Bulletin of Mathematical Biology最新文献

{"title":"A Data-Informed Mathematical Model of Microglial Cell Dynamics During Ischemic Stroke in the Middle Cerebral Artery.","authors":"Sara Amato, Andrea Arnold","doi":"10.1007/s11538-025-01412-6","DOIUrl":"10.1007/s11538-025-01412-6","url":null,"abstract":"<p><p>Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this study, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"31"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022270","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":"Bayesian Inference of Phylogenetic Distances: Revisiting the Eigenvalue Approach.","authors":"Matthew J Penn, Neil Scheidwasser, Christl A Donnelly, David A Duchêne, Samir Bhatt","doi":"10.1007/s11538-024-01403-z","DOIUrl":"10.1007/s11538-024-01403-z","url":null,"abstract":"<p><p>Using genetic data to infer evolutionary distances between molecular sequence pairs based on a Markov substitution model is a common procedure in phylogenetics, in particular for selecting a good starting tree to improve upon. Many evolutionary patterns can be accurately modelled using substitution models that are available in closed form, including the popular general time reversible model (GTR) for DNA data. For more complex biological phenomena, such as variations in lineage-specific evolutionary rates over time (heterotachy), other approaches such as the GTR with rate variation (GTR <math><mrow><mo>+</mo> <mi>Γ</mi></mrow> </math> ) are required, but do not admit analytical solutions and do not automatically allow for likelihood calculations crucial for Bayesian analysis. In this paper, we derive a hybrid approach between these two methods, incorporating <math><mrow><mi>Γ</mi> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>α</mi> <mo>)</mo></mrow> </math> -distributed rate variation and heterotachy into a hierarchical Bayesian GTR-style framework. Our approach is differentiable and amenable to both stochastic gradient descent for optimisation and Hamiltonian Markov chain Monte Carlo for Bayesian inference. We show the utility of our approach by studying hypotheses regarding the origins of the eukaryotic cell within the context of a universal tree of life and find evidence for a two-domain theory.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"32"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11759294/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022272","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 Innate Immunity Causing Chronic Inflammation and Tissue Damage.","authors":"Kosei Matsuo, Yoh Iwasa","doi":"10.1007/s11538-024-01410-0","DOIUrl":"10.1007/s11538-024-01410-0","url":null,"abstract":"<p><p>Mathematical models of immune responses have traditionally focused on adaptive immunity and pathogen-immune dynamics. However, recent advances in immunology have highlighted the critical role of innate immunity. In response to physical damage or pathogen attacks, innate immune cells circulating throughout the body rapidly migrate from blood vessels and accumulate at the site of injury, triggering inflammation. These cells engulf, break down, and eliminate pathogens. This innate immune response occurs much faster than adaptive immune responses, which require time for cell activation and proliferation. While inflammation helps eliminate pathogens, it can sometimes lead to chronic inflammation by triggering excessive immune responses, ultimately causing tissue damage. In this study, we examine a simple dynamical model of innate immunity. The analysis indicates that when an infection occurs, it triggers inflammation, which activates the innate immune system and initiates the activation cycle. Consequently, pathogens may be eradicated, leaving behind persistent chronic inflammation. Alternatively, the pathogens may not be eradicated, with their abundance either stabilizing at a positive level or oscillating indefinitely. The dynamics exhibit both transcritical and Hopf bifurcations. When innate immunity is activated in the absence of inflammation, pathogens are eradicated more easily, and the likelihood of oscillations in inflammation, immune responses, and pathogen abundance is reduced.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"34"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11760608/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022276","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 the Impact of Seasonality on Mosquito Population Dynamics: Insights for Vector Control Strategies.","authors":"Joseph Baafi, Amy Hurford","doi":"10.1007/s11538-024-01409-7","DOIUrl":"10.1007/s11538-024-01409-7","url":null,"abstract":"<p><p>Mosquitoes are important vectors for the transmission of some major infectious diseases of humans, i.e., malaria, dengue, West Nile Virus and Zika virus. The burden of these diseases is different for different regions, being highest in tropical and subtropical areas, which have high annual rainfall, warm temperatures, and less pronounced seasonality. The life cycle of mosquitoes consists of four distinct stages: eggs, larvae, pupae, and adults. These life stages have different mortality rates and only adults can reproduce. Seasonal weather may affect the population dynamics of mosquitoes, and the relative abundance of different mosquito stages. We developed a stage-structured model that considers laboratory experiments describing how temperature and rainfall affects the reproduction, maturation and survival of different Anopheles mosquito stages, the species that transmits the parasite that causes malaria. We consider seasonal temperature and rainfall patterns and describe the stage-structured population dynamics of the Anopheles mosquito in Ain Mahbel, Algeria, Cape Town, South Africa, Nairobi, Kenya and Kumasi, Ghana. We find that