A Modified Inhomogeneous Stochastic Simulation Algorithm to Model Reactive Boundary Conditions

The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.

Strong Convergence and Speed up of Nested Stochastic Simulation Algorithm

In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.

L-leap:accelerating the stochastic simulation of chemically reacting systems

Presented here is an L-leap method for accelerating stochastic simulation of well-stirred chemically reacting systems, in which the number of reactions occurring in a reaction channel with the largest propensity function is calculated from the leap condition and the number of reactions occurring in the other reaction channels are generated by using binomial random variables during a leap. The L-leap method can better satisfy the leap condition. Numerical simulation results indicate that the L-leap method can obtain better performance than established methods.

“Final all possible steps”approach for accelerating stochastic simulation of coupled chemical reactions

In this paper, we develop a modified accelerated stochastic simulation method for chemically reacting systems, called the ＂final all possible steps＂ （FAPS） method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of chemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existing methods.

Reducing Stochastic Discrete Models of Biochemical Networks

Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.

Effective Finite-Difference Techniques for Estimating Sensitivities for Stochastic Biochemical Systems

Cellular environments are in essence stochastic, owing to the random character of the biochemical reaction events in a single cell. Stochastic fluctuations may substantially contribute to the dynamics of systems with small copy numbers of some biochemical species. Then, stochastic models are indispensable for properly portraying the behaviour of the system. Sensitivity analysis is one of the central tools for studying stochastic models of cellular dynamics. Here, we propose some finite-difference strategies for estimating parametric sensitivities of higher-order moments of the system state for stochastic discrete biochemical kinetic models. To reduce the variance of the sensitivity estimator, we employ various coupling techniques. The advantages of the proposed methods are illustrated in several models of biochemical systems of practical relevance.

An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics

We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.

Stochastic Simulation of the Cell Cycle Model for Budding Yeast

We use the recently proposed Nested Stochastic Simulation Algorithm(Nested SSA)to simulate the cell cycle model for budding yeast.The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

An Accelerated Method for Simulating Population Dynamics

We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.