Bulletin of Mathematical Biology最新文献

{"title":"Theoretical Study of Retinoblastoma in the Hereditary and Non-hereditary Processes Including the Cancer Growth.","authors":"Hiroshi Toki, Yoshiharu Yonekura, Yuichi Tsunoyama, Masako Bando","doi":"10.1007/s11538-025-01483-5","DOIUrl":"10.1007/s11538-025-01483-5","url":null,"abstract":"<p><p>The two-hit model proposed by Knudson for retinoblastoma has been widely recognized as a standard model for cancer incidence. It successfully predicted the existence of the tumor suppressor gene known as \"Rb1\" by effectively demonstrating the overall patterns observed in clinical data covering both bilateral and unilateral retinoblastoma cases. However, it is important to note that the model's prediction currently deviates significantly from clinical data, both qualitatively and quantitatively. Regrettably, this disparity has remained unresolved. In light of this, we conducted a thorough re-evaluation of Knudson's two-hit model and arrived at a plausible solution that an additional somatic mutation mechanism is required to accurately replicate the magnitude and age dependence observed in both bilateral and unilateral retinoblastoma cases. This revelation offers a fresh and valuable perspective on the development of cancer, highlighting the significance of mutations not only during the cell growth period but also after the retina organ has reached maturity. We refer to this phase as the \"mature period,\" during which the mutation rate has been observed to surpass that of the growth period. With this enhanced understanding of retinoblastoma (Rb), we believe we have shed light on the intricate relationship between somatic and germline mutations. Moreover, this insight provides a promising clue for further exploration into the broader context of cancer incidence resulting from genetic mutations.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 8","pages":"103"},"PeriodicalIF":2.0,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144494687","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":"Nutrient-Driven Adaptive Evolution of Foraging Traits Impacts Producer-Grazer Dynamics.","authors":"Oluwagbemisola Oladepo, Angela Peace","doi":"10.1007/s11538-025-01482-6","DOIUrl":"10.1007/s11538-025-01482-6","url":null,"abstract":"<p><p>This study investigates the nutrient-driven adaptability of foraging efforts in producer-grazer dynamics. We develop two stoichiometric producer-grazer models: a base model incorporating a fixed energetic cost of feeding and an adaptive model where feeding costs vary over time in response to environmental conditions. By comparing these models, we examine the effects of adaptive foraging strategies on population dynamics. Our adaptive model suggests a potential mechanism for evolutionary rescue, where the population dynamically adjusts to environmental changes, such as fluctuations in food quality, by modifying its feeding strategies. However, when population densities oscillate in predator-prey limit cycles, fast adaptation can lead to very wide amplitude cycles, where populations are in danger of stochastic extinction. Overall, this increases our understanding of the conditions under which nutrient-driven adaptive foraging strategies can yield benefits to grazers.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 8","pages":"102"},"PeriodicalIF":2.0,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12198312/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144483217","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":"The Pathogenesis of Papilledema: Review of the Literature and a New Hypothesis.","authors":"David N Levine, Ari I Rapalino","doi":"10.1007/s11538-025-01465-7","DOIUrl":"10.1007/s11538-025-01465-7","url":null,"abstract":"<p><p>Since the first description of swelling of the optic nerve head in patients with increased intracranial pressure, our understanding of its pathogenesis has undergone significant changes. Early theories postulated that the swelling was caused by excessive extracellular fluid, but these views were disproved when electron microscopy showed that the swelling arose from dilated optic nerve axons, and autoradiography demonstrated blocked axonal transport at the posterior lamina cribrosa. This led to the currently prevailing view that the axonal swelling is caused by the damming back of axoplasm. However, this theory cannot account for the extent of swelling, its rate of development, and the variety of morphological changes in papilledema. It also cannot explain the differing patterns of swelling in papilledema and acute glaucoma despite identically located blockages of axonal transport. We conducted a biomechanical analysis, in which we calculated the stresses induced in a cylindrical nerve by external compression and the effect of these stresses on the nerve's axons and the axoplasm within them. We propose a new theory in which the axial gradient of tissue pressure causes displacement of axoplasm from the extraocular to the intraocular segment of the nerve, accounting for the intraocular axonal swelling. In addition, a sharply localized axial shear stress disrupts the axonal cytoskeleton to block axonal transport. Although the pressure gradient and the shear stress are both caused by the external compression of the nerve, they differ in their relative magnitudes across the nerve cross-section. The proposed hypothesis resolves the difficulties with the damming back hypothesis.