neglecting seasonality leads to significant overestimation or underestimation of mosquito abundance. We find that depending on the region, mosquito abundance: peaks one, two or four times a year, periods of low abundance are predicted to occur for durations ranging from six months (Ain Mahbel) to not at all (Nairobi); and seasonal patterns of relative abundance of stages are substantially different. The region with warmer temperatures and higher rainfall across the year, Kumasi, Ghana, is predicted to have higher mosquito abundance, which is broadly consistent with reported malaria deaths relative to the other countries considered by our study. Our analysis reveals distinct patterns in mosquito abundance across different months and regions. Control strategies often target one specific life stage, for example, applying larvicides to kill mosquito larvae, or spraying insecticides to kill adult mosquitoes. Our findings suggest that differences in seasonal weather affect mosquito stage structure, and that the best approaches to vector control may differ between regions in timing, duration, and efficacy.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"33"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022280","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":"Mechanical Cell Interactions on Curved Interfaces.","authors":"Pascal R Buenzli, Shahak Kuba, Ryan J Murphy, Matthew J Simpson","doi":"10.1007/s11538-024-01406-w","DOIUrl":"10.1007/s11538-024-01406-w","url":null,"abstract":"<p><p>We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models of flat epithelia to investigate the influence of curvature for mechanical relaxation. We represent the mechanics of a cell body either by straight springs, or by curved springs that follow the curve's shape. To understand the collective dynamics of the cells, we devise an appropriate continuum limit in which the number of cells and the length of the substrate are constant but the number of springs tends to infinity. In this limit, cell density is governed by a diffusion equation in arc length coordinates, where diffusion may be linear or nonlinear depending on the choice of the spring restoring force law. Our results have important implications about modelling cells on curved geometries: (i) curved and straight springs can lead to different dynamics when there is a finite number of springs, but they both converge quadratically to the dynamics governed by the diffusion equation; (ii) in the continuum limit, the curvature of the tissue does not affect the mechanical relaxation of cells within the layer nor their tangential stress; (iii) a cell's normal stress depends on curvature due to surface tension induced by the tangential forces. Normal stress enables cells to sense substrate curvature at length scales much larger than their cell body, and could induce curvature dependences in experiments.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"29"},"PeriodicalIF":2.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11706888/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142944992","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 3D Computational Study on the Formation and Progression of Tumor Cells in Diffuse Gastric Cancer.","authors":"Valéria Lopes, Joana Figueiredo, Patrícia Carneiro, Marcos Gouveia, Rui D M Travasso, João Carvalho","doi":"10.1007/s11538-024-01405-x","DOIUrl":"10.1007/s11538-024-01405-x","url":null,"abstract":"<p><p>Hereditary diffuse gastric cancer is characterized by an increased risk of diffuse gastric cancer and lobular breast cancer, and is caused by pathogenic germline variants of E-cadherin and <math><mi>α</mi></math> -E-catenin, which are key regulators of cell-cell adhesion. However, how the loss of cell-cell adhesion promotes cell dissemination remains to be fully understood. Therefore, a three-dimensional computer model was developed to describe the initial steps of diffuse gastric cancer development. In this model, we have implemented a cellular Potts approach that contemplates cell adhesion to other cells and to the extracellular matrix, cell extrusion from the gastric epithelia, and subsequent proliferation. We demonstrate that early disease features are determined by decreased adhesion of mutant cells to their normal epithelial neighbors, with concomitant increased attachment to matrix components. Importantly, our simulation shows how mechanical pressure and uncontrolled proliferation of mutant cells lead to modifications in cell shape and in gastric gland morphology. In conclusion, this work underscores the potential of computational models to elucidate the role of cellular and noncellular components in gastric cancer that may be relevant targets in therapeutic interventions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"28"},"PeriodicalIF":2.0,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142926550","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 Effect of Vaccination on the Competitive Advantage of Two Strains of an Infectious Disease.","authors":"Matthew D Johnston, Bruce Pell, Jared Pemberton, David A Rubel","doi":"10.1007/s11538-024-01378-x","DOIUrl":"10.1007/s11538-024-01378-x","url":null,"abstract":"<p><p>We investigate the impact of differential vaccine effectiveness, waning immunity, and natural cross-immunity on the capacity for vaccine-induced strain replacement in two-strain models of infectious disease spread. We focus specifically on the case where the first strain is more transmissible but the second strain is more immune-resistant. We consider two cases on vaccine-induced immunity: (1) a monovalent model where the second strain has immune escape with respect to vaccination; and (2) a bivalent model where the vaccine remains equally effective against both strains. Our analysis reaffirms the capacity for vaccine-induced strain replacement under a variety of circumstances; surprisingly, however, we find that which strain is preferred depends sensitively on the degree of differential vaccine effectiveness. In general, the monovalent model favors the more immune-resistant strain at high vaccination levels while the bivalent model favors the more transmissible strain at high vaccination levels. To further investigate this phenomenon, we parametrize the bifurcation space between the monovalent and bivalent model.