Bulletin of Mathematical Biology最新文献

The global spread of the Zika virus (ZIKV), compounded by the absence of effective antiviral drugs or widely available vaccines, highlights the importance of understanding its transmission dynamics to implement effective public health strategies. The transmission of the Zika virus is attributable to the heterogeneity of sexual contacts and the lack of miracle drugs or vaccines. We develop a degree-based mathematical network model which takes account of heterogeneity of sexual contacts and the adoption of preventive measures. We derive analytical expressions for the basic reproduction number for three scenarios: mosquito-borne transmission only, sexual transmission only, and a combined scenario where both transmission routes coexist. In particular, we demonstrate that the basic reproduction number is proportional to the degree of network heterogeneity when the Zika virus transmission is solely driven by sexual contacts. Our proposed model possesses infinitely many disease-free equilibrium points, and we prove that these collectively form a locally attracting set under specified conditions. Finally, we present numerical simulations, calibrated with Zika epidemic data from Brazil (2015-2016), which indicate that increasing the number of individuals who take comprehensive protective measures (using screens, mosquito nets, insect repellent, condoms, etc.) can significantly reduce the final epidemic size.

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulate processes such as hybridisation or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain properties are very difficult. A new way to encode a large class of networks, using "expanding covers", may provide a way to approach such problems. Expanding covers encode a large class of phylogenetic networks, called labellable networks. This class does not include all networks, but does include many familiar classes, including orchard, normal, tree-child and tree-sibling networks. As expanding covers are a combinatorial structure, it is possible that they can be used as a tool for counting such classes for a fixed number of leaves and reticulations, for which, in many cases, a closed formula has not yet been found. More recently, a new class of networks was introduced, called spinal networks, which are analogous to caterpillar trees for phylogenetic trees and can be fully described using covers. In the present article, we describe a method for counting networks that are both spinal and belong to some more familiar class, with the hope that these form a base case from which to attack the more general classes.

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a binary, rooted phylogenetic tree topology as an integer vector. OLA encoding and decoding take linear time in the number of leaf nodes, and the set of vectors corresponding to trees is a simply-described subset of integer sequences. The OLA encoding is unique compared to other existing encodings in having these properties. The integer vector encoding induces a distance on the set of trees, and we investigate this distance in relation to the NNI and SPR distances.

Kinetic modeling of microbial growth is essential for the design, optimization, and scale-up of industrial bioprocesses. Classical empirical models often lack biologically interpretable parameters or fail to capture complex multiphasic (polyauxic) behaviors, while fully mechanistic models are impractical for systems involving complex substrates and mixed cultures. This study proposes a unified mathematical framework that reformulates the canonical Boltzmann and Gompertz equations into semi-mechanistic forms, explicitly defining the maximum specific reaction rate and lag phase duration. Polyauxic growth is represented as a weighted sum of sigmoidal phases, subject to stringent constraints that ensure parameter identifiability, temporal consistency, and biological plausibility. The methodology integrates a workflow to address nonlinear regression in high-dimensional parameter spaces. A two-stage optimization strategy using Differential Evolution for global search followed by L-BFGS-B for local refinement avoid bias and heuristic parameter initialization. A Charbonnier loss function and the Robust Regression and Outlier Removal procedure are employed to identify and mitigate experimental outliers. Model parsimony is enforced using Akaike (AIC, AICc) and Bayesian (BIC) information criteria to select the optimal number of growth phases and avoid overparameterization. The framework was evaluated using experimental anaerobic digestion datasets, demonstrating that conventional single-phase models can obscure relevant metabolic transitions in co-digestion systems.

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.

Thermal reaction norms, or thermal performance curves (TPCs), describe how ectothermic organisms respond to temperature variation. Here, we investigate how stochastic environmental noise, by modulating competitive interactions among individuals with differing TPC shapes, can drive long-term evolutionary changes in thermal performance. We develop a Ricker competition model within the framework of adaptive dynamics to examine how environmental variability, corresponding to the joint effect of both periodic and stochastic temperature fluctuations, influences the evolution of competition TPCs. Growth, carrying capacity and competitive interactions are all temperature-dependent, with competition coefficients defined by the ratio of individuals' thermal performance curve at the prevailing temperature. Competition TPCs are modelled using a beta probability density function. Previous results from periodically (i.e., deterministically) fluctuating environments established that the thermal optimum converges to the mean environmental temperature, while performance breadth collapses under constant conditions. In contrast, we show that under stochastic environments, increasing thermal noise broadens competition TPCs and shifts the thermal optimum leftward, away from the environmental mean. This results in right-skewed competition TPCs and suggests an evolutionary bias towards cooler temperature optima for competition under moderate to high environmental noise. Alongside the broadening of competition TPCs to buffer against thermal fluctuations, the shift towards cooler optima reflects a more conservative thermal strategy for competition performance in the face of environmental uncertainty.

