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The Role of Viral Dynamics and Infectivity in Models of Oncolytic Virotherapy for Tumours with Different Motility. 病毒动力学和感染性在不同运动性肿瘤的溶瘤病毒治疗模型中的作用。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-25 DOI: 10.1007/s11538-026-01630-6
David Morselli, Federico Frascoli, Marcello E Delitala

The use of ad-hoc engineered viruses in the fight against tumours is one of the greatest ideas in cancer therapeutics within the last three decades. Although some remarkable successes have been obtained, it is still not entirely clear how to achieve reliable protocols that can be routinely employed with confidence on a significant range of tumours. In this work, we concentrate on the study of different mathematical descriptions of virotherapy with the aim of better understanding the role of viral infectivity and viral dynamics in positive therapeutic outcomes. In particular, we compare probabilistic, individual approaches with continuous, spatially inhomogeneous models and investigate the importance of different tumour motility and different mathematical representations of viral infectivity. Some of these formulations also allow us to arrive at better analytical characterisation of how waves of viral infections arise and propagate in tumours, providing interesting insights into therapy dynamics. Similarly to previous studies, oscillatory behaviours, stochasticity and cancers' diffusivities are all central to the eradication or the escape of tumours under virotherapy. Here, though, our results also show that the ability of viruses to infect tumours seems, in certain cases, more important to a final positive outcome than tumours' motility or even reproductivity. This could hopefully represent a first step into better insights into viral dynamics that may help clinicians to achieve consistently better outcomes.

在对抗肿瘤中使用特设工程病毒是过去三十年来癌症治疗领域最伟大的想法之一。尽管已经取得了一些显著的成功,但我们仍然不完全清楚如何实现可靠的方案,使其能够在很大范围内的肿瘤上得到可靠的常规应用。在这项工作中,我们专注于研究病毒治疗的不同数学描述,目的是更好地理解病毒感染性和病毒动力学在积极治疗结果中的作用。特别地,我们比较了概率、个体方法与连续的、空间非均匀的模型,并研究了不同肿瘤运动性和病毒感染性的不同数学表示的重要性。其中一些公式还使我们能够更好地分析病毒感染波是如何在肿瘤中产生和传播的,为治疗动力学提供了有趣的见解。与先前的研究类似,振荡行为、随机性和癌症的扩散性都是病毒治疗下肿瘤根除或逃逸的核心。然而,在这里,我们的结果也表明,在某些情况下,病毒感染肿瘤的能力似乎比肿瘤的运动性甚至繁殖能力对最终的积极结果更重要。这可能是更好地了解病毒动力学的第一步,这可能有助于临床医生获得一贯更好的结果。
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引用次数: 0
Integrating Mechanistic Modeling and Machine Learning to Study CD4+/CD8+ CAR-T Cell Dynamics with Tumor Antigen Regulation. 结合机制建模和机器学习研究CD4+/CD8+ CAR-T细胞动力学与肿瘤抗原调控。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-25 DOI: 10.1007/s11538-026-01633-3
Saranya Varakunan, Melissa Stadt, Mohammad Kohandel

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden. Building on a recent model of antigen-regulated memory-effector-exhaustion transitions in CAR-T cells, our system of differential equations incorporates CD4+-mediated modulation of CD8+ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8+ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naïve baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

