Novel domain expansion methods to improve the computational efficiency of the solution of Chemical Master Equation for large biological networks.

Background: Numerical solutions of the chemical master equation (CME) are important to understand the stochasticity of biochemical systems. However, solving CMEs is a formidable task due to the nonlinear nature of the reactions and size of the networks that result in different realisations and, most importantly, the exponential growth of the size of the state-space with respect to the number of different species in the system. When the size of the biochemical system is very large in terms of the number of variables, the solution to the CME becomes intractable. Therefore, 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 to describe the dynamic behaviour of the system. 𝐼𝑆𝑃 is based on a state-space search and the data structure standards of artificial intelligence (𝐴𝐼) 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. Results: To show the acceptability and effectiveness of our method, we apply the 𝐼𝑆𝑃 to several biological models previously discussed in the literature. According to the results of our computational experiments, we show that 𝐼𝑆𝑃 is effective in terms of speed and accuracy of the expansion, accuracy of the solution, and provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions: The 𝐼𝑆𝑃 is the de-novo method to address the accuracy as well as the performance problems for the solution of the CME. It systematically expands the projection space based on predefined inputs, which are useful in providing accuracy in the approximation and an exact analytical solution at the time of interest. The 𝐼𝑆𝑃 was more effective in terms of predicting the behaviour of the state-space of the system and in performance management, which is a vital step towards modelling large biochemical systems.