Fig. 2. ANN-aided stochastic model approximation of various models of transcription.

a Illustration of three models of transcription. The models describe initiation, elongation and termination and specifically predict the numbers of nascent RNAs (equivalently the number of RNAP polymerases, Pol IIs) at the gene locus. In all models, a nascent RNA molecule detaches after a constant time has elapsed from its binding to the promoter. The models differ in how they model Pol II binding: in Model I, the binding is modelled as a Poisson process, hence one at a time; in Model II, binding occurs in bursts, whose size conforms to a geometric distribution; in Model III, the gene switches between active and inactive states, and only the active state permits Pol II binding. b For all models, the FSP solution of the NN-CME derived by the ANN-aided procedure is in excellent agreement with the SSA of the delay CME. The accuracy is independent of the modality and skewness of the distribution. The rate constants and other parameters related to the ANN’s training are specified in SI Table 1.