Bulletin of Mathematical Biology最新文献

{"title":"Algebraic Representation of Mitochondrial Dynamics.","authors":"Raphael Mostov, Greyson Lewis, Gabriel Sturm, Wallace F Marshall","doi":"10.1007/s11538-026-01738-9","DOIUrl":"10.1007/s11538-026-01738-9","url":null,"abstract":"<p><p>This paper addresses the increasing need for comprehensive mathematical descriptions of cell organization by examining the algebraic structure of mitochondrial network dynamics. Mitochondria are cellular structures involved in metabolism that take the form of a network of membrane-based tubes that undergo continuous re-arrangement by a set of morphological processes, including fission and fusion, carried out by protein-based machinery. Because of their network structure, mitochondria can be represented as graphs, and the morphological operations that take place in the cell, referred to as mitochondrial dynamics, can be represented by changes to the graphs. Prior studies have classified mitochondrial graphs based on graph-theoretic features, but an alternative approach is to focus not on the graphs themselves but on the set of morphological operations inducing mitochondrial dynamics, since this may provide a simpler representation. Moreover, the operations are what determine the graphs that will be generated in a biological system. Here we show that mitochondrial dynamics give rise to a category in which the objects are equivalence classes of graphs defined by one of the morphological operations and morphisms are mappings between these equivalence classes defined by the remaining morphological operations. For mitochondria consisting of a single component this gives rise to a particularly simple representation. Using these formalisms we define a distance metric for similarity between mitochondrial structures based on an edit distance, and demonstrate how this representation can be used for visualization and statistical analysis of biological data. In the course of defining these structures we provide a mathematical motivation for new experimental questions regarding mitochondrial fusion, the impacts of cell division on mitochondrial morphology, and the presence of a single giant component in some cell types. This work points to a general strategy for formulating a cell structure state-space, based not on the shapes of cellular structures, but on relations between the dynamic operations that produce them.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13545136/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148891042","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":"How AI Can Advance Mathematical Biology: Opportunities, Challenges, and Future Directions.","authors":"Kobra Rabiei, Grzegorz A Rempala, Reinhard Laubenbacher, Wenrui Hao","doi":"10.1007/s11538-026-01744-x","DOIUrl":"10.1007/s11538-026-01744-x","url":null,"abstract":"<p><p>Mathematical biology has long relied on mechanistic models, including ordinary and partial differential equations, stochastic systems, and agent-based models, to study biological processes across scales. These approaches remain central because they provide structure, interpretability, and biological insight. However, modern biological and biomedical data, including longitudinal clinical records, medical imaging, and multi-omics measurements, are often high-dimensional, noisy, heterogeneous, and incomplete. These features make model calibration, simulation, and uncertainty quantification increasingly difficult. As a result, artificial intelligence (AI) and machine learning (ML) are playing a growing role in mathematical biology, not as replacements for mechanistic modeling, but as complementary tools that can support prediction, hybrid modeling, inference, and control. In this review, we organize these uses of AI from a mathematical biology perspective and examine how data-driven and mechanistic approaches interact across different modeling tasks. The selected examples span biomedical, epidemiological, ecological, evolutionary, biochemical, and population-level systems, while the review is intended to be representative rather than exhaustive. We emphasize recurring challenges that strongly affect biological credibility and practical usefulness, including interpretability, identifiability, generalization, and uncertainty quantification. Our goal is to clarify the roles AI can play in mathematical biology and to highlight the opportunities and limitations that arise when flexible learning methods are integrated with biologically grounded modeling.