Abstract
Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.
Highlights
Most of the events in and around the biological cell are inherently noisy
We want to investigate what happens if we use the Quasi-steady-state approximation (QSSA) approach to quantify the intrinsic noise for relatively complex biological networks? Under what conditions the QSSA approach will quantify the intrinsic noise as accurately as the stochastic simulation algorithm (SSA) performed using the mechanistic version of the model and when the result will differ significantly?
We have performed the stochastic simulation at J0 = 3 min-1 where we do have only one stable steady state and measured the steady state distribution of the total protein (X) to compare the QSSA and mechanistic models (The corresponding time courses for the two situations are given in S1A Fig)
Summary
Most of the events in and around the biological cell are inherently noisy. The sources of noise in the biological systems are diverse and can be mainly classified into two different classes [1,2,3,4,5], namely intrinsic and extrinsic noise. Gillespie’s stochastic simulation algorithm (SSA) [16] provides fundamentally the most accurate and correct description of the intrinsic noise for a biological network if all the terms in the corresponding model are based on mass action kinetics This means as the biological network grows in size and complexities, it will be computationally highly time consuming to simulate every reaction event using SSA. Quasi-steady-state approximation (QSSA) is one of such methods where one reduces the detailed mechanistic model of a complex biological network depending on the time scales of the reactions in the concerned system and as a result effectively cut short the number of molecular species and reactions to simulate stochastically [15,19]. We want to investigate what happens if we use the QSSA approach to quantify the intrinsic noise for relatively complex biological networks? Under what conditions the QSSA approach will quantify the intrinsic noise as accurately as the SSA performed using the mechanistic version of the model and when the result will differ significantly?
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