Angiogenesis and vascular remodelling in normal and cancerous tissues (2009)
Owen, M R, Alarcon, T, Maini, P K, Byrne, H M
Vascular development and homeostasis are underpinned by two fundamental features: the generation of new vessels to meet the metabolic demands of under-perfused regions and the elimination of vessels...
Angiogenesis and vascular remodelling in normal and cancerous tissues (2009)
Owen, M. R., Alarcon, T., Maini, P. K., Byrne, H. M.
Vascular development and homeostasis are underpinned by two fundamental features: the generation of new vessels to meet the metabolic demands of under-perfused regions and the elimination of vessels...
Modeling the skin pattern of fishes (2009)
Barrio, R. A., Baker, Ruth E., Tribuzy, K., De Carvalho, M. R., Bassanezi, R., ...
Complicated patterns showing various spatial scales have been obtained in the past by coupling Turing systems in such a way that the scales of the independent systems resonate. This produces...
Inherent noise can facilitate coherence in collective swarm motion (2009)
Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, J., Kevrekidis, I. G., ...
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional...
Baker, Ruth E., Schnell, S., Maini, P. K.
In this article we will discuss the integration of developmental patterning mechanisms with waves of competency that control the ability of a homogeneous field of cells to react to pattern forming...
Reptile scale paradigm: Evo-Devo, pattern formation and regeneration (2009)
Chang, C., Wu, P., Baker, Ruth E., Maini, P. K., Alibardi, L., Chuong, C. M.
The purpose of this perspective is to highlight the merit of the reptile integument as an experimental model. Reptiles represent the first amniotes. From stem reptiles, extant reptiles, birds and...
Directional persistence & the optimality of run-and-tumble chemotaxis (2009)
Nicolau Jr, D.V., Armitage, J.P., Maini, P K
E. coli does chemotaxis by performing a biased random walk composed of alternating periods of swimming (runs) and reorientations (tumbles). Tumbles are typically modelled as complete directional...
An integrative computational model for intestinal tissue renewal (2009)
Mirams, G R, Walter, A, Fletcher, A, Murray, P, Osbourne, J, ...
Objectives: The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality,...
Chaste: a test-driven approach to software development for physiological modelling (2009)
Pitt-Francis, J, Pathmanathan, P, Bernabeu, M O, Bordas, R, Cooper, J, Fletcher, A, ...
Chaste is a software library and set of test suites for modelling phenomena in the domain of computational biology. Specifically these the modelling problems arise in the fields of cancer modelling,...
Thomas, K, Sudhakar, K, Maini, P K
After two phases of AIDS control activities in India, the third phase of the National AIDS Control Programme (NACP III) was launched in July 2007. Our focus here is to predict the number of people...
Lin, C.M, Jiang, T.X., Baker, R.E., Maini, P.K., Widelitz, R.B., Chunong, C.M.
A key issue in stem cell biology is the differentiation of homogeneous stem cells towards different fates which are also organized into desired configurations. Little is known about the mechanisms...
Thomas, K, Sudhakar, K, Maini, P K
After two phases of AIDS control activities in India, the third phase of the National AIDS Control Programme (NACP III) was launched in July 2007. Our focus here is to predict the number of people...
From a discrete to a continuum model of cell dynamics in one dimension (2009)
Murray, P J, Edwards, C M, Tindall, M J, Maini, P K
Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell...
Inherent noise can facilitate coherence in collective swarm motion (2009)
Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, J., Kevrekidis, I. G., ...
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional...
Inherent noise can facilitate coherence in collective swarm motion (2009)
Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, J., Kevrekidis, I. G., ...
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional...
Chaste: a test-driven approach to software development for biological modelling (2009)
Pitt-Francis, J, Pathmanathan, P, Bernabeu, M O, Bordas, R, Cooper, J, Fletcher, A G, ...
Chaste (‘Cancer, heart and soft-tissue environment’) is a software library and a set of test suites for computational simulations in the domain of biology. Current functionality has arisen from...
Spatiotemporal modelling of CheY complexes in escherichia coli chemotaxis (2009)
Tindall, M. J., Porter, S. L., Wadhams, G H, Maini, P. K., Armitage, J. P.
The chemotaxis pathway of Escherichia coli is one of the best studied and modelled biological signalling pathways. Here we extend existing modelling approaches by explicitly including a description...
Mathematical modelling of tumour acidity (2008)
Smallbone, K., Gatenby, R.A., Maini, P.K.
Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as...
The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy (2008)
B. Ribba, T. Alarcón, K. Marron, P. K. Maini, Z. Agur
Abstract. The Hybrid Cellular Automata (HCA) modelling framework can be an efficient approach to a number of biological problems, particularly those which involve the integration of multiple spatial...
A MULTIPLE SCALE MODEL FOR TUMOR GROWTH ∗ (2008)
T. Alarc Ón, H. M. Byrne, P. K. Maini
Abstract. We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction...
Turbulent luminance in impassioned van Gogh paintings (2008)
Aragón, J L, Naumis, G G, Bai, M, Torres, M, Maini, P K
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function...
A simple mechanistic model of sprout spacing in tumour-associated angiogenesis (2008)
Addison-Smith, B, McElwain, D L S, Maini, P K
This paper develops a simple mathematical model of the siting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive...
Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration (2008)
Plikus, M V, Mayer, J A, Baker, R E, Maini, P K, Maxson, R, ...
In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult...
On the foundations of cancer modelling: selected topics, speculations, & perspectives (2008)
Bellomo, N, Li, N K, Maini, P K
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some...
A theoretical study of the response of vascular tumours to different types of chemotherapy (2008)
Panovska, J, Byrne, H M, Maini, P K
In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a...
Modelling multiscale aspects of colorectal cancer (2008)
Byrne, H M, Johnston, M D, Edwards, C M, Chapman, S J, Bodmer, W F, ...
Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and...
Modelling aspects of solid cancer growth (2008)
The modelling of cancer provides an enormous mathematical challenge because of its inherent multiscale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which...
Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell (2008)
Tindall, M J, Porter, S L, Maini, P K, Gaglia, G, Armitage, J P
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of...
Overview of mathematical approaches used to model bacterial chemotaxis II: the single cell (2008)
Tindall, M J, Porter, S L, Maini, P K, Gaglia, G, Armitage, J P
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized...
A new neurosurgical tool incorporating differential geometry and cellular automata techniques (2008)
Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to...
Mathematical modelling of tumour acidity (2008)
Smallbone, K, Gatenby, R A, Maini, P K
Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as...
'Extremotaxis': Computing with a bacterial-inspired algorithm (2008)
Nicolau Jr, D V, Burrage, K, Nicolau, D V, Maini, P K
We present a general-purpose optimization algorithm inspired by “run-and-tumble”, the biased random walk chemotactic swimming strategy used by the bacterium Escherichia coli to locate regions of...
Partial differential equations for self-organization in cellular and developmental biology (2008)
Baker, R E, Gaffney, E A, Maini, P K
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying...
Intracellular signalling during bacterial chemotaxis (2008)
Tindall, M J, Maini, P K, Armitage, J P, Singleton, C, Mason, A
n/a
Multiscale modelling of solid tumour growth (2008)
Byrne, H M, Owen, M R, Alarcon, T, Maini, P K
n/a
Non-linear transmission, mortality and stability of discrete-time infectious disease models (2008)
Korobeinikov, A, Maini, P K, Walker, W J
n/a
A simple mechanistic model of sprout spacing in tumour-associated angiogenesis (2008)
Addison-Smith, B., McElwain, D. L. S., Maini, P. K.
This paper develops a simple mathematical model of the siting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive...
Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration (2008)
Plikus, M. V., Mayer, J. A., Baker, Ruth E., Maini, P. K., Maxson, R., ...
In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult...
Turbulent luminance in impassioned van Gogh paintings (2008)
Aragón, J. L., Naumis, G. G., Bai, M., Torres, M., Maini, P. K.
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function...
On the foundations of cancer modelling: selected topics, speculations, & perspectives (2008)
Bellomo, N., Li, N. K., Maini, P. K.
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some...
A theoretical study of the response of vascular tumours to different types of chemotherapy (2008)
Panovska, J., Byrne, H. M., Maini, P. K.
In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a...
Modelling multiscale aspects of colorectal cancer (2008)
Byrne, H. M., Johnston, M. D., Edwards, C. M., Chapman, S. J., Bodmer, W. F., ...
Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and...
Modelling aspects of solid cancer growth (2008)
The modelling of cancer provides an enormous mathematical challenge because of its inherent multiscale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which...
Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell (2008)
Tindall, M. J., Porter, S. L., Maini, P. K., Gaglia, G., Armitage, J. P.
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of...
Overview of mathematical approaches used to model bacterial chemotaxis II: the single cell (2008)
Tindall, M. J., Porter, S. L., Maini, P. K., Gaglia, G., Armitage, J. P.
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized...
A new neurosurgical tool incorporating differential geometry and cellular automata techniques (2008)
Oshmyansky, A. R., Maini, P. K.
Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to...
Mathematical modelling of tumour acidity (2008)
Smallbone, K., Gatenby, R. A., Maini, P. K.
Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as...
'Extremotaxis': Computing with a bacterial-inspired algorithm (2008)
Nicolau Jr, D. V., Burrage, K., Nicolau, D. V., Maini, P. K.
We present a general-purpose optimization algorithm inspired by “run-and-tumble”, the biased random walk chemotactic swimming strategy used by the bacterium Escherichia coli to locate regions of...
Partial differential equations for self-organization in cellular and developmental biology (2008)
Baker, Ruth E., Gaffney, E. A., Maini, P. K.
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying...
Intracellular signalling during bacterial chemotaxis (2008)
Tindall, M. J., Maini, P. K., Armitage, J. P., Singleton, C., Mason, A.
n/a
Multiscale modelling of solid tumour growth (2008)
Byrne, H. M., Owen, M. R., Alarcon, T., Maini, P. K.
n/a
Non-linear transmission, mortality and stability of discrete-time infectious disease models (2008)
Korobeinikov, A., Maini, P. K., Walker, W. J.
n/a
on The Mathematical Modelling of Cell Kinetics in Corneal Epithelial Wound Healing (2007)
E. A. Gaffney, P. K. Maini, J. A. Sherratt, S. Tuft
This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a...
Digital Object Identifier (DOI): (2007)
K. J. Painter, P. K. Maini, H. G. Othmer
Development and applications of a model for cellular response to multiple chemotactic cues
Speed of reaction diffusion in embryogenesis (2007)
Page, K.M., Monk, N.A., Maini, P.K.
Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns...
Yamada, H., Nakagaki, T., Baker, R.E., Maini, P.K.
In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals....
Yamada, H., Nakagaki, T., Baker, R.E., Maini, P.K.
In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals....
Mathematical models of avascular cancer (2007)
Roose, T., Chapman, S.J., Maini, P.K.
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing...
Mathematical models of avascular cancer (2007)
Roose, T., Chapman, S. J., Maini, P. K.
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing...
Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K., Chapman, S. J.
Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome, and subsequent unbounded growth. We...
Maini, P K, Chaplain, M, Dosanjh, A
The last year has been a very busy one for the BMB. We have published 140 articles online, which is over twice the publication rate of the previous year. This reflects the increase in the submission...
Metabolic changes during carcinogenesis: Potential impact on invasiveness (2007)
Smallbone, K, Gatenby, R A, Gillies, R J, Maini, P K, Gavaghan, D J
Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the...
Multiscale modeling in biology (2007)
Schnell, S, Grima, R, Maini, P K
The 1966 science-fction film Fantastic Voyage captured the public imagination with a clever idea: what fantastic things might we see and do if we could minaturize ourselves and travel through the...
Oscillatory Turing Patterns in a Simple Reaction-Diffusion System (2007)
Liu, R T, Liaw, S S, Maini, P K
Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a...
Johnston, M D, Edwards, C M, Bodmer, W F, Maini, P K, Chapman, S J
Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome, and subsequent unbounded growth. We...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P K, Alarcon, T, Byrne, H M, Owen, M R, Murphy, J
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P K, Alarcon, T, Byrne, H M, Owen, M R, Murphy, J
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P K, Alarcon, T, Byrne, H M, Owen, M R, Murphy, J
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
A mechanism for morphogen-controlled domain growth (2007)
Many developmental systems are organised via the action of graded distributions of morphogens. In the Drosophila wing disc, for example, recent experimental evidence has shown that graded expression...
A biomimetic algorithm for the improved detection of microarray features, (2007)
Nicolau, D V Jr, Nicolau, D V, Maini, P K
One the major difficulties of microarray technology relate to the processing of large and - importantly - error-loaded images of the dots on the chip surface. Whatever the source of these errors,...
Mathematical models of avascular tumor growth (2007)
Roose, T, Chapman, S J, Maini, P K
This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models...
