  Stochastic effect in cellular systems has been an important topic in systems
biology. Stochastic modeling and simulation methods are important tools to
study stochastic effect. Given the low efficiency of stochastic simulation
algorithms, the hybrid method, which combines an ordinary differential equation
(ODE) system with a stochastic chemically reacting system, shows its unique
advantages in the modeling and simulation of biochemical systems. The
efficiency of hybrid method is usually limited by reactions in the stochastic
subsystem, which are modeled and simulated using Gillespie's framework and
frequently interrupt the integration of the ODE subsystem. In this paper we
develop an efficient implementation approach for the hybrid method coupled with
traditional ODE solvers. We also compare the efficiency of hybrid methods with
three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments
with three biochemical models are presented. A detailed discussion is presented
for the performances of three ODE solvers.
