Pub Date : 2025-02-04DOI: 10.1016/j.mbs.2025.109384
Xueying Wang , Xiao-Qiang Zhao
In the field of population dynamics, target reproduction number is a crucial metric that dictates the necessary control efforts for achieving specific prevention, intervention, or control goals. Recently, the concept of the target reproduction number has undergone significant extensions. Lewis et al. [1] presented a general framework of the target reproduction number for nonnegative matrices, and Wang and Zhao [2] further developed it to positive operators on an ordered Banach space. These extensions encompass fundamental metrics like basic reproduction number and type reproduction number, along with other threshold parameters from existing literature, elucidating their roles in population control. In the current paper, we establish the theory of target reproduction number for a large class of compartmental population models with time delay in the case where control is targeted toward either new infection/production or internal evolution/transition. It turns out that the target reproduction number of the original time-delayed population model can be viewed as a basic reproduction number of some modified system. At the end, we apply these analytic results to three epidemic models, which enhances our theoretical understanding and provides valuable insights for effective strategies in population-based interventions and control measures.
{"title":"Target reproduction numbers for time-delayed population systems","authors":"Xueying Wang , Xiao-Qiang Zhao","doi":"10.1016/j.mbs.2025.109384","DOIUrl":"10.1016/j.mbs.2025.109384","url":null,"abstract":"<div><div>In the field of population dynamics, target reproduction number is a crucial metric that dictates the necessary control efforts for achieving specific prevention, intervention, or control goals. Recently, the concept of the target reproduction number has undergone significant extensions. Lewis et al. <span><span>[1]</span></span> presented a general framework of the target reproduction number for nonnegative matrices, and Wang and Zhao <span><span>[2]</span></span> further developed it to positive operators on an ordered Banach space. These extensions encompass fundamental metrics like basic reproduction number and type reproduction number, along with other threshold parameters from existing literature, elucidating their roles in population control. In the current paper, we establish the theory of target reproduction number for a large class of compartmental population models with time delay in the case where control is targeted toward either new infection/production or internal evolution/transition. It turns out that the target reproduction number of the original time-delayed population model can be viewed as a basic reproduction number of some modified system. At the end, we apply these analytic results to three epidemic models, which enhances our theoretical understanding and provides valuable insights for effective strategies in population-based interventions and control measures.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109384"},"PeriodicalIF":1.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143344367","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2025.109377
Hyunjoong Kim , Manoj Subedi , Krešimir Josić
Foraging strategies are shaped by interactions with the environment, and evolve under metabolic constraints. Optimal strategies for isolated and competing organisms have been studied extensively in the absence of evolution. Much less is understood about how metabolic constraints shape the evolution of an organism’s ability to detect and reach food. To address this question, we introduce a minimal agent-based model of the coevolution of two phenotypic attributes critical for successful foraging in crowded environments: movement speed and perceptual acuity. Under competition higher speed and acuity lead to better foraging success, but at higher metabolic cost. We derive the optimal foraging strategy for a single agent, and show that this strategy is no longer optimal for foragers in a group. We show that mutation and selection can lead to the coexistence of two strategies: A metabolically costly strategy with high acuity and velocity, and a metabolically cheap strategy. Generally, in evolving populations speed and acuity co-vary. Therefore, even under metabolic constraints, trade-offs between metabolically expensive traits are not guaranteed.