A study of the temperature dependence of bienzyme systems and enzymatic chains (2007)
Kotov, N V, Baker, R E, Platov, K V, Valeyev, N V, Skorinkin, A I, Maini, P K
It is known that most enzyme-facilitated reactions are highly temperature dependent processes. In general, the temperature coefficient, Q10, of a simple reaction reaches 2.0-3.0. Nevertheless, some...
Yamada, H, Nakagaki, T, Baker, R E, Maini, P K
In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals....
Speed of reaction diffusion in embryogenesis (2007)
Page, K.M., Monk, N.A.M., Maini, P.K.
Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns...
Reaction-diffusion systems have been widely studied in developmental biology, chemistry and more recently in financial mathematics. Most of these systems comprise nonlinear reaction terms which makes...
Travelling gradients in interacting morphogen systems (2007)
Morphogen gradients are well known to play several important roles in development; however the mechanisms underlying the formation and maintenance of these gradients are often not well understood. In...
Aggregative movement and front propagation for bi-stable population models (2007)
Maini, P K, Malaguti, L, Marcelli, C, Matucci, S
Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling...
Kulesa, P M, Schnell, S, Rudloff, S, Baker, R E, Maini, P K
One of the most visually striking patterns in the early developing embryo is somite segmentation. Somites form as repeated, periodic structures in pairs along nearly the entire caudal vertebrate...
Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer (2007)
Gatenby, R A, Smallbone, K, Maini, P K, Rose, F, Averill, J, Nagle, R B, ...
Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are...
Aggregative movement and front propagation for bi-stable population models (2007)
Maini, P K, Malaguti, L, Marcelli, C, Matucci, S
Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling...
Pigmentation pattern formation in butterfly wigns: Global patterns on fore- and hind-wing (2007)
Sekimura, T, Madzvamuse, A, Maini, P K
Pigmentation patterns in butterfly wings are one of the most spectacular & vivid examples of pattern formation in biology. In this chapter, we devote our attention to the mechanisms for generating...
Mathematical modelling of vascular tumour growth and implications for therapy (2007)
Panovska, J, Byrne, H M, Maini, P K
In this chapter we briefly discuss the results of a mathematical model formulated in [22] that incorporates many processes associated with tumour growth. The deterministic model, a system of coupled...
Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions (2007)
We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction...
Modelling spatio-temporal starch degradation patterns in apples during fruit growth (2007)
Scheerlinck, N, Escudero, C, Baker, R E, Maini, P K
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Modelling the role of angiogenesis and vasculogenesis in solid tumuour growth (2007)
Stamper, I J, Byrne, H M, Maini, P K
Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs)...
Quiescience as a mechanism for cyclical hypoxia and acidosis (2007)
Smallbone, K, Gavaghan, D J, Maini, P K, Brady, J M
Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads...
Pomitaxis: Computing with a bacterial-inspired algorithm (2007)
We present a general-purpose optimisation algorithm inspired by "run-and-tumble2, the biased random chemotactic swimming strategy used by the bacterium E coli to locate regions of high nutrient...
Mathematical models for somite formation (2007)
Baker, R E, Schnell, S, Maini, P K
Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides...
A mathematical basis for the clock and wavefront model for somitogenesis (2007)
Baker, R E, Schnell, S, Maini, P K
n/a
Maini, P. K., Chaplain, M., Dosanjh, A.
The last year has been a very busy one for the BMB. We have published 140 articles online, which is over twice the publication rate of the previous year. This reflects the increase in the submission...
Metabolic changes during carcinogenesis: Potential impact on invasiveness (2007)
Smallbone, K., Gatenby, R. A., Gillies, R. J., Maini, P. K., Gavaghan, D. J.
Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the...
Multiscale modeling in biology (2007)
Schnell, S., Grima, R., Maini, P. K.
The 1966 science-fction film Fantastic Voyage captured the public imagination with a clever idea: what fantastic things might we see and do if we could minaturize ourselves and travel through the...
Oscillatory Turing Patterns in a Simple Reaction-Diffusion System (2007)
Liu, R. T., Liaw, S. S., Maini, P. K.
Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a...
Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K., Chapman, S. J.
Colorectal cancer is initiated in colonic crypts. A succession of genetic mutations or epigenetic changes can lead to homeostasis in the crypt being overcome, and subsequent unbounded growth. We...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P. K., Alarcon, T., Byrne, H. M., Owen, M. R., Murphy, J.
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P. K., Alarcon, T., Byrne, H. M., Owen, M. R., Murphy, J.
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
Structural adaptation in normal and cancerous vasculature (2007)
Maini, P. K., Alarcon, T., Byrne, H. M., Owen, M. R., Murphy, J.
The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been...
A mechanism for morphogen-controlled domain growth (2007)
Many developmental systems are organised via the action of graded distributions of morphogens. In the Drosophila wing disc, for example, recent experimental evidence has shown that graded expression...
A biomimetic algorithm for the improved detection of microarray features, (2007)
Nicolau, D. V. Jr, Nicolau, D. V., Maini, P. K.
One the major difficulties of microarray technology relate to the processing of large and - importantly - error-loaded images of the dots on the chip surface. Whatever the source of these errors,...
Mathematical models of avascular tumor growth (2007)
Roose, T., Chapman, S. J., Maini, P. K.
This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models...
A study of the temperature dependence of bienzyme systems and enzymatic chains (2007)
Kotov, N. V., Baker, Ruth E., Platov, K. V., Valeyev, N. V., Skorinkin, A. I., Maini, P. K.
It is known that most enzyme-facilitated reactions are highly temperature dependent processes. In general, the temperature coefficient, Q10, of a simple reaction reaches 2.0-3.0. Nevertheless, some...
Yamada, H., Nakagaki, T., Baker, Ruth E., Maini, P. K.
In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals....
Speed of reaction diffusion in embryogenesis (2007)
Page, K. M., Monk, N. A. M., Maini, P. K.
Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns...
Reaction-diffusion systems have been widely studied in developmental biology, chemistry and more recently in financial mathematics. Most of these systems comprise nonlinear reaction terms which makes...
Travelling gradients in interacting morphogen systems (2007)
Morphogen gradients are well known to play several important roles in development; however the mechanisms underlying the formation and maintenance of these gradients are often not well understood. In...
Aggregative movement and front propagation for bi-stable population models (2007)
Maini, P. K., Malaguti, L., Marcelli, C., Matucci, S.
Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling...
Kulesa, P. M., Schnell, S., Rudloff, S., Baker, Ruth E., Maini, P. K.
One of the most visually striking patterns in the early developing embryo is somite segmentation. Somites form as repeated, periodic structures in pairs along nearly the entire caudal vertebrate...
Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer (2007)
Gatenby, R. A., Smallbone, K., Maini, P. K., Rose, F., Averill, J., Nagle, R. B., ...
Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are...
Aggregative movement and front propagation for bi-stable population models (2007)
Maini, P. K., Malaguti, L., Marcelli, C., Matucci, S.
Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling...
Pigmentation pattern formation in butterfly wigns: Global patterns on fore- and hind-wing (2007)
Sekimura, T., Madzvamuse, A., Maini, P. K.
Pigmentation patterns in butterfly wings are one of the most spectacular & vivid examples of pattern formation in biology. In this chapter, we devote our attention to the mechanisms for generating...
Mathematical modelling of vascular tumour growth and implications for therapy (2007)
Panovska, J., Byrne, H. M., Maini, P. K.
In this chapter we briefly discuss the results of a mathematical model formulated in [22] that incorporates many processes associated with tumour growth. The deterministic model, a system of coupled...
Examples of mathematical modeling tales from the crypt (2007)
Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K., Chapman, S. J.
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal...
Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions (2007)
Maini, P. K., Wei, J., Winter, M.
We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction...
Modelling spatio-temporal starch degradation patterns in apples during fruit growth (2007)
Scheerlinck, N., Escudero, C., Baker, Ruth E., Maini, P. K.
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Examples of mathematical modeling tales from the crypt (2007)
Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K., Chapman, S. J.
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal...
Modelling the role of angiogenesis and vasculogenesis in solid tumuour growth (2007)
Stamper, I. J., Byrne, H. M., Maini, P. K.
Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs)...
Quiescience as a mechanism for cyclical hypoxia and acidosis (2007)
Smallbone, K., Gavaghan, D. J., Maini, P. K., Brady, J. M.
Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads...
Pomitaxis: Computing with a bacterial-inspired algorithm (2007)
We present a general-purpose optimisation algorithm inspired by "run-and-tumble2, the biased random chemotactic swimming strategy used by the bacterium E coli to locate regions of high nutrient...
Mathematical models for somite formation (2007)
Baker, Ruth E., Schnell, S., Maini, P. K.
Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides...
A mathematical basis for the clock and wavefront model for somitogenesis (2007)
Baker, Ruth E., Schnell, S., Maini, P. K.
n/a
The impact of cell crowding and active cell movement on vascular tumour growth (2006)
Betteridge, R, Owen, M R, Byrne, H M, Alarcon, T, Maini, P K
A multiscale model for vascular tumour growth is presented which includes systems of ordinary differential equations for the cell cycle and regulation of apoptosis in individual cells, coupled to...
The impact of cell crowding and active cell movement on vascular tumour growth (2006)
Betteridge, R., Owen, M. R., Byrne, H. M., Alarcon, T., Maini, P. K.
A multiscale model for vascular tumour growth is presented which includes systems of ordinary differential equations for the cell cycle and regulation of apoptosis in individual cells, coupled to...
Distinct mechanisms underlie pattern formation in the skin and skin appendages (2006)
Widelitz, R B, Baker, R E, Plikus, M, Lin, C, Maini, P K, Paus, R, ...
Patterns form with the break of homogeneity and lead to the emergence of new structure or arrangement. There are different physiological and pathological mechanisms that lead to the formation of...
Diffusion-aggregation processes with mono-stable reaction terms (2006)
Maini, P K, Malaguti, L, Marcelli, C, Matucci, S
This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$...
Distinct mechanisms underlie pattern formation in the skin and skin appendages (2006)
Widelitz, R. B., Baker, Ruth E., Plikus, M., Lin, C., Maini, P. K., Paus, R., ...
Patterns form with the break of homogeneity and lead to the emergence of new structure or arrangement. There are different physiological and pathological mechanisms that lead to the formation of...
Diffusion-aggregation processes with mono-stable reaction terms (2006)
Maini, P. K., Malaguti, L., Marcelli, C., Matucci, S.
This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$...
Modelling the response of vascular tumours to chemotherapy: A multiscale approach (2006)
Byrne, H M, Owen, M R, Alarcon, T A, Murphy, J, Maini, P K
An existing multiscale model is extended to study the response of a vascularised tumour to treatment with chemotherapeutic drugs which target proliferating cells. The underlying hybrid cellular...
Mode transitions in a model reaction-diffusion system driven by domain growth and noise (2006)
Barrass, I, Crampin, E J, Maini, P K
Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven...
Two-stage Turing model for generating pigment patterns on the leopard and the jaguar (2006)
Liu, R T, Liaw, S S, Maini, P K
Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we...
What is the biological basis of pattern formation of skin lesions? (2006)
Chuong, C M, Dhouailly, D, Gilmore, S, Forest, L, Shelly, W B, Stenn, K S, ...
Pattern recognition is at the heart of clinical dermatology and dermatopathology. Yet, while every practitioner of the art of dermatological diagnosis recognizes the supreme value of diagnostic cues...
Modelling the response of vascular tumours to chemotherapy: A multiscale approach (2006)
Byrne, H. M., Owen, M. R., Alarcon, T. A., Murphy, J., Maini, P. K.
An existing multiscale model is extended to study the response of a vascularised tumour to treatment with chemotherapeutic drugs which target proliferating cells. The underlying hybrid cellular...
Mode transitions in a model reaction-diffusion system driven by domain growth and noise (2006)
Barrass, I., Crampin, E. J., Maini, P. K.
Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven...
Two-stage Turing model for generating pigment patterns on the leopard and the jaguar (2006)
Liu, R. T., Liaw, S. S., Maini, P. K.
Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we...
What is the biological basis of pattern formation of skin lesions? (2006)
Chuong, C. M., Dhouailly, D., Gilmore, S., Forest, L., Shelly, W. B., Stenn, K. S., ...
Pattern recognition is at the heart of clinical dermatology and dermatopathology. Yet, while every practitioner of the art of dermatological diagnosis recognizes the supreme value of diagnostic cues...
Turbulent luminance in impassioned van Gogh paintings (2006)
Aragón, J. L., Naumis, Gerardo G., Bai, M., Torres, M., Maini, P. K.
Everything in the last period of Vincent van Gogh paintings seems to be moving; this dynamical style served to transmit his own feelings about a figure or a landscape. Since the early impressionism,...
Modelling aspects of cancer dynamics: a review (2006)
Byrne, H M, Alarcon, T, Owen, M R, Webb, S D, Maini, P K
Cancer is a complex disease in which a variety of factors interact over a wide range of spatial and temporal scales with huge datasets relating to the different scales available. However, these data...
McDougall, S, Dallon, J, Sherratt, J, Maini, P K
The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular...
