Biology subjects

Zabaikina, I.

Publications and source records attributed to Zabaikina, I..

7 recordsLinked to original sources

bioRxiv2026

Gene Expression Variability with Feedback Regulation Implemented via Protein-Dependent Cell Growth

Variability in gene expression among single cells and growing cell populations can arise from the stochastic nature of protein synthesis, which often occurs in random bursts. This study investigates the variability in the expression of a growth-sustaining protein, whose concentration is regulated by a negative feedback loop due to cell growth-induced dilution. We model the distribution of protein concentration using a Chapman-Kolmogorov equation for single cells and a population balance equation for growing cell populations. For single cells, we derive an explicit solution for the protein concentration distribution in state space and represent it as a Bessel function in Laplace space. For growing populations, we find that the distribution satisfies a Heun differential equation with singular boundary conditions. By addressing the central connection problem for the Heun equation, we quantify the population-level protein distribution and determine the Mathusian parameter, which characterizes population growth. This work provides a comprehensive analytical framework for understanding how stochastic protein synthesis impacts gene expression variability and population dynamics.

systems biology↗

bioRxiv2025

Stochastic Gene Expression under Sequestration: Noise Reduction and Emergent Distributions

Gene expression noise can be modulated by protein sequestration, a mechanism we investigate through a stochastic modeling framework. We examine how the distribution of free (non-sequestered) protein depends on sequestration cooperativity (monomers, dimers, multimers) and on the timescale separation between sequestration and protein turnover. For non-cooperative sequestration, faster kinetics drive the distribution from a high-noise to a lower-noise gamma form, while the right-tail remains governed by the high-noise limit -- revealing a non-commutativity between tail asymptotics and fast sequestration. For cooperative sequestration, the distribution departs from gamma, exhibiting left skewness or multi-modality. These results highlight how sequestration mechanisms shape protein variability in nontrivial ways.

systems biology↗

bioRxiv2025

Bursty Gene Expression in Single Cells and Expanding Populations: A Discrete Approach

Bursty protein production is a key source of gene expression noise. In this study, we analyze a Markovian model of cellular protein dynamics, where proteins are produced in geometrically distributed bursts. Extending this model, we incorporate a feedback mechanism by assuming that higher protein levels reduce both cell growth and protein decay rates. We study both single-cell dynamics and an expanding cell population. Without feedback, the protein level follows a negative binomial distribution with the same parameters in both cases. With feedback, however, single-cell and population-level distributions differ, each expressible as a mixture of two negative binomial distributions with framework-dependent parameters. Using numerical integration of the master and population balance equations, we calculate the time-dependent distributions in both settings. This work extends previous continuous models and provides new insights into how population expansion influences intrinsic cellular heterogeneity.

systems biology↗

bioRxiv2024

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

systems biology↗

bioRxiv2023

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

We consider a protein that negatively regulates the rate with which a cell grows. Since less growth means less protein dilution, this mechanism forms a positive feedback loop on the protein concentration. We couple the feedback model with a simple description of the cell cycle, in which a division event is triggered when the cell volume reaches a critical threshold. Following the division we either track only one of the daughter cells (single cell framework) or both cells (population frame-work). For both frameworks, we find an exact time-independent distribution of protein concentration and cell volume. We explore the consequences of dilution feedback on ergodicity, population growth rate, and the bias of the population distribution towards faster growing cells with less protein.

systems biology↗

bioRxiv2022

Quantifying noise modulation from coupling of stochastic expression to cellular growth: An analytical approach

The overexpression of many proteins can often have a detrimental impact on cellular growth. This expression-growth coupling leads to positive feedback - any increase of intracellular protein concentration reduces the growth rate of cell size expansion that in turn enhances the concentration via reduced dilution. We investigate how such feedback amplifies intrinsic stochasticity in gene expression to drive a skewed distribution of the protein concentration. Our results provide an exact solution to this distribution by analytically solving the Chapman-Kolmogorov equation, and we use it to quantify the enhancement of noise/skewness as a function of expression-growth coupling. This analysis has important implications for the expression of stress factors, where high levels provide protection from stress, but come at the cost of reduced cellular proliferation. Finally, we connect these analytical results to the case of an actively degraded gene product, where the degradation machinery is working close to saturation.

systems biology↗

bioRxiv2019

Optimal bang--bang feedback for bursty gene expression

Stochasticity in gene expression poses a critical challenge to the precise control of cellular function. In this paper we examine how precisely can a stochastically expressed protein attain a given target expression level. We consider a protein which is produced in bursts and which is able to control its expression via a negative feedback loop; we specifically focus on feedback of a bang-bang type which turns off the production of the protein whenever its concentration exceeds a given threshold. Using a piecewise deterministic mathematical formalism, we derive explicit expressions for the probabilistic distribution of the protein concentration, and for the mean square deviation from the target level. Employing a combination of analytic and numerical optimization, we identify the optimal value of the bang-bang threshold, in terms of minimising the deviation, and examine the dependence of the optimal value on the target level and the sub-threshold burst frequency. The systematic analysis allows us to formulate a number of quantitative and qualitative conclusions about the controllability of burst like gene expression. Finally, we outline directions for future research into the topic.

systems biology↗