{"title":"Emergence of multiple foraging strategies under competition","authors":"Hyunjoong Kim , Manoj Subedi , Krešimir Josić","doi":"10.1016/j.mbs.2025.109377","DOIUrl":"10.1016/j.mbs.2025.109377","url":null,"abstract":"<div><div>Foraging strategies are shaped by interactions with the environment, and evolve under metabolic constraints. Optimal strategies for isolated and competing organisms have been studied extensively in the absence of evolution. Much less is understood about how metabolic constraints shape the evolution of an organism’s ability to detect and reach food. To address this question, we introduce a minimal agent-based model of the coevolution of two phenotypic attributes critical for successful foraging in crowded environments: movement speed and perceptual acuity. Under competition higher speed and acuity lead to better foraging success, but at higher metabolic cost. We derive the optimal foraging strategy for a single agent, and show that this strategy is no longer optimal for foragers in a group. We show that mutation and selection can lead to the coexistence of two strategies: A metabolically costly strategy with high acuity and velocity, and a metabolically cheap strategy. Generally, in evolving populations speed and acuity co-vary. Therefore, even under metabolic constraints, trade-offs between metabolically expensive traits are not guaranteed.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109377"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967499","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109372
Manuela Aguiar , Ana Dias , Ian Stewart
We classify connected 3-node restricted excitatory–inhibitory networks, extending our previous paper (Aguiar et al., 2024). We assume that there are two node-types and two arrow-types, excitatory and inhibitory; all excitatory arrows are identical and all inhibitory arrows are identical; and excitatory (resp. inhibitory) nodes can only output excitatory (resp. inhibitory) arrows. The classification is performed under the following two network perspectives: ODE-equivalence and minimality; and valence . The results of this and the previous work constitute a first step towards analyzing dynamics and bifurcations of excitatory–inhibitory networks and have potential applications to biological network models.
我们对连接的3节点限制性兴奋-抑制网络进行了分类，扩展了我们之前的论文（Aguiar et al., 2024）。我们假设有两种节点类型和两种箭头类型，兴奋性和抑制性；所有兴奋性箭头是相同的所有抑制性箭头也是相同的；和兴奋（反应）。抑制性节点只能输出兴奋性节点。抑制)箭头。在两个网络视角下进行分类：ode等效性和极小性；价≤2。这一结果和之前的工作构成了分析兴奋-抑制网络的动力学和分支的第一步，并有潜在的应用于生物网络模型。
{"title":"Classification of 3-node restricted excitatory–inhibitory networks","authors":"Manuela Aguiar , Ana Dias , Ian Stewart","doi":"10.1016/j.mbs.2024.109372","DOIUrl":"10.1016/j.mbs.2024.109372","url":null,"abstract":"<div><div>We classify connected 3-node restricted excitatory–inhibitory networks, extending our previous paper (Aguiar et al., 2024). We assume that there are two node-types and two arrow-types, excitatory and inhibitory; all excitatory arrows are identical and all inhibitory arrows are identical; and excitatory (resp. inhibitory) nodes can only output excitatory (resp. inhibitory) arrows. The classification is performed under the following two network perspectives: ODE-equivalence and minimality; and valence <span><math><mrow><mo>≤</mo><mn>2</mn></mrow></math></span>. The results of this and the previous work constitute a first step towards analyzing dynamics and bifurcations of excitatory–inhibitory networks and have potential applications to biological network models.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109372"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142908051","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2025.109374
Bei Sun , Daozhou Gao , Xueying Wang , Yijun Lou
Amphibian decline and extinction have been observed on a global scale, highlighting the urgency of identifying the underlying factors. This issue has long been recognized as a critical concern in conservation ecology and continues to receive significant attention. Pathogen infection, in particular the chytrid fungus Batrachochytrium dendrobatidis, is postulated as a key factor contributing to the decline of certain species within specific regions. In this paper, we focus on identifying the pathogen characteristics that can drive host species extinction. Both deterministic and stochastic modeling frameworks based on a susceptible-infectious-pathogen epidemic model are proposed, to assess the influence of pathogen infection on species decline and extinction. Various indices, including the reproduction numbers of the host species, the replication of the pathogen, and the transmission of the pathogen are derived. Theoretical analysis includes the stability of equilibria, the extinction and persistence of host species in the deterministic model, and the evaluation of extinction probability and average extinction time in the stochastic model. Additionally, numerical simulations are conducted to quantify the effects of various factors on host decline and extinction, as well as the probabilities of extinction. We find two crucial conditions for a pathogen to drive host extinction: (i) the pathogen’s self-reproduction capacity in the environment, and (ii) the pathogen’s impact on the fecundity and survival of the infected host. These findings provide insights that could aid in the design and implementation of effective conservation strategies for amphibians.
