Transient hysteresis and inherent stochasticity in gene regulatory networks

A Kinetic Finite Volume Discretization of the Multidimensional PIDE Model for Gene Regulatory Networks

In this paper, a finite volume discretization scheme for partial integro-differential equations (PIDEs) describing the temporal evolution of protein distribution in gene regulatory networks is proposed. It is shown that the obtained set of ODEs can be formally represented as a compartmental kinetic system with a strongly connected reaction graph. This allows the application of the theory of nonnegative and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, it is straightforward to show the existence, uniqueness and stability of equilibria. Moreover, the computation of the stationary probability distribution can be traced back to the solution of linear equations. The discretization scheme is presented for one and multiple dimensional models separately. Illustrative computational examples show the precision of the approach, and good agreement with previous results in the literature.

Effects of microRNA-mediated negative feedback on gene expression noise

MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA-mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA-based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case.

Qualitative analysis of a Filippov wild-sterile mosquito population model with immigration

Effectively combating mosquito-borne diseases necessitates innovative strategies beyond traditional methods like insecticide spraying and bed nets. Among these strategies, the sterile insect technique (SIT) emerges as a promising approach. Previous studies have utilized ordinary differential equations to simulate the release of sterile mosquitoes, aiming to reduce or eradicate wild mosquito populations. However, these models assume immediate release, leading to escalated costs. Inspired by this, we propose a non-smooth Filippov model that examines the interaction between wild and sterile mosquitoes. In our model, the release of sterile mosquitoes occurs when the population density of wild mosquitoes surpasses a specified threshold. We incorporate a density-dependent birth rate for wild mosquitoes and consider the impact of immigration. This paper unveils the complex dynamics exhibited by the proposed model, encompassing local sliding bifurcation and the presence of bistability, which entails the coexistence of regular equilibria and pseudo-equilibria, as crucial model parameters, including the threshold value, are varied. Moreover, the system exhibits hysteresis phenomena when manipulating the rate of sterile mosquito release. The existence of three types of limit cycles in the Filippov system is ruled out. Our main findings indicate that reducing the threshold value to an appropriate level can enhance the effectiveness of controlling wild insects. This highlights the economic benefits of employing SIT with a threshold policy control to impede the spread of disease-carrying insects while bolstering economic outcomes.

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.

Mechanistic modelling of within-mosquito viral dynamics: Insights into infection and dissemination patterns

Vector or host competence can be defined as the ability of an individual to become infected and subsequently transmit a pathogen. Assays to measure competence play a key part in the assessment of the factors affecting mosquito-borne virus transmission and of potential pathogen-blocking control tools for these viruses. For mosquitoes, competence for arboviruses can be measured experimentally and results are usually analysed using standard statistical approaches. Here we develop a mechanistic approach to studying within-mosquito virus dynamics that occur during vector competence experiments. We begin by developing a deterministic model of virus replication in the mosquito midgut and subsequent escape and replication in the hemocoel. We then extend this to a stochastic model to capture the between-individual variation observed in vector competence experiments. We show that the dose-response of the probability of mosquito midgut infection and variation in the dissemination rate can be explained by stochastic processes generated from a small founding population of virions, caused by a relatively low rate of virion infection of susceptible cells. We also show that comparing treatments or species in competence experiments by fitting mechanistic models could provide further insight into potential differences. Generally, our work adds to the growing body of literature emphasizing the importance of intrinsic stochasticity in biological systems.

A subcellular biochemical model for T6SS dynamics reveals winning competitive strategies

The type VI secretion system (T6SS) is a broadly distributed interbacterial weapon that can be used to eliminate competing bacterial populations. Although unarmed target populations are typically used to study T6SS function in vitro, bacteria most likely encounter other T6SS-armed competitors in nature. However, the connection between subcellular details of the T6SS and the outcomes of such mutually lethal battles is not well understood. Here, we incorporate biological data derived from natural competitors of Vibrio fischeri light organ symbionts to build a biochemical model for T6SS at the single-cell level, which we then integrate into an agent-based model (ABM). Using the ABM, we isolate and experiment with strain-specific physiological differences between competitors in ways not possible with biological samples to identify winning strategies for T6SS-armed populations. Through in vitro experiments, we discover that strain-specific differences exist in T6SS activation speed. ABM simulations corroborate that faster activation is dominant in determining survival during competition. Once competitors are fully activated, the energy required for T6SS creates a tipping point where increased weapon building and firing becomes too costly to be advantageous. Through ABM simulations, we identify the threshold where this transition occurs in the T6SS parameter space. We also find that competitive outcomes depend on the geometry of the battlefield: unarmed target cells survive at the edges of a range expansion where unlimited territory can be claimed. Alternatively, competitions within a confined space, much like the light organ crypts where natural V. fischeri compete, result in the rapid elimination of the unarmed population.

