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On the reduction of stochastic chemical reaction networks. 关于随机化学反应网络的约化。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-28 DOI: 10.1007/s00285-025-02320-y
Justin Eilertsen, Wylie Stroberg

The linear noise approximation (LNA) describes the random fluctuations from the mean-field concentrations of a chemical reaction network due to intrinsic noise. It is also used as a test probe to determine the accuracy of reduced formulations of the chemical master equation and to understand the relationship between timescale disparity and model reduction in stochastic environments. Although several reduced LNAs have been proposed, they have not been placed into a general theory concerning the accuracy of reduced LNAs derived from center manifold and singular perturbation theory. This has made it difficult to understand why certain reductions of the master or Langevin equations fail or succeed. In this work, we develop a deeper understanding of slow manifold projection in the linear noise regime by answering a straightforward but open question: In the presence of eigenvalue disparity, does the appropriate oblique projection of the LNA onto the slow eigenspace accurately approximate the first and second moments of complete LNA, and if not, why? Although most studies concentrate on the role of eigenvalue disparity arising from the drift matrix, we go further and examine the interplay between disparate 'drift" eigenvalues and the eigenvalues of the diffusion matrix, the latter of which may or may not be disparate. Furthermore, we place the previously established reductions of the LNA into a more general framework and formulate the necessary and sufficient conditions for the projected LNA to accurately approximate the first and second moments of the complete LNA.

线性噪声近似(LNA)描述了由本征噪声引起的化学反应网络平均场浓度的随机波动。它还被用作测试探针,以确定化学主方程简化公式的准确性,并了解随机环境中时间尺度差异与模型简化之间的关系。虽然已经提出了几种约化lna,但它们还没有被纳入一个关于由中心流形和奇异摄动理论推导的约化lna精度的一般理论。这使得很难理解为什么主方程或朗之万方程的某些约简会失败或成功。在这项工作中,我们通过回答一个直接但开放的问题,对线性噪声体系中的慢流形投影有了更深入的理解:在特征值视差存在的情况下,LNA在慢特征空间上的适当斜投影是否准确地近似完整LNA的第一和第二矩,如果不是,为什么?虽然大多数研究都集中在漂移矩阵产生的特征值差异的作用上,但我们进一步研究了不同的“漂移”特征值和扩散矩阵的特征值之间的相互作用,后者可能是不同的,也可能不是。此外,我们将先前建立的LNA缩减纳入更一般的框架,并制定了预测LNA准确近似完整LNA的第一和第二矩的必要和充分条件。
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引用次数: 0
Dynamical mechanisms of inflammatory spatial distribution and its association with recurrence in Crohn's disease. 炎症空间分布的动力学机制及其与克罗恩病复发的关系
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-25 DOI: 10.1007/s00285-025-02319-5
Mengqi Peng, Weihua Jiang

Crohn's disease (CD) is a recurrent chronic autoimmune disease, which is an inflammatory disease of the intestine with epithelial granulomas. The number of patients has been increasing significantly, and its pathogenesis and treatments are arousing hot discussions in the academic community. Taking into account the spatial heterogeneity of lesion distribution and the periodic recurrence, this paper uses a partial functional differential system with the free diffusion of bacteria and immunocytes and immune response latency to model the process of CD, based on the Lauffenburger-Kennedy bacterial infection model. In order to describe the spatial distribution and recurrence, we analyze the stability of the inflammation equilibrium state, and deduce the diffusion-driven Turing bifurcations and delay-driven Hopf bifurcations, drive the critical conditions for occurrence. Furthermore, through the analysis of Turing-Hopf bifurcations, the coupling effect of two factors is explored to obtain spatiotemporal patterns that better reflect clinical manifestations of CD. In addition, both theoretical and numerical results reveal that the motility is a necessary factor in the production of intestinal epithelial granulomas, while the immune response latency is an important factor in the recurrence. A small effective diffusion rate and a large time delay would lead to two spatially non-homogeneous steady states and a stable periodic solution, ultimately giving rise to a pair of stable spatially non-homogeneous periodic solutions through Turing-Hopf bifurcations. Our conclusions may provide some insights into the control mechanisms for Crohn's disease.

克罗恩病(CD)是一种复发性慢性自身免疫性疾病,是一种肠上皮肉芽肿的炎症性疾病。患者数量显著增加,其发病机制和治疗方法引起了学术界的热议。考虑到病变分布的空间异质性和周期性复发,本文在lauffenburg - kennedy细菌感染模型的基础上,采用具有细菌和免疫细胞自由扩散和免疫反应潜伏期的部分功能微分系统来模拟CD的过程。为了描述炎症平衡状态的空间分布和递推性,分析了炎症平衡状态的稳定性,推导出扩散驱动的图灵分岔和延迟驱动的Hopf分岔,驱动发生的临界条件。进一步,通过图灵- hopf分岔分析,探讨两因素的耦合效应,获得更能反映CD临床表现的时空模式。此外,理论和数值结果均表明,肠上皮肉芽肿的运动是产生肠上皮肉芽肿的必要因素,而免疫反应潜伏期是复发的重要因素。小的有效扩散速率和大的时间延迟会导致两个空间非齐次稳态和一个稳定周期解,最终通过图灵-霍普夫分岔得到一对空间非齐次稳定周期解。我们的结论可能为克罗恩病的控制机制提供一些见解。
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引用次数: 0
Analytical Insights into Ephaptic Coupling and Its Effect on Conduction Velocity. 触觉耦合及其对传导速度影响的分析见解。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-25 DOI: 10.1007/s00285-025-02315-9
Ning Wei, Yoichiro Mori

