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Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.

ABSTRACT: Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.

SUBMITTER: Gursoy G

PROVIDER: S-EPMC5563493 | biostudies-other | 2016 Aug

REPOSITORIES: biostudies-other

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Project description:BackgroundNumerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system's dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states.ResultsTo demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns.ConclusionsThe ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.

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Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.

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