Modelling aspects of cancer dynamics: a review (2006)
Byrne, H. M., Alarcon, T., Owen, M. R., Webb, S. D., Maini, P. K.
Cancer is a complex disease in which a variety of factors interact over a wide range of spatial and temporal scales with huge datasets relating to the different scales available. However, these data...
McDougall, S., Dallon, J., Sherratt, J., Maini, P. K.
The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular...
Alarcon, T, Owen, M R, Byrne, H M, Maini, P K
Following the poor clinical results of antiangiogenic drugs, particularly when applied in isolation, tumour biologists and clinicians are now turning to combinations of therapies in order to obtain...
Miura, T, Shiota, K, Morriss-Kay, G, Maini, P K
It has been suggested that the Turing reaction–diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the...
Alarcon, T., Owen, M. R., Byrne, H. M., Maini, P. K.
Following the poor clinical results of antiangiogenic drugs, particularly when applied in isolation, tumour biologists and clinicians are now turning to combinations of therapies in order to obtain...
Miura, T., Shiota, K., Morriss-Kay, G., Maini, P. K.
It has been suggested that the Turing reaction–diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the...
Mathematical models in physiology (2006)
Gavaghan, D, Garny, A, Maini, P K, Kohl, P
Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with...
Mathematical models in physiology (2006)
Gavaghan, D., Garny, A., Maini, P. K., Kohl, P.
Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with...
A clock and wavefront mechanism for somite formation (2006)
Baker, R E, Schnell, S, Maini, P K
Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that...
A clock and wavefront mechanism for somite formation (2006)
Baker, Ruth E., Schnell, S., Maini, P. K.
Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that...
Mathematical modelling of the HIF-1 mediated hypoxic response in tumours (2006)
Kooner, P, Maini, P K, Gavaghan, D J
Solid tumours frequently display areas of low oxygen concentration (hypoxia) due to their uncontrolled proliferation and the fact that the new blood vessels they develop are irregular and have poor...
Cancer disease: integrative modelling approaches (2006)
Byrne, H M, Owen, M R, Alarcon, T, Maini, P K
Cancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of...
A mathematical investigation of a clock and wavefront model for somitogenesis (2006)
Baker, R E, Schnell, S, Maini, P K
Abstract Somites are transient blocks of cells that form sequentially along the antero-posterior axis of vertebrate embryos. They give rise to the vertebrae, ribs and other associated features of the...
Mathematical modelling of the HIF-1 mediated hypoxic response in tumours (2006)
Kooner, P., Maini, P. K., Gavaghan, D. J.
Solid tumours frequently display areas of low oxygen concentration (hypoxia) due to their uncontrolled proliferation and the fact that the new blood vessels they develop are irregular and have poor...
Cancer disease: integrative modelling approaches (2006)
Byrne, H. M., Owen, M. R., Alarcon, T., Maini, P. K.
Cancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of...
A mathematical investigation of a clock and wavefront model for somitogenesis (2006)
Baker, Ruth E., Schnell, S., Maini, P. K.
Abstract Somites are transient blocks of cells that form sequentially along the antero-posterior axis of vertebrate embryos. They give rise to the vertebrae, ribs and other associated features of the...
Roose, T, Chapman, S J, Maini, P K
The landmark paper by Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527-1530, 1999) presented experimental investigations to show that not only can...
An analysis of B cell selection mechanisms in germinal centres (2006)
Meyer-Hermann, M E, Maini, P K, Iber, D
Affinity maturation of antibodies during immune responses is achieved by multiple rounds of somatic hypermutation and subsequent preferential selection of those B cells that express B cell receptors...
Modelling aspects of vascular cancer development (2006)
Maini, P K, Alarcon, T, Byrne, H M
The modelling of cancer provides an enormous mathematical challenge because of its inherent multi-scale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which...
Mathematical modelling of angiogenesis and vascular adaptation (2006)
Alarcon, T, Byrne, H M, Maini, P K, Panovska, J
n/a
The turing model comes of molecular age (2006)
Maini, P K, Baker, R E, Chuong, C M
Molecular analysis of hair follicle formation provide evidence to support the most well-known mathematical model for biological pattern formation.
Roose, T., Chapman, S. J., Maini, P. K.
The landmark paper by Hirose et al. (Hirose, K., Kadowaki, S., Tanabe, M., Takeshima, H., Iino, M., Science 284:1527-1530, 1999) presented experimental investigations to show that not only can...
An analysis of B cell selection mechanisms in germinal centres (2006)
Meyer-Hermann, M. E., Maini, P. K., Iber, D.
Affinity maturation of antibodies during immune responses is achieved by multiple rounds of somatic hypermutation and subsequent preferential selection of those B cells that express B cell receptors...
Modelling aspects of vascular cancer development (2006)
Maini, P. K., Alarcon, T., Byrne, H. M.
The modelling of cancer provides an enormous mathematical challenge because of its inherent multi-scale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which...
Mathematical modelling of angiogenesis and vascular adaptation (2006)
Alarcon, T., Byrne, H. M., Maini, P. K., Panovska, J.
n/a
The turing model comes of molecular age (2006)
Maini, P. K., Baker, Ruth E., Chuong, C. M.
Molecular analysis of hair follicle formation provide evidence to support the most well-known mathematical model for biological pattern formation.
An evolving network model with community structure (2005)
Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable...
An evolving network model with community structure (2005)
Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable...
Cluster formation for multi-strain infections with cross-immunity (2005)
Calvez, V., Korobeinikov, A., Maini, P.K.
Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of...
Mathematical models of avascular cancer (2005)
Roose, T., Chapman, S.J., Maini, P.K.
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing...
The Penna bit-string model successfully encompasses many phenomena of population evolution, including inheritance, mutation, evolution, and aging. If we consider social interactions among individuals...
Modelling rain forest diversity: the role of competition (2005)
Bampfylde, C J, Brown, N D, Gavaghan, D J, Maini, P K
Rain forests exhibit enormous species diversity, but the mechanisms for establishing and maintaining such diversity are unknown. Models involving both exploitative and pre-emptive competition have...
Madzvamuse, A, Maini, P K, Wathen, A J
Numerical techniques for moving meshes are many and varied. In this paper we present a novel application of a moving grid finite element method applied to biological problems related to pattern...
Interpreting two-photon imaging data of lymphocyte motility (2005)
Meyer-Hermann, M E, Maini, P K
Recently, using two-photon imaging it has been found that the movement of B and T cells in lymph nodes can be described by a random walk with persistence of orientation in the range of 2 minutes. We...
Nonlinear incidence and stability of infectious disease models (2005)
In this paper we consider the impact of the form of the non-linearity of the infectious disease incidence rate on the dynamics of epidemiological models. We consider a very general form of the...
The role of acidity in solid tumour growth and invasion (2005)
Smallbone, K, Gavaghan, D J, Gatenby, R A, Maini, P K
Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional...
Different populations of RNA polymerase II in living mammalian cells (2005)
Cook, P R, Hieda, M, Winstanley, H, Maini, P K, Iborra, F J
RNA polymerase II is responsible for transcription of most eukaryotic genes, but, despite exhaustive analysis, little is known about how it transcribes natural templates in vivo. We studied...
A design principle for vascular beds: the effects of complex blood rheology (2005)
Alarcon, T, Byrne, H M, Maini, P K
We propose a design principle that extends Murray's original optimization principle for vascular architecture to account for complex blood rheology. Minimization of an energy dissipation function...
A multiscale model for collagen alignment in wound healing (2005)
Maini, P K, Dallon, J C, Sherratt, J A
It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this...
Cancer modelling: Getting to the heart of the problem (2005)
Byrne, H, Alarcon, T A, Maini, P K
Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate...
Complex pattern formation in reaction diffusion systems with spatially-varying parameters (2005)
Page, K M, Maini, P K, Monk, N A M
Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes...
Cutting edge: back to "one-way" germinal centers (2005)
Meyer-Hermann, M E, Maini, P K
The present status of germinal center (GC) research is revisited using in silico simulations based on recent lymphocyte motility data in mice. The generally adopted view of several rounds of somatic...
A multiple scale model for tumor growth (2005)
Alarcon, T, Byrne, H M, Maini, P K
We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between...
Ribba, B, Marron, K, Agur, Z, Alarcon, T, Maini, P K
Doxorubicin treatment outcomes for non-Hodgkin’s lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature...
Cluster formation for multi-strain infections with cross-immunity (2005)
Clavez, V, Korobeinikov, A, Maini, P K
Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of...
Extracellular volume regulation and growth (2005)
Hajek, D, Kolar, P, Maini, P K, Starha, P
We have formalized extracellular and intracellular volume interaction with each other and the influence of these processes on the type of cell growth. The linearized model was verified by stereo...
Analysis of B cell selection mechanisms in the adaptive immune response (2005)
Meyer-Hermann, M, Maini, P K, Iber, D
The essential task of a germinal centre reaction is the selection of those B cells that bind the antigen with high affinity. The exact mechanisms of B cell selection is still unknown and rather...
Mathematical models of avascular cancer (2005)
Roose, T., Chapman, S. J., Maini, P. K.
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing...
The Penna bit-string model successfully encompasses many phenomena of population evolution, including inheritance, mutation, evolution, and aging. If we consider social interactions among individuals...
Modelling rain forest diversity: the role of competition (2005)
Bampfylde, C. J., Brown, N. D., Gavaghan, D. J., Maini, P. K.
Rain forests exhibit enormous species diversity, but the mechanisms for establishing and maintaining such diversity are unknown. Models involving both exploitative and pre-emptive competition have...
Madzvamuse, A., Maini, P. K., Wathen, A. J.
Numerical techniques for moving meshes are many and varied. In this paper we present a novel application of a moving grid finite element method applied to biological problems related to pattern...
Interpreting two-photon imaging data of lymphocyte motility (2005)
Meyer-Hermann, M. E., Maini, P. K.
Recently, using two-photon imaging it has been found that the movement of B and T cells in lymph nodes can be described by a random walk with persistence of orientation in the range of 2 minutes. We...
Nonlinear incidence and stability of infectious disease models (2005)
Korobeinikov, A., Maini, P. K.
In this paper we consider the impact of the form of the non-linearity of the infectious disease incidence rate on the dynamics of epidemiological models. We consider a very general form of the...
The role of acidity in solid tumour growth and invasion (2005)
Smallbone, K., Gavaghan, D. J., Gatenby, R. A., Maini, P. K.
Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional...
Different populations of RNA polymerase II in living mammalian cells (2005)
Cook, P. R., Hieda, M., Winstanley, H., Maini, P. K., Iborra, F. J.
RNA polymerase II is responsible for transcription of most eukaryotic genes, but, despite exhaustive analysis, little is known about how it transcribes natural templates in vivo. We studied...
A design principle for vascular beds: the effects of complex blood rheology (2005)
Alarcon, T., Byrne, H. M., Maini, P. K.
We propose a design principle that extends Murray's original optimization principle for vascular architecture to account for complex blood rheology. Minimization of an energy dissipation function...
A multiscale model for collagen alignment in wound healing (2005)
Maini, P. K., Dallon, J. C., Sherratt, J. A.
It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this...
Cancer modelling: Getting to the heart of the problem (2005)
Byrne, H., Alarcon, T. A., Maini, P. K.
Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate...
Complex pattern formation in reaction diffusion systems with spatially-varying parameters (2005)
Page, K. M., Maini, P. K., Monk, N. A. M.
Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes...
Cutting edge: back to "one-way" germinal centers (2005)
Meyer-Hermann, M. E., Maini, P. K.
The present status of germinal center (GC) research is revisited using in silico simulations based on recent lymphocyte motility data in mice. The generally adopted view of several rounds of somatic...
A multiple scale model for tumor growth (2005)
Alarcon, T., Byrne, H. M., Maini, P. K.
We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between...
Ribba, B., Marron, K., Agur, Z., Alarcon, T., Maini, P. K.
Doxorubicin treatment outcomes for non-Hodgkin’s lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature...
Cluster formation for multi-strain infections with cross-immunity (2005)
Clavez, V., Korobeinikov, A., Maini, P. K.
Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of...
Extracellular volume regulation and growth (2005)
Hajek, D., Kolar, P., Maini, P. K., Starha, P.
We have formalized extracellular and intracellular volume interaction with each other and the influence of these processes on the type of cell growth. The linearized model was verified by stereo...
Analysis of B cell selection mechanisms in the adaptive immune response (2005)
Meyer-Hermann, M., Maini, P. K., Iber, D.
The essential task of a germinal centre reaction is the selection of those B cells that bind the antigen with high affinity. The exact mechanisms of B cell selection is still unknown and rather...
The effect of growth and curvature on pattern formation (2004)
Plaza, R, Sánchez-Garduño, F, Padilla, P, Barrio, R A, Maini, P K
Abstract Based on first principles, we derive a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and...
Bampfylde, C J, Brown, N D, Gavaghan, D J, Maini, P K
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Ribba, B, Alarcon, T, Marron, K, Maini, P K, Agur, Z
The Hybrid Cellular Automata (HCA) modelling framework can be an efficient approach to a number of biological problems, particularly those which involve the integration of multiple spatial and...
