Accounting for Diffusion in Agent Based Models of Reaction-Diffusion Systems with Application to Cytoskeletal Diffusion

Mohammad Azimi,Yousef Jamali,Mohammad R K Mofrad

doi:10.1371/journal.pone.0025306

Mohammad Azimi, Yousef Jamali + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0025306

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Journal: PLoS ONE	Publication Date: Sep 23, 2011
Citations: 49	License type: CC BY 4.0

Affiliation: University of California, Berkeley

Abstract

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.

Highlights

Diffusion is a key driver of many biological processes in living systems where ions and molecules move down concentration gradients as a result of their thermal motion within solutions
Other techniques with applications to modeling cellular pathways include partial differential equation (PDE), chemical master equation (CME) and reaction-diffusion master equation (RDME) models that are capable of accounting for spatial varying levels of spatial detail and stochasticity at the cost of increased computational time. These techniques are well-suited for modeling a range of biological phenomena (ODE/PDE methods are ideal for metabolic network models, CME/RDME methods are ideal for gene expression models), with each technique limited by spatial, stochastic and computational cost constraints [1,2,3,4,5]
On the other end of the modeling spectrum are more accurate Brownian dynamics (BD) and Langevin dynamics (LD) models that explicitly account for the diffusion and interaction of individual molecules with the ability to track these individual molecules and assess the effects of spatial and environmental properties that result in the emergence of phenomena such as molecular crowding

Summary

Introduction

Diffusion is a key driver of many biological processes in living systems where ions and molecules move down concentration gradients as a result of their thermal motion within solutions.

Results

Conclusion