  The recent development of single-cell transcriptomics has enabled gene
expression to be measured in individual cells instead of being
population-averaged. Despite this considerable precision improvement, inferring
regulatory networks remains challenging because stochasticity now proves to
play a fundamental role in gene expression. In particular, mRNA synthesis is
now acknowledged to occur in a highly bursty manner. We propose to view the
inference problem as a fitting procedure for a mechanistic gene network model
that is inherently stochastic and takes not only protein, but also mRNA levels
into account. We first explain how to build and simulate this network model
based upon the coupling of genes that are described as piecewise-deterministic
Markov processes. Our model is modular and can be used to implement various
biochemical hypotheses including causal interactions between genes. However, a
naive fitting procedure would be intractable. By performing a relevant
approximation of the stationary distribution, we derive a tractable procedure
that corresponds to a statistical hidden Markov model with interpretable
parameters. This approximation turns out to be extremely close to the
theoretical distribution in the case of a simple toggle-switch, and we show
that it can indeed fit real single-cell data. As a first step toward inference,
our approach was applied to a number of simple two-gene networks simulated in
silico from the mechanistic model and satisfactorily recovered the original
networks. Our results demonstrate that functional interactions between genes
can be inferred from the distribution of a mechanistic, dynamical stochastic
model that is able to describe gene expression in individual cells. This
approach seems promising in relation to the current explosion of single-cell
expression data.
