Modelling Molecular Processes by Individual-Based Simulations Applied to Actin Polymerisation - Simulation and Modeling Methodologies, Technologies and Application - page 176

Fig. 1. The physical size of the actin molecule determines the size of an agent in the simulation.
For the two dimensional simulation the width and height of an actin agent is set to 50 A × 50 A [18].

dynamics to analyse the self-assembly process of actin and the dynamics of long fila-
ments [11]. The distribution of the length of actin filaments inside a cell was analysed
with a discrete and continuous model [5]. Different models using stochastic π -calculus
as a representative of process algebra, have also been published [2].
In this paper we describe simulations using an agent-based approach with commu-
nicating X-machines [9], implemented in a software called Flexible Large-scale Agent-
based Modelling Environment (FLAME) [13]. This allows us to analyse the spatial and
time dependent behaviour during the composition of the filament structure by free actin
with a high degree of physical realism. The outline of the paper is as follows. Section
2 explains the three models in detail. Section 3 discusses the output of the models and
Section 4 sums up the conclusions and gives a brief outlook for further studies.

2 Agent-Based Simulation

An agent is formally defined as an finite-state machine. Because the finite-state ma-
chine model is too restrictive for general system specification, an extension with a
memory, the so called X-machine promise a better implementation [12]. If a system
contains more than one agent, the particular X-machines must be able to communi-
cate together and this leads to a communication X-machine system [9]. This concept is
implemented in the software named Flexible Large-scale Agent-based Modelling Envi-
ronment (FLAME) [13].
Using the actin model generated by X-ray analysis [18] we fix the size of one
molecule to 50 A 50 A. The dimension of the molecule is shown in Figure 1. Each

agent contains an identification number and two binding sides to connect to another
agent, namely bottom-bound (BB) and top-bound (TB) and can switch between three
different states (free, bottom-bound, fully bound). A free binding side is denoted with
the constant

×

− 1 (free), the agent
is randomly rotating and moving around in a distance of 1-200 A, which is an ap-
proximation for the computational expensive calculation of Brownian dynamics. If a

− 1 . As long as both binding sides are marked with