Gilberto L. Thomas

CompuCell, a multi-model framework for simulation of morphogenesis

MOTIVATION CompuCell is a multi-model software framework for simulation of the development of multicellular organisms known as morphogenesis. It models the interaction of the gene regulatory network with generic cellular mechanisms, such as cell adhesion, division, haptotaxis and chemotaxis. A combination of a state automaton with stochastic local rules and a set of differential equations, including subcellular ordinary differential equations and extracellular reaction-diffusion partial differential equations, model gene regulation. This automaton in turn controls the differentiation of the cells, and cell-cell and cell-extracellular matrix interactions that give rise to cell rearrangements and pattern formation, e.g. mesenchymal condensation. The cellular Potts model, a stochastic model that accurately reproduces cell movement and rearrangement, models cell dynamics. All these models couple in a controllable way, resulting in a powerful and flexible computational environment for morphogenesis, which allows for simultaneous incorporation of growth and spatial patterning. RESULTS We use CompuCell to simulate the formation of the skeletal architecture in the avian limb bud. AVAILABILITY Binaries and source code for Microsoft Windows, Linux and Solaris are available for download from http://sourceforge.net/projects/compucell/

Multi-scale modeling of tissues using CompuCell3D.

The study of how cells interact to produce tissue development, homeostasis, or diseases was, until recently, almost purely experimental. Now, multi-cell computer simulation methods, ranging from relatively simple cellular automata to complex immersed-boundary and finite-element mechanistic models, allow in silico study of multi-cell phenomena at the tissue scale based on biologically observed cell behaviors and interactions such as movement, adhesion, growth, death, mitosis, secretion of chemicals, chemotaxis, etc. This tutorial introduces the lattice-based Glazier-Graner-Hogeweg (GGH) Monte Carlo multi-cell modeling and the open-source GGH-based CompuCell3D simulation environment that allows rapid and intuitive modeling and simulation of cellular and multi-cellular behaviors in the context of tissue formation and subsequent dynamics. We also present a walkthrough of four biological models and their associated simulations that demonstrate the capabilities of the GGH and CompuCell3D.

Rounding of aggregates of biological cells: Experiments and simulations

The influence of surface tension and size on rounding of cell aggregates is studied using chick embryonic cells and numerical simulations based on the cellular Potts model. Our results show exponential relaxation in both cases as verified in previous studies using 2D Hydra cell aggregates. The relaxation time decreases with higher surface tension as expected from hydrodynamics laws. However, it increases faster than linearly with aggregate size. The results provide an additional support to the validity of the cellular Potts model for non-equilibrium situations and indicate that aggregate shape relaxation is not governed by the hydrodynamics of viscous liquids.

Computer simulations of cell sorting due to differential adhesion.

The actions of cell adhesion molecules, in particular, cadherins during embryonic development and morphogenesis more generally, regulate many aspects of cellular interactions, regulation and signaling. Often, a gradient of cadherin expression levels drives collective and relative cell motions generating macroscopic cell sorting. Computer simulations of cell sorting have focused on the interactions of cells with only a few discrete adhesion levels between cells, ignoring biologically observed continuous variations in expression levels and possible nonlinearities in molecular binding. In this paper, we present three models relating the surface density of cadherins to the net intercellular adhesion and interfacial tension for both discrete and continuous levels of cadherin expression. We then use then the Glazier-Graner-Hogeweg (GGH) model to investigate how variations in the distribution of the number of cadherins per cell and in the choice of binding model affect cell sorting. We find that an aggregate with a continuous variation in the level of a single type of cadherin molecule sorts more slowly than one with two levels. The rate of sorting increases strongly with the interfacial tension, which depends both on the maximum difference in number of cadherins per cell and on the binding model. Our approach helps connect signaling at the molecular level to tissue-level morphogenesis.

Multi-model simulations of chicken limb morphogenesis

Early development of multicellular organisms (morphogenesis) is a complex phenomenon. We present COMPUCELL, a multi-model software framework for simulations of morphogenesis. As an example, we simulate the formation of the skeletal pattern in the avian limb bud, which requires simulations based on interactions of the genetic regulatory network with generic cellular mechanisms (cell adhesion, haptotaxis, and chemotaxis). A combination of a rule-based state automaton and sets of differential equations, both subcellular ordinary differential equations (ODEs) and domain-level reaction-diffusion partial differential equations (PDEs) models genetic regulation. This regulation controls the differentiation of cells, and also cell-cell and cell-extracellular matrix interactions that give rise to cell pattern formation and cell rearrangements such as mesenchymal condensation. The cellular Potts model (CPM) models cell dynamics (cell movement and rearrangement). These models couple; COMPUCELL provides an integrated framework for such computations. Binaries for Microsoft Windows and Solaris are available. Source code is available on request, via email: compucell@cse.nd.edu.

Growth Laws and Self-Similar Growth Regimes of Coarsening Two-Dimensional Foams: Transition from Dry to Wet Limits

We study the topology and geometry of two-dimensional coarsening foam with an arbitrary liquid fraction. To interpolate between the dry limit described by von Neumanns law and the wet limit described by Marqusees equation, the relevant bubble characteristics are the Plateau border radius and a new variable: the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau border interfaces. The resulting prediction is successfully tested, without an adjustable parameter, using extensive bidimensional Potts model simulations. The simulations also show that a self-similar growth regime is observed at any liquid fraction, and they also determine how the average size growth exponent, side number distribution, and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals, and other domains with coarsening that is driven by curvature.

Bursts and cavity formation in Hydra cells aggregates: experiments and simulations

We present experimental results and a simulation in two dimensions of the expansion and bursting of aggregates of Hydra cells formed from an initially disordered mixture. In the experiments, after cell sorting, the aggregate rounds and swells until violent bursts occur, forcibly expelling internal fluid and loose cells. We use Monte Carlo techniques to simulate the bursts in two dimensions. Initially, we consider a ring made of a monolayer of cells enveloping an internal fluid. Each cell and the internal medium have their areas controlled by target area size. Increasing the target area of the internal cavity causes the aggregate to swell. We observe that aggregates of cells with higher surface tension generate higher internal pressure. In the simulations the cell ring bursts when it is too thin to endure fluctuations in the cellular membranes. The process is relevant to embryonic development.

Emergent Stratification in Solid Tumors Selects for Reduced Cohesion of Tumor Cells: A Multi-Cell, Virtual-Tissue Model of Tumor Evolution Using CompuCell3D.

Tumor cells and structure both evolve due to heritable variation of cell behaviors and selection over periods of weeks to years (somatic evolution). Micro-environmental factors exert selection pressures on tumor-cell behaviors, which influence both the rate and direction of evolution of specific behaviors, especially the development of tumor-cell aggression and resistance to chemotherapies. In this paper, we present, step-by-step, the development of a multi-cell, virtual-tissue model of tumor somatic evolution, simulated using the open-source CompuCell3D modeling environment. Our model includes essential cell behaviors, microenvironmental components and their interactions. Our model provides a platform for exploring selection pressures leading to the evolution of tumor-cell aggression, showing that emergent stratification into regions with different cell survival rates drives the evolution of less cohesive cells with lower levels of cadherins and higher levels of integrins. Such reduced cohesivity is a key hallmark in the progression of many types of solid tumors.

Dibaryons as axially symmetric skyrmions

Abstract Dibaryon configurations are studied in the framework of the bound-state soliton model. A generalized axially symmetric ansatz is used to determine the soliton background. We show that once the constraints imposed by the symmetries of the lowest-energy torus configuration are satisfied, all spurious states are removed from the dibaryon spectrum. In particular, we show that the lowest allowed state in the S = −2 channel carries the quantum numbers of the H-particle. We find that, within our approximations, this particle is slightly bound in the model. We discuss, however, that vacuum effects neglected in the present calculation are very likely to unbind the H.Dibaryons configurations are studied in the framework of the bound state soliton model. A generalized axially symmetric ansatz is used to determine the soliton background. We show that once the constraints imposed by the symmetries of the lowest energy torus configuration are satisfied all spurious states are removed from the dibaryon spectrum. In particular, we show that the lowest allowed state in the

SCALING IN A CONTINUOUS TIME MODEL FOR BIOLOGICAL AGING

S=-2