arXiv subjects

Ulysse Herbach

Publications and source records attributed to Ulysse Herbach.

6 recordsLinked to original sources

arXiv2026

Efficient stochastic simulation of gene regulatory networks using hybrid models of transcriptional bursting

Single-cell data reveal the presence of biological stochasticity between cells of identical genome and environment, in particular highlighting the transcriptional bursting phenomenon. To account for this property, gene expression may be modeled as a continuous-time Markov chain where biochemical species are described in a discrete way, leading to Gillespie's stochastic simulation algorithm (SSA) which turns out to be computationally expensive for realistic mRNA and protein copy numbers. Alternatively, hybrid models based on piecewise-deterministic Markov processes (PDMPs) offer an effective compromise for capturing cell-to-cell variability, but their simulation remains limited to specialized mathematical communities. With a view to making them more accessible, we present here a simple simulation method that is reminiscent of SSA, while allowing for much lower computational cost. We detail the algorithm for a bursty PDMP describing an arbitrary number of interacting genes, and prove that it simulates exact trajectories of the model. As an illustration, we use the algorithm to simulate a two-gene toggle switch: this example highlights the fact that bimodal distributions as observed in real data are not explained by transcriptional bursting per se, but rather by distinct burst frequencies that may emerge from interactions between genes.

q-bio.MN↗

arXiv2026

Quantitative ergodicity for gene regulatory networks with transcriptional bursting

We study the long-term behavior of two piecewise-deterministic Markov processes used to model stochastic gene regulatory networks with bursting dynamics. Under regularity assumptions on the jump rate, we prove the existence and uniqueness of the stationary distribution for an arbitrary number of interacting genes and an arbitrary strength of interaction. Using coupling methods, we also provide explicit upper bounds for the convergence to equilibrium in terms of Wasserstein distances.

math.PR↗

arXiv2023

Harissa: stochastic simulation and inference of gene regulatory networks based on transcriptional bursting

Gene regulatory networks, as a powerful abstraction for describing complex biological interactions between genes through their expression products within a cell, are often regarded as virtually deterministic dynamical systems. However, this view is now being challenged by the fundamentally stochastic, 'bursty' nature of gene expression revealed at the single cell level. We present a Python package called Harissa which is dedicated to simulation and inference of such networks, based upon an underlying stochastic dynamical model driven by the transcriptional bursting phenomenon. As part of this tool, network inference can be interpreted as a calibration procedure for a mechanistic model: once calibrated, the model is able to capture the typical variability of single-cell data without requiring ad hoc external noise, unlike ordinary or even stochastic differential equations frequently used in this context. Therefore, Harissa can be used both as an inference tool, to reconstruct biologically relevant networks from time-course scRNA-seq data, and as a simulation tool, to generate quantitative gene expression profiles in a non-trivial way through gene interactions.

q-bio.MN↗

arXiv2021

Gene regulatory network inference from single-cell data using a self-consistent proteomic field

The well-known issue of reconstructing regulatory networks from gene expression measurements has been somewhat disrupted by the emergence and rapid development of single-cell data. Indeed, the traditional way of seeing a gene regulatory network as a deterministic system affected by small noise is being challenged by the highly stochastic, bursty nature of gene expression revealed at single-cell level. In previous work, we described a promising strategy in which network inference is seen as a calibration procedure for a mechanistic model driven by transcriptional bursting: this model inherently captures the typical variability of single-cell data without requiring ad hoc external noise, unlike ordinary or even stochastic differential equations often used in this context. The resulting algorithm, based on approximate resolution of the related master equation using a self-consistent field, was derived in detail but only applied as a proof of concept to simulated two-gene networks. Here we derive a simplified version of the algorithm and apply it, in more relevant situations, to both simulated and real single-cell RNA-Seq data. We point out three interesting features of this approach: it is computationally tractable with realistic numbers of cells and genes, it provides inferred networks with biological interpretability, and the underlying mechanistic model allows testable predictions to be made. A practical implementation of the inference procedure, together with an efficient stochastic simulation algorithm for the model, is available as a Python package.

q-bio.MN↗

arXiv2019

Stochastic gene expression with a multistate promoter: breaking down exact distributions

We consider a stochastic model of gene expression in which transcription depends on a multistate promoter, including the famous two-state model and refractory promoters as special cases, and focus on deriving the exact stationary distribution. Building upon several successful approaches, we present a more unified viewpoint that enables us to simplify and generalize existing results. In particular, the original jump process is deeply related to a multivariate piecewise-deterministic Markov process that may also be of interest beyond the biological field. In a very particular case of promoter configuration, this underlying process is shown to have a simple Dirichlet stationary distribution. In the general case, the corresponding marginal distributions extend the well-known class of Beta products, involving complex parameters that directly relate to spectral properties of the promoter transition matrix. Finally, we illustrate these results with biologically plausible examples.

math.PR↗

arXiv2017

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

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.

q-bio.MN↗