arXiv subjects

Manuel Eduardo Hernández-García

Publications and source records attributed to Manuel Eduardo Hernández-García.

8 recordsLinked to original sources

arXiv2026

Telegraph Processes with Extrinsic Fluctuations: Burst Dynamics and an Application to Domestic Cat Activity

Animal activity often consists of intermittent bursts separated by prolonged periods of inactivity. Here, we describe this behavior using a two-state telegraph process with extrinsically fluctuating transition rates. We derived analytical expressions for the stationary behavior of the system and characterized how stationary fluctuations in the effective transition rates modified the activity and residence time statistics. In particular, we show that whereas fixed transition rates lead to exponential residence-time distributions, stationary rate fluctuations generate effective Lomax distributions with heavier tails. We also found that fluctuations can either increase or decrease the mean occupancy of the active state, and that when the fluctuations in the two transition rates are equal, their effect on the stationary occupancy becomes indistinguishable from the case without fluctuations. We assessed the parameter inference using synthetic data and applied the framework to observations of a domestic cat. For synthetic data, accounting for extrinsic fluctuations substantially improved the recovery of the kinetic parameters used to generate the data. In the experimental data, the inferred variability of the inactive-to-active transition rate was substantially larger than that of the active-to-inactive rate. These results establish a tractable framework for studying stochastic switching systems in which extrinsic variability reshapes burst and residence-time statistics.

q-bio.QM↗

arXiv2026

Oscillations and Spatial Patterns in Large-Scale Stochastic Gene Regulatory Networks

Gene regulatory networks (GRNs) are fundamental to cellular growth and tissue formation, orchestrating spatially and temporally regulated gene expression during development. These networks are inherently subject to intrinsic fluctuations arising from molecular noise, making the analysis of their stability essential for understanding robust pattern formation and developmental dynamics of the organism. In this study, we analyze the stability and dynamics of cyclic GRNs with negative feedback and diffusion, considering both deterministic and stochastic approaches. In the deterministic case, the system exhibits a bifurcation between stability and instability, leading to Hopf instability in the absence of diffusion and to Turing-Hopf instability when diffusion is included. It was observed that the discretization of the spatial domain introduces additional unstable modes, enabling a wider range of patterns. The stochastic framework based on the second-moment approach, which incorporates intrinsic fluctuations, reveals that for small system sizes, fluctuations can dominate the dynamics and induce stochastic Turing instability, even when the system is stable in the absence of diffusion. Notably, Turing instabilities can emerge even when all variables have the same diffusion rate. The developed framework provides a systematic method for analyzing the stability of high-dimensional stochastic systems with diffusion, thereby simplifying the prediction of Turing and Turing-Hopf instabilities. These findings contribute to a deeper understanding of the complex dynamics and pattern formation in GRNs, with potential implications for biological processes, such as cellular differentiation and development.

q-bio.MN↗

arXiv2026

Oscillation Criteria in Large-Scale Gene Regulatory Networks with Intrinsic Fluctuations

Gene Regulatory Networks(GRNs) with feedback are essential components of many cellular processes and may exhibit oscillatory behavior. Analyzing such systems becomes increasingly complex as the number of components increases. Since gene regulation often involves a small number of molecules, fluctuations are inevitable. Therefore, it is important to understand how fluctuations affect the oscillatory dynamics of cellular processes, as this will allow comprehension of the mechanisms that enable cellular functions to remain even in the presence of fluctuations or, failing that, to determine the limit of fluctuations that permits various cellular functions. In this study, we investigated the conditions under which GRNs with feedback and intrinsic fluctuations exhibit oscillatory behavior. Our focus was on developing a procedure that would be both manageable and practical, even for extensive regulatory networks, that is, those comprising numerous nodes. Using the second-moment approach, we described the stochastic dynamics through a set of ordinary differential equations for the mean concentration and its second central moment. The system can attain either a stable equilibrium or oscillatory behavior, depending on its scale and, consequently, the intensity of fluctuations. To illustrate the procedure, we analyzed two relevant systems: a repressilator with three nodes and a system with five nodes, both incorporating intrinsic fluctuations. In both cases, it was observed that for very small systems, which therefore exhibit significant fluctuations, oscillatory behavior is inhibited. The procedure presented here for analyzing the stability of oscillations under fluctuations enables the determination of the critical minimum size of GRNs at which intrinsic fluctuations do not eliminate their cyclical behavior.

q-bio.MN↗

arXiv2025

An Exact Moment-Based Approach for Chemical Reaction-Diffusion Networks: From Mass Action to Hill Functions

Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic models such as the chemical master equation are commonly used to study these systems. However, analytical solutions are limited to specific cases, and stochastic simulations require significant computational resources. To mitigate these challenges, approximation methods, such as the moment approach, reduce the system to a set of ordinary differential equations, thereby lowering the computational requirements. This study investigates the conditions under which the second-moment approach yields exact results during the dynamic evolution of chemical reaction-diffusion networks. The analysis encompasses second-order or higher-order reactions and Hill functions without relying on higher-order moment estimations or closure approximations. Starting with stationary states, we extended the analysis to a dynamic evolution. An enzymatic process and an antithetic feedback system were examined for purely reactive systems, demonstrating the approach's accuracy in capturing system behavior and quantifying errors. The study was further extended to genetic regulatory networks governed by Hill functions, including both purely reactive and reaction-diffusion systems, validating the method in spatially distributed contexts. This framework enables precise characterization of biochemical systems, avoiding information loss typically associated with approximations and allowing for stability analysis under fluctuations. These findings optimize computational strategies while providing insights into intracellular signaling and regulatory processes, paving the way for efficient and accurate stochastic modeling in biochemical systems.

q-bio.MN↗

arXiv2024

Relationship between Decimal Hill Coefficient, Intermediate Processes and Mesoscopic Fluctuations

The Hill function is relevant for describing enzyme binding and other processes in gene regulatory networks. Despite its theoretical foundation, it is often empirically used as a useful fitting function. Theoretical predictions suggest that the Hill coefficient should be an integer. However, it is often assigned a decimal value. The deterministic approximation of binding processes leads to the derivation of the Hill function, which can be expanded around the fluctuation magnitude to derive mesoscopic corrections. This study establishes the relationships between intermediate processes and the decimal Hill coefficient through a direct relationship between the dissociation constants, both with and without fluctuations. This outcome contributes to a deeper understanding of the underlying processes associated with the decimal Hill coefficient while also enabling the prediction of an effective value of the Hill coefficient from the underlying mechanism. This procedure allows us to have a simplified effective description of complex systems.

q-bio.MN↗

arXiv2024

Corrected Hill Function in Stochastic Gene Regulatory Networks

Describing reaction rates in stochastic bio-circuits is commonly done by directly introducing the deterministically deduced Hill function into the master equation. However, when fluctuations in enzymatic reaction rates are not neglectable, the Hill function must be derived, considering all the involved stochastic reactions. In this work, we derived the stochastic version of the Hill function from the master equation of the complete set of reactions that, in the macroscopic limit, lead to the Hill function reaction rate. We performed a series expansion around the average values of the concentrations, which allowed us to find corrections for the deterministic Hill function. This process allowed us to quantify the fluctuations of enzymatic reactions. We found that the underlying variability in propensity rates of gene regulatory networks has an important non-linear effect that reduces the intrinsic fluctuations of the mRNA and protein concentrations.

q-bio.MN↗

arXiv2024

Extrinsic Fluctuations in the p53 Cycle

Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the Master Equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues.

q-bio.MN↗

arXiv2024

Exact Solutions for Small Systems: Urns Models

In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed.

cond-mat.stat-mech↗