Bulletin of Mathematical Biology最新文献

{"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}

{"title":"Transformations to Simplify Phylogenetic Networks.","authors":"Johanna Heiss, Daniel H Huson, Mike Steel","doi":"10.1007/s11538-024-01398-7","DOIUrl":"10.1007/s11538-024-01398-7","url":null,"abstract":"<p><p>The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or lateral gene transfer events between lineages, and so the history of life is more accurately described by a rooted phylogenetic network. Nevertheless, phylogenetic networks may be complex and difficult to interpret, so biologists sometimes prefer a tree that summarises the central tree-like trend of evolution. In this paper, we formally investigate methods for transforming an arbitrary phylogenetic network into a tree (on the same set of leaves) and ask which ones (if any) satisfy a simple consistency condition. This consistency condition states that if we add additional species into a phylogenetic network (without otherwise changing this original network) then transforming this enlarged network into a rooted phylogenetic tree induces the same tree on the original set of species as transforming the original network. We show that the LSA (lowest stable ancestor) tree method satisfies this consistency property, whereas several other commonly used methods (and a new one we introduce) do not. We also briefly consider transformations that convert arbitrary phylogenetic networks to another simpler class, namely normal networks.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"20"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920694","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":"Negligible Long-Term Impact of Nonlinear Growth Dynamics on Heterogeneity in Models of Cancer Cell Populations.","authors":"Stefano Giaimo, Saumil Shah, Michael Raatz, Arne Traulsen","doi":"10.1007/s11538-024-01395-w","DOIUrl":"10.1007/s11538-024-01395-w","url":null,"abstract":"<p><p>Linear compartmental models are often employed to capture the change in cell type composition of cancer cell populations. Yet, these populations usually grow in a nonlinear fashion. This begs the question of how linear compartmental models can successfully describe the dynamics of cell types. Here, we propose a general modeling framework with a nonlinear part capturing growth dynamics and a linear part capturing cell type transitions. We prove that dynamics in this general model are asymptotically equivalent to those governed only by its linear part under a wide range of assumptions for nonlinear growth.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"18"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11698897/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920613","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 Theoretical Analysis of Mass Testing Strategies to Control Epidemics.","authors":"Michela Sabbatino, Simone De Reggi, Andrea Pugliese","doi":"10.1007/s11538-024-01387-w","DOIUrl":"10.1007/s11538-024-01387-w","url":null,"abstract":"<p><p>One of the strategies used in some countries to contain the COVID-19 epidemic has been the test-and-isolate policy, generally coupled with contact tracing. Such strategies have been examined in several simulation models, but a theoretical analysis of their effectiveness in simple epidemic model is, to our knowledge, missing. In this paper, we present four epidemic models of either SIR or SEIR type, in which it is assumed that at fixed times the whole population (or a part of the population) is tested and, if positive, isolated. We find the conditions for an epidemic to go extinct under such a strategy; for these types of models we provide an appropriate definition of <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , that can be computed either analytically or numerically. Finally, we show numerically that the final-size relation of SIR models approximately holds for the four models, over a large parameter range.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"22"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920493","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 Residual Fertility Impacts the Efficiency of Crop Pest Control by the Sterile Insect Technique.","authors":"Marine A Courtois, Ludovic Mailleret, Suzanne Touzeau, Louise van Oudenhove, Frédéric Grognard","doi":"10.1007/s11538-024-01401-1","DOIUrl":"10.1007/s11538-024-01401-1","url":null,"abstract":"<p><p>The sterile insect technique (SIT) is a biological control technique based on mass-rearing, radiation-based sterilization that can induce fitness costs, and releases of the pest species targeted for population control. Sterile matings, between females and sterilized males, can reduce the overall population growth rate and cause a fall in population density. However, a proportion of irradiated males may escape sterilization, resulting in what is called residual fertility. Our aim in this study was to examine the impact of residual fertility on pest control employing a modeling approach. We modeled pest population dynamics with three generic differential equations representing sterilized males, wild males and wild females. We explored the impact of residual fertility, in the presence or absence of fitness costs, on potential pest control outcomes using a scenario with <math><mrow><mn>100</mn> <mo>%</mo></mrow> </math> male sterilization as our standard of reference. We carried out a detailed mathematical analysis of the model's dynamics by calculating model equilibria and the latter's stability. Bifurcation analyses were performed with parameters for the Mediterranean fruit fly Ceratitis capitata. We showed that, when residual fertility is below a threshold value, wild populations can be eradicated by flooding the landscape with irradiated males. This threshold is higher when residual fertility is associated with fitness costs. Too high a level of residual fertility makes SIT less effective and hinders population eradication. That said, substantial decreases in population density can be achieved even when residual fertility is much larger than the above threshold.