A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance. We show that the hybrid approach yields accurate results for sufficiently large molecule counts, while reducing the computational effort from one ordinary differential equation for each state to one partial differential equation for each mode of the system. Furthermore, we give an analytical steady-state solution of the hybrid model for the case of a self-regulatory gene.

BackgroundDiscrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years several methods for accurately approximating the statistical moments of such models have become very popular since they allow an efficient analysis of complex networks.ResultsWe propose a generalized method of moments approach for inferring the parameters of reaction networks based on a sophisticated matching of the statistical moments of the corresponding stochastic model and the sample moments of population snapshot data. The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when a large number of samples is available. We demonstrate the usefulness and efficiency of the inference method on two case studies.ConclusionsThe generalized method of moments provides accurate and fast estimations of unknown parameters of reaction networks. The accuracy increases when also moments of order higher than two are considered. In addition, the variance of the estimator decreases, when more samples are given or when higher order moments are included.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0342-8) contains supplementary material, which is available to authorized users.

Abstract. DNA methylation is an epigenetic mechanism whose important role in development has been widely recognized. This epigenetic modification results in heritable changes in gene expression not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood and recently different mechanistic models of enzyme activities responsible for DNA methylation have been proposed. Here we extend existing Hidden Markov Models (HMMs) for DNA methylation by describing the occurrence of spatial methylation patterns over time and propose several models with different neighborhood dependencies. We perform numerical analysis of the HMMs applied to bisulfite sequencing measurements and accurately predict wild-type data. In addition, we find evidence that the enzymes' activities depend on the left 5' neighborhood but not on the right 3' neighborhood.

DNA methylation is an epigenetic mark whose important role in development has been widely recognized. This epigenetic modification results in heritable information not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood. Several mechanistic models of enzyme activities responsible for DNA methylation have been proposed. Here, we extend existing Hidden Markov Models (HMMs) for DNA methylation by describing the occurrence of spatial methylation patterns over time and propose several models with different neighborhood dependences. Furthermore, we investigate correlations between the neighborhood dependence and other genomic information. We perform numerical analysis of the HMMs applied to comprehensive hairpin and non-hairpin bisulfite sequencing measurements and accurately predict wild-type data. We find evidence that the activities of Dnmt3a and Dnmt3b responsible for de novo methylation depend on 5' (left) but not on 3' (right) neighboring CpGs in a sequencing string.

In this work we study a microtubule (MT) model, whose length is regulated by the action of processive kinesin motors. We treat the case of infinite processivity, i.e. particle exchange in the bulk is neglected. The exact results can be obtained for model parameters which correspond to a finite length of the MT. In contrast to the model with particle exchange we find that the lengths of the MT are exponentially distributed in this parameter regime. The remaining parameter space of the model, which corresponds to diverging MT lengths, is analyzed by means of extensive Monte Carlo simulations and a macroscopic approach. For divergent MTs we find a complex structure of the phase diagram in terms of shapes of the density profile.