Mathematical Biosciences最新文献

{"title":"The roles of continuous and discontinuous proliferations on hepatitis B virus infection","authors":"Rupchand Sutradhar,&nbsp;D.C. Dalal","doi":"10.1016/j.mbs.2025.109448","DOIUrl":"10.1016/j.mbs.2025.109448","url":null,"abstract":"<div><div>The proliferation of both uninfected and infected hepatocytes, as well as the recycling effects of rcDNA-containing capsids are two key mechanisms playing significant roles in the persistence and clearance of hepatitis B virus (HBV) infection. In this study, the temporal dynamics of this viral infection is investigated through two intercellular mathematical models considering proliferation of both types of hepatocytes (uninfected and infected) and recycling effects of capsids. Both models are formulated on the basis of a key finding in the existing literature: mitosis of an infected hepatocytes yields in two uninfected progenies. In the first model (defined by P-model), we examine the continuous proliferation (which occur continuously), while the second one (defined by M-model) deals with the discontinuous proliferation (happen when the concentration of liver cells decreases to less than 70% of its initial concentration). The proposed models are calibrated with the experimental data obtained from an adult chimpanzee. Results of this study suggest that when both hepatocytes proliferate with equal rate, proliferation helps the individual in a rapid recovery from the acute infection whereas in case of chronic infection, the severity of the infection increases. On the other hand, if the infected hepatocytes proliferate at a different rate that of uninfected hepatocytes, the proliferation of uninfected hepatocytes contributes to increase the infection, but the proliferation of infected hepatocytes acts to reduce the infection from the long-term perspective. The global sensitivity analysis also shows the same results. Furthermore, it is also observed that the differences between the outcomes of continuous and discontinuous proliferations are significant and noteworthy.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109448"},"PeriodicalIF":1.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical differences in rod and cone photoresponses","authors":"Miguel Castillo García,&nbsp;Eugenio Urdapilleta","doi":"10.1016/j.mbs.2025.109445","DOIUrl":"10.1016/j.mbs.2025.109445","url":null,"abstract":"<div><div>Understanding how photoreceptor cells respond to light is crucial for comprehending the intricacies of vision. These cells, known as rods and cones, play a pivotal role as they convert light into electrical signals that the brain can interpret. If these cells share this exquisite machinery, how can photoresponses be so different? In this work, we study the factors influencing the dynamics of photoreceptor responses. Based on a detailed model of the underlying biochemical steps, we analyzed the impact of various processes on the response, with particular emphasis on the cyclase feedback. Our study focused on the transition between monophasic and biphasic regimes in photoreceptor responses. Critically, the influence of intracellular messengers’ turnover rates, such as for Ca²⁺ and cGMP, initial concentrations, maximum currents, and the modulation by other parameters was studied in depth. By analyzing both dark-adapted and light-adapted responses for rods and cones, we highlighted the importance of Ca²⁺ concentration and the cGMP turnover in darkness to determine bi- or mono-phasic responses. Through this systematic exploration, we aimed to provide valuable insights about the underlying mechanisms driving the dynamic behavior of photoresponses and to answer why similar experiments give rise to different dynamical behaviors.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109445"},"PeriodicalIF":1.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Biological pattern formation in cell dynamics under cross-diffusion: An Isogeometric analysis perspective","authors":"Ilham Asmouh","doi":"10.1016/j.mbs.2025.109444","DOIUrl":"10.1016/j.mbs.2025.109444","url":null,"abstract":"<div><div>This note presents an efficient numerical method based on isogeometric analysis (IgA) and an operator splitting approach for solving nonlinear reaction–diffusion systems with cross-diffusion. Such problems are often used in mathematical modeling of developmental biology and are subject to highly rigid reactive and diffusive terms. Similarly, the interactions between substances produce complex morphologies (Roth, 2011) <span><span>[1]</span></span>. In this note we present two different types of solutions. Mainly, the Turing patterns and the traveling waves, which are a direct result of the presence of linear diffusion and/or cross-diffusion in the dynamical system. To deal with the multiphysical nature of the nonlinear system, we propose a time-splitting method. The spatial discretization is