Framework to simulate gene regulatory networks with stochastic molecular kinetics and to infer steady-state network structure

Abstract

BackgroundThe temporal progression of many fundamental processes in cells and organisms, including homeostasis, differentiation and development, are governed by gene regulatory networks (GRNs). GRNs balance fluctuations in the output of their genes, which trace back to the stochasticity of molecular interactions. Although highly desirable to understand life processes, predicting the temporal progression of gene products within a GRN is challenging when considering stochastic events such as transcription factor - DNA interactions or protein production and degradation. ResultsWe report CaiNet, a fast computer-aided interactive network simulation environment optimized to set up, simulate and infer GRNs at molecular detail. In our approach, we consider each network element to be isolated from other elements during small time intervals, after which we synchronize molecule numbers between all network elements. Thereby, the temporal behaviour of network elements is decoupled and can be treated by local stochastic or deterministic solutions. We demonstrate the working principle of the modular approach of CaiNet with a repressive gene cascade comprising four genes. By considering a deterministic time evolution within each time interval for all elements, our method approaches the solution of the system of deterministic differential equations associated with the GRN. By allowing genes to stochastically switch between on and off states or by considering stochastic production of gene outputs, we are able to include increasing levels of stochastic detail and approximate the solution of a Gillespie simulation. Notably, our modular approach further allows for a simple consideration of deterministic delays. We further infer relevant regulatory connections and steady-state parameters of a GRN of up to ten genes from steady-state measurements by identifying each gene of the network with a single perceptron in an artificial neuronal network and using a gradient decent method originally designed to train recurrent neural networks. ConclusionCaiNet constitutes a user-friendly framework to simulate GRNs at molecular detail and to infer the topology and steady-state parameters of GRNs. Thus, it should prove helpful to analyze or predict the temporal progression of reaction networks or GRNs in cellular and organismic biology. CaiNet is freely available at https://gitlab.com/GebhardtLab/CaiNet.