{"title":"Infection-induced host extinction: Deterministic and stochastic models for environmentally transmitted pathogens","authors":"Bei Sun , Daozhou Gao , Xueying Wang , Yijun Lou","doi":"10.1016/j.mbs.2025.109374","DOIUrl":"10.1016/j.mbs.2025.109374","url":null,"abstract":"<div><div>Amphibian decline and extinction have been observed on a global scale, highlighting the urgency of identifying the underlying factors. This issue has long been recognized as a critical concern in conservation ecology and continues to receive significant attention. Pathogen infection, in particular the chytrid fungus <em>Batrachochytrium dendrobatidis</em>, is postulated as a key factor contributing to the decline of certain species within specific regions. In this paper, we focus on identifying the pathogen characteristics that can drive host species extinction. Both deterministic and stochastic modeling frameworks based on a susceptible-infectious-pathogen epidemic model are proposed, to assess the influence of pathogen infection on species decline and extinction. Various indices, including the reproduction numbers of the host species, the replication of the pathogen, and the transmission of the pathogen are derived. Theoretical analysis includes the stability of equilibria, the extinction and persistence of host species in the deterministic model, and the evaluation of extinction probability and average extinction time in the stochastic model. Additionally, numerical simulations are conducted to quantify the effects of various factors on host decline and extinction, as well as the probabilities of extinction. We find two crucial conditions for a pathogen to drive host extinction: (i) the pathogen’s self-reproduction capacity in the environment, and (ii) the pathogen’s impact on the fecundity and survival of the infected host. These findings provide insights that could aid in the design and implementation of effective conservation strategies for amphibians.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109374"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143019034","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109371
Alex Busalacchi , Maya Weissman , Feng-Bin Wang , Naveen K. Vaidya
Black band disease (BBD) is one of the most prevalent diseases causing significant destruction of coral reefs. Coral reefs acquire this deadly disease from bacteria in the microbiome community, the composition of which is highly affected by the environmental temperature. While previous studies have provided valuable insights into various aspects of BBD, the temperature-dependent microbiome composition has not been considered in existing BBD models. We developed a transmission dynamics model, incorporating the effects of temperature on the microbiome composition and, subsequently, on BBD in coral reefs. Based on our non-autonomous model systems, we calculate the infection invasion threshold, providing an environmental condition for the disease to persist in the coral reef community. Our results suggest that temperature significantly impacts coral reef health, with microbiome-favored moderate environmental temperatures resulting in more BBD-infected corals. Our model and related results help investigate potential strategies to protect reef ecosystems from stressors, including BBD.
