Reduction of chemical reaction networks through delay distributions

Abstract

Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional “backward” bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or “forward” bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research.

Exact Probability Distributions of Selected Species in Stochastic Chemical Reaction Networks

“…As noted in Barrio et al (2013), the matrix above is a real tridiagonal matrix with positive off diagonal elements and, hence, it is similar to an Hermitian matrix (Veselić 1979; Bernstein 2009, p. 359). This implies that has real, simple eigenvalues.…”

“…It should be noted that Leier et al (2014) and Barrio et al (2013) tackled the problem of exactly reducing general monomolecular reaction networks and unbranched monomolecular reaction networks, respectively, into one monomolecular reaction. This reduced representation is characterised by a constant reaction rate and a time delay sampled from a defined distribution.…”

“…However, we note that such approaches use the delay stochastic simulation algorithm (DSSA, see Cai 2007; Barrio et al 2006, 2010, for instance). In contrast, our methodology obtains an exact, analytical solution of the CME of the reaction network studied in Barrio et al (2013) and additional topologies, hence avoiding the computational burden of the (D)SSA.…”

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

“…Examples where these features would be of special importance include the analysis of system robustness, model reduction, and parameter calibration. 4,[34][35][36][37][38] The application of the proposed method to complex stochastic systems remains challenging because of the sampling effort. Even though the method is trivial to implement in parallel, future works should focus on the improvement of the methods to lower its computational complexity.…”

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

“…Recently, a model with non-constant time delay has been derived to simplify the translational process of multistep reactions35. In addition, research work has been conducted for exact model reduction with time delay; and closed form distribution and extension have been derived for fully bi-directional monomolecular reactions3637. In spite of these advances, more work is still needed to address the issue of accuracy for modelling multistep reaction systems.…”