Bulletin of Mathematical Biology最新文献

{"title":"Problems, Progress and Perspectives in Mathematical and Computational Biology.","authors":"Qixuan Wang, Hans G Othmer, Philip K Maini","doi":"10.1007/s11538-026-01620-8","DOIUrl":"https://doi.org/10.1007/s11538-026-01620-8","url":null,"abstract":"<p><p>For this Special Collection we invited experts in the area of mathematical and computational biology to share their views on the major problems in their areas of interest and their recent research results - focusing on the development of state-of-the-art modeling approaches and computational techniques applied to problems in the life sciences - and to present their vision of the new directions needed for addressing unsolved problems. Papers in this Special Collection address mathematical and computational problems in several areas of the life sciences, including theoretical neuroscience, cancer modeling, and cell and developmental systems. With respect to methodologies, these papers cover dynamical systems, differential equations, stochastic processes, and modern computational techniques, all with an emphasis on techniques in modern modeling and computational methodologies. This Special Collection is jointly hosted by the Bulletin of Mathematical Biology and the Journal of Mathematical Biology.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147622023","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":"How Does Genetic Information Enable Life?","authors":"Robert Gatenby","doi":"10.1007/s11538-026-01636-0","DOIUrl":"10.1007/s11538-026-01636-0","url":null,"abstract":"<p><p>Life requires genetic information to maintain a stable, highly ordered state far from thermodynamic equilibrium, but the general principles and specific mechanisms governing these dynamics are not well established. Here, the role of information in maintaining the unique thermodynamic state of living systems is examined in enzyme-accelerated reactions. Thermodynamically, reaction rates are governed by temperature and activation energy in the empirically derived Arrhenius equation. Living systems use genetically encoded enzymes to accelerate reactions up to 15 orders of magnitude without increased temperature. This is quantified in the Arrhenius equation as decreased activation energy but achieved physically by optimizing quantum interactions of substrate molecules to increase the probability of reaction. This scale transition from molecular mechanics in the information encoded amino acid sequence to quantum mechanics in substrate interactions represents \"fine graining\" which, as the opposite of coarse graining, requires added information. This is hypothesized to emerge from the cell's molecular machinery that controls folding kinetics to ensure (with high probability) the genetically encoded string of amino acids folds to a single enzymatically functional 3-dimensional configuration from all other thermodynamically possible states thus increasing Shannon information. Enzyme-accelerated reactions alter concentrations of substrate and products without increased temperature to generate a Boltzmann distribution that is highly improbable for, and therefore, not in equilibrium with the cell's thermodynamic state (temperature). Failure to maintain this non-equilibrium results in death, enabling evolutionary feedback. Furthermore, since protein function governs organism fitness, evolutionary selection is applied to both the gene that encodes the protein and cellular mechanisms that control its folding. By altering probabilistic quantum states during chemical reactions and producing statistical mechanics (Boltzmann distribution) inconsistent with the cellular thermodynamic state, the probability functions of Shannon information in the genome act at microscopic/macroscopic interfaces to enable the ordered, non-equilibrium state necessary for life.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13050764/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147621989","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":"Estimating the Growth Rate of a Birth and Death Process Using data From a Small Sample.","authors":"Carola Sophia Heinzel, Jason Schweinsberg","doi":"10.1007/s11538-026-01626-2","DOIUrl":"10.1007/s11538-026-01626-2","url":null,"abstract":"<p><p>The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of n individuals has been considered by several authors (Stadler in Journal of Theoretical Biology 261(1):58-66, 2009: Williams et al in Nature 602 (7895):162-168, 2022: Mitchell et al in Nature 606(7913):343-350, 2022: Johnson et al in Bioinformatics 39(9):btad561, 2023). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, Johnson et al Bioinformatics 39(9):btad561, 2023) proposed an analytical method for estimating the growth rate using the theory of coalescent point processes, which has comparable accuracy to more computationally intensive methods when the sample size n is large. We use a similar approach to obtain an estimate of the growth rate that is not based on the assumption that n is large. We demonstrate, through simulations using the R package cloneRate, that our estimator of the growth rate performs well in comparison with previous approaches when n is small.