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 8","pages":"101"},"PeriodicalIF":2.0,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12198279/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144483218","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":"Fluid Dynamics of Multiple Fast-Firing Extrusomes : Fast extrusomes.","authors":"Addie Harrison, Wanda Strychalski, Christina Hamlet, Laura Miller","doi":"10.1007/s11538-025-01474-6","DOIUrl":"https://doi.org/10.1007/s11538-025-01474-6","url":null,"abstract":"<p><p>The contact and puncturing of cells and organisms in fluid at microscales are difficult due to viscous-dominated effects and the interactions of boundary layers. This challenge can be overcome in part through the ultra-fast firing of organelles such as the nematocysts of jellyfish. Such super-fast extrusive organelles found in cnidarians, protists, and dinoflagellates are known as extrusomes. It has previously been shown that a single barb at the cellular microscale must be fired fast enough to reach the inertial regime to contact prey. The fluid physics of multiple-fired extrusomes has not been carefully studied, however. The simultaneous firing of extrusomes can be seen in nature, with one example being the dinoflagellate Nematodunium, where each nematocyst consists of a ring of parallel sub-capsules similar to a Gatling gun. In this paper, the immersed boundary method was used to numerically simulate the dynamics of one, two, and three barb-like structures that are accelerated and released towards a passive elastic prey in two dimensions. We considered the simultaneous release of all three barbs as well as a sequential release of the barbs. We also vary the Reynolds number of the simulation for several orders of magnitude to consider the biologically relevant range of extrusome firing, given that different organelles are fired at different speeds and that some extrusomes are fired in viscous mucus. For multiple barbs, we found that there is a nonmonotonic relationship between the distance between the top of the center barb and the prey and the Reynolds number when fired simultaneously. This is because the prey is not pushed out of the way by boundary effects at higher Reynolds numbers, while barbs at lower Reynolds numbers entrain more fluid and are carried farther. Furthermore, the center barbs at the highest Reynolds numbers always hit the prey and are robust to firing order and the spacing between barbs. Overall, our simple model shows that the extreme nonlinearity of the fluid at this scale results in nonmonotonic relationships between the distance to the prey and various parameters.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"100"},"PeriodicalIF":2.0,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144473970","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 Dynamics of Coral and Macroalgae: Analyzing Extinction and Resilience in Coral Reef Ecosystems.","authors":"Ning Wang, Li Yang, Shengqiang Liu","doi":"10.1007/s11538-025-01479-1","DOIUrl":"10.1007/s11538-025-01479-1","url":null,"abstract":"<p><p>Understanding the interactions between coral and macroalgae and the influence of environmental factors is critical for the conservation and restoration of coral reef ecosystems. This study introduces a stochastic model that systematically investigates the combined effects of external coral recruitment, macroalgae grazing pressure, and environmental stochasticity on coral-macroalgae dynamics. The analysis begins with deterministic dynamics, followed by an evaluation of long-term stochastic behavior with and without external coral recruitment. A critical stochastic threshold with external coral recruitment, <math><mi>λ</mi></math> , is identified, which characterizes stochastic persistence, extinction, and ergodicity within the system. Simulation results indicate tipping points associated with variations in coral and macroalgae biomass. The analysis reveals that increased external coral recruitment and grazing of macroalgae facilitate macroalgae extinction, effectively reversing blooms. Furthermore, changes in noise intensity (either reduced noise for coral or increased noise for macroalgae) accelerate macroalgae extinction and drive a shift in coral biomass from low to high levels. These dynamics underscore the reversibility of macroalgal blooms and the opposite effects of different noise types on ecosystem behavior. Additionally, coral reef resilience is significantly influenced by initial biomass conditions, with high macroalgae biomass combined with low coral biomass markedly diminishing resilience and complicating recovery, while higher coral biomass enhances the tolerable range for system recovery. The results yield theoretical insights and offer practical strategies for coral reef conservation and restoration.