嵌合抗原受体(CAR) T细胞治疗在血液系统恶性肿瘤中显示出显著的成功,但患者的反应仍然高度可变,CD4+和CD8+亚群的作用尚不完全清楚。我们提出了CAR-T细胞动力学的扩展数学框架,明确地模拟CD4+辅助细胞和CD8+细胞毒性谱系及其与肿瘤抗原负荷的相互作用。基于CAR-T细胞中抗原调控的记忆-效应-耗竭转换的最新模型,我们的微分方程系统结合了CD4+介导的CD8+增殖、细胞毒性和通过生物基础饱和相互作用的记忆再生的调节。敏感性分析确定效应增殖、抗原周转和CD8+扩增率是治疗结果的主要驱动因素。虚拟患者模拟恢复了CAR-T组成的定性趋势,包括与仅CD8制剂相比,定义CD4:CD8产物的扩增和肿瘤清除增强,同时也揭示了患者间的可变性和时间依赖性效应。为了评估参数不确定性下患者水平预测的实际限制,我们在关键参数中引入了受控噪声,并表明直接的机制分类会迅速退化。然后,我们证明了一个简单的前馈神经网络可以从噪声输入中部分恢复预测信号,优于naïve基线,同时保持与机械灵敏度一致。这项工作将扩展模型定位为假设生成器,并说明了当参数不确定性限制预测置信度时,数据驱动方法如何补充机制建模。
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引用次数: 0
Final-Size Solutions for SIRI Models with Vaccination. 带有疫苗的SIRI模型的最终尺寸解决方案。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-24 DOI: 10.1007/s11538-026-01610-w
Maria A Gutierrez, Julia R Gog

In the classic SIR model, infection gives full immunity against any possible reinfection. However, for many important epidemiological situations, immunity is only partial and reinfection is possible. Though these models are mathematically more complex, we are able to find expressions for the epidemic final size. We also generalise these expressions to include vaccination, with a fraction of the population vaccinated before the epidemic, where vaccinees are less susceptible to primary infections than unvaccinated hosts.Partial immunity can be interpreted at the population level as providing either full or no protection to each host, in some proportion (all-or-none immunity). In this scenario, we give analytical expressions (mathematically similar to the SIR final-size) for the cumulative primary infections and the cumulative reinfections in unvaccinated and vaccinated hosts. Alternatively, partial immunity can be interpreted as providing homogeneous imperfect protection to each host (leaky immunity). For this other scenario, we again obtain an implicit equation for the final epidemic size. We break down, in terms of the final size, the number of infections in hosts with or without prior immunity (vaccine- or infection- induced), as well as the number of primary infections and reinfections. Under the leaky immunity assumption, we find a form of reinfection threshold. If the relative host susceptibility to reinfection is above this threshold (which is the inverse of the pathogen's basic reproduction number), transmission rates are high enough to support an endemic disease. Below the reinfection threshold, epidemics are transient. In the all-or-none model, epidemics are always transient.