Epigenetic landscapes (ELs) are defined by the pattern of epigenetic marks (acetylation, methylation, etc.) layed over large chromatin regions. The information contained in the ELs is essential to sustain the patterns of gene expression that shape cell fate and identity. EL maintenance requires the precise regulation of chromatin-modifying enzymes (ChME) and their metabolic cofactors (McF). Competition for ChME or dysregulation of McF abundance can lead to degradation of ELs, triggering large-scale changes in the cell fate information contained in EL. Thus, predicting impending epigenetic tipping points (ETPs) by identifying early warning signals (EWS) may help to anticipate the onset of cell identity loss during aging and cancer. Since ELs are formed (and maintained) by a systems of writer/eraser enzymes that interact both in cis (local) and trans (long-range) modes, their mathematical description involves a high-dimensional dynamical system, where identifying ETPs and characterising the biological mechanisms that control them remains challenging. Here, we develop a general mathematical framework that incorporates different connectivity patterns generated by the 3D chromatin folding structure to analyze competition-induced ETP in large EL. This framework allows us to measure the sensitivity and robustness of ETP to the availability of metabolic cofactors and to identify potential EWS. Using a dimension reduction method, we derived coarse-grained (CG) equations for the collective observables associated with chromatin modifications. Analysis of the CG system allows the prediction of global transitions that shape the large-scale features of EL, accurately reproduce the corresponding microscopic benchmarks, and reveal the existence of tipping points under conditions of ChME competition. We applied the CG method to predict ETP under different connectivity patterns, including heterogeneous profiles such as those found in Hi-C data. Although a robustness measure for stable EL was derived from the CG dynamics in bistable regimes, sensitivity analysis revealed that metabolic cofactors have the greatest impact on EL robustness. In particular, we identified the metabolic cofactors SAM and acetyl-CoA as potential EWS for the catastrophic loss of hyperacetylated EL induced by ChME competition. The ability to predict global ETP can facilitate the discovery of predictive biomarkers and inform metabolic interventions aimed at limiting and reversing pathological cell fate decisions.

Bioeconomic systems are inherently governed by fast-slow dynamics, arising from the interplay between rapid market adjustments and slower ecological processes. In this paper, we analyze a four-dimensional fishery model that couples predator-prey dynamics with fishing effort subject to capacity constraints and market-clearing prices. Using geometric singular perturbation theory, we show that the separation of timescales leads to a split critical manifold. The system's operational mode is determined by a single dimensionless bioeconomic parameter, which acts as a structural selector between an Internally-Regulated regime and a Capacity-Saturated regime. Beyond equilibrium stability, we focus on transient behaviors by deriving a closed-form approximation for the transient response time to external shocks. This analytical metric explicitly links recovery duration to the effective net growth budget. Our results demonstrate that while the Capacity-Saturated regime may sustain a stable equilibrium, it incurs significantly larger cumulative ecological deficits and slower recovery rates following perturbations. These findings quantify the trade-off between harvest intensity and system responsiveness, offering a dynamical basis for the vulnerability of high-effort fisheries.

Cell fate decisions typically occur at critical tipping points during development. Identifying these points offers valuable insights into the underlying mechanisms that govern cell fate determination. In this study, we introduce a novel approach called Network Relative Entropy (NRE), which is designed to detect crucial time points during development by analyzing variations in network structures between consecutive time points. After validating the NRE method using simulation data, we apply it to experimental datasets to discern the critical points of early embryonic development. Our findings indicate that the predictions made by the NRE method closely match experimental observations. Furthermore, by ranking the NREs, we identify distinct gene subsets, which we refer to as signaling genes. Statistical analysis reveals a notable divergence in the expression patterns of these signaling genes at the critical points compared to their preceding states. Additionally, we map the correlation coefficients of these signaling genes onto the known protein-protein interaction (PPI) networks. Notably, the correlations among signaling genes exhibit a significant increase at the critical points. These observations provide additional evidence for the reliability of the NRE method from an alternative perspective.

The pregnane X receptor (PXR) regulates the expression of cytochrome P450 (CYP) enzymes and plays a crucial role in the metabolism of various drugs. Rifampicin (RIF) is a PXR ligand that forms the primary metabolite, 25-desacetyl rifampicin (25-DRIF), which retains the antimicrobial activity of the original drug. In this study, we quantified PXR activation and its associated effects on CYP3A4, CYP2C9, and CYP2B6 enzymes in response to 25-DRIF treatment by combining mathematical modeling with long-term mRNA expression analysis of these enzymes in 3D primary human hepatocyte (3D PHH) spheroids. Our estimates suggest that 25-DRIF activates PXR at a rate 20 times lower than RIF. The PXR-dependent rate constant for CYP3A4 transcription was estimated to be higher in 3D PHHs treated with 25-DRIF than in those treated with RIF and also higher than that for CYP2B6 transcription in 3D PHHs treated with 25-DRIF. The rate constants driving PXR-dependent transcription of CYP2C9 were comparable in RIF- and 25-DRIF-treated 3D PHHs. These results demonstrate the ligand-specific nature of PXR activation and suggest that the transcription of PXR-controlled CYP enzymes is ligand- and CYP-specific in 3D PHHs. Finally, we showed that the half-maximal effective concentration ( ${\text{EC}}_{50}$ ) evaluated from our mathematical predictions was time-dependent, which was further validated by CYP3A4 gene reporter assays that measured RIF-induced PXR activity.