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"99"},"PeriodicalIF":2.0,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144339904","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 Mechanical Model for the Failure of Reconstructive Breast Implant Surgery Due to Capsular Contracture.","authors":"Yuqi Xiao, Leah Edelstein-Keshet, Alain Goriely, Kathryn V Isaac","doi":"10.1007/s11538-025-01473-7","DOIUrl":"10.1007/s11538-025-01473-7","url":null,"abstract":"<p><p>Capsular contracture is a pathological response to implant-based reconstructive breast surgery, where the \"capsule\" (tissue surrounding an implant) painfully thickens, contracts and deforms. It is known to affect breast-cancer survivors at higher rates than healthy women opting for cosmetic breast augmentation with implants. We model the early stages of capsular contracture based on stress-dependent recruitment of contractile and mechanosensitive cells to the implant site. We derive a one-dimensional continuum spatial model for the spatio-temporal evolution of cells and collagen densities away from the implant surface. Various mechanistic assumptions are investigated for linear versus saturating mechanical cell responses and cell traction forces. Our results point to specific risk factors for capsular contracture, and indicate how physiological parameters, as well as initial states (such as inflammation after surgery) contribute to patient susceptibility.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"98"},"PeriodicalIF":2.0,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144332484","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":"Steady-State and Dynamical Behavior of a PDE Model of Multilevel Selection with Pairwise Group-Level Competition.","authors":"Konstantinos Alexiou, Daniel B Cooney","doi":"10.1007/s11538-025-01476-4","DOIUrl":"10.1007/s11538-025-01476-4","url":null,"abstract":"<p><p>Evolutionary competition often occurs simultaneously at multiple levels of organization, in which traits or behaviors that are costly for an individual can provide collective benefits to groups to which the individual belongs. Building off of recent work that has used ideas from game theory to study evolutionary competition within and among groups, we study a PDE model for multilevel selection that considers group-level evolutionary dynamics through a pairwise conflict depending on the strategic composition of the competing groups. This model allows for incorporation of group-level frequency dependence, facilitating the exploration for how the form of probabilities for victory in a group-level conflict can impact the long-time support for cooperation via multilevel selection. We characterize well-posedness properties for measure-valued solutions of our PDE model and apply these properties to show that the population will converge to a delta-function at the all-defector equilibrium when between-group selection is sufficiently weak. We further provide necessary conditions for the existence of bounded steady state densities for the multilevel dynamics of Prisoners' Dilemma and Hawk-Dove scenarios, using a mix of analytical and numerical techniques to characterize the relative strength of between-group selection required to ensure the long-time survival of cooperation via multilevel selection. We also see that the average payoff at steady state appears to be limited by the average payoff of the all-cooperator group, even for games in which groups achieve maximal average payoff at intermediate levels of cooperation, generalizing behavior that has previously been observed in PDE models of multilevel selection with frequency-independent group-level competition.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"97"},"PeriodicalIF":2.0,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12179033/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144324562","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":"A SIMPL Model of Phage-Bacteria Interactions Accounting for Mutation and Competition.","authors":"Carli Peterson, Darsh Gandhi, Austin Carlson, Aaron Lubkemann, Emma Richardson, John Serralta, Michael S Allen, Souvik Roy, Christopher M Kribs, Hristo V Kojouharov","doi":"10.1007/s11538-025-01478-2","DOIUrl":"https://doi.org/10.1007/s11538-025-01478-2","url":null,"abstract":"<p><p>Pseudomonas aeruginosa is an opportunistically pathogenic bacteria that causes fatal infections and outbreaks in hospital environments. Due to the increasing prevalence of antibiotic-resistant strains of P. aeruginosa, the need for alternative therapies