performed using IgA-based Non-Uniform Ratinal B-spline (NURBS) functions, where the semidiscrete problem is integrated using an implicit scheme. The nonlinear terms are treated by an adaptive fourth-order Runge–Kutta method. The well-known FitzHugh–Nagumo and Gray–Scott models are used to study the performance of the new method. The results obtained demonstrate the ability of our algorithm to accurately maintain the shape of the solution in the presence of complex patterns arising from biological cells on complex geometries. Furthermore, the energy dissipation in the Allen-Cahn equation is analyzed and the new method clarifies the effect of the geometry on the formed patterns and on the energy decay for the considered benchmarks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109444"},"PeriodicalIF":1.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trophic flow of contamination: A nontrivial weapon for species coexistence","authors":"Amit Samadder ,&nbsp;Arnab Chattopadhyay ,&nbsp;Arindam Mandal ,&nbsp;Yun Kang ,&nbsp;Sabyasachi Bhattacharya","doi":"10.1016/j.mbs.2025.109443","DOIUrl":"10.1016/j.mbs.2025.109443","url":null,"abstract":"<div><div>In the modern age of human-induced environmental changes, ecologists are increasingly alarmed about the potential disruption of ecosystems through toxicological processes. As humanity’s footprint on the natural world expands, understanding these dynamics becomes crucial. While recent ecotoxicology research has mainly focused on entirely contaminated ecosystems, overlooking the effects of aquatic contamination on terrestrial predators with access to uncontaminated prey, our study addresses this gap. We present a prey–predator model for partially contaminated communities, where predators face a trade-off in prey preference between contaminated and uncontaminated sources. Through mathematical analysis and numerical simulations, we uncover some interpretable findings: (1) In uncontaminated environments, predation pressure may cause the extinction of one prey species. However, when even a small contamination level exists in alternative prey, endangered prey species can coexist with others. (2) Survival under high contamination depends on the predator’s preference. A very low preference for contaminated prey trivially allows the predator to persist, while low or high preferences lead to the predator’s exclusion. Surprisingly, intermediate preference leads to bi-stability between contaminated prey and predator extinction equilibrium, resulting in a trade-off between the presence of contaminated prey or the predator. (3) Our results confirm the abrupt extinction of predators due to contamination, driven by bistability between predator-free and coexisting states. However, our observation reveals that the likelihood of sudden predator extinction increases with a higher preference for contaminated prey. Additionally, we explore the robustness of these outcomes by considering flexible model assumptions and alternative parameter sets. In summary, our study offers valuable insights into the ecotoxicological processes within partially contaminated communities, shedding light on direct and indirect species interactions.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109443"},"PeriodicalIF":1.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homeostasis in input-output networks: Structure, Classification and Applications","authors":"Fernando Antoneli ,&nbsp;Martin Golubitsky ,&nbsp;Jiaxin Jin ,&nbsp;Ian Stewart","doi":"10.1016/j.mbs.2025.109435","DOIUrl":"10.1016/j.mbs.2025.109435","url":null,"abstract":"<div><div>Homeostasis is concerned with regulatory mechanisms, present in biological systems, where some specific variable is kept close to a set value as some external disturbance affects the system. Many biological systems, from gene networks to signaling pathways to whole tissue/organism physiology, exhibit homeostatic mechanisms. In all these cases there are homeostatic regions where the variable is relatively to insensitive external stimulus, flanked by regions where it is sensitive. Mathematically, the notion of homeostasis can be formalized in terms of an input–output function that maps the parameter representing the external disturbance to the output variable that must be kept within a fairly narrow range. This observation inspired the introduction of the notion of infinitesimal homeostasis, namely, the derivative of the input–output function is zero at an isolated point. This point of view allows for the application of methods from singularity theory to characterize infinitesimal homeostasis points (i.e. critical points of the input–output function). In this paper we review the infinitesimal approach to the study of homeostasis in input–output networks. An input–output network is a network with two distinguished nodes ‘input’ and ‘output’, and the dynamics of the network determines the