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"25"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920496","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":"Modelling the Impact of HIF on Metabolism and the Extracellular Matrix: Consequences for Tumour Growth and Invasion.","authors":"Kévin Spinicci, Gibin Powathil, Angélique Stéphanou","doi":"10.1007/s11538-024-01391-0","DOIUrl":"10.1007/s11538-024-01391-0","url":null,"abstract":"<p><p>The extracellular matrix (ECM) is a complex structure involved in many biological processes with collagen being the most abundant protein. Density of collagen fibers in the matrix is a factor influencing cell motility and migration speed. In cancer, this affects the ability of cells to migrate and invade distant tissues which is relevant for designing new therapies. Furthermore, increased cancer cell migration and invasion have been observed in hypoxic conditions. Interestingly, it has been revealed that the Hypoxia Inducible Factor (HIF) can not only impact the levels of metabolic genes but several collagen remodeling genes as well. The goal of this paper is to explore the impact of the HIF protein on both the tumour metabolism and the cancer cell migration with a focus on the Warburg effect and collagen remodelling processes. Therefore, we present an agent-based model (ABM) of tumour growth combining genetic regulations with metabolic and collagen-related processes involved in HIF pathways. Cancer cell migration is influenced by the extra-cellular collagen through a biphasic response dependant on collagen density. Results of the model showed that extra-cellular collagen within the tumour was mainly influenced by the local cellular density while collagen also influenced the shape of the tumour. In our simulations, proliferation was reduced with higher extra-cellular collagen levels or with lower oxygen levels but reached a maximum in the absence of cell-cell adhesion. Interestingly, combining lower levels of oxygen with higher levels of collagen further reduced the proliferation of the tumour. Since HIF impacts the metabolism and may affect the appearance of the Warburg Effect, we investigated whether different collagen conditions could lead to the adoption of the Warburg phenotype. We found that this was not the case, results suggested that adoption of the Warburg phenotype seemed mainly controlled by inhibition of oxidative metabolism by HIF combined with oscillations of oxygen.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"27"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11698809/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920454","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":"Prevalence Estimation Methods for Time-Dependent Antibody Kinetics of Infected and Vaccinated Individuals: A Markov Chain Approach.","authors":"Prajakta Bedekar, Rayanne A Luke, Anthony J Kearsley","doi":"10.1007/s11538-024-01402-0","DOIUrl":"10.1007/s11538-024-01402-0","url":null,"abstract":"<p><p>Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalence combine non-trivially to govern antibody levels sampled from a population. Time-dependence and disease prevalence pose considerable modeling challenges that need to be addressed to provide a rigorous mathematical underpinning of the underlying biology. We propose a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for antibody kinetics and demonstrate its use in a setting in which individuals can be infected or vaccinated but not both. We conduct prevalence estimation via transition probability matrices using synthetic data. This approach is ideal to model sequences of infections and vaccinations, or personal trajectories in a population, making it an important first step towards a mathematical characterization of reinfection, vaccination boosting, and cross-events of infection after vaccination or vice versa.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"26"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11698776/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920658","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":"Ecosystem Knowledge Should Replace Coexistence and Stability Assumptions in Ecological Network Modelling.","authors":"Sarah A Vollert, Christopher Drovandi, Matthew P Adams","doi":"10.1007/s11538-024-01407-9","DOIUrl":"10.1007/s11538-024-01407-9","url":null,"abstract":"<p><p>Quantitative population modelling is an invaluable tool for identifying the cascading effects of conservation on an ecosystem. When population data from monitoring programs is not available, deterministic ecosystem models have often been calibrated using the theoretical assumption that ecosystems have a stable, coexisting equilibrium. However, a growing body of literature suggests these theoretical assumptions are inappropriate for conservation contexts. Here, we develop an alternative for data-free population modelling that relies on expert-elicited knowledge of species populations. Our new Bayesian algorithm systematically removes model parameters that lead to impossible predictions, as defined by experts, without incurring excessive computational costs. We demonstrate our framework on an ordinary differential equation model by limiting predicted population sizes and their ability to change rapidly, utilising readily available knowledge from field observations and experts rather than relying on theoretical ecosystem properties. Our results show that using only coexistence and stability requirements can lead to unrealistic population dynamics, which can be avoided by switching to expert-derived information. We demonstrate how this change can dramatically impact population predictions, expected responses to management, conservation decision-making, and long-term ecosystem behaviour. Without data, we argue that field observations and expert knowledge are more trustworthy for representing ecosystems observed in nature, improving the precision and confidence in predictions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"17"},"PeriodicalIF":2.0,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142909431","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}