Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

Modeling tumor cell migration: from microscopic to macroscopic

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several millions of cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in details the conditions of validity of the approximations used in the derivation and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids and jamming systems.Comment: Final published version; 14 pages, 7 figure

A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin

Residential equilibrium in a multifractal metropolitan area

A residential location model derived from urban economics is combined with the geometry of a multifractal Sierpinski carpet to represent and model a metropolitan area. This area is made up of a system of built-up patches hierarchically organised around a city centre, and green areas arranged in an inverse hierarchical order (large open-spaces in the periphery). An analytical solution is obtained by using a specific geographic coding system for computing distances. The values of the parameters used in the model are based on the French medium sized metropolitan areas; a realistic benchmark is proposed and comparative-statics simulations are performed. The results show that the French peri-urbanisation process (which took place from 1970 onward) can be explained by an increase in income and a reduction in transport costs. Nevertheless, changes in household preferences, in particular an increased taste for open spaces, can also contribute to urban sprawl by making the gradient of land rents less steep and by making peripheral household locations more desirableperi-urban, residential localisation, fractal geometry, amenities

Selectively advantageous instability in biotic and pre-biotic systems and implications for evolution and aging

Rules of biology typically involve conservation of resources. For example, common patterns such as hexagons and logarithmic spirals require minimal materials, and scaling laws involve conservation of energy. Here a relationship with the opposite theme is discussed, which is the selectively advantageous instability (SAI) of one or more components of a replicating system, such as the cell. By increasing the complexity of the system, SAI can have benefits in addition to the generation of energy or the mobilization of building blocks. SAI involves a potential cost to the replicating system for the materials and/or energy required to create the unstable component, and in some cases, the energy required for its active degradation. SAI is well-studied in cells. Short-lived transcription and signaling factors enable a rapid response to a changing environment, and turnover is critical for replacement of damaged macromolecules. The minimal gene set for a viable cell includes proteases and a nuclease, suggesting SAI is essential for life. SAI promotes genetic diversity in several ways. Toxin/antitoxin systems promote maintenance of genes, and SAI of mitochondria facilitates uniparental transmission. By creating two distinct states, subject to different selective pressures, SAI can maintain genetic diversity. SAI of components of synthetic replicators favors replicator cycling, promoting emergence of replicators with increased complexity. Both classical and recent computer modeling of replicators reveals SAI. SAI may be involved at additional levels of biological organization. In summary, SAI promotes replicator genetic diversity and reproductive fitness, and may promote aging through loss of resources and maintenance of deleterious alleles

Design Guidelines for Agent Based Model Visualization

In the field of agent-based modeling (ABM), visualizations play an important role in identifying, communicating and understanding important behavior of the modeled phenomenon. However, many modelers tend to create ineffective visualizations of Agent Based Models (ABM) due to lack of experience with visual design. This paper provides ABM visualization design guidelines in order to improve visual design with ABM toolkits. These guidelines will assist the modeler in creating clear and understandable ABM visualizations. We begin by introducing a non-hierarchical categorization of ABM visualizations. This categorization serves as a starting point in the creation of an ABM visualization. We go on to present well-known design techniques in the context of ABM visualization. These techniques are based on Gestalt psychology, semiology of graphics, and scientific visualization. They improve the visualization design by facilitating specific tasks, and providing a common language to critique visualizations through the use of visual variables. Subsequently, we discuss the application of these design techniques to simplify, emphasize and explain an ABM visualization. Finally, we illustrate these guidelines using a simple redesign of a NetLogo ABM visualization. These guidelines can be used to inform the development of design tools that assist users in the creation of ABM visualizations.Visualization, Design, Graphics, Guidelines, Communication, Agent-Based Modeling

A Cellular Automata Model of Enantiomer Interactions with beta-Cyclodextrin

The binding mechanisms of molecules to cyclodextrins continues to be studied to better explain the interactions occurring. The majority of published models focus on one-to-one molecular binding thermodynamics to explain experimental results. They rely on physical concepts of energies and forces to guide the actions of molecules expressed mathematically in terms of differential and non-linear equations. These models are limited in scope due to their complexity and are not easily expanded to study many diverse analytes. Conversely, cellular automata uses simple mathematical idealizations of systems governed by deterministic and probabilistic rules that are easily adaptable to many types of molecular interactions. The primary goal of this research is to develop a model that is easy to use in the prediction of beta-cyclodextrin chromatographic separations of enantiomers. The model uses variegated square cells to simulate the physical environment of the molecules involved, evolving by a series of discrete time-steps referred to as iterations. Governing probabilistic rules define the physical and chemical interactions. Rules are randomly applied to all the cells of the system during each iteration and the system is updated accordingly. Micro and macro visual analysis is possible in addition to statistical output. Results demonstrate the model’s capability to use probabilistic rules for breaking of analyte-to-cyclodextrin complexes that were correlated to published experimentally determined equilibrium constants. The model was further expanded to predict the strength of interactions between enantiomer pairs to beta-cyclodextrin and their potential separation. The model accurately predicted the order of strength for six enantiomer pairs. To truly predict chromatographic separation of enantiomers, the model was expanded from one-to-one interactions between enantiomers and beta-cyclodextrin to a larger modeled chromatographic scale. At this scale enantiomer separation was modeled and evaluated for peak resolution and selectivity while varying column temperature, mobile phase pH and flow, and injection volumes. All results agreed well with published laboratory results. With the cost of research and development increasing, ongoing budget cuts, and the rush to get products to market first, an analytical model that can run multiple chromatographic simulations in minutes versus days could prove a valuable tool to many industries

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast