Ariel Balter

Magnetization to Morphogenesis: A Brief History of the Glazier-Graner-Hogeweg Model

This chapter discusses the history and development of what we propose to rename the Glazier-Graner-Hogeweg model (GGH model), starting with its ancestors, simple models of magnetism, and concluding with its current state as a powerful, cell-oriented method for simulating biological development and tissue physiology. We will discuss some of the choices and accidents of this development and some of the positive and negative consequences of the model’s pedigree.

Modeling gastrulation in the chick embryo: formation of the primitive streak.

The body plan of all higher organisms develops during gastrulation. Gastrulation results from the integration of cell proliferation, differentiation and migration of thousands of cells. In the chick embryo gastrulation starts with the formation of the primitive streak, the site of invagination of mesoderm and endoderm cells, from cells overlaying Kollers Sickle. Streak formation is associated with large-scale cell flows that carry the mesoderm cells overlying Kollers sickle into the central midline region of the embryo. We use multi-cell computer simulations to investigate possible mechanisms underlying the formation of the primitive streak in the chick embryo. Our simulations suggest that the formation of the primitive streak employs chemotactic movement of a subpopulation of streak cells, as well as differential adhesion between the mesoderm cells and the other cells in the epiblast. Both chemo-attraction and chemo-repulsion between various combinations of cell types can create a streak. However, only one combination successfully reproduces experimental observations of the manner in which two streaks in the same embryo interact. This finding supports a mechanism in which streak tip cells produce a diffusible morphogen which repels cells in the surrounding epiblast. On the other hand, chemotactic interaction alone does not reproduce the experimental observation that the large-scale vortical cell flows develop simultaneously with streak initiation. In our model the formation of large scale cell flows requires an additional mechanism that coordinates and aligns the motion of neighboring cells.

Multicell Simulations of Development and Disease Using the CompuCell3D Simulation Environment

Mathematical modeling and computer simulation have become crucial to biological fields from genomics to ecology. However, multicell, tissue-level simulations of development and disease have lagged behind other areas because they are mathematically more complex and lack easy-to-use software tools that allow building and running in silico experiments without requiring in-depth knowledge of programming. This tutorial introduces Glazier-Graner-Hogeweg (GGH) multicell simulations and CompuCell3D, a simulation framework that allows users to build, test, and run GGH simulations.

The Glazier-Graner-Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study

One of the reasons for the enormous success of the Glazier-Graner-HogewegGlazier-Graner-Hogeweg Model (GGH) model is that it is a framework for model building rather than a specific biological model. Thus new ideas constantly emerge for ways to extend it to describe new biological (and non-biological) phenomena. The GGH model automatically integrates extensions with the whole body of prior GGH work, a flexibility which makes it unusually simple and rewarding to work with. In this chapter we discuss some possible future directions to extend GGH modeling. We discuss off-lattice extensions to the GGH model, which can treat fluids and solids, new classes of model objects, approaches to increasing computational efficiency, parallelization, and new model-development platforms that will accelerate our ability to generate successful models. We also discuss a non-GGH, but GGH-inspired, model of plant development by Merks and collaborators, which uses the Hamiltonian and Monte-Carlo approaches of the GGH but solves them using Finite Element (FE) methods.

Effect of nonlinearity in hybrid kinetic Monte Carlo–continuum models

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

Probing soap-film friction with two-phase foam flow

We have created a novel, stable pattern of quasi-two-dimensional (2D) foam flow that enables us to measure the relationship between the drag force on a soap-film sliding on a glass plate and the drag force on a soap-film sliding on another soap-film. We created a flowing homogenous 2D foam by supplying bubbles at a steady rate into one end of a Hele–Shaw cell. Part of the way along the midline of the cell, we injected air through the upper plate, inflating bubbles as they flowed by. These bubbles formed a constant-width band along the midline of the cell that moved with the background flow at low injection rates and faster than the background flow at higher injection rates. Fitting our experimental data to a simple theoretical model based on linear drag and minimization of frictional dissipation, we show that the drag force from the wetting layer on the glass plates is an order of magnitude smaller than the drag from other soap-films.

Multinomial diffusion equation

We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N→∞, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.