Stochastic SIR model predicts the evolution of COVID-19 epidemics from public health and wastewater data in small and medium-sized municipalities: A one year study

The level of unpredictability of the COVID-19 pandemics poses a challenge to effectively model its dynamic evolution. In this study we incorporate the inherent stochasticity of the SARS-CoV-2 virus spread by reinterpreting the classical compartmental models of infectious diseases (SIR type) as chemical reaction systems modeled via the Chemical Master Equation and solved by Monte Carlo Methods. Our model predicts the evolution of the pandemics at the level of municipalities, incorporating for the first time (i) a variable infection rate to capture the effect of mitigation policies on the dynamic evolution of the pandemics (ii) SIR-with-jumps taking into account the possibility of multiple infections from a single infected person and (iii) data of viral load quantified by RT-qPCR from samples taken from Wastewater Treatment Plants. The model has been successfully employed for the prediction of the COVID-19 pandemics evolution in small and medium size municipalities of Galicia (Northwest of Spain).

Wastewater and marine bioindicators surveillance to anticipate COVID-19 prevalence and to explore SARS-CoV-2 diversity by next generation sequencing: One-year study

This study presents the results of SARS-CoV-2 surveillance in sewage water of 11 municipalities and marine bioindicators in Galicia (NW of Spain) from May 2020 to May 2021. An integrated pipeline was developed including sampling, pre-treatment and biomarker quantification, RNA detection, SARS-CoV-2 sequencing, mechanistic mathematical modeling and forecasting. The viral load in the inlet stream to the wastewater treatment plants (WWTP) was used to detect new outbreaks of COVID-19, and the data of viral load in the wastewater in combination with data provided by the health system was used to predict the evolution of the pandemic in the municipalities under study within a time horizon of 7 days. Moreover, the study shows that the viral load was eliminated from the treated sewage water in the WWTP, mainly in the biological reactors and the disinfection system. As a result, we detected a minor impact of the virus in the marine environment through the analysis of seawater, marine sediments and, wild and aquacultured mussels in the final discharge point of the WWTP.

Synchronization of gene expression across eukaryotic communities through chemical rhythms

The synchronization is a recurring phenomenon in neuroscience, ecology, human sciences, and biology. However, controlling synchronization in complex eukaryotic consortia on extended spatial-temporal scales remains a major challenge. Here, to address this issue we construct a minimal synthetic system that directly converts chemical signals into a coherent gene expression synchronized among eukaryotic communities through rate-dependent hysteresis. Guided by chemical rhythms, isolated colonies of yeast Saccharomyces cerevisiae oscillate in near-perfect synchrony despite the absence of intercellular coupling or intrinsic oscillations. Increased speed of chemical rhythms and incorporation of feedback in the system architecture can tune synchronization and precision of the cell responses in a growing cell collectives. This synchronization mechanism remain robust under stress in the two-strain consortia composed of toxin-sensitive and toxin-producing strains. The sensitive cells can maintain the spatial-temporal synchronization for extended periods under the rhythmic toxin dosages produced by killer cells. Our study provides a simple molecular framework for generating global coordination of eukaryotic gene expression through dynamic environment.

Pareto optimality between growth-rate and lag-time couples metabolic noise to phenotypic heterogeneity in Escherichia coli

Despite mounting evidence that in clonal bacterial populations, phenotypic variability originates from stochasticity in gene expression, little is known about noise-shaping evolutionary forces and how expression noise translates to phenotypic differences. Here we developed a high-throughput assay that uses a redox-sensitive dye to couple growth of thousands of bacterial colonies to their respiratory activity and show that in Escherichia coli, noisy regulation of lower glycolysis and citric acid cycle is responsible for large variations in respiratory metabolism. We found that these variations are Pareto optimal to maximization of growth rate and minimization of lag time, two objectives competing between fermentative and respiratory metabolism. Metabolome-based analysis revealed the role of respiratory metabolism in preventing the accumulation of toxic intermediates of branched chain amino acid biosynthesis, thereby supporting early onset of cell growth after carbon starvation. We propose that optimal metabolic tradeoffs play a key role in shaping and preserving phenotypic heterogeneity and adaptation to fluctuating environments.

Gene Families With Stochastic Exclusive Gene Choice Underlie Cell Adhesion in Mammalian Cells

Exclusive stochastic gene choice combines precision with diversity. This regulation enables most T-cells to express exactly one T-cell receptor isoform chosen from a large repertoire, and to react precisely against diverse antigens. Some cells express two receptor isoforms, revealing the stochastic nature of this process. A similar regulation of odorant receptors and protocadherins enable cells to recognize odors and confer individuality to cells in neuronal interaction networks, respectively. We explored whether genes in other families are expressed exclusively by analyzing single-cell RNA-seq data with a simple metric. This metric can detect exclusivity independently of the mean value and the monoallelic nature of gene expression. Chromosomal segments and gene families are more likely to express genes concurrently than exclusively, possibly due to the evolutionary and biophysical aspects of shared regulation. Nonetheless, gene families with exclusive gene choice were detected in multiple cell types, most of them are membrane proteins involved in ion transport and cell adhesion, suggesting the coordination of these two functions. Thus, stochastic exclusive expression extends beyond the prototypical families, permitting precision in gene choice to be combined with the diversity of intercellular interactions.