Vo Hong Thanh

Efficient rejection-based simulation of biochemical reactions with stochastic noise and delays

We propose a new exact stochastic rejection-based simulation algorithm for biochemical reactions and extend it to systems with delays. Our algorithm accelerates the simulation by pre-computing reaction propensity bounds to select the next reaction to perform. Exploiting such bounds, we are able to avoid recomputing propensities every time a (delayed) reaction is initiated or finished, as is typically necessary in standard approaches. Propensity updates in our approach are still performed, but only infrequently and limited for a small number of reactions, saving computation time and without sacrificing exactness. We evaluate the performance improvement of our algorithm by experimenting with concrete biological models.

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm.

We address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajectory is exact by exploiting the rejection-based mechanism. We benchmark tRSSA on different biological systems with varying forms of reaction rates to demonstrate its applicability and efficiency. We reveal that for nontrivial cases, the selection of reaction firings in existing algorithms introduces approximations because the integration of reaction rates is very computationally demanding and simplifying assumptions are introduced. The selection of the next reaction firing by our approach is easier while preserving the exactness.

Tree-based search for stochastic simulation algorithm

In this paper, we present an efficient tree-based formulation for exact stochastic simulation algorithm (SSA) to improve the search for the next reaction firing. There are two implementations considered: one based on a complete binary tree and one based on the Huffman tree, an optimal tree for data compression.

Efficient Constant-Time Complexity Algorithm for Stochastic Simulation of Large Reaction Networks

Exact stochastic simulation is an indispensable tool for a quantitative study of biochemical reaction networks. The simulation realizes the time evolution of the model by randomly choosing a reaction to fire and update the system state according to a probability that is proportional to the reaction propensity. Two computationally expensive tasks in simulating large biochemical networks are the selection of next reaction firings and the update of reaction propensities due to state changes. We present in this work a new exact algorithm to optimize both of these simulation bottlenecks. Our algorithm employs the composition-rejection on the propensity bounds of reactions to select the next reaction firing. The selection of next reaction firings is independent of the number reactions while the update of propensities is skipped and performed only when necessary. It therefore provides a favorable scaling for the computational complexity in simulating large reaction networks. We benchmark our new algorithm with the state of the art algorithms available in literature to demonstrate its applicability and efficiency.

Adaptive tree-based search for stochastic simulation algorithm

Stochastic modelling and simulation is a well-known approach for predicting the behaviour of biochemical systems. Its main applications lie in those systems wherein the inherently random fluctuations of some species are significant, as often is the case whenever just a few macromolecules have a large effect on the rest of the system. The Gillespies stochastic simulation algorithm (SSA) is a standard method to properly realise the stochastic nature of reactions. In this paper we propose an improvement to SSA based on the Huffman tree, a binary tree which is used to define an optimal data compression algorithm. We exploit results from that area to devise an efficient search for next reactions, moving from linear time complexity to logarithmic complexity. We combine this idea with others from literature, and compare the performance of our algorithm with previous ones. Our experiments show that our algorithm is faster, especially on large models.

Accelerating rejection-based simulation of biochemical reactions with bounded acceptance probability

Stochastic simulation of large biochemical reaction networks is often computationally expensive due to the disparate reaction rates and high variability of population of chemical species. An approach to accelerate the simulation is to allow multiple reaction firings before performing update by assuming that reaction propensities are changing of a negligible amount during a time interval. Species with small population in the firings of fast reactions significantly affect both performance and accuracy of this simulation approach. It is even worse when these small population species are involved in a large number of reactions. We present in this paper a new approximate algorithm to cope with this problem. It is based on bounding the acceptance probability of a reaction selected by the exact rejection-based simulation algorithm, which employs propensity bounds of reactions and the rejection-based mechanism to select next reaction firings. The reaction is ensured to be selected to fire with an acceptance rate greater than a predefined probability in which the selection becomes exact if the probability is set to one. Our new algorithm improves the computational cost for selecting the next reaction firing and reduces the updating the propensities of reactions.

Efficient stochastic simulation of biochemical reactions with noise and delays

The stochastic simulation algorithm has been used to generate exact trajectories of biochemical reaction networks. For each simulation step, the simulation selects a reaction and its firing time according to a probability that is proportional to the reaction propensity. We investigate in this paper new efficient formulations of the stochastic simulation algorithm to improve its computational efficiency. We examine the selection of the next reaction firing and reduce its computational cost by reusing the computation in the previous step. For biochemical reactions with delays, we present a new method for computing the firing time of the next reaction. The principle for computing the firing time of our approach is based on recycling of random numbers. Our new approach for generating the firing time of the next reaction is not only computationally efficient but also easy to implement. We further analyze and reduce the number of propensity updates when a delayed reaction occurred. We demonstrate the applicability of our improvements by experimenting with concrete biological models.

Stochastic Simulation of Biochemical Reaction Systems

This chapter presents the foundational theory of the stochastic chemical kinetics for modeling biochemical reaction networks, of which the discreteness in population of species and the randomness of reactions are treated as an intrinsic part. The dynamical behavior of the biochemical reactions, based on the fundamental premise of the stochastic chemical kinetics, is exactly described by the chemical master equation (CME). A class of Monte Carlo simulation techniques originating from the stochastic simulation algorithm (SSA) has been developed to realize the time evolution of the reaction networks.

Implementations of the Stochastic Simulation Algorithm

The stochastic simulation algorithm (SSA) is a stochastic, discrete event simulation strategy where a reaction is randomly selected to update the system state. It has the nice property of producing an exact realization (with respect to the chemical master equation) of the temporal dynamics of biochemical reactions. The heart of SSA is the Monte Carlo step for sampling the next reaction firing and its firing time from the joint reaction probability density function.

Hybrid Simulation Algorithms

In this chapter we will introduce hybrid simulation strategies as a combination of previously introduced simulation algorithms. Hybrid simulation combines the advantages of complementary simulation approaches: a system is partitioned into subsystems that are simulated with different methods.