{"title":"Modeling the role of temperature-dependent microbiome composition in black band disease transmission among coral reefs","authors":"Alex Busalacchi , Maya Weissman , Feng-Bin Wang , Naveen K. Vaidya","doi":"10.1016/j.mbs.2024.109371","DOIUrl":"10.1016/j.mbs.2024.109371","url":null,"abstract":"<div><div>Black band disease (BBD) is one of the most prevalent diseases causing significant destruction of coral reefs. Coral reefs acquire this deadly disease from bacteria in the microbiome community, the composition of which is highly affected by the environmental temperature. While previous studies have provided valuable insights into various aspects of BBD, the temperature-dependent microbiome composition has not been considered in existing BBD models. We developed a transmission dynamics model, incorporating the effects of temperature on the microbiome composition and, subsequently, on BBD in coral reefs. Based on our non-autonomous model systems, we calculate the infection invasion threshold, providing an environmental condition for the disease to persist in the coral reef community. Our results suggest that temperature significantly impacts coral reef health, with microbiome-favored moderate environmental temperatures resulting in more BBD-infected corals. Our model and related results help investigate potential strategies to protect reef ecosystems from stressors, including BBD.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109371"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901513","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109352
Jacob Curran-Sebastian , Frederik Mølkjær Andersen , Samir Bhatt
The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity in the early phase of an outbreak into account in order to adequately capture the uncertainty in disease forecasts. We propose a general branching process model of disease spread that includes host-level heterogeneity, and that can be straightforwardly tailored to capture the salient aspects of a particular disease outbreak. We combine this with a model of case importation that occurs via an independent marked Poisson process. We use this framework to investigate the impact of different control strategies, particularly on the time to establishment of an invading, exogenous strain, using parameters taken from the literature for COVID-19 as an example. We also demonstrate how to combine our model with a deterministic approximation, such that longer term projections can be generated that still incorporate the uncertainty from the early growth phase of the epidemic. Our approach produces meaningful short- and medium-term projections of the course of a disease outbreak when model parameters are still uncertain and when stochasticity still has a large effect on the population dynamics.
{"title":"Modelling the stochastic importation dynamics and establishment of novel pathogenic strains using a general branching processes framework","authors":"Jacob Curran-Sebastian , Frederik Mølkjær Andersen , Samir Bhatt","doi":"10.1016/j.mbs.2024.109352","DOIUrl":"10.1016/j.mbs.2024.109352","url":null,"abstract":"<div><div>The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity in the early phase of an outbreak into account in order to adequately capture the uncertainty in disease forecasts. We propose a general branching process model of disease spread that includes host-level heterogeneity, and that can be straightforwardly tailored to capture the salient aspects of a particular disease outbreak. We combine this with a model of case importation that occurs via an independent marked Poisson process. We use this framework to investigate the impact of different control strategies, particularly on the time to establishment of an invading, exogenous strain, using parameters taken from the literature for COVID-19 as an example. We also demonstrate how to combine our model with a deterministic approximation, such that longer term projections can be generated that still incorporate the uncertainty from the early growth phase of the epidemic. Our approach produces meaningful short- and medium-term projections of the course of a disease outbreak when model parameters are still uncertain and when stochasticity still has a large effect on the population dynamics.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109352"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793018","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109368
Ann Osi, Navid Ghaffarzadegan
The transmission dynamics of infectious diseases and human responses are intertwined, forming complex feedback loops. However, many epidemic models fail to endogenously represent human behavior change. In this study, we introduce a novel behavioral epidemic model that incorporates various behavioral phenomena into SEIR models, including risk-response dynamics, shifts in containment policies, adherence fatigue, and societal learning, alongside disease transmission dynamics. By testing our model against data from 8 countries, where extensive behavioral data were available, we simultaneously replicate death rates, mobility trends, fatigue levels, and policy changes, both in-sample and out-of-sample. Our model offers a comprehensive depiction of changes in multiple behavioral measures along with the spread of the disease. We assess the explanatory power of each model mechanism in capturing data variability. Our findings demonstrate that the comprehensive model that includes all mechanisms provides the most insightful perspective for understanding the influence of human behavior during pandemics.