corresponding input–output function of the system. This class of dynamical systems provides an appropriate framework to study homeostasis and several important biological systems can be formulated in this context. Moreover, this approach, coupled to graph-theoretic ideas from combinatorial matrix theory, provides a systematic way for classifying different types of homeostasis (homeostatic mechanisms) in input–output networks, in terms of the network topology. In turn, this leads to new mathematical concepts, such as, homeostasis subnetworks, homeostasis patterns, homeostasis mode interaction. We illustrate the usefulness of this theory with several biological examples: biochemical networks, chemical reaction networks (CRN), gene regulatory networks (GRN), Intracellular metal ion regulation and so on.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109435"},"PeriodicalIF":1.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Foraging dynamics in social insect colonies: Mechanisms of backward bifurcations and impacts of stochasticity","authors":"Tao Feng ,&nbsp;Yun Kang","doi":"10.1016/j.mbs.2025.109436","DOIUrl":"10.1016/j.mbs.2025.109436","url":null,"abstract":"<div><div>This investigation presents a two-dimensional collective foraging model alongside its stochastic counterpart, simplifying the previous more complex three-dimensional framework utilized to examine foraging behaviors within social insect colonies. We first conduct a thorough examination of the global dynamics of the deterministic model. The results show that the two-dimensional model exhibits equilibrium dynamics, with the possibility of coexistence between non-foraging and foraging equilibrium states. This finding highlights the parallelism between the two-dimensional model and the traditional three-dimensional framework. Following this, an extensive exploration into the long-term collective foraging dynamics within a stochastic environment is conducted, elucidating the interplay between stochasticity and the transitions across distinct stable foraging states. Additionally, the investigation assesses the risk of foraging cessation across varying initial worker populations, subsequently delineating foraging termination warning thresholds. The findings illuminate the multifaceted influence of environmental stochasticity on the collective foraging dynamics observed in harvester ant colonies. Grasping these dynamics furnishes valuable understanding of ecological resilience and the adaptive strategies deployed by collective entities in navigating environmental fluctuations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109436"},"PeriodicalIF":1.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deciphering Akt activation: Insights from a mean-field model","authors":"Catheryn W. Gray,&nbsp;Adelle C.F. Coster","doi":"10.1016/j.mbs.2025.109434","DOIUrl":"10.1016/j.mbs.2025.109434","url":null,"abstract":"<div><div>Being at the right place at the right time is vital for any signalling system component. Akt/PKB is a well-known low-threshold switch in the mammalian insulin signalling pathway. The activation of Akt is essential for the uptake of glucose, however, data concerning this vital system is very sparse, particularly with regards to cellular location and activation state. Here we present a parsimonious mathematical model that captures the current experimental understanding of Akt dynamics. The system operates on two distinct timescales (signalling and physical transport), with the transportation of Akt constituting the rate-limiting step in most circumstances. The model outputs are consistent with observations of the steady state behaviour of the system and display the transient overshoot behaviour which is a necessary characteristic of the activation of Akt.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109434"},"PeriodicalIF":1.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adipocyte size distribution: Mathematical model of a tissue property","authors":"Aloïs Dauger ,&nbsp;Hedi Soula ,&nbsp;Chloe Audebert","doi":"10.1016/j.mbs.2025.109433","DOIUrl":"10.1016/j.mbs.2025.109433","url":null,"abstract":"<div><div>White adipose tissue is in charge of storing excess of energy in form of lipids. The main cells involved in the process – the adipocytes – adapt their sizes up to <span><math><mrow><mn>200</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span> of diameter to accommodate the storage. In addition, their size distribution is bimodal. A previous mathematical model based on lipid fluxes provided size distribution bimodality. However, the variability within cell population was not fully explored. In the previous model, bimodality was considered a consequence of a bistable distribution of cell sizes at equilibrium: meaning that adipocytes had to have two stable sizes. In this study, we first provide a computational method to evaluate equilibria taking into account cells variability. Our results suggest that this variability is key to provide realistic distributions. In addition, we show that size distributions with a proportion of cell with bi-stable profile are not in good agreement with the measurements. We find that mono-stable (i.e. one equilibrium size) profile within the adipose tissue is enough to explain bimodality and to reproduce qualitatively size distribution data. We thus show that bimodality of adipose tissue size distribution does not arise directly from cellular bi-stability but rather from a tissue property.