arXiv subjects

Tomás Alarcón

Publications and source records attributed to Tomás Alarcón.

9 recordsLinked to original sources

arXiv2025

Stochastic modelling reveals that chromatin folding buffers epigenetic landscapes against sirtuin depletion during DNA damage

Epigenetic landscapes, represented by patterns of chemical modifications on histone tails, are essential for maintaining cell identity and tissue homeostasis. These landscapes are shaped by multiple factors, including local biochemical signals and the three-dimensional organisation of chromatin. However, their response to genomic stress, such as DNA double-strand breaks (DSBs), remains incompletely understood. Here, we use a stochastic model of histone modification dynamics integrated with chromatin architecture to investigate how local depletion of sirtuins, histone deacetylases involved in DSB repair, destabilises epigenetic patterns. Our simulations recapitulate experimental findings in which sirtuin relocalisation to DSB sites leads to the epigenetic erosion and suggest that the resulting landscape depends on enzyme levels and chromatin geometry. Importantly, chromatin regions with large domains of long-range contacts are more resilient to epigenetic destabilisation. These findings suggest that chromatin folding can buffer against relocation of histone-modifying enzymes, highlighting a structural mechanism for preserving epigenetic integrity under stress.

q-bio.QM↗

arXiv2024

Hybrid methods in reaction-diffusion equations

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems, accounting for each individual is inefficient. If the number of entities is large enough, random effects are negligible, and often partial differential equations (PDEs) are used in which the fluctuations are neglected. When the system is heterogeneous, so that the number of individuals is large in certain regions and small in others, the PDE description becomes inaccurate in certain regions. To overcome this problem, the so-called hybrid schemes have been proposed that couple a stochastic description in parts of the domain with its mean field limit in the others. In this chapter, we review the different formulations of this approach and our recent contributions to overcome several of the limitations of previous schemes, including the extension of the concept to multiscale models of cell populations.

q-bio.QM↗

arXiv2024

Understanding how chromatin folding and enzyme competition affect rugged epigenetic landscapes

Epigenetics plays a key role in cellular differentiation and maintaining cell identity, enabling cells to regulate their genetic activity without altering the DNA sequence. Epigenetic regulation occurs within the context of hierarchically folded chromatin, yet the interplay between the dynamics of epigenetic modifications and chromatin architecture remains poorly understood. In addition, it remains unclear what mechanisms drive the formation of rugged epigenetic patterns, characterised by alternating genomic regions enriched in activating and repressive marks. In this study, we focus on post-translational modifications of histone H3 tails, particularly H3K27me3, H3K4me3, and H3K27ac. We introduce a mesoscopic stochastic model that incorporates chromatin architecture and competition of histone-modifying enzymes into the dynamics of epigenetic modifications in small genomic loci comprising several nucleosomes. Our approach enables us to investigate the mechanisms by which epigenetic patterns form on larger scales of chromatin organisation, such as loops and domains. Through bifurcation analysis and stochastic simulations, we demonstrate that the model can reproduce uniform chromatin states (open, closed, and bivalent) and generate previously unexplored rugged profiles. Our results suggest that enzyme competition and chromatin conformations with high-frequency interactions between distant genomic loci can drive the emergence of rugged epigenetic landscapes. Additionally, we hypothesise that bivalent chromatin can act as an intermediate state, facilitating transitions between uniform and rugged landscapes. This work offers a powerful mathematical framework for understanding the dynamic interactions between chromatin architecture and epigenetic regulation, providing new insights into the formation of complex epigenetic patterns.

q-bio.QM↗

arXiv2024

Computational modelling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modelling has contributed to unravelling its complexity. Many existing theoretical models of angiogenic sprouting are based on the 'snail-trail' hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate towards low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modelling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modelling components such models should include in order to investigate its functional role.

q-bio.TO↗

arXiv2022

Semiclassical theory explains stochastic ghosts scaling

Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time delay towards equilibrium. Specifically the duration of the transient, $τ$, close to this bifurcation in deterministic systems follows scaling laws of the form $τ\sim |ε- ε_c|^{-1/2}$, where $ε$ is the bifurcation or control parameter, and $ε_c$ its critical value. For systems undergoing a saddle-node bifurcation, the mechanism involves transients getting trapped by a so-called ghost. In a recent article we explored how intrinsic noise affected the deterministic picture. Extensive numerical simulations showed that, although scaling behaviour persisted in the presence of noise, the scaling law was more complicated than a simple power law. In order to gain deeper insight into this scaling behaviour, we resort to the WKB asymptotic approximation of the Master Equation. According to this approximation, the behaviour of the system is given as the weighted sum of \emph{trajectories} within the phase space of the Hamiltonian associated to the corresponding Hamilton-Jacobi equation. By analysing the flight time of the Hamilton equations, we show that the statistically significant paths follow a scaling function that exactly matches the one observed in the stochastic simulations. We therefore put forward that the properties of the flight times of the Hamiltonian system underpin the scaling law of the underlying stochastic system, and that the same properties should extend in a universal way to all stochastic systems whose associated Hamiltonian exhibits the same behaviour.

math.DS↗

arXiv2021

A method to coarse-grain multi-agent stochastic systems with regions of multistability

Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally expensive. Traditional techniques to reduce the computational intensity of such models can lead to a reduction in the richness of the dynamics observed, compared to the original system. Here we use large deviation theory to decrease the computational cost of a spatially-extended multi-agent stochastic system with a region of multi-stability by coarse-graining it to a continuous time Markov chain on the state space of stable steady states of the original system. Our technique preserves the original description of the stable steady states of the system and accounts for noise-induced transitions between them. We apply the method to a bistable system modelling phenotype specification of cells driven by a lateral inhibition mechanism. For this system, we demonstrate how the method may be used to explore different pattern configurations and unveil robust patterns emerging on longer timescales. We then compare the full stochastic, coarse-grained and mean-field descriptions via pattern quantification metrics and in terms of the numerical cost of each method. Our results show that the coarse-grained system exhibits the lowest computational cost while preserving the rich dynamics of the stochastic system. The method has the potential to reduce the computational complexity of hybrid multiscale models, making them more tractable for analysis, simulation and hypothesis testing.

q-bio.QM↗

arXiv2018

Local migration quantification method for scratch assays

Motivation: The scratch assay is a standard experimental protocol used to characterize cell migration. It can be used to identify genes that regulate migration and evaluate the efficacy of potential drugs that inhibit cancer invasion. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. A drawback of this methodology is the lack of its reproducibility resulting in irregular cell-free areas with crooked leading edges. Existing quantification methods deal poorly with such resulting irregularities present in the data. Results: We introduce a new quantification method that can analyse low quality experimental data. By considering in-silico and in-vitro data, we show that the method provides a more accurate statistical classification of the migration rates than two established quantification methods. The application of this method will enable the quantification of migration rates of scratch assay data previously unsuitable for analysis. Availability and Implementation: The source code and the implementation of the algorithm as a GUI along with an example dataset and user instructions, are available in https://bitbucket.org/anavictoria-ponce/local_migration_quantification_scratch_assays/src/master/. The datasets are available in https://ganymed.math.uni-heidelberg.de/~victoria/publications.shtml.

q-bio.QM↗

arXiv2016

Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age. The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. We then formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size: cells consume oxygen which in turns fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. This allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.

physics.bio-ph↗

arXiv2015

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the Chemical Master Equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provide the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species are order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.

physics.bio-ph↗