在经典的SIR模型中,感染会对任何可能的再感染产生完全的免疫力。然而,对于许多重要的流行病学情况,免疫只是部分的,并且有可能再次感染。虽然这些模型在数学上更复杂,但我们能够找到流行病最终规模的表达式。我们还将这些表达推广到包括疫苗接种,在疫情前接种疫苗的一小部分人口中,接种疫苗的人比未接种疫苗的人更不容易受到原发性感染。在人口层面,部分免疫可以解释为在一定比例上为每个宿主提供完全保护或不提供保护(要么完全免疫,要么完全不免疫)。在这种情况下,我们给出了未接种疫苗和接种疫苗的宿主中累积原发感染和累积再感染的解析表达式(数学上类似于SIR最终大小)。或者,部分免疫可以解释为向每个宿主提供均匀的不完全保护(漏性免疫)。对于另一种情况,我们再次得到最终流行病规模的隐式方程。根据最终大小,我们分解了有或没有事先免疫(疫苗或感染诱导)的宿主的感染数量,以及原发性感染和再感染的数量。在免疫漏洞假设下,我们发现了一种再感染阈值的形式。如果宿主对再感染的相对易感性高于这个阈值(与病原体的基本繁殖数相反),传播率就高到足以支持一种地方病。在再感染阈值以下,流行病是短暂的。在全有或全无模型中,流行病总是短暂的。
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引用次数: 0
Emergence of Bursting and Delay-Induced Spiral Patterns in Eco-Epidemiological Systems. 生态流行病学系统中爆发型和延迟型螺旋型的出现。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-24 DOI: 10.1007/s11538-026-01627-1
Namrata Mani Tripathi, Ranjit Kumar Upadhyay, Dipesh Barman, Anotida Madzvamuse
<p><p>Understanding the spatio-temporal dynamics of interacting populations is crucial for studying ecological systems. In this work, we develop an eco-epidemic system of susceptible and infected preys and predators, incorporating memory-driven delays due to a carryover effect <math><mrow><mo>(</mo> <msub><mi>f</mi> <mn>1</mn></msub> <mo>)</mo></mrow> </math> in susceptible prey and a predator-induced fear <math><mrow><mo>(</mo> <msub><mi>f</mi> <mn>2</mn></msub> <mo>)</mo></mrow> </math> , along with a recovery process of infected preys parametrized by a constant recovery rate ( <math><mi>γ</mi></math> ). We prove the existence and boundedness of solutions and establish Hopf bifurcation conditions for four cases of time delays, which are also verified numerically. Without delays, the temporal system exhibits saddle-node and Hopf bifurcations with respect to <math><msub><mi>f</mi> <mn>1</mn></msub> </math> and <math><msub><mi>f</mi> <mn>2</mn></msub> </math> , where higher carryover stabilizes and higher fear destabilizes the dynamics, as shown numerically, while variations in the recovery rate significantly influence population densities by increasing susceptible prey and suppressing predator persistence under different transmission rates. In the presence of delays and in the absence of recovery ( <math><mrow><mi>γ</mi> <mo>=</mo> <mn>0</mn></mrow> </math> ), delays do not affect the stability of an initially stable temporal system; however, in unstable regimes, carryover and fear delays lead to chaotic oscillations, confirmed by the computation of Lyapunov exponents, and bursting dynamics, respectively. When the recovery rate is nonzero and exceeds a threshold value, temporal stability becomes independent of the delays. PRCC-based global sensitivity analysis identifies key parameters that significantly influence coexistence and system stability. Beyond temporal dynamics, small delays induce Turing instability and generate diverse spatial patterns in a reaction-diffusion framework, where increasing fear-induced delay <math><mrow><mo>(</mo> <msub><mi>τ</mi> <mn>2</mn></msub> <mo>)</mo></mrow> </math> enhances aggregation by transforming micro-spirals into dense clusters, carryover delay <math><mrow><mo>(</mo> <msub><mi>τ</mi> <mn>1</mn></msub> <mo>)</mo></mrow> </math> stabilizes larger spirals, and their combined effects produce four-headed spirals at high prey diffusion <math><mrow><mo>(</mo> <msub><mi>D</mi> <mi>S</mi></msub> <mo>)</mo></mrow> </math> that become denser at lower diffusion; increasing recovery shifts large spirals to micro-spirals, confirming the existence of a critical recovery rate beyond which the destabilizing effects of <math><msub><mi>τ</mi> <mn>1</mn></msub> </math> and <math><msub><mi>τ</mi> <mn>2</mn></msub> </math> are suppressed. Overall, this study shows that time delays and recovery jointly govern ecosystem stability, driving transitions between regular, chaotic, and patterned dynamics, and offering insights for ec
了解种群相互作用的时空动态对研究生态系统至关重要。在这项工作中,我们开发了一个易感和受感染猎物和捕食者的生态流行病系统,结合了由于易感猎物的携带效应(f1)和捕食者引起的恐惧(f2)而导致的记忆驱动延迟,以及受感染猎物的恢复过程,该过程由恒定的恢复率(γ)参数化。证明了四种时滞情况解的存在性和有界性,建立了Hopf分岔条件,并进行了数值验证。在没有延迟的情况下,时间系统相对于f1和f2表现出鞍节点和Hopf分岔,其中较高的携带性稳定,较高的恐惧性不稳定,如数值所示,而恢复率的变化通过增加易感猎物和抑制捕食者在不同传播率下的持久性显著影响种群密度。在存在延迟和不存在恢复(γ = 0)的情况下,延迟不会影响初始稳定的时间系统的稳定性;然而,在不稳定的状态下,结转和恐惧延迟导致混沌振荡,分别由李雅普诺夫指数和爆破动力学的计算证实。当恢复速率非零且超过阈值时,时间稳定性与延迟无关。基于prc的全局敏感性分析确定了显著影响共存和系统稳定性的关键参数。除了时间动力学之外,小的延迟还会导致图灵不稳定性,并在反应-扩散框架中产生不同的空间模式,其中增加的恐惧引起的延迟(τ 2)通过将微螺旋转变为密集的簇来增强聚集性,携带延迟(τ 1)稳定较大的螺旋,它们的综合作用产生在高猎物扩散(ds)时变得更密集的四头螺旋;增加恢复将大螺旋转变为微螺旋,证实了临界恢复速率的存在,超过该临界恢复速率,τ 1和τ 2的不稳定效应被抑制。总体而言,该研究表明,时间延迟和恢复共同控制着生态系统的稳定性,驱动着规则、混沌和模式动态之间的转变,并为生态管理和疾病控制提供了见解。