The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The...
It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern...
Bulletin of Mathematical Biology - facts, figures and comparisons (2004)
Maini, P K, Schnell, S, Jolliffe, S
The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB...
A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells (2004)
Alarcon, T, Byrne, H M, Maini, P K
The evolution of the cell-cycle is known to be influenced by environmental conditions, including lack of extracellular oxygen (hypoxia). Notably, hypoxia appears to have different effects on normal...
Maini, P K, McElwain, S, Leavesley, D
The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over...
McInerney, D, Schnell, S, Baker, R, Maini, P K
In this work we present an analysis, supported by numerical simulations, of the formulation of the cell-cycle model for somitogenesis proposed in Collier et al.(J. Theor. Biol. 207 (2000),...
Travelling waves in a wound healing assay (2004)
Maini, P K, McElwain, S, Leavesley, D
Several authors have predicted that cell propagation in a number of biological contexts, for example, wound healing, tumour cell invasion, angiogenesis etc., occurs due to a constant speed travelling...
Towards whole-organ modelling of tumour growth (2004)
Alarcon, T, Byrne, H M, Maini, P K
Multiscale approaches to modelling biological phenomena are growing rapidly. We present here some recent results on the formulation of a theoretical framework which can be developed into a fully...
Using mathematical models to help understand biological pattern formation (2004)
One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has...
Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form $\beta I_p S_q$ for the case p
The effect of growth and curvature on pattern formation (2004)
Plaza, R., Sánchez-Garduño, F., Padilla, P., Barrio, R. A., Maini, P. K.
Abstract Based on first principles, we derive a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and...
Bampfylde, C. J., Brown, N. D., Gavaghan, D. J., Maini, P. K.
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Ribba, B., Alarcon, T., Marron, K., Maini, P. K., Agur, Z.
The Hybrid Cellular Automata (HCA) modelling framework can be an efficient approach to a number of biological problems, particularly those which involve the integration of multiple spatial and...
The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The...
It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern...
Bulletin of Mathematical Biology - facts, figures and comparisons (2004)
Maini, P. K., Schnell, S., Jolliffe, S.
The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB...
A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells (2004)
Alarcon, T., Byrne, H. M., Maini, P. K.
The evolution of the cell-cycle is known to be influenced by environmental conditions, including lack of extracellular oxygen (hypoxia). Notably, hypoxia appears to have different effects on normal...
Maini, P. K., McElwain, S., Leavesley, D.
The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over...
McInerney, D., Schnell, S., Baker, Ruth E., Maini, P. K.
In this work we present an analysis, supported by numerical simulations, of the formulation of the cell-cycle model for somitogenesis proposed in Collier et al.(J. Theor. Biol. 207 (2000),...
Travelling waves in a wound healing assay (2004)
Maini, P. K., McElwain, S., Leavesley, D.
Several authors have predicted that cell propagation in a number of biological contexts, for example, wound healing, tumour cell invasion, angiogenesis etc., occurs due to a constant speed travelling...
Towards whole-organ modelling of tumour growth (2004)
Alarcon, T., Byrne, H. M., Maini, P. K.
Multiscale approaches to modelling biological phenomena are growing rapidly. We present here some recent results on the formulation of a theoretical framework which can be developed into a fully...
Using mathematical models to help understand biological pattern formation (2004)
One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has...
Korobeinikov, A., Maini, P. K.
Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form $\beta I_p S_q$ for the case p
McInerney, D., Schnell, S., Baker, R. E., Maini, P. K.
In this work we present an analysis, supported by numerical simulations, of the formulation of the cell‐cycle model for somitogenesis proposed in Collier et al.(J. Theor. Biol. 207 (2000),...
Estimation of effective vaccination rate : pertussis in New Zealand as a case study (2003)
Korobeinikov, A., Maini, P.K., Walker, W.J.
In some cases vaccination is unreliable. For example vaccination against pertussis has comparatively high level of primary and secondary failures. To evaluate efficiency of vaccination we introduce...
Pattern formation in spatially heterogeneous Turing reaction–diffusion models (2003)
Page, K.M., Maini, P.K., Monk, N.A.M.
The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially...
Formation of vertebral precursors: Past models and future predictions (2003)
Baker, R E, Schnell, S, Maini, P K
Disruption of normal vertebral development results from abnormal formation and segmentation of the vertebral precursors, called somites. Somitogenesis, the sequential formation of a periodic pattern...
A cellular automaton model for tumour growth in inhomogeneous environment (2003)
Alarcon, T, Byrne, H M, Maini, P K
Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this...
Response kinetics of tethered bacteria to stepwise changes in nutrient concentration (2003)
Chernova, A A, Armitage, J P, Maini, P K
We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial...
Pigmentation pattern formation in butterflies: experiments and models (2003)
Nijhout, H F, Maini, P K, Madzvamuse, A, Wathen, A J, Sekimura, T
Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who...
A moving grid finite element method applied to a model biological pattern generator (2003)
Madzvamuse, A, Wathen, A J, Maini, P K
Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we...
Estimation of effective vaccination rate for pertussis in New Zealand as a case study (2003)
Korobeinikov, A, Maini, P K, Walker, M J
In some cases vaccination is unreliable. For example vaccination against pertussis has comparatively high level of primary and secondary failures. To evaluate efficiency of vaccination we introduce...
How the mouse got its stripes (2003)
Acentral issue in developmental biology is the understanding of how various processes interact to produce spatio-temporal patterns in the embryo. To even observe these dynamical patterns directly is...
Pigmentation pattern formation in the buttery wing of Papilio dardanus (2003)
Sekimura, T, Madzvamuse, A, Wathen, A J, Maini, P K
n/a
Implications of domain growth in morphogenesis (2003)
Maini, P K, Crampin, E J, Madzvamuse, A, Wathen, A J, Thomas, R D K
Domain growth can play an important role in pattern formation during early embryonic development. By considering the Turing reaction-diffusion model for pattern formation, we show how growth can...
Pattern formation in spatially heterogeneous Turing reaction-diffusion models (2003)
Page, K, Maini, P K, Monk, N A M
The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially...
A century of enzyme kinetics. Should we believe in the Km and vmax estimates? (2003)
The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The...
www.elsevier.com/locate/aml Travelling Waves in a Wound Healing Assay (2003)
Communicated by G. Wake Abstract-- Several authors have predicted that cell propagation in a number of biological con-texts, for example, wound healing, turnout cell invasion, angiogenesis etc.,...
Formation of vertebral precursors: Past models and future predictions (2003)
Baker, Ruth E., Schnell, S., Maini, P. K.
Disruption of normal vertebral development results from abnormal formation and segmentation of the vertebral precursors, called somites. Somitogenesis, the sequential formation of a periodic pattern...
A cellular automaton model for tumour growth in inhomogeneous environment (2003)
Alarcon, T., Byrne, H. M., Maini, P. K.
Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this...
Response kinetics of tethered bacteria to stepwise changes in nutrient concentration (2003)
Chernova, A. A., Armitage, J. P., Maini, P. K.
We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial...
Pigmentation pattern formation in butterflies: experiments and models (2003)
Nijhout, H. F., Maini, P. K., Madzvamuse, A., Wathen, A. J., Sekimura, T.
Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who...
A moving grid finite element method applied to a model biological pattern generator (2003)
Madzvamuse, A., Wathen, A. J., Maini, P. K.
Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we...
Estimation of effective vaccination rate for pertussis in New Zealand as a case study (2003)
Korobeinikov, A., Maini, P. K., Walker, M. J.
In some cases vaccination is unreliable. For example vaccination against pertussis has comparatively high level of primary and secondary failures. To evaluate efficiency of vaccination we introduce...
How the mouse got its stripes (2003)
Acentral issue in developmental biology is the understanding of how various processes interact to produce spatio-temporal patterns in the embryo. To even observe these dynamical patterns directly is...
Pigmentation pattern formation in the buttery wing of Papilio dardanus (2003)
Sekimura, T., Madzvamuse, A., Wathen, A. J., Maini, P. K.
n/a
Implications of domain growth in morphogenesis (2003)
Maini, P. K., Crampin, E. J., Madzvamuse, A., Wathen, A. J., Thomas, R. D. K.
Domain growth can play an important role in pattern formation during early embryonic development. By considering the Turing reaction-diffusion model for pattern formation, we show how growth can...
Pattern formation in spatially heterogeneous Turing reaction-diffusion models (2003)
Page, K., Maini, P. K., Monk, N. A. M.
The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially...
A century of enzyme kinetics. Should we believe in the Km and vmax estimates? (2003)
The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The...
Making sense of complex phenomena in biology, (2002)
The remarkable advances in biotechnology over the past two decades have resulted in the generation of a huge amount of experimental data. It is now recognized that, in many cases, to extract...
A mathematical model for germinal centre kinetics and affinity maturation (2002)
We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction....
Investigating a simple model of cutaneous wound healing angiogenesis (2002)
Gaffney, E A, Pugh, K, Maini, P K, Arnold, F
A simple model of wound healing angiogenesis is presented, and investigated using numerical and asymptotic techniques. The model captures many key qualitative features of the wound healing angiogenic...
Mathematical models for cell-matrix interactions during dermal wound healing (2002)
Maini, P K, Olsen, L, Sherratt, J A
This paper contains a review of our recent work on the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing. The models are of...
A predictive model for color pattern formation in the buttery wing of Papilio dardanus (2002)
Madzvamuse, A, Maini, P K, Wathen, A J, Sekimura, T
Previously, we have proposed a mathematical model based on a modified Turing mechanism to account for pigmentation patterning in the butterfly wing of Papilio dardanus, well-known for the spectacular...
Size dependent symmetry breaking in models for morphogenesis (2002)
Barrio, R A, Maini, P K, Aragon, J L, Torres, M
A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed...
Pattern formation in reaction-diffusion models with nonuniform growth (2002)
Crampin, E J, Hackborn, W W, Maini, P K
Recent examples of biological pattern formation where a pattern changes qualitatively as the underlying domain grows have given rise to renewed interest in the reaction-diffusion (Turing) model for...
How to generate pentagonal symmetry using Turing systems (2002)
Aragon, J L, Torres, M, Gil, D, Barrio, R A, Maini, P K
We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of...
Madzvamuse, A, Thomas, R D K, Maini, P K, Wathen, A J
In this paper, we employ the novel application of a reaction-diffusion model on a growing domain to examine growth patterns of the ligaments of arcoid bivalves (marine molluscs) using realistic...
The dynamics and pinning of a spike for a reaction-diffusion system (2002)
Ward, M J, McInerney, D, Houston, P, Gavaghan, D, Maini, P K
The motion of a one-spike solution to a simplified form of the Gierer--Meinhardt activator-inhibitor model is studied in both a one-dimensional and a two-dimensional domain. The pinning effect on the...
Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology (2002)
Schnell, S, Maini, P K, McInerney, D, Gavaghan, D, Houston, P
Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study...
Gatenby, R A, Maini, P K, Gawlinski, E T
We use a novel “inverse problem” technique to construct a basic mathematical model of the interacting populations at the tumor-host interface. This approach assumes that invasive cancer is a...
Breast Cancer: Modelling and Detection (2002)
Gavaghan, D J, Brady, J M, Behrenbruch, C P, Highnam, R P, Maini, P K
This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection....
Crampin, E J, Gaffney, E A, Maini, P K
Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates...
Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations (2002)
Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter space in the positive initial enzyme-initial substrate...
Pattern formation and wound healing (2002)
One of the main immediate challenges in the biomedical sciences is the synthesis of the vast amount of data now available at the molecular and cellular levels for development, regulation and repair....
Making sense of complex phenomena in biology, (2002)
The remarkable advances in biotechnology over the past two decades have resulted in the generation of a huge amount of experimental data. It is now recognized that, in many cases, to extract...
A mathematical model for germinal centre kinetics and affinity maturation (2002)
We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction....
Investigating a simple model of cutaneous wound healing angiogenesis (2002)
Gaffney, E. A., Pugh, K., Maini, P. K., Arnold, F.
A simple model of wound healing angiogenesis is presented, and investigated using numerical and asymptotic techniques. The model captures many key qualitative features of the wound healing angiogenic...
Mathematical models for cell-matrix interactions during dermal wound healing (2002)
Maini, P. K., Olsen, L., Sherratt, J. A.
This paper contains a review of our recent work on the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing. The models are of...
A predictive model for color pattern formation in the buttery wing of Papilio dardanus (2002)
Madzvamuse, A., Maini, P. K., Wathen, A. J., Sekimura, T.
Previously, we have proposed a mathematical model based on a modified Turing mechanism to account for pigmentation patterning in the butterfly wing of Papilio dardanus, well-known for the spectacular...
Size dependent symmetry breaking in models for morphogenesis (2002)
Barrio, R. A., Maini, P. K., Aragón, J. L., Torres, M.