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13046663/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147590200","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":"Modeling Epithelial-Mesenchymal Transition with Partial Differential Equations: Implications for Metastatic Progression and Treatment Strategies.","authors":"Ruixuan Sun, Yongzhen Pei, Changguo Li, Han Lu, Yonghui Liu","doi":"10.1007/s11538-026-01616-4","DOIUrl":"https://doi.org/10.1007/s11538-026-01616-4","url":null,"abstract":"<p><p>Metastatic tumors-secondary malignancies arising from the hematogenous or lymphatic dissemination of cancer cells from primary lesions to distant sites-account for nearly 90% of cancer-associated mortality worldwide. Consequently, studying the effect of epithelial-mesenchymal transition (EMT) on metastatic tumors using experimental data and partial differential equation (PDE) modeling is essential. This study innovatively established a phenotype- and density-regulated chemotaxis coefficient to develop a PDE model characterizing cancer cell migration, proliferation, and EMT, enabling analysis of EMT behavior within the tumor microenvironment and its impact on spreading patterns. Subsequently, incorporating the mechanisms of anti-TGF <math><mi>β</mi></math> RII and cyclophosphamide (CTX), three therapeutic models for tumor metastasis were constructed, with parameter estimation based on experimental data. To predict primary tumor distant metastasis risk, we originally established a tumor metastasis incidence index, thereby evaluating the critical roles of EMT-targeting and cytotoxic chemotherapeutic drugs in tumor progression. Our findings demonstrate that appropriate pharmacological intervention effectively suppresses tumor dissemination, with therapeutic efficacy significantly enhanced upon EMT inhibition. This study establishes a theoretical framework for designing cancer treatment strategies and provides foundational insights for developing personalized therapeutic regimens.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147580791","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":"A Practical Identifiability Criterion Leveraging Weak-Form Parameter Estimation.","authors":"Nora Heitzman-Breen, Vanja Dukic, David M Bortz","doi":"10.1007/s11538-026-01639-x","DOIUrl":"10.1007/s11538-026-01639-x","url":null,"abstract":"<p><p>In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This criterion is better able to encompass changes in the quality of the parameter estimate(s) due to increased noise in the data (compared to existing criteria based solely on average relative errors). We illustrate the usefulness of the criteria in several challenging identifiability studies, involving parameter estimation in partially observed systems. Furthermore, we leverage a weak-form equation error-based method of parameter estimation for systems with unobserved variables to assess practical identifiability far more quickly in comparison to output error-based parameter estimation. We do so by generating weak-form input-output equations using differential algebra techniques, as previously proposed by Boulier et al. (2014), and then applying Weak form Estimation of Nonlinear Dynamics (WENDy) to obtain parameter estimates. This method is computationally efficient and robust to noise, as demonstrated through two classical biological modeling examples.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13035585/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147580649","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":"Mathematical Modeling of p27-Regulated Quiescent-to-Proliferative Transition: Parameter Uncertainty Quantification, Propagation, and Dynamic Curve Analysis.","authors":"Shuli Guo, Haoran Hu, Huifang Wen, Jing Zhang, Yongqi Song, Kaiqun Wang, Di Huang, Yanhu Shan","doi":"10.1007/s11538-026-01631-5","DOIUrl":"https://doi.org/10.1007/s11538-026-01631-5","url":null,"abstract":"<p><p>The cellular transition from quiescence to proliferation is a tightly regulated process orchestrated primarily by activated CyclinD- and CyclinE-associated kinase complexes. However, the p27-mediated activation mechanism of these complexes, particularly in the context of governing this quiescent-to-proliferative switch, remains incompletely characterized. To tackle this challenge, we established an ordinary differential equation (ODE) model to characterize p27-regulated activation of CyclinD- and CyclinE-associated kinase complexes. Model parameters were estimated via the quantile-based PINN method by fitting to experimental data from the existing literature. The associated uncertainty of estimated parameters and outputs were then quantified. Parameters displayed distinct modal values alongside variations in the width of kernel density estimation (KDE) curves, which was likely attributable to the interplay between model structure and the quality of experimental data. Variable- and time-dependent predictive uncertainty was propagated from parameter uncertainties through a combination of independent and correlated pathways. Consequently, this establishes reliable ranges for parameters and predictions, thereby enhancing the suitability of the model results for real-world scenarios. Our study has advanced our quantitative understanding of p27-mediated cell cycle control mechanisms and provides an interpretable quantitative framework to potentially guide future investigations into tumor-targeted intervention strategies, thereby facilitating the rational design of therapeutic approaches targeting cell cycle dysregulation in cancer.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147572595","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":"From Outbreak to Endemicity or Control: Tracking First Passage Time in Infectious Diseases.","authors":"Olusegun Michael Otunuga","doi":"10.1007/s11538-026-01635-1","DOIUrl":"https://doi.org/10.1007/s11538-026-01635-1","url":null,"abstract":"<p><p>This study investigates the transition from outbreak to endemic states or endemic control by analyzing the effective reproduction number R(t) within a stochastic epidemic framework. We derive the transition and stationary probability density functions of R(t), which are then used to characterize the first passage time (FPT) of R(t) across a boundary Z. These are later used to calculate the distribution of the first time that infection will dominate (or be controlled) in a population. Analytical expressions for some properties of the distribution provide quantitative measures of when endemic transition is likely to emerge under stochastic fluctuations. For a fixed threshold Z, the crossing time marks the moment R(t) first signals sustained endemic behavior. We further extend the analysis to a time-varying threshold Z(t) representing a moving barrier shaped by dynamic epidemiological or policy conditions. In this setting, crossing corresponds to the moment the disease process keeps pace with a shifting target. By linking epidemic dynamics with stochastic first-passage