Inferring gene regulatory networks from single-cell data: a mechanistic approach

Ulysse Herbach,Thibault Espinasse,Arnaud Bonnaffoux,Olivier Gandrillon

doi:10.1186/s12918-017-0487-0

Abstract

BackgroundThe 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.ResultsWe 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.ConclusionsOur 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.

Highlights

The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged
Taking advantage of the latent structure of proteins, we can deal with missing data in a natural way: if the mRNA measurement of gene i is invalid in a cell k owing to technical problems, it is possible to ignore it by removing the i-th term in the conditional distribution of mRNAs (12). This only modifies the definition of v for cell k in Eq (13), ensuring that all valid data is effectively used for each cell. In this part, we first compare the distribution of the mechanistic model (4) to the mRNA quasi-steady state combined with Hartree approximation for proteins, on a simple toggle-switch example
We show that the single-gene model with auto-activation can fit marginal mRNA distributions from real data better than the constant-kon model

Summary

Introduction

The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged. As the mean is not sufficient to account for a population of cells, a deterministic model – e.g. ordinary differential equation (ODE) systems, often used in inference [8, 9] – is unlikely to faithfully inform about an underlying gene regulatory network. Whether such a deterministic approach could still be a valid approximation or not is a difficult question that may require some biological insight into the system under consideration [10]. Another key aspect when considering individual cells is that they generally have to be killed for measurements: from a statistical point of view, temporal single-cell data should

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