Developmental biology. The Turing model comes of molecular age.
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Animals↗
Biomedical subjects
Philip K Maini
Publications and source records attributed to Philip K Maini.
Metabolic changes during carcinogenesis: potential impact on invasiveness.
Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane. We find that selective forces in tumoural regions furthest from the blood supply act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. The model predicts three phases of somatic evolution. Initially, cell survival and proliferation is limited due to diminished oxygen levels. This promotes adaptation to a second phase of growth dominated by cells with constitutively up-regulated glycolysis, less reliant on oxygen for ATP production. Increased glycolysis induces acidification of the local environment, limiting proliferation and inducing cell death through necrosis and apoptosis. This promotes a third phase of cellular evolution, with emergence of phenotypes resistant to acid-induced toxicity. This emergent cellular phenotype has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. The model's results suggest this sequence is essential in the transition from self-limited premalignant growth to invasive cancer, and, therefore, that this transition may be delayed or prevented through novel strategies directed towards interrupting the hypoxia-glycolysis-acidosis cycle.
Adenosine Triphosphate↗
Mode transitions in a model reaction-diffusion system driven by domain growth and noise.
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 by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.
Animals↗
An analysis of B cell selection mechanisms in germinal centers.
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 with improved binding characteristics for the antigen. The mechanism underlying B cell selection has not yet been defined. By employing an agent-based model, we show that for physiologically reasonable parameter values affinity maturation can be driven by competition for neither binding sites nor antigen--even in the presence of competing secreted antibodies. Within the tested mechanisms, only clonal competition for T cell help or a refractory time for the interaction of centrocytes with follicular dendritic cells is found to enable affinity maturation while generating the experimentally observed germinal centre characteristics and tolerating large variations in the initial antigen density.
Animals↗
Mathematical models in physiology.
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 more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.
Computer Simulation↗
Distinct mechanisms underlie pattern formation in the skin and skin appendages.
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 patterns. Here, we first introduce the basics of pattern formation and their possible biological basis. We then discuss different categories of skin patterns and their potential underlying molecular mechanisms. Some patterns, such as the lines of Blaschko and Naevus, are based on cell lineage and genetic mosaicism. Other patterns, such as regionally specific skin appendages, can be set by distinct combinatorial molecular codes, which in turn may be set by morphogenetic gradients. There are also some patterns, such as the arrangement of hair follicles (hair whorls) and fingerprints, which involve genetics as well as stochastic epigenetic events based on physiochemical principles. Many appendage primordia are laid out in developmental waves. In the adult, some patterns, such as those involving cycling hair follicles, may appear as traveling waves in mice. Since skin appendages can renew themselves in regeneration, their size and shape can still change in the adult via regulation by hormones and the environment. Some lesion patterns are based on pathological changes involving the above processes and can be used as diagnostic criteria in medicine. Understanding the different mechanisms that lead to patterns in the skin will help us appreciate their full significance in morphogenesis and medical research. Much remains to be learned about complex pattern formation, if we are to bridge the gap between molecular biology and organism phenotypes.
Animals↗
Mixed-mode pattern in Doublefoot mutant mouse limb--Turing reaction-diffusion model on a growing domain during limb development.
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 present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction-diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction-diffusion model. Finally, we make some experimentally testable predictions.
Animals↗
Complex networks generated by the Penna bit-string model: emergence of small-world and assortative mixing.
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 in the Penna model, the population will form a complex network. In this paper, we first modify the Verhulst factor to control only the birth rate, and introduce activity-based preferential reproduction of offspring in the Penna model. The social interactions among individuals are generated by both inheritance and activity-based preferential increase. Then we study the properties of the complex network generated by the modified Penna model. We find that the resulting complex network has a small-world effect and the assortative mixing property.
Journal Article↗
Interpreting two-photon imaging data of lymphocyte motility.
