arXiv subjects

Guillaume Le Treut

Publications and source records attributed to Guillaume Le Treut.

4 recordsLinked to original sources

arXiv2023

Markov-bridge generation of transition paths and its application to cell-fate choice

We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master equation for Markov bridges, which exhibits the original transition rates scaled by a time-dependent factor. Trajectories can then be generated using a refined version of the Gillespie algorithm. We illustrate the benefits of our method by sampling trajectories in the Müller-Brown potential. This allows us to generate transition paths which would otherwise be obtained at a high computational cost with standard Kinetic Monte Carlo methods because commitment to a transition path is essentially a rare event. We then apply our method to a single-cell RNA sequencing dataset from mouse pancreatic cells to investigate the cell differentiation pathways of endocrine-cell precursors. By sampling Markov bridges for a specific differentiation pathway we obtain a time-resolved dynamics that can reveal features such as cell types which behave as bottlenecks. The ensemble of trajectories also gives information about the fluctuations around the most likely path. For example, we quantify the statistical weights of different branches in the differentiation pathway to alpha cells.

cond-mat.stat-mech↗

arXiv2020

A polymer model for the quantitative reconstruction of 3d chromosome architecture from Hi-C and GAM data

It is widely believed that the folding of the chromosome in the nucleus has a major effect on genetic expression. For example co-regulated genes in several species have been shown to colocalize in space despite being far away on the DNA sequence. In this manuscript, we present a new method to model the three-dimensional structure of the chromosome in live cells, based on DNA-DNA interactions measured in high-throughput chromosome conformation capture experiments (Hi-C) and genome architecture mapping experiments (GAM). Our approach incorporates a polymer model, and directly uses the contact probabilities measured in Hi-C and GAM experiments rather than estimates of average distances between genomic loci. Specifically, we model the chromosome as a Gaussian polymer with harmonic interactions and extract the coupling coefficients best reproducing the experimental contact probabilities. In contrast to existing methods, we give an exact expression of the contact probabilities at thermodynamic equilibrium. The Gaussian effective model (GEM) reconstructed with our method reproduces experimental contacts with high accuracy. We also show how Brownian Dynamics simulations of our reconstructed GEM can be used to study chromatin organization, and possibly give some clue about its dynamics.

q-bio.QM↗

arXiv2018

Models of chromosome architecture and connection with the regulation of genetic expression

Increasing evidence suggests that chromosome folding and genetic expression are intimately connected. For example, the co-expression of a large number of genes can benefit from their spatial co-localization in the cellular space. Furthermore, functional structures can result from the particular folding of the chromosome. Such phenomena have in common to result from the binding of divalent proteins that can bridge regions sometimes far away on the DNA sequence. The physical system consisting of the chromosome interacting with divalent proteins can be very complex. As such, most of the mechanisms responsible for chromosome folding and for the formation of functional structures have remained elusive. Using methods from statistical physics, we investigated models of chromosome architecture. A common denominator of our approach has been to represent the chromosome as a polymer with bending rigidity and consider its interaction with a solution of DNA-binding proteins. Structures entailed by the binding of such proteins were then characterized at the thermodynamical equilibrium. Furthermore, we complemented theoretical results with Brownian dynamics simulations, allowing to reproduce more of the biological complexity. The main contributions of this thesis have been: (i) to provide a model for the existence of transcription factories characterized in vivo with fluorescence microscopy; (ii) to propose a physical basis for a conjectured regulatory mechanism of the transcription involving the formation of DNA hairpin loops by the H-NS protein as characterized with atomic-force microscopy experiments; (iii) to propose a physical model of the chromosome that reproduces contacts measured in chromosome conformation capture (CCC) experiments. Consequences on the regulation of transcription are discussed in each of these studies.

cond-mat.soft↗

arXiv2015

Phase behaviour of DNA in presence of DNA-binding proteins

To characterize the thermodynamical equilibrium of DNA chains interacting with a solution of non-specific binding proteins, a Flory-Huggins free energy model was implemented. We explored the dependence on DNA and protein concentrations of the DNA collapse. For physiologically relevant values of the DNA-protein affinity, this collapse gives rise to a biphasic regime with a dense and a dilute phase; the corresponding phase diagram was computed. Using an approach based on Hamiltonian paths, we show that the dense phase has either a molten globule or a crystalline structure, depending on the DNA bending rigidity, which is influenced by the ionic strength. These results are valid at the thermodynamical equilibrium and should therefore be consistent with many biological processes, whose characteristic timescales range typically from 1 ms to 10 s. Our model may thus be applied to biological phenomena that involve DNA-binding proteins, such as DNA condensation with crystalline order, which occurs in some bacteria to protect their chromosome from detrimental factors; or transcription initiation, which occurs in clusters called transcription factories that are reminiscent of the dense phase characterized in this study.

cond-mat.soft↗