arXiv subjects

Cesar Nieto

Publications and source records attributed to Cesar Nieto.

4 recordsLinked to original sources

arXiv2025

Stochastic multi-step cell size homeostasis model for cycling human cells

Measurements of cell size dynamics have established the adder principle as a robust mechanism of cell size homeostasis. In this framework, cells add a nearly constant amount of size during each cell cycle, independent of their size at birth. Theoretical studies have shown that the adder principle can be achieved when cell-cycle progression is coupled to cell size. Here, we extend this framework by considering a general growth law modeled as a Hill-type function of cell size. This assumption introduces growth saturation to the model, such that very large cells grow approximately linearly rather than exponentially. Additionally, to capture the sequential nature of division, we implement a stochastic multi-step adder model in which cells progress through internal regulatory stages before dividing. From this model, we derive exact analytical expressions for the moments of cell size distributions. Our results show that stronger growth saturation increases the mean cell size in steady state, while slightly reducing fluctuations compared to exponential growth. Importantly, despite these changes, the adder property is preserved. This emphasizes that the reduction in size variability is a consequence of~the growth law rather than simple scaling with mean size. Finally, we analyze stochastic clonal proliferation and find that growth saturation influences both single-cell size statistics and variability across populations. Our results provide a generalized framework for connecting multi-step adder mechanisms with proliferation dynamics, extending size control theory beyond exponential growth.

q-bio.QM↗

arXiv2025

Intrinsic limits of timekeeping precision in gene regulatory cascades

Multiple cellular processes are triggered when the concentration of a regulatory protein reaches a critical threshold. Previous analyses have characterized timing statistics for single-gene systems. However, many biological timers are based on cascades of genes that activate each other sequentially. Here, we develop an analytical framework to describe the timing precision of such cascades using a burst-dilution hybrid stochastic model. We first revisit the single-gene case and recover the known result of an optimal activation threshold that minimizes first-passage-time (FPT) variability. Extending this concept to two-gene cascades, we identify three distinct optimization regimes determined by the ratio of intrinsic noise levels and the protein dilution rate, defining when coupling improves or worsens timing precision compared to a single-gene strategy. Generalizing to cascades of arbitrary gene length, we obtain a simple mathematical condition that determines when a new gene in the cascade can decrease the timing noise based on its intrinsic noise and protein dilution rate. In the specific case of a cascade of identical genes, our analytical results predict suppression of FPT noise with increasing cascade length and the existence of a mean time that decreases relative timing fluctuations. Together, these results define the intrinsic limits of timekeeping precision in gene regulatory cascades and provide a minimal analytical framework to explore timing control in biological systems.

q-bio.OT↗

arXiv2025

Dynamical Inference of Cell Size Regulation Parameters

Cells achieve size homeostasis by regulating their division timing based on their size, added size, and cell cycle time. Previous research under steady-state conditions demonstrated the robustness of these mechanisms. However, their dynamic responses in fluctuating environments, such as nutrient depletion due to population growth, remain challenging to fully characterize. Currently, advances in single-cell microscopy have revealed various cellular division strategies whose underlying molecular mechanisms are complex and not always available. This study introduces a novel approach to model cell size dynamics using a piecewise deterministic Markov chain framework, where cell division events are modeled as stochastic jumps determined by a division propensity dependent on both current cell size and added size since birth. We propose a three-parameter characterization for the division process: scale (target added size at division), shape (division stochasticity), and division strategy (relevance of cell size, added size, or cell cycle duration). We derive analytical formulas for the probability of division, and with this probability, we develop a maximum likelihood estimation (MLE) framework. We implement a systematic investigation of the accuracy of inference as a function of sample size. The model's performance is studied across various scenarios, including those exhibiting dynamical changes in one or more parameters, suggesting its broad applicability for analyzing new experimental data on cell size regulation in dynamic environments.

q-bio.QM↗

arXiv2025

Information and fitness in two-state systems: self-replicating individuals in a fluctuating environment

A population of individuals with the same genes can present heterogeneous traits (phenotypes). The prevalence of this heterogeneity can be explained as a bet-hedging strategy that improves the population proliferation rate (fitness) in fluctuating environments. The phenotype distribution is influenced by factors such as competition between phenotypes, the duration of environmental states, and the rate of phenotype-switching. We illustrate these effects in a system where both the environment and the phenotype can adopt two states. This system includes scenarios such as symmetric bet-hedging and dormant-proliferating phenotypes. We examine how environmental and phenotypic states share mutual information, measured in bits, and explore the relationship between this information and population fitness. We propose that when fitness is measured relative to the case where phenotype and environment are independent, information and fitness can be treated as equivalent measures. We investigate strategies that individuals can use to improve this information, such as adjusting the rates of proliferation and phenotype-switching relative to the environmental fluctuation rate. Through these strategies, with fixed marginal distributions, an increase in information implies an increase in population fitness. We also identify limits to the maximum achievable fitness and information and discuss the value of the information in terms of this new normalized fitness. Our framework offers new insights into how organisms adapt to fluctuating environmental conditions.

q-bio.PE↗