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13541877/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148886527","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":"Probability of Antibiotic Resistance During Treatment in Stochastic PK/PD-Based Bacterial Model with Distinct Drug and Mutation Modes.","authors":"Chimezie Izuazu, Cameron Browne","doi":"10.1007/s11538-026-01729-w","DOIUrl":"10.1007/s11538-026-01729-w","url":null,"abstract":"<p><p>Mathematical models, e.g., differential equations and stochastic processes, have gained considerable attention for understanding evolution of antibiotic resistance. However, most existing models assume standing genetic variation and do not consider the possibility of random or drug-induced mutation of reference bacterial strains. Therefore, we propose a pharmacokinetics/pharmacodynamics (PK/PD)-based continuous-time Markov chain considering the competition and mutation between sensitive and resistant bacterial within an infected host during treatment. The proposed model is approximated as a generalized birth-death process with immigration, allowing for explicit derivation of the probability resistant population establishes during treatment. Besides capturing the stochasticity of de novo emergence of a resistant bacterial strain, we explore the effects of different antibiotic modes of action, horizontal gene transfer, nutrient availability and drug pharmacokinetics on antibiotic resistance. We find that replication-targeting (biostatic) drugs suppress resistance more than death-targeting (biocidal) drugs. Like prior works, we obtain maximized resistance at intermediate drug concentrations, however the consideration of de novo mutation magnifies the superiority of higher doses in preventing resistance emergence.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148886657","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":"Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.","authors":"Yuxuan Zhao, Kaisheng Zhu, Yefei Zhang, Daniel B Cooney","doi":"10.1007/s11538-026-01733-0","DOIUrl":"10.1007/s11538-026-01733-0","url":null,"abstract":"<p><p>The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13541878/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148886519","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":"mTORC1 Promotes SARS-CoV-2 Replication and Attenuates Type I Interferon Responses in the Alveolar Epithelium: A Computational and Experimental Study.","authors":"Achyudhan R Kutuva, Henrique Al Ribeiro, Felipe T Lima, Matthew A Schaller, Borna Mehrad, Reinhard Laubenbacher","doi":"10.1007/s11538-026-01701-8","DOIUrl":"10.1007/s11538-026-01701-8","url":null,"abstract":"<p><p>The mechanistic target of rapamycin complex 1 (mTORC1) has been implicated in coronavirus pathogenesis, yet its precise role in shaping antiviral defenses in pneumocytes remains unresolved. This study combines ex vivo human lung tissue assays with a literature-curated, logic-based (Boolean) signaling model to study how mTORC1 influences SARS-CoV-2 replication and type-I interferon (IFN) responses. Our in-vitro data showed that pharmacologic inhibition of mTORC1 with sirolimus was associated with reduced viral replication and increased IFN- <math><mi>β</mi></math> expression across donor samples. To interpret these data, we constructed a network integrating inflammation, stress, apoptosis, and RIG-I-IFN signaling, and evaluated four mechanistic hypotheses for explaining our experiments in which mTORC1 either promotes replication, inhibits IFN, both, or neither. The model was constructed according to the best evidence in the literature and evaluated against 56 independent protein/phosphoprotein readouts from 26 studies not used for model construction; the model achieved high qualitative accuracy overall (F1 <math><mrow><mo>≳</mo> <mn>0.75</mn></mrow> </math> ) and on live-virus experiments (F1 <math><mrow><mo>≳</mo> <mn>0.9</mn></mrow> </math> ). We found that the hypotheses where mTORC1 promotes viral replication, inhibits IFN, or both were able to qualitatively reproduce the empirical data, i.e., mTORC1 inhibition by sirolimus leads to lower viral replication and higher IFN expression. We queried the robustness of those predictions through a systematic edge knock-in/knockout screen generating 6,328 network variants per scenario (25,312 total). We found that the scenario where mTORC1 enhances viral replication is the more plausible, due to parsimony (this mechanism is also observed in other viral infections), higher robustness (more variants still reproduce the result), and stronger inhibition that is more likely to be observed in biological experiments with low statistical power. This scenario supports the idea that the mTORC1 effects on IFN expression are indirectly mediated by viral replication itself.