{"title":"A simultaneous simulation of human behavior dynamics and epidemic spread: A multi-country study amidst the COVID-19 pandemic","authors":"Ann Osi, Navid Ghaffarzadegan","doi":"10.1016/j.mbs.2024.109368","DOIUrl":"10.1016/j.mbs.2024.109368","url":null,"abstract":"<div><div>The transmission dynamics of infectious diseases and human responses are intertwined, forming complex feedback loops. However, many epidemic models fail to endogenously represent human behavior change. In this study, we introduce a novel behavioral epidemic model that incorporates various behavioral phenomena into SEIR models, including risk-response dynamics, shifts in containment policies, adherence fatigue, and societal learning, alongside disease transmission dynamics. By testing our model against data from 8 countries, where extensive behavioral data were available, we simultaneously replicate death rates, mobility trends, fatigue levels, and policy changes, both in-sample and out-of-sample. Our model offers a comprehensive depiction of changes in multiple behavioral measures along with the spread of the disease. We assess the explanatory power of each model mechanism in capturing data variability. Our findings demonstrate that the comprehensive model that includes all mechanisms provides the most insightful perspective for understanding the influence of human behavior during pandemics.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109368"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840714","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109344
Francis C. Motta , Kevin McGoff , Breschine Cummins , Steven B. Haase
Synchronized behavior among individuals, broadly defined, is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be made of complex, dynamic populations. Despite the importance to analyzing and modeling populations, existing notions of synchrony often lack rigorous definitions, may be specialized to a particular experimental system and/or measurement, or may have undesirable properties that limit their utility. Here we introduce a notion of synchrony for populations of individuals occupying a compact metric space that depends on the Fréchet variance of the distribution of individuals across the space. We establish several fundamental and desirable mathematical properties of our proposed measure of synchrony, including continuity and invariance to metric scaling. We establish a general approximation result that controls the disparity between synchrony in the true space and the synchrony observed through a discretization of state space, as may occur when observable states are limited by measurement constraints. We develop efficient algorithms to compute synchrony for distributions in a variety of state spaces, including all finite state spaces and empirical distributions on the circle, and provide accessible implementations in an open-source Python module. To demonstrate the usefulness of the synchrony measure in biological applications, we investigate several biologically relevant models of mechanisms that can alter the dynamics of population synchrony over time, and reanalyze published experimental and model data concerning the dynamics of the intraerythrocytic developmental cycles of Plasmodium parasites. We anticipate that the rigorous definition of population synchrony and the mathematical and biological results presented here will be broadly useful in analyzing and modeling populations in a variety of contexts.
{"title":"Generalized measures of population synchrony","authors":"Francis C. Motta , Kevin McGoff , Breschine Cummins , Steven B. Haase","doi":"10.1016/j.mbs.2024.109344","DOIUrl":"10.1016/j.mbs.2024.109344","url":null,"abstract":"<div><div>Synchronized behavior among individuals, broadly defined, is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be made of complex, dynamic populations. Despite the importance to analyzing and modeling populations, existing notions of synchrony often lack rigorous definitions, may be specialized to a particular experimental system and/or measurement, or may have undesirable properties that limit their utility. Here we introduce a notion of synchrony for populations of individuals occupying a compact metric space that depends on the Fréchet variance of the distribution of individuals across the space. We establish several fundamental and desirable mathematical properties of our proposed measure of synchrony, including continuity and invariance to metric scaling. We establish a general approximation result that controls the disparity between synchrony in the true space and the synchrony observed through a discretization of state space, as may occur when observable states are limited by measurement constraints. We develop efficient algorithms to compute synchrony for distributions in a variety of state spaces, including all finite state spaces and empirical distributions on the circle, and provide accessible implementations in an open-source Python module. To demonstrate the usefulness of the synchrony measure in biological applications, we investigate several biologically relevant models of mechanisms that can alter the dynamics of population synchrony over time, and reanalyze published experimental and model data concerning the dynamics of the intraerythrocytic developmental cycles of <em>Plasmodium</em> parasites. We anticipate that the rigorous definition of population synchrony and the mathematical and biological results presented here will be broadly useful in analyzing and modeling populations in a variety of contexts.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109344"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901511","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109362
Pablo Saez , Pallavi U. Shirke , Jyoti R. Seth , Jorge Alegre-Cebollada , Abhijit Majumder
Cell migration regulates central life processes including embryonic development, tissue regeneration, and tumor invasion. To establish the direction of migration, cells follow exogenous cues. Durotaxis, the directed cell migration towards elastic stiffness gradients, is the classical example of mechanical taxis. However, whether gradients of the relaxation properties in the extracellular matrix may also induce tactic responses (viscotaxis) is not well understood. Moreover, whether and how durotaxis and viscotaxis interact with each other has never been investigated. Here, we integrate clutch models for cell adhesions with an active gel theory of cell migration to reveal the mechanisms that govern viscotaxis. We show that viscotaxis is enabled by an asymmetric expression of cell adhesions that further polarize the intracellular motility forces to establish the cell front, similar to durotaxis. More importantly, when both relaxation and elastic gradients coexist, durotaxis appears more efficient in controlling directed cell migration, which we confirm with experimental results. However, the presence of opposing relaxation gradients to an elastic one can arrest or shift the migration direction. Our model rationalizes for the first time the mechanisms that govern viscotaxis and its competition with durotaxis through a mathematical model.