{"title":"Emergence of Bursting and Delay-Induced Spiral Patterns in Eco-Epidemiological Systems.","authors":"Namrata Mani Tripathi, Ranjit Kumar Upadhyay, Dipesh Barman, Anotida Madzvamuse","doi":"10.1007/s11538-026-01627-1","DOIUrl":"https://doi.org/10.1007/s11538-026-01627-1","url":null,"abstract":"&lt;p&gt;&lt;p&gt;Understanding the spatio-temporal dynamics of interacting populations is crucial for studying ecological systems. In this work, we develop an eco-epidemic system of susceptible and infected preys and predators, incorporating memory-driven delays due to a carryover effect &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; in susceptible prey and a predator-induced fear &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; , along with a recovery process of infected preys parametrized by a constant recovery rate ( &lt;math&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/math&gt; ). We prove the existence and boundedness of solutions and establish Hopf bifurcation conditions for four cases of time delays, which are also verified numerically. Without delays, the temporal system exhibits saddle-node and Hopf bifurcations with respect to &lt;math&gt;&lt;msub&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;/math&gt; and &lt;math&gt;&lt;msub&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;/math&gt; , where higher carryover stabilizes and higher fear destabilizes the dynamics, as shown numerically, while variations in the recovery rate significantly influence population densities by increasing susceptible prey and suppressing predator persistence under different transmission rates. In the presence of delays and in the absence of recovery ( &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt; &lt;/math&gt; ), delays do not affect the stability of an initially stable temporal system; however, in unstable regimes, carryover and fear delays lead to chaotic oscillations, confirmed by the computation of Lyapunov exponents, and bursting dynamics, respectively. When the recovery rate is nonzero and exceeds a threshold value, temporal stability becomes independent of the delays. PRCC-based global sensitivity analysis identifies key parameters that significantly influence coexistence and system stability. Beyond temporal dynamics, small delays induce Turing instability and generate diverse spatial patterns in a reaction-diffusion framework, where increasing fear-induced delay &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;τ&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; enhances aggregation by transforming micro-spirals into dense clusters, carryover delay &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;τ&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; stabilizes larger spirals, and their combined effects produce four-headed spirals at high prey diffusion &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt; &lt;mi&gt;S&lt;/mi&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; that become denser at lower diffusion; increasing recovery shifts large spirals to micro-spirals, confirming the existence of a critical recovery rate beyond which the destabilizing effects of &lt;math&gt;&lt;msub&gt;&lt;mi&gt;τ&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;/math&gt; and &lt;math&gt;&lt;msub&gt;&lt;mi&gt;τ&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;/math&gt; are suppressed. Overall, this study shows that time delays and recovery jointly govern ecosystem stability, driving transitions between regular, chaotic, and patterned dynamics, and offering insights for ec","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147509824","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}
引用次数: 0
Modelling and Simulation of Collective Cell Migration with Non-Local Interactions on Time-Dependent Spatial Domains. 时变空间域上非局部相互作用的集体细胞迁移建模与仿真。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-24 DOI: 10.1007/s11538-026-01628-0
Alf Gerisch