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109433"},"PeriodicalIF":1.9,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizing symmetry transitions in systems with dynamic morphology","authors":"Maria-Veronica Ciocanel ,&nbsp;Punit Gandhi ,&nbsp;Karl Niklas ,&nbsp;Adriana T. Dawes","doi":"10.1016/j.mbs.2025.109431","DOIUrl":"10.1016/j.mbs.2025.109431","url":null,"abstract":"<div><div>The accurate quantification of symmetry is a key goal in biological inquiries because symmetry can affect biological performance and can reveal insights into development and evolutionary history. Recently, we proposed a versatile measure of symmetry, transformation information (<span><math><mi>TI</mi></math></span>), which provides an entropy-based measure of deviations from exact symmetry with respect to a parameterized family of transformations. Here we develop this measure further to quantify approximate symmetries and maximal symmetries represented by critical points in <span><math><mi>TI</mi></math></span> as a function of a transformation parameter. This framework allows us to characterize the evolution of symmetry by tracking qualitative changes with respect to these critical points. We apply <span><math><mi>TI</mi></math></span> to increasingly complex settings, from mathematically tractable probability distributions to differential equation models with emergent behaviors that are inspired by developmental biology and formulated in both static and growing domains. Our analysis of the qualitative changes in symmetry properties indicates a potential pathway toward a general mathematical framework for characterizing symmetry transitions akin to bifurcation theory for dynamical systems. The results reveal deep connections between observed symmetry transitions, subtle changes in morphology, and the underlying mechanisms that govern the dynamics of the system.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109431"},"PeriodicalIF":1.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143756705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Testing-isolation interventions will likely be insufficient to contain future novel disease outbreaks","authors":"Jeffery Demers ,&nbsp;William F. Fagan ,&nbsp;Sriya Potluri ,&nbsp;Justin M. Calabrese","doi":"10.1016/j.mbs.2025.109432","DOIUrl":"10.1016/j.mbs.2025.109432","url":null,"abstract":"<div><div>Rapid identification and isolation of infected individuals with diagnostic testing plays a critical role in combating invasions of novel human pathogens. Unfortunately, unprepared health agencies may struggle to meet the massive testing capacity demands imposed by an outbreaking novel pathogen, potentially resulting in a failure of epidemic containment as occurred with COVID-19. Despite the critical importance of understanding the likelihood of such an outcome, it remains unclear how the particular characteristics of a novel disease will impact the magnitude of resource constraints on controllability. Specifically, is the failure of testing-isolation unique to COVID-19, or is this a likely outcome across the spectrum of disease traits that may constitute future epidemics? Here, using a generalized mathematical model parameterized for seven different human diseases and variants, we show that testing-isolation strategies will typically fail to contain epidemic outbreaks at practicably achievable testing capacities. From this analysis, we identify three key disease characteristics that govern controllability under resource constraints; the basic reproduction number, mean latent period, and non-symptomatic transmission index. Interactions among these characteristics play prominent roles in both explaining controllability differences among diseases and enhancing the efficacy of testing-isolation in combination with transmission-reduction measures. This study provides broad guidelines for managing controllability expectations during future novel disease invasions, describing which classes of diseases are most amenable to testing-isolation strategies alone and which will necessitate additional transmission-reduction measures like social distancing.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109432"},"PeriodicalIF":1.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143756729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}