2023

1. Trajectory inference for a branching SDE model of cell differentiation

   Elias Ventre, Aden Forrow, Nitya Gadhiwala, Parijat Chakraborty, Omer Angel, Geoffrey Schiebinger

   arXiv, 2023

   Abs DOI

   A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory inference methods cannot distinguish variability in net proliferation from cell differentiation dynamics, and hence require accurate prior knowledge of the proliferation rate. Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation. In particular, when there is neither death nor subsampling of cells, we show that we extend gWOT to the case with proliferation with similar theoretical guarantees and computational cost, without requiring any prior information. In the case of death and/or subsampling, our method introduces a bias, that we describe explicitly and argue to be inherent to these lineage tracing data. We demonstrate in both cases the ability of this method to reliably reconstruct the landscape of a branching SDE from time-courses of simulated datasets with lineage tracing, outperforming even a benchmark using the experimentally unavailable true branching rates.

2023

1. Convergence of the Sinkhorn algorithm when the Schrödinger problem has no solution

   Aymeric Baradat, Elias Ventre

   Annales de la Faculté des sciences de Toulouse, 2023

   Abs DOI

   The Sinkhorn algorithm is the most popular algorithm for solving the Schröodinger problem: it is known to converge as soon as the latter has a solution, and with a linear rate when the solution has the same support as the reference coupling. Motivated by recent applications of the Schrödinger problem where structured stochastic processes lead to degenerate situations with possibly no solution, we show that the Sinkhorn algorithm still gives rise in this case to exactly two limit points, that can be used to compute the solution of a relaxed version of the Schr\"odinger problem, appearing as the Gamma-limit of a problem where the marginal constraints are replaced by marginal penalizations. These results also allow to develop a theoretical procedure for characterizing the support of the solution, both in the original and in the relaxed problem, for any reference coupling and marginal constraints. We showcase promising numerical applications related to a model used in cell biology.

2023

1. One model fits all: combining inference and simulation of gene regulatory networks

   Elias Ventre, Ulysse Herbach, Thibault Espinasse, Gérard Benoit, Olivier Gandrillon

   PLOS Computational Biology, 2023

   Abs DOI

   The rise of single-cell data highlights the need for a nondeterministic view of gene expression, while offering new opportunities regarding gene regulatory network inference. We recently introduced two strategies that specifically exploit time-course data, where single-cell profiling is performed after a stimulus: HARISSA, a mechanistic network model with a highly efficient simulation procedure, and CARDAMOM, a scalable inference method seen as model calibration. Here, we combine the two approaches and show that the same model driven by transcriptional bursting can be used simultaneously as an inference tool, to reconstruct biologically relevant networks, and as a simulation tool, to generate realistic transcriptional profiles emerging from gene interactions. We verify that CARDAMOM quantitatively reconstructs causal links when the data is simulated from HARISSA, and demonstrate its performance on experimental data collected on in vitro differentiating mouse embryonic stem cells. Overall, this integrated strategy largely overcomes the limitations of disconnected inference and simulation.

2022

1. Evidence for close molecular proximity between reverting and undifferentiated cells

   Souad Zreika, Camille Fourneaux, Elodie Vallin, Laurent Modolo, Rémi Seraphin, Alice Moussy, Elias Ventre, Matteo Bouvier, Anthony Ozier-Lafontaine, Arnaud Bonnaffoux, Franck Picard, Olivier Gandrillon, Sandrine Giraud