We extend the formulation of a non-local PDE model of collective cell migration involving attracting or repelling cellular interactions to the case of time-dependent spatial domains as present, for instance, in modelling developmental processes from embryology. We restrict to a spatially one-dimensional setting, as is appropriate for the modelling of neural crest cell invasion, and focus on the case of spatially homogeneous domain change as this already highlights many of the modelling and numerical challenges. The approach is illustrated and numerical simulations are presented and discussed for a model of an aggregating cellular population and for a simple model of neural crest cell invasion accounting for contact inhibition of locomotion.

我们将涉及吸引或排斥细胞相互作用的集体细胞迁移的非局部PDE模型的公式扩展到现有的时间依赖空间域的情况下,例如,在胚胎学的发育过程建模中。我们限制在空间一维的设置,这是适合于神经嵴细胞入侵的建模,并专注于空间均匀域变化的情况,因为这已经突出了许多建模和数值挑战。本文对该方法进行了说明,并对一个聚集细胞群体模型和一个考虑运动接触抑制的神经嵴细胞侵袭的简单模型进行了数值模拟。
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引用次数: 0
Effect of Preventive Measures and Heterogeneity of Sexual Contacts on Zika virus Transmission. 预防措施及性接触异质性对寨卡病毒传播的影响
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-18 DOI: 10.1007/s11538-026-01622-6
Qiaojuan Jia, Ling Xue, Jichen Yang, Junyuan Yang, James M Hyman

The global spread of the Zika virus (ZIKV), compounded by the absence of effective antiviral drugs or widely available vaccines, highlights the importance of understanding its transmission dynamics to implement effective public health strategies. The transmission of the Zika virus is attributable to the heterogeneity of sexual contacts and the lack of miracle drugs or vaccines. We develop a degree-based mathematical network model which takes account of heterogeneity of sexual contacts and the adoption of preventive measures. We derive analytical expressions for the basic reproduction number for three scenarios: mosquito-borne transmission only, sexual transmission only, and a combined scenario where both transmission routes coexist. In particular, we demonstrate that the basic reproduction number is proportional to the degree of network heterogeneity when the Zika virus transmission is solely driven by sexual contacts. Our proposed model possesses infinitely many disease-free equilibrium points, and we prove that these collectively form a locally attracting set under specified conditions. Finally, we present numerical simulations, calibrated with Zika epidemic data from Brazil (2015-2016), which indicate that increasing the number of individuals who take comprehensive protective measures (using screens, mosquito nets, insect repellent, condoms, etc.) can significantly reduce the final epidemic size.

寨卡病毒(ZIKV)在全球的传播,加上缺乏有效的抗病毒药物或广泛获得的疫苗,凸显了了解其传播动态以实施有效公共卫生战略的重要性。寨卡病毒的传播可归因于性接触的异质性以及缺乏特效药物或疫苗。我们开发了一个基于程度的数学网络模型,该模型考虑了性接触的异质性和预防措施的采用。我们推导了三种情况下基本繁殖数的解析表达式:蚊媒传播、性传播和两种传播途径并存的组合情况。特别是,我们证明了当寨卡病毒传播仅由性接触驱动时,基本繁殖数与网络异质性程度成正比。我们所提出的模型具有无穷多个无病平衡点,并证明了这些平衡点在一定条件下共同形成一个局部吸引集。最后,我们以巴西2015-2016年的寨卡疫情数据进行了数值模拟,结果表明,采取综合防护措施(使用纱窗、蚊帐、驱蚊剂、避孕套等)的人数增加,可以显著减少最终的疫情规模。
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引用次数: 0
Counting Spinal Phylogenetic Networks. 计算脊柱系统发育网络。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-18 DOI: 10.1007/s11538-026-01624-4
Andrew Francis, Michael Hendriksen