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"19"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920722","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 Dynamical Analysis of the Alignment Mechanism Between Two Interacting Cells.","authors":"Vivienne Leech, Mohit P Dalwadi, Angelika Manhart","doi":"10.1007/s11538-024-01397-8","DOIUrl":"10.1007/s11538-024-01397-8","url":null,"abstract":"<p><p>In this work we analytically investigate the alignment mechanism of self-propelled ellipse-shaped cells in two spatial dimensions interacting via overlap avoidance. By considering a two-cell system and imposing certain symmetries, we obtain an analytically tractable dynamical system, which we mathematically analyse in detail. We find that for elongated cells there is a half-stable steady state corresponding to perfect alignment between the cells. Whether cells move towards this state (i.e., become perfectly aligned) or not is determined by where in state space the initial condition lies. We find that a separatrix splits the state space into two regions, which characterise these two different outcomes. We find that some self-propulsion is necessary to achieve perfect alignment, however too much self-propulsion hinders alignment. Analysing the effect of small amounts of self-propulsion offers an insight into the timescales at play when a trajectory is moving towards the point of perfect alignment. We find that the two cells initially move apart to avoid overlap over a fast timescale, and then the presence of self-propulsion causes them to move towards a configuration of perfect alignment over a much slower timescale. Overall, our analysis highlights how the interaction between self-propulsion and overlap avoidance is sufficient to generate alignment.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"23"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11698796/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920490","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 Role of Cytonemes and Diffusive Transport in the Establishment of Morphogen Gradients.","authors":"Jay Stotsky, Hans G Othmer","doi":"10.1007/s11538-024-01388-9","DOIUrl":"10.1007/s11538-024-01388-9","url":null,"abstract":"<p><p>Spatial distributions of morphogens provide positional information in developing systems, but how the distributions are established and maintained remains an open problem. Transport by diffusion has been the traditional mechanism, but recent experimental work has shown that cells can also communicate by filopodia-like structures called cytonemes that make direct cell-to-cell contacts. Here we investigate the roles each may play individually in a complex tissue and how they can jointly establish a reliable spatial distribution of a morphogen. To this end, we formulate models that capture fundamental aspects of various cytoneme-based transport mechanisms. In simple cases, exact solutions are attainable, and in more complex cases, we discuss results of numerical simulations.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"21"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920727","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":"Integration of Immune Cell-Target Cell Conjugate Dynamics Changes the Time Scale of Immune Control of Cancer.","authors":"Qianci Yang, Arne Traulsen, Philipp M Altrock","doi":"10.1007/s11538-024-01400-2","DOIUrl":"10.1007/s11538-024-01400-2","url":null,"abstract":"<p><p>The human immune system can recognize, attack, and eliminate cancer cells, but cancers can escape this immune surveillance. Variants of ecological predator-prey models can capture the dynamics of such cancer control mechanisms by adaptive immune system cells. These dynamical systems describe, e.g., tumor cell-effector T cell conjugation, immune cell activation, cancer cell killing, and T cell exhaustion. Target (tumor) cell-T cell conjugation is integral to the adaptive immune system's cancer control and immunotherapy. However, whether conjugate dynamics should be explicitly included in mathematical models of cancer-immune interactions is incompletely understood. Here, we analyze the dynamics of a cancer-effector T cell system and focus on the impact of explicitly modeling the conjugate compartment to investigate the role of cellular conjugate dynamics. We formulate a deterministic modeling framework to compare possible equilibria and their stability, such as tumor extinction, tumor-immune coexistence (tumor control), or tumor escape. We also formulate the stochastic analog of this system to analyze the impact of demographic fluctuations that arise when cell populations are small. We find that explicit consideration of a conjugate compartment can (i) change long-term steady-state, (ii) critically change the time to reach an equilibrium, (iii) alter the probability of tumor escape, and (iv) lead to very different extinction time distributions. Thus, we demonstrate the importance of the conjugate compartment in defining tumor-effector T cell interactions. Accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"24"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11698905/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920451","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}