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 interpret this new class of lymphocyte motility data within a theoretical model. The model considers cell movement to be composed of the movement of subunits of the cell membrane. In this way movement and deformation of the cell are correlated to each other. We find that, indeed, the lymphocyte movement in lymph nodes can best be described as a random walk with persistence of orientation. The assumption of motility induced cell elongation is consistent with the data. Within the framework of our model the two-photon data suggest that T and B cells are in a single velocity state with large stochastic width. The alternative of three different velocity states with frequent changes of their state and small stochastic width is less likely. Two velocity states can be excluded.
Algorithms↗
Non-linear incidence and stability of infectious disease models.
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 non-linear incidence rate (in fact, we assumed that the incidence rate is given by an arbitrary function f (S, I, N) constrained by a few biologically feasible conditions) and a variety of epidemiological models. We show that under the constant population size assumption, these models exhibit asymptotically stable steady states. Precisely, we demonstrate that the concavity of the incidence rate with respect to the number of infective individuals is a sufficient condition for stability. If the incidence rate is concave in the number of the infectives, the models we consider have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case the infection-free equilibrium state is stable. For the incidence rate of the form g(I)h(S), we prove global stability, constructing a Lyapunov function and using the direct Lyapunov method. It is remarkable that the system dynamics is independent of how the incidence rate depends on the number of susceptible individuals. We demonstrate this result using a SIRS model and a SEIRS model as case studies. For other compartment epidemic models, the analysis is quite similar, and the same conclusion, namely stability of the equilibrium states, holds.
Animals↗
The role of acidity in solid tumour growth and invasion.
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 tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Analysis of the model allows us to assess novel therapies directed towards changing the level of acidity within the tumour.
Cell Proliferation↗
Cutting edge: back to "one-way" germinal centers.
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 hypermutations and positive selection is analyzed with special emphasis on the spatial organization of the GC reaction. We claim that the development of dark zones is not necessary for successful GC reactions to develop. We find that a recirculation of positively selected centrocytes to the dark zone is rather unlikely. Instead we propose a scenario that combines a multiple-step mutation and selection concept with a "one-way" GC in the sense of cell migration.
Animals↗
Extracellular volume regulation and growth.
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 metric solution and the results were compared with experimental data. Two theoretical solutions were found: Solution 1, extracellular volume (ECV) was calculated to be about 23% of total body volume (TV). Stereo metric solution suggested the cubic cell cluster formed by 8-cells. This hypothesis (Solution l) explains the ECV to be compatible with the widely accepted value (about 23% of TV). In addition, the 8-cell cluster hypothesis explains the existence of ECV oscillation with the period of about seven days. This hypothesis probably describes the dominant type of growth in humans. Solution 2, in this type of growth, ECV fills about 77% per cent of TV. Instead of the 8-cell cube, in this type of proliferation 4-cells could form a tetrahedron. This type of growth could be beneficial in processes where free space in tissue or organ must be filled for example in peptic ulcer healing and namely in repopulating of free space in a bone after high dose chemotherapy.
Cell Growth Processes↗
A design principle for vascular beds: the effects of complex blood rheology.
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 enables us to determine how rheology affects the morphology of simple branching networks. The behavior of various physical quantities associated with the networks, such as the wall shear stress and the flow velocity, is also determined. Our results are shown to be qualitatively and quantitatively compatible with independent experimental observations and simulations.
Blood Circulation Time↗
Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells.
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 appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells-reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formation where the quantitative parameters are difficult to obtain.
Animals↗
Bulletin of mathematical biology-facts, figures and comparisons.
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 annual meeting in Dundee the Society asked the editor of the BMB to produce an analysis of impact factor, subject matter of papers, submission rates etc. Other members of the society were interested in the handling times of articles and wanted comparisons with other (appropriate) journals. In this article we present a brief history of the journal and report on how the journal impact factor has grown substantially in the last few years. We also present an analysis of subject areas of published papers over the past two years. We finally present data on times from receipt of paper to acceptance, acceptance to print (and to online publication) and compare these data with some other journals.
Biometry↗
Using mathematical models to help understand biological pattern formation.
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 been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.
Animals↗
Periodic pattern formation in reaction-diffusion systems: an introduction for numerical simulation.
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 reaction-diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction-diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.
Algorithms↗