Modeling Theory and Software Architecture of theE-CELL Simulation SystemKouichi Takahashi 12
shafi@sfc.keio.ac.jp
Katsuyuki Yugi 13

t95980ky@sfc.keio.ac.jp
123
4

Tom Shimizu 14
tom@sfc.keio.ac.jp
Masaru Tomita 13
mt@sfc.keio.ac.jp

Laboratory for Bioinformatics
Graduate School of Media and Governance
Department of Environmental Information
Keio University, 5322 Endo, Fujisawa 252-8520, Japan
Department

ofZoology,

UniversityofCambridge,

CB2

3EJ,

United Kingdom

1 Introduction

We have been developing E-CELL, a generic software environment for whole cell modeling and simulation. E-CELL simulates the behavior of model cell by computing interactions among molecularspecies it contains. E-CELL allows the user to de ne chemically discrete compartments such as membranes, chromosomes and cytoplasm. The collection of substance quantity values in all of the cellularcompartments comprises internal representation of the cell state, which can be monitored and/ormanipulated using the various graphical user interfaces. E-CELL attempts to provide a framework
not only for modeling metabolic pathways, but also for higher-order cellular phenomena such as gene
regulation network, DNA replication, and other occurrence in the cell cycle. A major challenge of theproject is to develop a method of modeling which is suciently robust to accommodate the drastic
di erence in time scale among these processes.
2 Modeling Theory

The E-CELL employs structured Substance-Reactor model to construct and simulate the cell model.
The structured Substance-Reactor model consists of three classes of objects, Substance, Reactor, andSystem, representing molecular species, reactions and functional/physical compartments, respectively.
To model chromosomes and other genetic materials, the system also has sophisticated data structures
such as Genome, GenomicElement, and Gene.
Assuming rapid equilibrium in each compartment, a state of the cell at a point in time anddynamics of the cell are represented as a set of concentration vectors and reaction kinetics, respectively.
Therefore, simulation of the cell can be viewed as integration of ordinary di erential equations (ODEs).
The numerical integration is performed in distributed form with Stepper and Integrator class objects
in the system. With this design, the system is capable of multi-compartment, multi-scheme andmulti-phase numerical integration. In other words, time step sizes and integration algorithm can vary
among di erent compartments, and therefore parallel computation can be applied to \sti " di erentialsystems like the cell.
The problem of sti ness occurs in a system where there are very di erent scales of the time
variable on which the dependent variables are changing. The sti ness often results in various kinds ofnumerical errors, some of which are fatal for the simulation. One of such problems is called Less Than250

SpreadSheetSoftware(CSV file)

Converter

CultureIntermediate
Code (eri file)

Interpreter

Converter
E-CellParser

GUI

Various Processors/Converters

Rule File

Lexical Analyzer

Graph Drawer/Editor

Compiler

User
AgentsKnowledge
Base
Etc....

E-Cell Manager

Figure 1: The E-CELL Simulation Environment.
Zero (LTZ) problem, in which concentration of substance becomes a negative value. More precisely,

it occurs when() <Sj t

X(fX( )) + ( v (t)) 1t

ij vi tikjk(1)g1k

where S (t) is concentration of j th substance, v (t) is velocity of ith reaction,  is stoichiometricconstant of the ith reaction for the j th substance, and 1t is time step size. The LTZ problem is
especially complicated when the substance is consumed by two or more reactions as their substrate.
We are trying to cope with the LTZ problem using the following three techniques: multi-compartment
numerical integration, adaptive step size control and partial recalculation.
jiij

3 Software Architecture

The E-CELL System is written in C++ and designed with object oriented MVC model, which facilitates independent development of the simulation engine, user interfaces and the cell model. Eachreaction kinetics are encapsulated into the Reactor class objects. In addition to general reaction
schema provided by the system, task-speci c reaction schema can be de ned by the user using C++
language without detailed knowledge about implementation of the other parts of the system.
The E-CELL simulation environment consists of several software components such as core simulation system (E-CELL System), E-CELL Manager, rule le compiler, and other various data converters/processors (Fig. 1). Besides the system speci c E-CELL Rule format, the user can now write simulation rules using any commercially/publicly available spread sheet software. The rules are compiled
into .eri (E-CELL Rule Intermediate) format, which can be interpreted by the simulation system. The
core system reads compiled rule, starts simulation and outputs logged data. The simulation process
can be automated using E-CELL Script language(.ecs). The whole process of rule writing, simulation,
and analysis is managed by the E-CELL Manager.
Acknowledgments

This work was supported in part by a Grant-in-Aid for Scienti c Research on Priority Areas `Genome
Science' from The Ministry of Education, Science, Sports and Culture in Japan.
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