Abstract
BackgroundBiochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities.ResultsIn this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments.ConclusionsThe Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.
Highlights
Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise
We compare them with the popular benchmark of the Euler τ -leap method (TL; most recent formulation)[14], and we selected two newer methods that are intended to be representative of the most current, fastest and most accurate methods
These are the θ -trapezoidal τ -leap (TTTL) [21], which has two stages and weak order two, and the unbiased τ -leap (UBTL) [19], which accurately estimates the mean and variance of the number of reactions that occur during one step
Summary
Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Stochasticity is a defining property of these processes, which can have so few component particles that random fluctuations dominate their behaviour [4,5]. Stochastic simulation methods take proper account of these fluctuations, as opposed to deterministic methods that assume a system does not deviate from its mean behaviour [6]; deterministic methods can often be useful for an approximate description of the dynamics. The stochastic simulation algorithm (SSA) of Gillespie [10] is a simple and exact method for generating Markov paths. Because it keeps track of each reaction, it can be too computationally costly for more complex systems or those with frequent reactions. Many approximate methods have since been developed, which use similar principles as the SSA but group many reactions into a single calculation, reducing computational time (for a recent review, see [11])
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