A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed...
Pattern formation in reaction-diffusion models with nonuniform growth (2002)
Crampin, E. J., Hackborn, W. W., Maini, P. K.
Recent examples of biological pattern formation where a pattern changes qualitatively as the underlying domain grows have given rise to renewed interest in the reaction-diffusion (Turing) model for...
How to generate pentagonal symmetry using Turing systems (2002)
Aragón, J. L., Torres, M., Gil, D., Barrio, R. A., Maini, P. K.
We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of...
Madzvamuse, A., Thomas, R. D. K., Maini, P. K., Wathen, A. J.
In this paper, we employ the novel application of a reaction-diffusion model on a growing domain to examine growth patterns of the ligaments of arcoid bivalves (marine molluscs) using realistic...
The dynamics and pinning of a spike for a reaction-diffusion system (2002)
Ward, M. J., McInerney, D., Houston, P., Gavaghan, D., Maini, P. K.
The motion of a one-spike solution to a simplified form of the Gierer--Meinhardt activator-inhibitor model is studied in both a one-dimensional and a two-dimensional domain. The pinning effect on the...
Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology (2002)
Schnell, S., Maini, P. K., McInerney, D., Gavaghan, D., Houston, P.
Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study...
Gatenby, R. A., Maini, P. K., Gawlinski, E. T.
We use a novel “inverse problem” technique to construct a basic mathematical model of the interacting populations at the tumor-host interface. This approach assumes that invasive cancer is a...
Breast Cancer: Modelling and Detection (2002)
Gavaghan, D. J., Brady, J. M., Behrenbruch, C. P., Highnam, R. P., Maini, P. K.
This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection....
Crampin, E. J., Gaffney, E. A., Maini, P. K.
Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates...
Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations (2002)
Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter space in the positive initial enzyme-initial substrate...
Pattern formation and wound healing (2002)
One of the main immediate challenges in the biomedical sciences is the synthesis of the vast amount of data now available at the molecular and cellular levels for development, regulation and repair....
Reaction-diffusion models for biological pattern formation (2001)
We consider the use of reaction-diffusion equations to model biological pattern formation and describe the derivation of the reaction-terms for several illustrative examples. After a brief discussion...
Applications of mathematical modelling to biological pattern formation, (2001)
The formation of spatiotemporal patterning in biology has intrigued experimentalists and theoreticians for many generations. Here we present a brief review of some mathematical models for pattern...
Modelling biological pattern formation: The role of domain growth (2001)
One of the central puzzles in developmental biology concerns the formation of spatio-temporal patterns during early embryogenesis. Although genes ultimately determine spatial structure and form, the...
Satnoianu, R A, Maini, P K, Menzinger, M
new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates...
Explaining rain forest diversity (2001)
Bampfylde, C J, Brown, N D, Gavaghan, D J, Maini, P K
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Dallon, J C, Sherratt, J A, Maini, P K
We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of transforming growth factor-β (TGFβ.) Our work extends...
Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation (2001)
Satnoianu, R A, Maini, P K, Sánchez-Garduño, F, Armitage, J P
We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting...
A model of primitive streak initiation in the chick embryo (2001)
Page, K M, Maini, P K, Monk, N A M, Stern, C D
Initiation of the primitive streak in avian embryos provides a well-studied example of a pattern-forming event that displays a striking capacity for regulation. The mechanisms underlying the...
Schnell, S, Painter, K J, Maini, P K, Othmer, H G
The basic body plan of a number of vertebrates results from two processes that occur early in the development of the blastoderm: large scale rearrangements of tissue via a process called...
Reaction-diffusion models for biological pattern formation (2001)
We consider the use of reaction-diffusion equations to model biological pattern formation and describe the derivation of the reaction-terms for several illustrative examples. After a brief discussion...
Applications of mathematical modelling to biological pattern formation, (2001)
The formation of spatiotemporal patterning in biology has intrigued experimentalists and theoreticians for many generations. Here we present a brief review of some mathematical models for pattern...
Modelling biological pattern formation: The role of domain growth (2001)
One of the central puzzles in developmental biology concerns the formation of spatio-temporal patterns during early embryogenesis. Although genes ultimately determine spatial structure and form, the...
Satnoianu, R. A., Maini, P. K., Menzinger, M.
new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates...
Explaining rain forest diversity (2001)
Bampfylde, C. J., Brown, N. D., Gavaghan, D. J., Maini, P. K.
This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The...
Dallon, J. C., Sherratt, J. A., Maini, P. K.
We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of transforming growth factor-β (TGFβ.) Our work extends...
Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation (2001)
Satnoianu, R. A., Maini, P. K., Sánchez-Garduño, F., Armitage, J. P.
We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting...
A model of primitive streak initiation in the chick embryo (2001)
Page, K. M., Maini, P. K., Monk, N. A. M., Stern, C. D.
Initiation of the primitive streak in avian embryos provides a well-studied example of a pattern-forming event that displays a striking capacity for regulation. The mechanisms underlying the...
Schnell, S., Painter, K. J., Maini, P. K., Othmer, H. G.
The basic body plan of a number of vertebrates results from two processes that occur early in the development of the blastoderm: large scale rearrangements of tissue via a process called...
A cell cycle model for somitogenesis: mathematical formulation and numerical simulation (2000)
Collier, J R, McInerney, D, Schnell, S, Maini, P K, Gavaghan, D J, Houston, P, ...
After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems...
Turing instabilities in general systems (2000)
Satnoianu, R A, Menzinger, M, Maini, P K
We present necessary and sufficient conditions on the stability matrix of a general n(S2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing...
Dallon, J, Sherratt, J, Maini, P K, Ferguson, M
We deveiop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a...
Development and applications of a model for cellular response to multiple chemotactic cues (2000)
Painter, K J, Maini, P K, Othmer, H G
The chemotactic response of a cell population to a single chemical species has been characterized experimentally for many cell types and has been extensively studied from a theoretical standpoint....
A model for colour pattern formation in the buttery wing of Papilio dardanus (2000)
Sekimura, T, Madzvamuse, A, Wathen, A J, Maini, P K
The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a...
Thomas, R D K, Madzvamuse, A, Maini, P K, Wathen, A J
The dorsal ligaments of arcoid bivalves typically consist of oblique, lamellar and fibrous sheets, alternating along the hinge so that their attachments form characteristic chevron patterns. New...
n/a
Clock and induction model for somitogenesis (2000)
After many years of research, somitogenesis is still one of the major unresolved problems in developmental biology. Recent experimental findings show a novel type of pattern formation in which a...
A chemotactic model for the advance and retreat of the primitive streak in avian development (2000)
Painter, K J, Maini, P K, Othmer, H G
The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective...
Enzyme kinetics at high enzyme concentrations (2000)
We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0...
Sekimura, T, Roose, T, Li, B, Maini, P K, Hara, T
Plants change their shapes, depending on their environment, for example, plant height increases with increasing population density. We examined the density-dependent plasticity in shoot morphology of...
An envelope method for analysing sequential pattern formation (2000)
Cruywagen, G C, Maini, P K, Murray, J D
We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady...
Dispersal can sharpen parapatric boundaries on a spatially varying environment (2000)
Garcia-Ramos, G, Sánchez-Garduño, F, Maini, P K
Parapatry describes a geographic pattern in which the ranges of two species have separate but contiguous distributions without any physical barriers between them. We present results from a study of...
A chemotactic model for the advance and retreat of the primitive streak in avian development (2000)
K. J. Painter, P. K. Maini, H. G. Othmer
The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective...
Enzyme kinetics at high enzyme concentration (2000)
We re-visit previous analyses of the classical Michaelis–Menten substrate–enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt...
A cell cycle model for somitogenesis: mathematical formulation and numerical simulation (2000)
Collier, J. R., McInerney, D., Schnell, S., Maini, P. K., Gavaghan, D. J., Houston, P., ...
After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems...
Turing instabilities in general systems (2000)
Satnoianu, R. A., Menzinger, M., Maini, P. K.
We present necessary and sufficient conditions on the stability matrix of a general n(S2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing...
Dallon, J., Sherratt, J., Maini, P. K., Ferguson, M.
We deveiop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a...
Development and applications of a model for cellular response to multiple chemotactic cues (2000)
Painter, K. J., Maini, P. K., Othmer, H. G.
The chemotactic response of a cell population to a single chemical species has been characterized experimentally for many cell types and has been extensively studied from a theoretical standpoint....
A model for colour pattern formation in the buttery wing of Papilio dardanus (2000)
Sekimura, T., Madzvamuse, A., Wathen, A. J., Maini, P. K.
The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a...
Thomas, R. D. K., Madzvamuse, A., Maini, P. K., Wathen, A. J.
The dorsal ligaments of arcoid bivalves typically consist of oblique, lamellar and fibrous sheets, alternating along the hinge so that their attachments form characteristic chevron patterns. New...
n/a
Clock and induction model for somitogenesis (2000)
After many years of research, somitogenesis is still one of the major unresolved problems in developmental biology. Recent experimental findings show a novel type of pattern formation in which a...
A chemotactic model for the advance and retreat of the primitive streak in avian development (2000)
Painter, K. J., Maini, P. K., Othmer, H. G.
The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective...
Enzyme kinetics at high enzyme concentrations (2000)
We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0...
Sekimura, T., Roose, T., Li, B., Maini, P. K., Hara, T.
Plants change their shapes, depending on their environment, for example, plant height increases with increasing population density. We examined the density-dependent plasticity in shoot morphology of...
An envelope method for analysing sequential pattern formation (2000)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady...
Dispersal can sharpen parapatric boundaries on a spatially varying environment (2000)
Garcia-Ramos, G., Sánchez-Garduño, F., Maini, P. K.
Parapatry describes a geographic pattern in which the ranges of two species have separate but contiguous distributions without any physical barriers between them. We present results from a study of...
Reaction and diffusion on growing domains: Scenarios for robust pattern formation (1999)
Crampin, E J, Gaffney, E A, Maini, P K
We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion...
Gaffney, E A, Maini, P K, McCaig, C D, Zhao, M, Forrester, J V
A new framework for the modelling of corneal epithelial wound healing is presented, which can include the presence of a physiological electric field. The difficulty inherent in the inclusion of this...
Dallon, J, Sherratt, J, Maini, P K
Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the...
Painter, K J, Maini, P K, Othmer, H G
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce...
Mathematical modelling of anisotropy in fibrous connective tissue (1999)
Olsen, L, Maini, P K, Sherratt, J A, Dallon, J
We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial...
A two-dimensional numerical study of spatial pattern formation in interacting Turing systems (1999)
Barrio, R A, Varea, C, Aragon, J L, Maini, P K
For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rôle...
The mathematical modelling of cell kinetics in corneal epithelial wound healing (1999)
Gaffney, E A, Maini, P K, Sherratt, J A, Tuft, S
This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a...
Sekimura, T, Zhu, M, Cook, J, Maini, P K
We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial...
Mathematical modelling of signalling in Dictyostelium discoideum (1999)
Sherratt, J A, Dallon, J C, Hofer, T, Maini, P K
n/a
Reaction and diffusion on growing domains: Scenarios for robust pattern formation (1999)
Crampin, E. J., Gaffney, E. A., Maini, P. K.
We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion...
Gaffney, E. A., Maini, P. K., McCaig, C. D., Zhao, M., Forrester, J. V.
A new framework for the modelling of corneal epithelial wound healing is presented, which can include the presence of a physiological electric field. The difficulty inherent in the inclusion of this...
Dallon, J., Sherratt, J., Maini, P. K.
Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the...
Painter, K. J., Maini, P. K., Othmer, H. G.
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce...
Mathematical modelling of anisotropy in fibrous connective tissue (1999)
Olsen, L., Maini, P. K., Sherratt, J. A., Dallon, J.
We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial...
A two-dimensional numerical study of spatial pattern formation in interacting Turing systems (1999)
Barrio, R. A., Varea, C., Aragón, J. L., Maini, P. K.
For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rôle...
The mathematical modelling of cell kinetics in corneal epithelial wound healing (1999)
Gaffney, E. A., Maini, P. K., Sherratt, J. A., Tuft, S.
This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a...
Sekimura, T., Zhu, M., Cook, J., Maini, P. K.
We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial...
Mathematical modelling of signalling in Dictyostelium discoideum (1999)
Sherratt, J. A., Dallon, J. C., Hofer, T., Maini, P. K.
n/a
GAFFNEY, E. A., MAINI, P. K., MCCAIG, C. D., ZHAO, M., FORRESTER, J. V.
A new framework for the modelling of corneal epithelial wound healing is presented, which can include the presence of a physiological electric field. The difficulty inherent in the inclusion of this...
Aragon, J L, Varea, C, Barrio, R A, Maini, P K
In this paper we extend the study of Turing models to investigate the rôle of boundary conditions, parameter modulation, domain growth, and coupling of models. Our numerical simulations show that...