theory, this framework highlights how fluctuations and dynamic thresholds jointly determine the timing of epidemic transitions. The results offer probabilistic tools for anticipating epidemic resurgence, assessing intervention durability, and designing adaptive public health strategies. Applied to a rhinovirus calibration (daily units), our result demonstrates that reducing the per-capita transmission rate effectively suppresses the amplification of stochastic fluctuations and accelerates the transition of the system into a non-epidemic regime. We calibrate the framework, using region-specific parameter estimates for each of the ten U.S. Department of Health and Human Services (HHS) regions over a late-winter to early-summer window, to analyze the weekly percent-positive of rhinovirus/enterovirus (RV/EV) activity in the United States. Our result shows that the modal FPT typically precedes the crest of the percent-positive curve while the mean FPT aligns with the beginning of the sustained decline or plateau.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147520147","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":"The Role of Viral Dynamics and Infectivity in Models of Oncolytic Virotherapy for Tumours with Different Motility.","authors":"David Morselli, Federico Frascoli, Marcello E Delitala","doi":"10.1007/s11538-026-01630-6","DOIUrl":"10.1007/s11538-026-01630-6","url":null,"abstract":"<p><p>The use of ad-hoc engineered viruses in the fight against tumours is one of the greatest ideas in cancer therapeutics within the last three decades. Although some remarkable successes have been obtained, it is still not entirely clear how to achieve reliable protocols that can be routinely employed with confidence on a significant range of tumours. In this work, we concentrate on the study of different mathematical descriptions of virotherapy with the aim of better understanding the role of viral infectivity and viral dynamics in positive therapeutic outcomes. In particular, we compare probabilistic, individual approaches with continuous, spatially inhomogeneous models and investigate the importance of different tumour motility and different mathematical representations of viral infectivity. Some of these formulations also allow us to arrive at better analytical characterisation of how waves of viral infections arise and propagate in tumours, providing interesting insights into therapy dynamics. Similarly to previous studies, oscillatory behaviours, stochasticity and cancers' diffusivities are all central to the eradication or the escape of tumours under virotherapy. Here, though, our results also show that the ability of viruses to infect tumours seems, in certain cases, more important to a final positive outcome than tumours' motility or even reproductivity. This could hopefully represent a first step into better insights into viral dynamics that may help clinicians to achieve consistently better outcomes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13018097/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147509829","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":"Integrating Mechanistic Modeling and Machine Learning to Study CD4+/CD8+ CAR-T Cell Dynamics with Tumor Antigen Regulation.","authors":"Saranya Varakunan, Melissa Stadt, Mohammad Kohandel","doi":"10.1007/s11538-026-01633-3","DOIUrl":"https://doi.org/10.1007/s11538-026-01633-3","url":null,"abstract":"<p><p>Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4⁺ and CD8⁺ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4⁺ helper and CD8⁺ cytotoxic lineages and their interactions with tumor antigen burden. Building on a recent model of antigen-regulated memory-effector-exhaustion transitions in CAR-T cells, our system of differential equations incorporates CD4⁺-mediated modulation of CD8⁺ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8⁺ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naïve baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147509819","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":"Final-Size Solutions for SIRI Models with Vaccination.","authors":"Maria A Gutierrez, Julia R Gog","doi":"10.1007/s11538-026-01610-w","DOIUrl":"10.1007/s11538-026-01610-w","url":null,"abstract":"<p><p>In the classic SIR model, infection gives full immunity against any possible reinfection. However, for many important epidemiological situations, immunity is only partial and reinfection is possible. Though these models are mathematically more complex, we are able to find expressions for the epidemic final size. We also generalise these expressions to include vaccination, with a fraction of the population vaccinated before the epidemic, where vaccinees are less susceptible to primary infections than unvaccinated hosts.Partial immunity can be interpreted at the population level as providing either full or no protection to each host, in some proportion (all-or-none immunity). In this scenario, we give analytical expressions (mathematically similar to the SIR final-size) for the cumulative primary infections and the cumulative reinfections in unvaccinated and vaccinated hosts. Alternatively, partial immunity can be interpreted as providing homogeneous imperfect protection to each host (leaky immunity). For this other scenario, we again obtain an implicit equation for the final epidemic size. We break down, in terms of the final size, the number of infections in hosts with or without prior immunity (vaccine- or infection- induced), as well as the number of primary infections and reinfections. Under the leaky immunity assumption, we find a form of reinfection threshold. If the relative host susceptibility to reinfection is above this threshold (which is the inverse of the pathogen's basic reproduction number), transmission rates are high enough to support an endemic disease. Below the reinfection threshold, epidemics are transient. In the all-or-none model, epidemics are always transient.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13013105/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147509768","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}