is critical. Bacteriophage therapy is emerging as a promising approach; however, it remains unapproved for clinical use and is hindered by limited understanding of the complex interactions between bacterial cells and phage virions. Mathematical models provide insight into these interactions. Through a system of ordinary differential equations, we successfully capture the dynamics observed between susceptible, infected, and mutated bacterial cells and bacteriophage virions in a microwell setting. Data fitting based on this model produced a set of parameter estimates unique to our experimental observations of a specific phage and P. aeruginosa strain. In translating observed optical density readings into bacterial concentrations, we also found that bacterial debris has a significant impact on optical density, with a lysed bacterium contributing roughly <math><mrow><mn>31</mn> <mo>%</mo></mrow> </math> as much to optical density readings as a living cell.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"96"},"PeriodicalIF":2.0,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144301136","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":"Perfect Taxon Sampling and Fixing Taxon Traceability: Introducing a Class of Phylogenetically Decisive Collections of Taxon Sets.","authors":"Mareike Fischer, Janne Pott","doi":"10.1007/s11538-025-01457-7","DOIUrl":"10.1007/s11538-025-01457-7","url":null,"abstract":"<p><p>Phylogenetically decisive collections of taxon sets have the property that if trees are chosen for each of their elements, as long as these trees are compatible, the resulting supertree is unique. This means that as long as the trees describing the phylogenetic relationships of the (input) species sets are compatible, they can only be combined into a common supertree in precisely one way. This setting is sometimes also referred to as \"perfect taxon sampling\". While for rooted trees, the decision if a given set of input taxon sets is phylogenetically decisive can be made in polynomial time, the decision problem to determine whether a collection of taxon sets is phylogenetically decisive concerning unrooted trees is unfortunately coNP-complete and therefore in practice hard to solve for large instances. This shows that recognizing such sets is often difficult. In this paper, we explain phylogenetic decisiveness and introduce a class of input taxon sets, namely so-called fixing taxon traceable sets, which are guaranteed to be phylogenetically decisive and which can be recognized in polynomial time. Using both combinatorial approaches as well as simulations, we compare properties of fixing taxon traceability and phylogenetic decisiveness, e.g., by deriving lower and upper bounds for the number of quadruple sets (i.e., sets of 4-tuples) needed in the input set for each of these properties. In particular, we correct an erroneous lower bound concerning phylogenetic decisiveness from the literature. We have implemented the algorithm to determine if a given collection of taxon sets is fixing taxon traceable in R and made our software package FixingTaxonTraceR publicly available.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"94"},"PeriodicalIF":2.0,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12152082/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144257348","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":"Analysis of Anaerobic Digestion Model With Two Serial Interconnected Chemostats.","authors":"Thamer Hmidhi, Radhouane Fekih-Salem, Jérôme Harmand","doi":"10.1007/s11538-025-01475-5","DOIUrl":"https://doi.org/10.1007/s11538-025-01475-5","url":null,"abstract":"<p><p>In this paper, we study a well-known two-step anaerobic digestion model in a configuration of two chemostats in series. The model is an eight-dimensional system of ordinary differential equations. Since the reaction system has a cascade structure, the model can be reduced to a four-dimensional one. Using general growth rates, we provide an in-depth mathematical analysis of the asymptotic behavior of the system. First, we determine all the equilibria of the model where there can be fifteen equilibria with a nonmonotonic growth rate. Then, the necessary and sufficient conditions of existence and local stability of all equilibria are established according to the operating parameters: the dilution rate, the input concentrations of the two nutrients, and the distribution of the total process volume considered. The operating diagrams are then theoretically analyzed to describe the asymptotic behavior of the process according to the four control parameters. The system exhibits a rich behavior with bistability, tri-stability, and the possibility of coexistence of the two microbial species in the two bioreactors.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"95"},"PeriodicalIF":2.0,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144257347","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}