Pattern formation in Lepidopteran wings (1998)
Sekimura, T, Maini, P K, Nardi, J B, Zhu, M, Murray, J D
Two different kinds of patterns have been studied in lepidopteran wings - color pattern and the spacing pattern of scale cells. These patterns exist on two different spatial scales. In the early...
Olsen, L, Maini, P K, Sherratt, J A, Marchant, B
We present a generic model to investigate alignment due to cell movement with specific application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions...
Pattern formation in a generalised chemotactic model (1998)
Myerscough, M R, Maini, P K, Painter, K J
Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to...
Spatially varying equilibria of mechanical models: Application to dermal wound contraction (1998)
Olsen, L, Maini, P K, Sherratt, J A
Mechanochemical models based on the Oster-Murray continuum framework have been applied to a variety of biological settings to obtain an understanding of the morphogenesis of living tissues....
Unravelling the Turing bifurcation using spatially varying diffusion coefficients (1998)
Benson, D L, Maini, P K, Sherratt, J A
The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors...
Olsen, L, Maini, P K, Sherratt, J A, Marchant, B
We present a generic model to investigate alignment due to cell movement with specific application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions...
Aragón, J. L., Varea, C., Barrio, R. A., Maini, P. K.
In this paper we extend the study of Turing models to investigate the rôle of boundary conditions, parameter modulation, domain growth, and coupling of models. Our numerical simulations show that...
Pattern formation in Lepidopteran wings (1998)
Sekimura, T., Maini, P. K., Nardi, J. B., Zhu, M., Murray, J. D.
Two different kinds of patterns have been studied in lepidopteran wings - color pattern and the spacing pattern of scale cells. These patterns exist on two different spatial scales. In the early...
Olsen, L., Maini, P. K., Sherratt, J. A., Marchant, B.
We present a generic model to investigate alignment due to cell movement with specific application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions...
Pattern formation in a generalised chemotactic model (1998)
Myerscough, M. R., Maini, P. K., Painter, K. J.
Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to...
Spatially varying equilibria of mechanical models: Application to dermal wound contraction (1998)
Olsen, L., Maini, P. K., Sherratt, J. A.
Mechanochemical models based on the Oster-Murray continuum framework have been applied to a variety of biological settings to obtain an understanding of the morphogenesis of living tissues....
Unravelling the Turing bifurcation using spatially varying diffusion coefficients (1998)
Benson, D. L., Maini, P. K., Sherratt, J. A.
The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors...
Olsen, L., Maini, P. K., Sherratt, J. A., Marchant, B.
We present a generic model to investigate alignment due to cell movement with specific application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions...
Spatial pattern formation in chemical and biological systems (1997)
Maini, P K, Painter, K J, Chau, H N P
One of the central issues in developmental biology is the formation of spatial pattern in the embryo. A number of theories have been proposed to account for this phenomenon. The most widely studied...
Dale, P D, Sherratt, J A, Maini, P K
Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which...
Streaming instability of slime mold amoebae: An analytical model (1997)
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a...
Olsen, L, Sherratt, J A, Maini, P K, Arnold, F
Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic...
Bones, feathers, teeth and coat marking: a unified model (1997)
The formation of structure within the developing embryo is perhaps the most important and remarkable phenomenon in science. From the almost uniform mass of dividing cells in the very early stage of...
A mechanochemical model for normal and abnormal dermal wound repair (1997)
Olsen, L, Maini, P K, Sherratt, J A
n/a
Hierarchically coupled ultradian oscillators generating robust circadian rhythms (1997)
Barrio, R A, Zhang, L, Maini, P K
Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many...
Models of Dictyostelium discoideum aggregation (1997)
Dallon, J C, Othmer, H G, Van Oss, C, Panfilov, A, Hogeweg, P, Hofer, T, ...
n/a
Boundary-driven instability (1997)
We analyse a reaction-diffusion system and show that complex spatial patterns can be generated by imposing Dirichlet boundary conditions on one or more of the reactant concentrations. This pattern...
Wound healing in the corneal epithelium: biological mechanisms and mathematical models (1997)
Gaffney, E A, Maini, P K, Sherratt, J A, Dale, P D
Corneal epithelium has a highly specialised wound-healing response. The biological aspects of this repair process are reviewed, and methods of modelling it mathematically are described. A model which...
Biological pattern formation on two-dimensional domains: A nonlinear bifurcation analysis (1997)
Cruywagen, G C, Maini, P K, Murray, J D
A tissue interaction model for skin organ pattern formation is presented. Possible spatially patterned solutions on rectangular domains are investigated. Linear stability analysis suggests that the...
Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations (1997)
Sánchez-Garduño, F, Maini, P K
In this paper we study the existence of one-dimensional travelling wave solutions $u(x,t)=\phi(x-ct)$ for the non-linear degenerate (at u=0) reaction-diffusion equation $u_t=[D(u)u_x]_x+g(u)$ where g...
Spatial pattern formation in chemical and biological systems (1997)
Maini, P. K., Painter, K. J., Chau, H. N. P.
One of the central issues in developmental biology is the formation of spatial pattern in the embryo. A number of theories have been proposed to account for this phenomenon. The most widely studied...
Dale, P. D., Sherratt, J. A., Maini, P. K.
Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which...
Streaming instability of slime mold amoebae: An analytical model (1997)
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a...
Olsen, L., Sherratt, J. A., Maini, P. K., Arnold, F.
Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic...
Bones, feathers, teeth and coat marking: a unified model (1997)
The formation of structure within the developing embryo is perhaps the most important and remarkable phenomenon in science. From the almost uniform mass of dividing cells in the very early stage of...
A mechanochemical model for normal and abnormal dermal wound repair (1997)
Olsen, L., Maini, P. K., Sherratt, J. A.
n/a
Hierarchically coupled ultradian oscillators generating robust circadian rhythms (1997)
Barrio, R. A., Zhang, L., Maini, P. K.
Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many...
Models of Dictyostelium discoideum aggregation (1997)
Dallon, J. C., Othmer, H. G., Van Oss, C., Panfilov, A., Hogeweg, P., Hofer, T., ...
n/a
Boundary-driven instability (1997)
Maini, P. K., Myerscough, M. R.
We analyse a reaction-diffusion system and show that complex spatial patterns can be generated by imposing Dirichlet boundary conditions on one or more of the reactant concentrations. This pattern...
Wound healing in the corneal epithelium: biological mechanisms and mathematical models (1997)
Gaffney, E. A., Maini, P. K., Sherratt, J. A., Dale, P. D.
Corneal epithelium has a highly specialised wound-healing response. The biological aspects of this repair process are reviewed, and methods of modelling it mathematically are described. A model which...
Biological pattern formation on two-dimensional domains: A nonlinear bifurcation analysis (1997)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
A tissue interaction model for skin organ pattern formation is presented. Possible spatially patterned solutions on rectangular domains are investigated. Linear stability analysis suggests that the...
Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations (1997)
Sánchez-Garduño, F., Maini, P. K.
In this paper we study the existence of one-dimensional travelling wave solutions $u(x,t)=\phi(x-ct)$ for the non-linear degenerate (at u=0) reaction-diffusion equation $u_t=[D(u)u_x]_x+g(u)$ where g...
Collier, J R, Monk, N A M, Maini, P K, Lewis, J H
In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can...
Dale, P D, Sherratt, J A, Maini, P K
Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3,...
Sánchez-Garduño, F, Kappos, E, Maini, P K
In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly...
A reaction-diffusion-advection model of multicellular morphogenesis during in the aggregation phase of the microorganism Dictyostelium discoideum is reviewed. Linear analysis identifies a novel...
A mathematical model for fibro-proliferative wound healing disorders (1996)
Olsen, L, Sherratt, J A, Maini, P K
The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as...
Sánchez-Garduño, F, Maini, P K, Kappos, E
In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x +...
The cellular slime mould Dictyostelium discoideum provides a paradin model system for the study of multicellular pattern formation. Its life cycle involves a route to primitive multicellular...
On a model mechanism for the spatial patterning of teeth primordia in the Alligator (1996)
Kulesa, P M, Cruywagen, G C, Lubkin, S R, Maini, P K, Sneyd, J, Ferguson, M W J, ...
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986,...
Spatial and spatiotemporal pattern formation in generalised Turing systems (1996)
Reaction-diffusion, or Turing, models have been proposed to account for a number of pattern formation phenomena in early development. However, there are a number of crucial morphogenetic phenomena...
Simple vs. sophisticated models of breath alcohol exhalation profiles (1996)
Lubkin, S R, Gullberg, R G, Logan, B K, Maini, P K, Murray, J D
For medicolegal purposes, breath alcohol content is typically determined from an end-expiratory sample. Measurements obtained by this method necessarily underestimate the alveolar breath alcohol...
Sánchez-Garduño, F, Maini, P K, Kappos, E
In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x +...
Collier, J. R., Monk, N. A. M., Maini, P. K., Lewis, J. H.
In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can...
Dale, P. D., Sherratt, J. A., Maini, P. K.
Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3,...
Sánchez-Garduño, F., Kappos, E., Maini, P. K.
In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly...
A reaction-diffusion-advection model of multicellular morphogenesis during in the aggregation phase of the microorganism Dictyostelium discoideum is reviewed. Linear analysis identifies a novel...
A mathematical model for fibro-proliferative wound healing disorders (1996)
Olsen, L., Sherratt, J. A., Maini, P. K.
The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as...
Sánchez-Garduño, F., Maini, P. K., Kappos, E.
In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x +...
The cellular slime mould Dictyostelium discoideum provides a paradin model system for the study of multicellular pattern formation. Its life cycle involves a route to primitive multicellular...
On a model mechanism for the spatial patterning of teeth primordia in the Alligator (1996)
Kulesa, P. M., Cruywagen, G. C., Lubkin, S. R., Maini, P. K., Sneyd, J., Ferguson, M. W. J., ...
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986,...
Spatial and spatiotemporal pattern formation in generalised Turing systems (1996)
Reaction-diffusion, or Turing, models have been proposed to account for a number of pattern formation phenomena in early development. However, there are a number of crucial morphogenetic phenomena...
Simple vs. sophisticated models of breath alcohol exhalation profiles (1996)
Lubkin, S. R., Gullberg, R. G., Logan, B. K., Maini, P. K., Murray, J. D.
For medicolegal purposes, breath alcohol content is typically determined from an end-expiratory sample. Measurements obtained by this method necessarily underestimate the alveolar breath alcohol...
Sánchez-Garduño, F., Maini, P. K., Kappos, E.
In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x +...
Travelling waves in wound healing (1995)
Dale, P D, Olsen, L, Maini, P K, Sherratt, J A
We illustrate the role of travelling waves in wound healing by considering three different cases. Firstly, we review a model for surface wound healing in the cornea and focus on the speed of healing...
A receptor based model for pattern formation in Hydra (1995)
Sherratt, J A, Maini, P K, Jager, W, Muller, W A
We propose a new theoretical model for pattern regulation in Hydra. Our model treats positional value and "head activation potential" as manifestations of the same cellular property, the amount of a...
Olsen, L, Sherratt, J A, Maini, P K
The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic...
The spread of viral infection in moths, (1995)
Roose, T, Maini, P K, Cory, J, Hails, R
To control insect pests with a virus, it is important to determine the optimum time for the treatment. However, before analysing this problem, a realistic model for the uninfected host must be...
Phase differences in reaction-diffusion-advection systems and applications to morphogenesis (1995)
Perumpanani, A J, Sherratt, J A, Maini, P K
The authors study the effect of advection on reaction-diffusion patterns. It is shown that the addition of advection to a two-variable reaction–diffusion system with periodic boundary conditions...
Cellular pattern formation during Dictyostelium aggregation (1995)
Hofer, T, Sherratt, J A, Maini, P K
The development of multicellularity in the life cycle of Dictyostelium discoideum provides a paradigm model system for biological pattern formation. Previously, mathematical models have shown how a...
Dictyostelium discoideum: Cellular self-organisation in an excitable medium (1995)
Hofer, T, Sherratt, J A, Maini, P K
The dynamics which govern the establishment of pattern and form in multicellular organisms remain a key problem of developmental biology. We study this question in the case of morphogenesis during...
Kulesa, P M, Cruywagen, G C, Lubkin, S R, Maini, P K, Sneyd, J S, Murray, J D
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies12–14 have shown that jaw...
A mechanochemical model for adult dermal wound contraction (1995)
Olsen, L, Sherratt, J A, Maini, P K
We propose a deterministic mathematical model to describe the biomechanics and cell biology of wound contraction, a ubiquitous feature in the normal healing of adult dermal excisional wounds. Our aim...
Corneal epithelial wound healing (1995)
Dale, P D, Sherratt, J A, Maini, P K
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
Hofer, T, Maini, P K, Sherratt, J A, Chaplain, M A J, Murray, J D
The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in...
Hierarchical models for spatial pattern formation in biology (1995)
We review some recent work investigating a hierarchy of patterning processes in which a reaction-diffusion model forms the top level. In one such hierarchy, it is assumed that the boundary is...