{"title":"Competing elastic and viscous gradients determine directional cell migration","authors":"Pablo Saez , Pallavi U. Shirke , Jyoti R. Seth , Jorge Alegre-Cebollada , Abhijit Majumder","doi":"10.1016/j.mbs.2024.109362","DOIUrl":"10.1016/j.mbs.2024.109362","url":null,"abstract":"<div><div>Cell migration regulates central life processes including embryonic development, tissue regeneration, and tumor invasion. To establish the direction of migration, cells follow exogenous cues. Durotaxis, the directed cell migration towards elastic stiffness gradients, is the classical example of mechanical taxis. However, whether gradients of the relaxation properties in the extracellular matrix may also induce tactic responses (viscotaxis) is not well understood. Moreover, whether and how durotaxis and viscotaxis interact with each other has never been investigated. Here, we integrate clutch models for cell adhesions with an active gel theory of cell migration to reveal the mechanisms that govern viscotaxis. We show that viscotaxis is enabled by an asymmetric expression of cell adhesions that further polarize the intracellular motility forces to establish the cell front, similar to durotaxis. More importantly, when both relaxation and elastic gradients coexist, durotaxis appears more efficient in controlling directed cell migration, which we confirm with experimental results. However, the presence of opposing relaxation gradients to an elastic one can arrest or shift the migration direction. Our model rationalizes for the first time the mechanisms that govern viscotaxis and its competition with durotaxis through a mathematical model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109362"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142866826","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}
Pub Date : 2025-02-01DOI: 10.1016/j.mbs.2024.109369
Matthias Christgen , Rodrigo A. Caetano , Michael Eisenburger , Arne Traulsen , Philipp M. Altrock
Lobular carcinoma in situ (LCIS) is a precursor of invasive lobular carcinoma of the breast. LCIS cells lack cell-cell cohesion due to the loss of E-cadherin. LCIS cells grow in mammary lobules rather than in ducts. The etiology of this pattern, especially its dependence on cellular cohesion, is incompletely understood. We simulated passive intra-glandular scattering of carcinoma in situ (CIS) cells in an ultra-simplified hollow mold tissue replica (HMTR) and a discrete-time mathematical model featuring particles of variable sizes representing single cells (LCIS-like particles) or groups of cohesive carcinoma cells (DCIS-like particles). The HMTR features structures reminiscent of a mammary duct with associated lobules. The discrete mathematical model characterizes spatial redistribution over time and includes transition probabilities between ductal or lobular localizations. Redistribution of particles converged toward an equilibrium depending on particle size. Strikingly, equilibrium proportions depended on particle properties, which we also confirm in a continuous-time mathematical model that considers controlling lobular properties such as crowding. Particles of increasing size, representing CIS cells with proficient cohesion, showed increasingly higher equilibrium ductal proportions. Our investigations represent two conceptual abstractions implying a link between loss of cell-cell cohesion and lobular localization of LCIS, which provide a much-needed logical foundation for studying the connections between collective cell behavior and cancer development in breast tissues. In light of the findings from our simplified modeling approach, we discuss multiple avenues for near-future research that can address and evaluate the redistribution hypothesis mathematically and empirically.
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