Inference of Kinetic Parameters of Delayed Stochastic Models of Gene Expression Using a Markov Chain Approximation

Gene expression dynamics is influenced by even small fluctuations on the levels of various molecular species, such as RNA polymerases and transcription factors. In some cases, even the presence of a single molecule can cause phenotypic switching [1]. This makes the cellular metabolism inherently stochastic [2].The stochasticity in the abundance of a substance is in general thought of being noise that obscures a signal that carries information relevant to the cell. However, recent evidence suggests that cells may be able to use the noise component in benefit of their survival [3]. Due to this, several modelling strategies have been proposed for accurately accounting for noise in the dynamics of gene regulatory networks (GRNs) [2, 4–7].The chemical master equation is a probabilistic description of the dynamics of interacting molecules that fully captures the stochasticity of their kinetics. However, it is intractable to solve in the biologically relevant cases.The stochastic simulation algorithm [8] (SSA) is a Monte Carlo simulation of the chemical master equation, allowing the study of complex models of gene expression. In the SSA, all chemical reactions are assumed instantaneous. However, several processes during the transcription and translation of a gene are highly complex, either involving many molecular species or involving reactions that are not bimolecular (e.g., the promoter open complex formation). To account for the effects of these events on the dynamics of RNA and proteins, the delayed SSA (DSSA) was proposed [5]. The ability of the DSSA to model chemical reactions with noninstantaneous events makes it a good tool to model GRN [6].Assessing a model's accuracy and validity is important [9]. Even if experimental data has been used in model building, one must also be able to quantitatively rank the models based on the data. This ranking can be used to determine realistic parameter values, if these have not been measured directly, and to choose between models