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulate processes such as hybridisation or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain properties are very difficult. A new way to encode a large class of networks, using "expanding covers", may provide a way to approach such problems. Expanding covers encode a large class of phylogenetic networks, called labellable networks. This class does not include all networks, but does include many familiar classes, including orchard, normal, tree-child and tree-sibling networks. As expanding covers are a combinatorial structure, it is possible that they can be used as a tool for counting such classes for a fixed number of leaves and reticulations, for which, in many cases, a closed formula has not yet been found. More recently, a new class of networks was introduced, called spinal networks, which are analogous to caterpillar trees for phylogenetic trees and can be fully described using covers. In the present article, we describe a method for counting networks that are both spinal and belong to some more familiar class, with the hope that these form a base case from which to attack the more general classes.

系统发育网络是表示涉及网状过程(如杂交或水平基因转移)的进化史的重要方式,但诸如有多少网络满足某些特性之类的基本问题非常困难。一种对大型网络进行编码的新方法,即使用“扩展覆盖”,可能为解决这类问题提供了一种方法。扩展覆盖编码了一大类系统发育网络,称为可标记网络。这个类不包括所有的网络,但包括许多熟悉的类,包括果园、正常、树-子和树-兄弟网络。由于扩展盖是一种组合结构,它们可能被用作一种工具,用于计算固定数量的叶子和网状的这类,在许多情况下,还没有找到一个封闭的公式。最近,一种新的网络被引入,称为脊柱网络,它类似于系统发育树的毛虫树,可以用覆盖物完全描述。在本文中,我们描述了一种计算神经网络的方法,这些神经网络既属于脊椎神经网络,又属于一些更熟悉的类,希望这些神经网络能形成一个基础案例,从中攻击更一般的类。
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引用次数: 0
Vector Encoding of Phylogenetic Trees by Ordered Leaf Attachment. 基于有序叶片附着的系统发育树矢量编码。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-18 DOI: 10.1007/s11538-026-01611-9
David Harry Richman, Cheng Zhang, Frederick A Matsen

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a binary, rooted phylogenetic tree topology as an integer vector. OLA encoding and decoding take linear time in the number of leaf nodes, and the set of vectors corresponding to trees is a simply-described subset of integer sequences. The OLA encoding is unique compared to other existing encodings in having these properties. The integer vector encoding induces a distance on the set of trees, and we investigate this distance in relation to the NNI and SPR distances.

作为将系统发育与机器学习联系起来的工作的一部分,最近对系统发育树的矢量编码产生了相当大的兴趣。我们提出了一种简单的新“有序叶连接”(OLA)方法,用于将二叉根系统发育树拓扑结构唯一地编码为整数向量。OLA的编码和解码在叶节点数量上占用线性时间,而树对应的向量集是整数序列的一个简单描述子集。与具有这些属性的其他现有编码相比,OLA编码是唯一的。整数向量编码在树的集合上产生一个距离,我们研究了这个距离与NNI和SPR距离的关系。
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引用次数: 0
Mono- and Polyauxic Growth Kinetics: A Semi-Mechanistic Framework for Complex Biological Dynamics. 单一和多元生长动力学:复杂生物动力学的半机械框架。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-18 DOI: 10.1007/s11538-026-01621-7
Gustavo Mockaitis