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13538202/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148879145","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":"Allee Effect and Oncolytic Virotherapy: Different Therapeutic Outcomes for Different Tumour Growth.","authors":"Jiawen Chen, Federico Frascoli, Tonghua Zhang","doi":"10.1007/s11538-026-01746-9","DOIUrl":"10.1007/s11538-026-01746-9","url":null,"abstract":"<p><p>Tumour recurrence after oncolytic virotherapy is a critical clinical challenge, as solid cancers tend to persist and spread after such therapies alone. Often, mathematical models consider tumour growth without taking possible cooperative cell behaviours into account. Instead, the well-known Allee effect has the ability to drive low-density tumour dynamics and affect therapeutic outcomes. For this reason, we here explore the contribution of Allee effects into two of the most common cancer growth paradigms, e.g. the logistic and the Gompertz frameworks. Our analysis reveals that density-dependent cooperation fundamentally alters virotherapy efficacy. Weak effects can enable pseudo-extinction states where tumour populations collapse to undetectable levels, whilst strong effects can interestingly create non trivial, bistable outcomes. Initial tumour burden seems to be determinant: bifurcation analysis shows scenarios where modest increase in infection or decrease in clearance rates can shift outcomes dramatically. Notably, the Gompertz model exhibits multistability under marginal Allee thresholds, pointing at a possible explanation for spontaneous remission that have been clinically observed. Overall, these findings suggest that Allee effects may be an important factor in the future to adjust dosing schedules, reduce viral loads, lower recurrence risk and shorten therapeutic times. Our framework may also offer quantitative guidance for patient-specific regimes for virotherapy and combination therapies.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13538181/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148879135","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":"Optimal Vaccination for Contagious Diseases with Seasonal Transmission.","authors":"Nir Gavish, Guy Katriel","doi":"10.1007/s11538-026-01741-0","DOIUrl":"10.1007/s11538-026-01741-0","url":null,"abstract":"<p><p>We study optimal periodic time-dependent vaccination strategies for seasonal epidemics with waning immunity, aiming to minimize the basic reproduction number under a fixed annual vaccine supply. Our analysis, which does not pre-assume the structure of the vaccination profile, reveals that the optimal time-periodic vaccination profile typically alternates between intervals of active, time-varying vaccination and intervals with no vaccination. Within the active periods, we derive an explicit expression for the optimal vaccination rate. For a wide class of continuous seasonal transmission rate functions, we show that the optimal solution does not exhibit pulse components. In contrast, when the transmission rate exhibits upward jump discontinuities, such as those arising from school-term forcing, the optimal strategy includes pulse components. These theoretical findings are supported by numerical computations of optimal vaccination profiles across a range of scenarios.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 10","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13538159/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148879112","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":"Chemotactic Feedback Controls Patterning in Hybrid Tumor-Stroma Model.","authors":"Jiguang Yu, Louis Shuo Wang, Zonghao Liu, Jingfeng Liu","doi":"10.1007/s11538-026-01745-w","DOIUrl":"10.1007/s11538-026-01745-w","url":null,"abstract":"<p><p>Motivated by an ongoing collaboration with clinical oncologists and pathologists, we develop a hybrid partial differential equation-ordinary differential equation (PDE-ODE) framework that captures (i) competition between susceptible and resistant phenotypes, (ii) stromal state switching, and (iii) a clinically realistic open-loop, single-dose therapeutic agent I with diffusion and clearance. Clinical management of solid tumors is increasingly limited by spatial heterogeneity and therapy-induced resistance niches that are difficult to predict from well-mixed models. We establish a rigorous mathematical backbone with forward invariance of the nonnegative cone and global-in-time well-posedness. Exploiting the decoupled drug equation <math> <mrow><msub><mi>∂</mi> <mi>t</mi></msub> <mi>I</mi> <mo>=</mo> <msub><mi>d</mi> <mi>I</mi></msub> <mi>Δ</mi> <mi>I</mi> <mo>-</mo> <msub><mi>γ</mi> <mi>I</mi></msub> <mi>I</mi></mrow> </math> , we prove a long-time reduction during washout and show that the damped base dynamics admit no diffusion-driven (Turing-type) instability. We then formulate a directionality-damping principle: unidirectional (open-loop) sensing yields at most transient focusing, whereas bidirectional (closed-loop) feedback reshapes the effective mobility and produces explicit thresholds separating stable homogeneity, finite-band patterning (resistance niche formation), and aggregation when strong parabolicity is violated. Reproducible simulations corroborate this classification and highlight when flux regularization is required for physical realism.