Rhythmic firing patterns in SCN: The role of circuit interactions (1995)
Zhang, L, Aguilar-Roblero, R, Barrio, R A, Maini, P K
The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological...
Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis (1995)
We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the...
Hofer, T, Maini, P K, Sherratt, J A, Chaplain, M A J, Murray, J D
The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in...
A mechanochemical model for adult dermal wound contraction (1995)
Olsen, L, Sherratt, J A, Maini, P K
We propose a deterministic mathematical model to describe the biomechanics and cell biology of wound contraction, a ubiquitous feature in the normal healing of adult dermal excisional wounds. Our aim...
Corneal epithelial wound healing (1995)
Dale, P D, Sherratt, J A, Maini, P K
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
Travelling waves in wound healing (1995)
Dale, P. D., Olsen, L., Maini, P. K., Sherratt, J. A.
We illustrate the role of travelling waves in wound healing by considering three different cases. Firstly, we review a model for surface wound healing in the cornea and focus on the speed of healing...
A receptor based model for pattern formation in Hydra (1995)
Sherratt, J. A., Maini, P. K., Jager, W., Muller, W. A.
We propose a new theoretical model for pattern regulation in Hydra. Our model treats positional value and "head activation potential" as manifestations of the same cellular property, the amount of a...
Olsen, L., Sherratt, J. A., Maini, P. K.
The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic...
The spread of viral infection in moths, (1995)
Roose, T., Maini, P. K., Cory, J., Hails, R.
To control insect pests with a virus, it is important to determine the optimum time for the treatment. However, before analysing this problem, a realistic model for the uninfected host must be...
Phase differences in reaction-diffusion-advection systems and applications to morphogenesis (1995)
Perumpanani, A. J., Sherratt, J. A., Maini, P. K.
The authors study the effect of advection on reaction-diffusion patterns. It is shown that the addition of advection to a two-variable reaction–diffusion system with periodic boundary conditions...
Cellular pattern formation during Dictyostelium aggregation (1995)
Hofer, T., Sherratt, J. A., Maini, P. K.
The development of multicellularity in the life cycle of Dictyostelium discoideum provides a paradigm model system for biological pattern formation. Previously, mathematical models have shown how a...
Dictyostelium discoideum: Cellular self-organisation in an excitable medium (1995)
Hofer, T., Sherratt, J. A., Maini, P. K.
The dynamics which govern the establishment of pattern and form in multicellular organisms remain a key problem of developmental biology. We study this question in the case of morphogenesis during...
Kulesa, P. M., Cruywagen, G. C., Lubkin, S. R., Maini, P. K., Sneyd, J. S., Murray, J. D.
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies12–14 have shown that jaw...
A mechanochemical model for adult dermal wound contraction (1995)
Olsen, L., Sherratt, J. A., Maini, P. K.
We propose a deterministic mathematical model to describe the biomechanics and cell biology of wound contraction, a ubiquitous feature in the normal healing of adult dermal excisional wounds. Our aim...
Hofer, T., Maini, P. K., Sherratt, J. A., Chaplain, M. A. J., Murray, J. D.
The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in...
Hierarchical models for spatial pattern formation in biology (1995)
We review some recent work investigating a hierarchy of patterning processes in which a reaction-diffusion model forms the top level. In one such hierarchy, it is assumed that the boundary is...
Rhythmic firing patterns in SCN: The role of circuit interactions (1995)
Zhang, L., Aguilar-Roblero, R., Barrio, R. A., Maini, P. K.
The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological...
Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis (1995)
We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the...
Hofer, T., Maini, P. K., Sherratt, J. A., Chaplain, M. A. J., Murray, J. D.
The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in...
A mechanochemical model for adult dermal wound contraction (1995)
Olsen, L., Sherratt, J. A., Maini, P. K.
We propose a deterministic mathematical model to describe the biomechanics and cell biology of wound contraction, a ubiquitous feature in the normal healing of adult dermal excisional wounds. Our aim...
Corneal epithelial wound healing (1995)
Dale, P. D., Sherratt, J. A., Maini, P. K.
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
Coupled models for spatial organization in development (1994)
Several simple models have been proposed to account for spatial organization in early development. Recently, a number of models have been proposed in which such patterning mechanisms are coupled....
A mathematical model for chemotactic movement and aggregation in cellular slime moulds (1994)
Hofer, T, Maini, P K, Sherratt, J A
The cellular slime mould Dictyostelium discoideum (Dd)is a widely studied organism. In starvation conditions, Dd amoebae aggregate into a slug-like body which can crawl some distance before forming a...
Bifurcating spatial patterns arising from travelling waves in a tissue interaction model (1994)
Cruywagen, G C, Maini, P K, Murray, J D
We analyse a tissue interaction model recently proposed to account for pattern formation in the morphogenesis of skin organ primordia. We show that the model can exhibit travelling wave solutions...
Travelling waves in a tissue interaction model for skin pattern formation (1994)
Cruywagen, G C, Maini, P K, Murray, J D
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for...
Sánchez-Garduño, F, Maini, P K
In this paper we use a dynamical systems approach to prove the existence of a unique critical value c * of the speed c for which the degenerate density-dependent diffusion equation $u_t = [D(u)u_x]_x...
A resolution of the chemotactic wave paradox (1994)
Hofer, T, Maini, P K, Sherratt, J A, Chaplain, M A J, Chauvet, P, Metevier, D, ...
We propose an extension of the standard model for cell chemotaxis which explicitly accounts for the adaptation of the chemotactic response. We show that this model resolves the “chemotactic wave...
Mathematical modelling of corneal epithelium wound healing (1994)
Dale, P D, Maini, P K, Sherratt, J A
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
The speed of corneal epithelial wound healing (1994)
Dale, P D, Sherratt, J A, Maini, P K
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
An approximation to a sharp type solution of a density-dependent diffusion equation (1994)
Sánchez-Garduño, F, Maini, P K
In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the...
Nonlinear diffusion of a growth inhibitory factor in multicell spheriods (1994)
Chaplain, M A J, Benson, D L, Maini, P K
A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The model is based on the assumption that the GIF diffuses within the spheroid in...
Travelling wave phenomena in some degenerate reaction-diffusion equations (1994)
Sánchez-Garduño, F, Maini, P K
In this paper we study the existence of travelling wave solutions (t.w.s.), $u(x, t)=\phi(x−ct)$ for the equation $u_t=[D(u)u_x]_x+g(u) (*)$ where the reactive part g(u) is as in the Fisher-KPP...
Dillon, R, Maini, P K, Othmer, H G
Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is...
Pattern formation in tissue interaction models (1994)
Murray, J D, Cruywagen, G C, Maini, P K
Embryogenesis depends on a series of processes which generate specific patterns at each stage of development. For example, gastrulation, chondrogenesis, formation of scale, feather and hair primordia...
Coupled models for spatial organization in development (1994)
Several simple models have been proposed to account for spatial organization in early development. Recently, a number of models have been proposed in which such patterning mechanisms are coupled....
A mathematical model for chemotactic movement and aggregation in cellular slime moulds (1994)
Hofer, T., Maini, P. K., Sherratt, J. A.
The cellular slime mould Dictyostelium discoideum (Dd)is a widely studied organism. In starvation conditions, Dd amoebae aggregate into a slug-like body which can crawl some distance before forming a...
Bifurcating spatial patterns arising from travelling waves in a tissue interaction model (1994)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
We analyse a tissue interaction model recently proposed to account for pattern formation in the morphogenesis of skin organ primordia. We show that the model can exhibit travelling wave solutions...
Travelling waves in a tissue interaction model for skin pattern formation (1994)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for...
Sánchez-Garduño, F., Maini, P. K.
In this paper we use a dynamical systems approach to prove the existence of a unique critical value c * of the speed c for which the degenerate density-dependent diffusion equation $u_t = [D(u)u_x]_x...
A resolution of the chemotactic wave paradox (1994)
Hofer, T., Maini, P. K., Sherratt, J. A., Chaplain, M. A. J., Chauvet, P., Metevier, D., ...
We propose an extension of the standard model for cell chemotaxis which explicitly accounts for the adaptation of the chemotactic response. We show that this model resolves the “chemotactic wave...
Mathematical modelling of corneal epithelium wound healing (1994)
Dale, P. D., Maini, P. K., Sherratt, J. A.
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
The speed of corneal epithelial wound healing (1994)
Dale, P. D., Sherratt, J. A., Maini, P. K.
We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically...
An approximation to a sharp type solution of a density-dependent diffusion equation (1994)
Sánchez-Garduño, F., Maini, P. K.
In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the...
Nonlinear diffusion of a growth inhibitory factor in multicell spheriods (1994)
Chaplain, M. A. J., Benson, D. L., Maini, P. K.
A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The model is based on the assumption that the GIF diffuses within the spheroid in...
Travelling wave phenomena in some degenerate reaction-diffusion equations (1994)
Sánchez-Garduño, F., Maini, P. K.
In this paper we study the existence of travelling wave solutions (t.w.s.), $u(x, t)=\phi(x−ct)$ for the equation $u_t=[D(u)u_x]_x+g(u) (*)$ where the reactive part g(u) is as in the Fisher-KPP...
Dillon, R., Maini, P. K., Othmer, H. G.
Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is...
Pattern formation in tissue interaction models (1994)
Murray, J. D., Cruywagen, G. C., Maini, P. K.
Embryogenesis depends on a series of processes which generate specific patterns at each stage of development. For example, gastrulation, chondrogenesis, formation of scale, feather and hair primordia...
Suicide substrate reaction-diffusion equations: varying the source (1993)
Burke, M A, Maini, P K, Murray, J D
The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of...
Travelling waves in density-dependent dispersion models (1993)
Maini, P K, Sánchez-Garduño, F
Many models have been proposed to account for the spatial dispersion of population of insects, bacteria, etc. Some species migrate from densely populated areas into sparsely populated regions to...
Benson, D L, Maini, P K, Sherratt, J A
We consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially...
Mathematical modelling of ethanol metabolism in normal subjects and chronic alcohol misusers (1993)
Smith, G D, Shaw, L J, Maini, P K, Ward, R J, Peters, T J, Murray, J D
The time course of ethanol disappearance from the blood has been examined in normal males and females and in alcohol misusers. Blood alcohol estimations were made over a period of 3 hr, following an...
Pattern formation in Turing systems with mixed boundary conditions (1993)
Maini, P K, Dillon, R, Othmer, H G
A central issue in developmental biology is the formation of pattern and form in the early embryo. From the apparently homogeneous mass of dividing cells that exists in the earliest stages of...
Steady-state patterns in a reaction diffusion system with mixed boundary conditions (1993)
Maini, P K, Dillon, R, Othmer, H G
A number of models for pattern formation and regulation are based on the hypothesis that a diffusible morphogen supplies positional information that can interpreted by cells. Such models fall into...
Wave patterns in one-dimensional nonlinear degenerate diffusion equations (1993)
Sánchez-Garduño, F, Maini, P K
Several different types of wave patterns occur in physiology, chemistry and biology. In many cases such phenomena are modelled by reactive-diffusive parabolic systems (see, for example, Fisher 1937;...
Sequential and synchronous skin pattern formation (1993)
Cruywagen, G C, Maini, P K, Murray, J D
Mathematical modelling has become a widely accepted method for examining how and why vertebrate skin structures are laid down in an orderly and organized fashion. Although various theoretical models...
Pattern formation in heterogeneous domains (1993)
Benson, D L, Maini, P K, Sherratt, J A
Development of spatial pattern in the early embryo results from the interaction of several processes in a complex hierarchy of mechanisms. Most models for morphogenesis to date have, however,...
Diffusion driven instability in an inhomogeneous domain (1993)
Benson, D L, Sherratt, J A, Maini, P K
Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of...
Bifurcating spatial patterns in a cell-chemotaxis model (1993)
Maini, P K, Winters, K H, Myerscough, M R, Murray, J D
Spatial pattern formation is a key issue in early embroynic development. Embroynic cells divide, migrate, and differentiate to form the various structures, markings and organs of the body. Perhaps...
Suicide substrate reaction-diffusion equations: varying the source (1993)
Burke, M. A., Maini, P. K., Murray, J. D.
The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of...
Travelling waves in density-dependent dispersion models (1993)
Maini, P. K., Sánchez-Garduño, F.
Many models have been proposed to account for the spatial dispersion of population of insects, bacteria, etc. Some species migrate from densely populated areas into sparsely populated regions to...
Benson, D. L., Maini, P. K., Sherratt, J. A.
We consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially...
Mathematical modelling of ethanol metabolism in normal subjects and chronic alcohol misusers (1993)
Smith, G. D., Shaw, L. J., Maini, P. K., Ward, R. J., Peters, T. J., Murray, J. D.
The time course of ethanol disappearance from the blood has been examined in normal males and females and in alcohol misusers. Blood alcohol estimations were made over a period of 3 hr, following an...