Kinetic modeling of microbial growth is essential for the design, optimization, and scale-up of industrial bioprocesses. Classical empirical models often lack biologically interpretable parameters or fail to capture complex multiphasic (polyauxic) behaviors, while fully mechanistic models are impractical for systems involving complex substrates and mixed cultures. This study proposes a unified mathematical framework that reformulates the canonical Boltzmann and Gompertz equations into semi-mechanistic forms, explicitly defining the maximum specific reaction rate and lag phase duration. Polyauxic growth is represented as a weighted sum of sigmoidal phases, subject to stringent constraints that ensure parameter identifiability, temporal consistency, and biological plausibility. The methodology integrates a workflow to address nonlinear regression in high-dimensional parameter spaces. A two-stage optimization strategy using Differential Evolution for global search followed by L-BFGS-B for local refinement avoid bias and heuristic parameter initialization. A Charbonnier loss function and the Robust Regression and Outlier Removal procedure are employed to identify and mitigate experimental outliers. Model parsimony is enforced using Akaike (AIC, AICc) and Bayesian (BIC) information criteria to select the optimal number of growth phases and avoid overparameterization. The framework was evaluated using experimental anaerobic digestion datasets, demonstrating that conventional single-phase models can obscure relevant metabolic transitions in co-digestion systems.

微生物生长的动力学建模对于工业生物过程的设计、优化和规模化至关重要。经典的经验模型往往缺乏生物学上可解释的参数,或者无法捕捉复杂的多相(多源)行为,而完全机械的模型对于涉及复杂底物和混合培养的系统是不切实际的。本研究提出了一个统一的数学框架,将规范的玻尔兹曼和冈珀兹方程重新表述为半机械形式,明确定义了最大比反应速率和滞后相持续时间。复合生长被表示为s型相的加权和,受到严格的约束,以确保参数可识别性、时间一致性和生物合理性。该方法集成了一个工作流来解决高维参数空间中的非线性回归问题。采用差分进化进行全局搜索,L-BFGS-B进行局部优化,避免了偏差和启发式参数初始化。采用Charbonnier损失函数和鲁棒回归和异常值去除程序来识别和减轻实验异常值。采用Akaike (AIC, AICc)和Bayesian (BIC)信息准则来实现模型的简约性,以选择最优生长阶段数,避免过度参数化。使用实验厌氧消化数据集对该框架进行了评估,表明传统的单相模型可以模糊共消化系统中的相关代谢转变。
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引用次数: 0
Effects of Multi-Phase Control Mechanism on Fibroblast Dynamics: A Segmented Mathematical Modeling Approach. 多相调控机制对成纤维细胞动力学的影响:分段数学建模方法。
IF 2.2 4区 数学 Q2 BIOLOGY Pub Date : 2026-03-18 DOI: 10.1007/s11538-026-01607-5
Shuqi Fan, Yuhong Zhang, Jinzhi Lei

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.

细胞大小是细胞生理的基本决定因素,影响细胞生长、分裂和功能等过程。在这项研究中,我们开发了一个分段的数学框架来研究不同的控制机制如何在细胞周期的多个阶段影响成纤维细胞群体动力学。基于我们之前的工作建模大小器、计时器和加法器策略,我们通过在S和G2阶段引入相位特定控制方案来扩展分析,其中包含非线性生长动力学和细胞死亡。使用基于智能体的随机模拟,我们研究了这些机制如何形成稳态尺寸分布并响应参数变化。我们的研究结果表明,稳态细胞大小分布主要由分裂核和阶段特异性控制策略控制,并且对细胞死亡模式具有显著的鲁棒性。我们确定了外在和内在生长反馈之间的基本权衡:虽然种群密度依赖的调节严格限制了细胞总数,但细胞大小依赖的调节作为一种比例稳态机制,抑制了相对大小的可变性。此外,我们还证明,保留具有增殖能力的大细胞可以加速种群恢复。这项研究为生长、分裂和体内平衡之间复杂的相互作用提供了生物学相关的见解,对理解组织修复和疾病进展具有重要意义。
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引用次数: 0
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Bulletin of Mathematical Biology
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