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148863629","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":"Stochastic Analysis of a Plant-Vector-Virus Model with Saturated Incidence Rate.","authors":"Sunil Maity","doi":"10.1007/s11538-026-01735-y","DOIUrl":"10.1007/s11538-026-01735-y","url":null,"abstract":"<p><p>Cassava mosaic disease (CMD), caused by the cassava mosaic virus (CMV) and transmitted primarily by the whitefly Bemisia tabaci, reflects the most severe and widespread viral threat to cassava cultivation. The emergence of CMD with a nonlinear saturated incidence of Holling type II form is stochastically modeled and analyzed in this paper utilizing the continuous-time Markov chain (CTMC) modeling approach. The most significant distinction between deterministic and stochastic models is that the deterministic model predicts disease persistence when the basic reproduction number <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> , whereas the stochastic model, characterized by the branching-process threshold <math><mrow><mi>ρ</mi> <mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </math> , indicates that disease extinction can still occur in finite time due to random fluctuations, even when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . The likelihood of disease extinction is determined using the Galton-Watson branching process (GWbp) approximation and compared to the estimated probability obtained from the stochastic model's 10,000 sample paths. This comparison reveals a substantial link between these probabilities. It is found that the disease has a higher probability of extinction when transmission occurs solely through infected vectors, as opposed to transmission through infected plants or both infected plants and vectors. In the stochastic settings, the implicit equation for the mean first passage time is derived to assess the typical time until the first state transition. Additionally, we evaluate both the quasi-stationary distribution of infected individuals and the probability distribution of the epidemic's ultimate size.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148856898","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":"Eco-Evolutionary Dynamics of Proliferation Heterogeneity: A Phenotype-Structured Model for Tumor Growth and Treatment Response.","authors":"Lara Schmalenstroer, Haojun Chen, Russell C Rockne, Farnoush Farahpour","doi":"10.1007/s11538-026-01740-1","DOIUrl":"10.1007/s11538-026-01740-1","url":null,"abstract":"<p><p>Intra-tumor heterogeneity in proliferation rates fundamentally influences cancer progression and treatment resistance. To investigate how continuous phenotypic variation shapes eco-evolutionary dynamics, we develop a phenotype-structured partial differential equation framework that explicitly models proliferation heterogeneity as a dynamic trait. Our model integrates three key biological principles: (1) phenotypic diffusion capturing heritable variation in proliferation rates, (2) global resource competition enforcing density-dependent growth constraints, and (3) an experimentally grounded life-history trade-off linking elevated proliferation to increased mortality. Using adaptive dynamics, we derive the optimum proliferation rate in a growing tumor, showing that the optimal phenotype dynamically shifts toward slower proliferation as tumors approach carrying capacity under control condition. We perform in silico treatment simulations for four different treatment regimes (uniform targeting, low-, mid-, and high-proliferation targeting) to show how therapeutic selective pressures reshape fitness landscapes. While all treatments slow down tumor growth, they induce divergent evolutionary trajectories. We connect these dynamics with changes in mean proliferation rates during and after treatment. Our work establishes a predictive, evolutionarily grounded framework for understanding how therapy reshapes tumor proliferation landscapes, offering a mechanistic basis for designing strategies that anticipate and counteract adaptive resistance.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13526070/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148856931","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}