TY - JOUR

T1 - Stochastic simulation of biological reactions, and its applications for studying actin polymerization

AU - Ichikawa, Kazuhisa

AU - Suzuki, Takashi

AU - Murata, Noboru

PY - 2010/12

Y1 - 2010/12

N2 - Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate Pr is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis-Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca2+ dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events.

AB - Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate Pr is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis-Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca2+ dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events.

UR - http://www.scopus.com/inward/record.url?scp=79551473812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551473812&partnerID=8YFLogxK

U2 - 10.1088/1478-3975/7/4/046010

DO - 10.1088/1478-3975/7/4/046010

M3 - Article

C2 - 21119218

AN - SCOPUS:79551473812

SN - 1478-3967

VL - 7

JO - Physical Biology

JF - Physical Biology

IS - 4

M1 - 046010

ER -