Pattern formation in Turing systems with mixed boundary conditions (1993)
Maini, P. K., Dillon, R., Othmer, H. G.
A central issue in developmental biology is the formation of pattern and form in the early embryo. From the apparently homogeneous mass of dividing cells that exists in the earliest stages of...
Steady-state patterns in a reaction diffusion system with mixed boundary conditions (1993)
Maini, P. K., Dillon, R., Othmer, H. G.
A number of models for pattern formation and regulation are based on the hypothesis that a diffusible morphogen supplies positional information that can interpreted by cells. Such models fall into...
Wave patterns in one-dimensional nonlinear degenerate diffusion equations (1993)
Sánchez-Garduño, F., Maini, P. K.
Several different types of wave patterns occur in physiology, chemistry and biology. In many cases such phenomena are modelled by reactive-diffusive parabolic systems (see, for example, Fisher 1937;...
Sequential and synchronous skin pattern formation (1993)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
Mathematical modelling has become a widely accepted method for examining how and why vertebrate skin structures are laid down in an orderly and organized fashion. Although various theoretical models...
Pattern formation in heterogeneous domains (1993)
Benson, D. L., Maini, P. K., Sherratt, J. A.
Development of spatial pattern in the early embryo results from the interaction of several processes in a complex hierarchy of mechanisms. Most models for morphogenesis to date have, however,...
Diffusion driven instability in an inhomogeneous domain (1993)
Benson, D. L., Sherratt, J. A., Maini, P. K.
Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of...
Bifurcating spatial patterns in a cell-chemotaxis model (1993)
Maini, P. K., Winters, K. H., Myerscough, M. R., Murray, J. D.
Spatial pattern formation is a key issue in early embroynic development. Embroynic cells divide, migrate, and differentiate to form the various structures, markings and organs of the body. Perhaps...
Suicide substrate reaction-diffusion equations: Varying the source (1993)
BURKE, MEGHAN A., MAINI, P. K., MURRAY, J. D.
The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of...
Sequential pattern formation in a model for skin morphogenesis (1992)
Cruywagen, G C, Maini, P K, Murray, J D
During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in...
Maini, P K, Benson, D L, Sherratt, J A
Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the...
Environmental instability in heterogeneous domains (1992)
Maini, P K, Benson, D L, Sherratt, J A
Species interaction models have been widely studied to investigate the phenomena of population fluctuations and extinction. To a great degree, these models have assumed that the environment is...
Sequential pattern formation in a model for skin morphogenesis (1992)
Cruywagen, G. C., Maini, P. K., Murray, J. D.
During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in...
Maini, P. K., Benson, D. L., Sherratt, J. A.
Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the...
Environmental instability in heterogeneous domains (1992)
Maini, P. K., Benson, D. L., Sherratt, J. A.
Species interaction models have been widely studied to investigate the phenomena of population fluctuations and extinction. To a great degree, these models have assumed that the environment is...
Sequential pattern formation in a model for skin morphogenesis (1992)
CRUYWAGEN, GERHARD C., MAINI, P. K., MURRAY, J. D.
During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in...
Maini, P K, Burke, Meghan, Murray, J D
We consider a recent extension to the validity of the quasi-steady-state assumption (QSSA) which includes the case where the ratio of the initial enzyme to substrate concentration is not necessarily...
Analysis of a risk based model for the growth of AIDS infection (1991)
De Young, G, Maini, P K, Nakamaye, M
Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the...
The spatial spread of the grey squirrel in Britain (1991)
Maini, P K, Okubo, A, Williamson, M H, Murray, J D
Around the turn of the century the North American grey squirrel, Sciurus carolinensis, was releasted from various sites in Britain. Since then the grey squirrel has successfully spread to colonize...
Tracking bifurcating solutions of a model biological pattern generator (1991)
Winters, K H, Myerscough, M R, Maini, P K, Murray, J D
We study heterogeneous steady-state solutions of a cell-chemotaxis model for generating biological spatial patterns in two-dimensional domains with zero flux boundary conditions. We use the...
Cellular mechanisms of pattern formation in the developing limb (1991)
Development of spatial pattern and form is an important, yet poorly understood phenomenon in embryology. Although genes ultimately control pattern formation, the study of the genetic aspects alone...
A comparison of reaction diffusion and mechanochemical models for limb development (1991)
Several theoretical models have been proposed to attempt to elucidate the underlying mechanisms involved in the spatial patterning of skeletal elements in the limb. Here, I briefly compare two such...
Maini, P K, Myerscough, M R, Murray, J D, Winters, K H
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude,...
Maini, P K, Myerscough, M R, Murray, J D, Winters, K H
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude,...
Maini, P. K., Burke, Meghan, Murray, J. D.
We consider a recent extension to the validity of the quasi-steady-state assumption (QSSA) which includes the case where the ratio of the initial enzyme to substrate concentration is not necessarily...
Analysis of a risk based model for the growth of AIDS infection (1991)
De Young, G., Maini, P. K., Nakamaye, M.
Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the...
The spatial spread of the grey squirrel in Britain (1991)
Maini, P. K., Okubo, A., Williamson, M. H., Murray, J. D.
Around the turn of the century the North American grey squirrel, Sciurus carolinensis, was releasted from various sites in Britain. Since then the grey squirrel has successfully spread to colonize...
Tracking bifurcating solutions of a model biological pattern generator (1991)
Winters, K. H., Myerscough, M. R., Maini, P. K., Murray, J. D.
We study heterogeneous steady-state solutions of a cell-chemotaxis model for generating biological spatial patterns in two-dimensional domains with zero flux boundary conditions. We use the...
Cellular mechanisms of pattern formation in the developing limb (1991)
Development of spatial pattern and form is an important, yet poorly understood phenomenon in embryology. Although genes ultimately control pattern formation, the study of the genetic aspects alone...
A comparison of reaction diffusion and mechanochemical models for limb development (1991)
Several theoretical models have been proposed to attempt to elucidate the underlying mechanisms involved in the spatial patterning of skeletal elements in the limb. Here, I briefly compare two such...
Maini, P. K., Myerscough, M. R., Murray, J. D., Winters, K. H.
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude,...
Maini, P. K., Myerscough, M. R., Murray, J. D., Winters, K. H.
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude,...
On the kinetics of suicide substrates (1990)
Burke, M, Maini, P K, Murray, J D
We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure...
Superposition of modes in a caricature of a model for morphogenesis (1990)
In a model proposed for cell pattern formation by Nagorcka et al. (J. Theor. Biol. 1987) linear analysis revealed the possibility of an initially spatially uniform cell density going unstable to...
Two dimensional pattern formation in a chemotactic system (1990)
Myerscough, M R, Maini, P K, Murray, J D, Winters, K H
Chemotaxis is known to be important in cell aggregation in a variety of contexts. We propose a simple partial differential equation model for a chemotactic system of two species, a population of...
On the kinetics of suicide substrates (1990)
Burke, M., Maini, P. K., Murray, J. D.
We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure...
Superposition of modes in a caricature of a model for morphogenesis (1990)
In a model proposed for cell pattern formation by Nagorcka et al. (J. Theor. Biol. 1987) linear analysis revealed the possibility of an initially spatially uniform cell density going unstable to...
Two dimensional pattern formation in a chemotactic system (1990)
Myerscough, M. R., Maini, P. K., Murray, J. D., Winters, K. H.
Chemotaxis is known to be important in cell aggregation in a variety of contexts. We propose a simple partial differential equation model for a chemotactic system of two species, a population of...
On the spatial spread of the grey squirrel in Britain (1989)
Okubo, A, Maini, P K, Williamson, M H, Murray, J D
We present a diffusion-competition model to describe the mteraction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from...
Spatial and spatio-temporal patterns in a cell-haptotaxis model (1989)
We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the...
Pattern formation mechanisms - a comparison of reaction diffusion and mechanochemical models (1989)
The elucidations of the underlying mechanisms that occur during morphogenesis is of fundamental importance in developmental biology. From the homogeneous mass of dividing cells of the early blastula,...
Splitting of cell clusters and bifurcation of bryozoan branches (1989)
Goldwasser, L, Maini, P K, Murray, J D
We present a cell mechanical model that exhibits the pattern-forming behaviour of a cluster of cells at the growing tips of bryozoan branches. The crucial event in the production of the overall...
On the spatial spread of the grey squirrel in Britain (1989)
Okubo, A., Maini, P. K., Williamson, M. H., Murray, J. D.
We present a diffusion-competition model to describe the mteraction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from...
Spatial and spatio-temporal patterns in a cell-haptotaxis model (1989)
We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the...
Pattern formation mechanisms - a comparison of reaction diffusion and mechanochemical models (1989)
The elucidations of the underlying mechanisms that occur during morphogenesis is of fundamental importance in developmental biology. From the homogeneous mass of dividing cells of the early blastula,...
Splitting of cell clusters and bifurcation of bryozoan branches (1989)
Goldwasser, L., Maini, P. K., Murray, J. D.
We present a cell mechanical model that exhibits the pattern-forming behaviour of a cluster of cells at the growing tips of bryozoan branches. The crucial event in the production of the overall...
We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration...
Mechanochemical models for generating biological pattern and form in development (1988)
Murray, J D, Maini, P K, Tranquillo, R T
The central issue in development is the formation of spatial patterns of cells in the early embryo. The mechanisms which generate these patterns are unknown. Here we describe the new Oster-Murray...
A nonlinear analysis of a mechanical model for pattern formation (1988)
This paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A...
We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration...
Mechanochemical models for generating biological pattern and form in development (1988)
Murray, J. D., Maini, P. K., Tranquillo, R. T.
The central issue in development is the formation of spatial patterns of cells in the early embryo. The mechanisms which generate these patterns are unknown. Here we describe the new Oster-Murray...
A nonlinear analysis of a mechanical model for pattern formation (1988)
This paper studies a simplified but biologically relevant version of a mechanical model for morphogenesis proposed by Oster, Murray, and Harris [J. Embryol. Exp. Morph., 78 (1983), pp. 83–125]. A...
Nonlinear pattern selection in a mechanical model for morphogenesis (1986)
Perelson, A S, Maini, P K, Murray, J D, Hyman, J M, Oster, G F
We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a...
A new approach to the generation of pattern and form in embryology (1986)
A central issue in developmental biology is the formation of spatial pattern in the early embryo. From the homogeneous mass of dividing cells in the very early stge of development, emerge the vast...
An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis (1986)
Maini, P K, Murray, J D, Oster, G F
In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically...
Nonlinear pattern selection in a mechanical model for morphogenesis (1986)
Perelson, A. S., Maini, P. K., Murray, J. D., Hyman, J. M., Oster, G. F.
We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a...
A new approach to the generation of pattern and form in embryology (1986)
A central issue in developmental biology is the formation of spatial pattern in the early embryo. From the homogeneous mass of dividing cells in the very early stge of development, emerge the vast...
An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis (1986)
Maini, P. K., Murray, J. D., Oster, G. F.
In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically...
A model for chondrogenic condensations in the developing limb (1985)
Oster, G F, Murray, J D, Maini, P K
The hyaluronate component of the extracellular matrix is a powerfully hydrophilic polymer, capable of osmotically swelling and deswelling by a volume factor of 5 or more. At the time of cartilage...
A mechanical model for biological pattern formation: A nonlinear bifurcation analysis (1985)
Maini, P K, Murray, J D, Oster, G F
We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on...
A model for chondrogenic condensations in the developing limb (1985)
Oster, G. F., Murray, J. D., Maini, P. K.
The hyaluronate component of the extracellular matrix is a powerfully hydrophilic polymer, capable of osmotically swelling and deswelling by a volume factor of 5 or more. At the time of cartilage...
A mechanical model for biological pattern formation: A nonlinear bifurcation analysis (1985)
Maini, P. K., Murray, J. D., Oster, G. F.
We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on...
Forces and pattern in limb morphogenesis (1984)
Oster, G F, Murray, J D, Maini, P K
Prior to cartilage and bone formation in the limb bud chondroblasts condense into foci which provide the pattern for subsequent bone development. Formation of these condensations is, finally, a...
Forces and pattern in limb morphogenesis (1984)
Oster, G. F., Murray, J. D., Maini, P. K.
Prior to cartilage and bone formation in the limb bud chondroblasts condense into foci which provide the pattern for subsequent bone development. Formation of these condensations is, finally, a...
Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis
Painter, K. J., Maini, P. K., Othmer, H. G.
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce...
Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis
Painter, K. J., Maini, P. K., Othmer, H. G.
Current interest in pattern formation can be traced to a seminal paper by Turing, who demonstrated that a system of reacting and diffusing chemicals, called morphogens, can interact so as to produce...
A model for colour pattern formation in the butterfly wing of Papilio dardanus.
Sekimura, T, Madzvamuse, A, Wathen, A J, Maini, P K
The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a...
Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer
Gatenby, R A, Smallbone, K, Maini, P K, Rose, F, Averill, J, Nagle, R B, ...
Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are...