   BMC Biology, 2022

   Abs DOI

   According to Waddington’s epigenetic landscape concept, the differentiation process can be illustrated by a cell akin to a ball rolling down from the top of a hill (proliferation state) and crossing furrows before stopping in basins or “attractor states” to reach its stable differentiated state. However, it is now clear that some committed cells can retain a certain degree of plasticity and reacquire phenotypical characteristics of a more pluripotent cell state. In line with this dynamic model, we have previously shown that differentiating cells (chicken erythrocytic progenitors (T2EC)) retain for 24 hours the ability to self-renew when transferred back in self-renewal conditions. Despite those intriguing and promising results, the underlying molecular state of those “reverting” cells remains unexplored. The aim of the present study was therefore to molecularly characterize the T2EC reversion process by combining advanced statistical tools to make the most of single cell transcriptomic data. For this purpose, T2EC, initially maintained in a self-renewal medium (0H), were induced to differentiate for 24h (24H differentiating cells); then a part of these cells was transferred back to the self-renewal medium (48H reverting cells) and the other part was maintained in the differentiation medium for another 24h (48H differentiating cells). For each time point, cell transcriptomes were generated using scRT-qPCR and scRNAseq. Our results showed a strong overlap between 0H and 48H reverting cells when applying dimensional reduction. Moreover, the statistical comparison of cell distributions and differential expression analysis indicated no significant differences between these two cell groups. Interestingly, gene pattern distributions highlighted that, while 48H reverting cells have gene expression pattern more similar to 0H cells, they retained traces of their engagement in the differentiation process. Finally, Sparse PLS analysis showed that only the expression of 3 genes discriminates 48H reverting and 0H cells. Altogether, we show that reverting cells return to an earlier molecular state almost identical to undifferentiated cells and demonstrate a previously undocumented physiological and molecular plasticity during the differentiation process, which most likely results from the dynamic behavior of the underlying molecular network.

2021

1. Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics

   Elias Ventre

   In Silico Biology, 2021

   Abs DOI

   Differentiation can be modeled at the single cell level as a stochastic process resulting from the dynamical functioning of an underlying Gene Regulatory Network (GRN), driving stem or progenitor cells to one or many differentiated cell types. Metastability seems inherent to differentiation process as a consequence of the limited number of cell types. Moreover, mRNA is known to be generally produced by bursts, which can give rise to highly variable non-Gaussian behavior, making the estimation of a GRN from transcriptional profiles challenging. In this article, we present CARDAMOM (Cell type Analysis from scRna-seq Data achieved from a Mixture MOdel), a new algorithm for inferring a GRN from timestamped scRNA-seq data, which crucially exploits these notions of metastability and transcriptional bursting. We show that such inference can be seen as the successive resolution of as many regression problem as timepoints, after a preliminary clustering of the whole set of cells with regards to their associated bursts frequency. We demonstrate the ability of CARDAMOM to infer a reliable GRN from in silico expression datasets, with good computational speed. To the best of our knowledge, this is the first description of a method which uses the concept of metastability for performing GRN inference.

2021

1. Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastability

   Elias Ventre, Thibault Espinasse, Charles-Edouard Bréhier, Vincent Calvez, Thomas Lepoutre, Olivier Gandrillon

   Journal of Mathematical Biology, 2021

   Abs DOI

   Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In this work we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit of which the basins of attraction can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an approximation of the stationary distribution of the PDMP system, which appears as a Beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types.

   PhD thesis

   2022

   1. Analysis, calibration and evaluation of stochastic models of gene expression

      Elias Ventre

      Hal, 2022

      Abs DOI

      Differentiation is the process by which a cell acquires a specific phenotype, through the expression of genes over time. It is now widely accepted that these dynamics results from the action of a gene regulatory network (GRN). New measurement technologies now make it possible to obtain gene expression levels within a single cell. These data have shown the existence of a large variability between cells with the same genotype, showing that population-based data are not sufficient for understanding the mechanisms of cell differentiation. The aim of this PhD project is to develop complementary methods to better understand the dynamics and structure of a GRN from single cell sequencing data. We study a stochastic process modeling the dynamics of a GRN within a cell by a system of coupled piecewise deterministic Markov processes (PDMPs), as well as some simplifications of this model. We first show how a large deviation analysis allows to reduce this molecular model to a discrete Markov chain on a limited number of cell types, thus connecting the GRN structure to the dynamics on these functional types. We then use this analysis to develop a reverse-engineering method of the model from time-course series of expression datasets. We show its efficiency on simulated and experimental data, as well as its biological interpretability. Finally, we develop a method for evaluating the model (once calibrated) against the data by studying the Schrödinger problem when the reference process is a system of PDMPs.