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A guide to modeling reaction-diffusion of molecules with Spatiocyte

Satya N. V. Arjunan
RIKEN Quantitative Biology Center, Furuedai, Suita, Osaka 565-0874, Japan

Abstract

The E-Cell System is an advanced platform intended for mathematical modeling and simulation of well-stirred biochemical systems. We have recently implemented the Spatiocyte method as a set of plug in modules to the E-Cell System, allowing simulations of complicated multicompartment dynamical processes with inhomogeneous molecular distributions. With Spatiocyte, the diffusion and reaction of each molecule can be handled individually at the microscopic scale. Here we describe the basic theory of the method and provide the installation and usage guides of the Spatiocyte modules. Where possible, model examples are also given to quickly familiarize the reader with spatiotemporal model building and simulation.

Keywords: spatial modeling, stochastic simulation, diffusion, membrane, multicompartment, intercompartment, Spatiocyte

Introduction

The E-Cell System version 3 can model and simulate both deterministic and stochastic biochemical processes (Takakashi et al., 2004). Simulated molecules are assumed to be dimensionless and homogeneously distributed in a compartment. Some processes such as cell signaling and cytokinesis, however, depend on cellular geometry and spatially localized molecules to carry out their functions. To reproduce such processes using spatially resolved models in silico, we have developed a lattice-based stochastic reaction-diffuson (RD) simulation method, called Spatiocyte (Arjunan and Tomita, 2010), and implemented it as a set of plug in modules to the E-Cell System (Arjunan and Tomita, 2009). Spatiocyte allows diffusion and reaction to take place between different compartments: for example, a volume molecule in the cytoplasm can diffuse and react with a surface molecule on the plasma membrane. Since molecules are represented as spheres with dimensions, it can also reproduce anomalous diffusion of molecules in a crowded compartment (Dix and Verkman, 2008, Hall and Hoshino, 2010). Using Spatiocyte simulated microscopy visualization feature, simulation results of spatiotemporal localization of molecules can be evaluated by directly comparing them with experimentally obtained fluorescent microscopy images.

The theory and algorithm of the Spatiocyte method are provided in (Arjunan and Tomita, 2010) while the implementation details are described in (Arjunan and Tomita, 2009). In this chapter, we provide a guide on how to build spatiotemporal RD models using Spatiocyte modules. We begin with the basic theory of the method and proceed with the installation procedures. The properties of each  module are outlined in the subsequent section. Some example models are given to familiarize the reader with the common model structures while describing the modules. We conclude this chapter by outlining the planned future directions of Spatiocyte development.