Cardiovascular disease continues to be the leading cause of death in the United States. A major contributing factor is cardiac arrhythmia, which results from irregular electrical activity in the heart. On a tissue level, cardiac conduction involves the spread of action potentials (AP) across the heart, enabling coordinated contraction of the myocardium. On a cellular level, the transmission of signals between cells is facilitated by low-resistance pathways formed by gap junctions (GJs). Recent experimental studies have sparked discussion on whether GJs play a dominant role in cell communication. Interestingly, research has revealed that GJ knockout mice can still demonstrate signal propagation in the heart, albeit more slowly and discontinuously, indicating the presence of an alternative mechanism for cardiac conduction. Unlike GJ-mediated propagation, ephaptic coupling (EpC) has emerged as a distinct form of electrical transmission, characterized by contactless electrochemical signaling across the narrow intercalated discs (IDs) between cardiomyocytes. Advancements in cardiac research have highlighted the crucial role of EpC in restoring conduction by increasing conduction velocity (CV), reducing conduction block (CB), and terminating reentry arrhythmias, particularly when GJs are impaired. However, most EpC studies are either numerical or experimental, while analytical studies on ephaptic conduction-an equally important aspect of understanding EpC-remain extremely limited. In this paper, we applied asymptotic theory to calculate the CV in the presence of weak EpC. To achieve this, we developed both continuous and discrete models to describe ephaptic conduction along a strand of cells. Ionic dynamics were modeled using the piecewise linear and cubic functions. The resulting system represents a bistable system with weak EpC. We calculated an expression for CV in the presence of weak EpC for both models, and validated our analytical results with numerical simulations. Additionally, we showed that under weak EpC, CV can increase if the distribution of INa is more prominent on the end membrane.

在美国,心血管疾病仍然是导致死亡的主要原因。一个主要因素是心律失常,这是由心脏电活动不规律引起的。在组织水平上,心脏传导涉及动作电位(AP)在心脏的传播,使心肌协调收缩。在细胞水平上,细胞间的信号传递是由间隙连接(GJs)形成的低电阻通路促进的。最近的实验研究引发了关于gj是否在细胞通讯中起主导作用的讨论。有趣的是,研究表明GJ基因敲除小鼠仍然可以在心脏中表现出信号传播,尽管速度较慢且不连续,这表明存在另一种心脏传导机制。与gj介导的传播不同,ephaptic偶联(EpC)已成为一种独特的电传输形式,其特征是通过心肌细胞之间狭窄的嵌入盘(IDs)的非接触电化学信号。心脏研究的进展强调了EpC在恢复传导中的关键作用,通过增加传导速度(CV),减少传导阻滞(CB)和终止再入性心律失常,特别是当gj受损时。然而,大多数EpC研究要么是数值研究,要么是实验研究,而对触觉传导的分析研究——理解EpC的一个同样重要的方面——仍然非常有限。本文应用渐近理论计算了弱EpC存在时的CV。为了实现这一目标,我们开发了连续和离散模型来描述沿着细胞链的触觉传导。采用分段线性和三次函数对离子动力学进行了建模。由此得到的系统是一个弱EpC的双稳态系统。我们计算了两种模型在弱EpC存在下的CV表达式,并通过数值模拟验证了我们的分析结果。此外,我们还发现,在弱EpC条件下,当端膜上的INa分布更突出时,CV也会增加。
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引用次数: 0
The importance of the individual's micro-environment in drug consumption : A novel conceptual framework applied to the modeling of binge drinking. 个人微环境在药物消费中的重要性:一个应用于酗酒建模的新概念框架。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-19 DOI: 10.1007/s00285-025-02313-x
R Gutiérrez, C Rojas-Jara

The identification of psychosocial risk and protective factors associated with substance use during adolescence is crucial for the prevention and treatment of addictive behaviors. However, in the mathematical modeling of addictions, these psychological and social dimensions are often addressed in isolation. By focusing on the immediate socialization environment of adolescents, comprising peers, parents and family, and school, and considering them as risk and protective factors, we mathematically model binge drinking behavior from interaction dynamics among individuals and their predisposition to consumption based on evolutionary and adaptive reasons. Our findings indicate that, in the face of negative peer influence, prosocial behaviors, as well as supportive attitudes from parents and family, and the school environment, have the potential to inhibit long-term binge drinking. This tendency is strengthened when protective situations are consistently promoted in response to risky scenarios, which is in line with both theoretical approaches to prevention and current public policy on drug consumption.

识别与青少年时期物质使用相关的社会心理风险和保护因素对于预防和治疗成瘾行为至关重要。然而,在成瘾的数学模型中,这些心理和社会层面往往被孤立地处理。通过关注青少年的直接社交环境,包括同伴、父母和家庭以及学校,并将其视为风险和保护因素,我们从个体之间的互动动态及其基于进化和适应原因的消费倾向出发,对酗酒行为进行数学建模。我们的研究结果表明,面对消极的同伴影响,亲社会行为,以及来自父母和家庭的支持态度,以及学校环境,都有可能抑制长期酗酒。如果针对危险情况不断促进保护性情况,这种趋势就会加强,这既符合预防的理论方法,也符合目前关于药物消费的公共政策。
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引用次数: 0
Multistability of small zero-one reaction networks. 小型零-一反应网络的多稳定性。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-18 DOI: 10.1007/s00285-025-02306-w
Yue Jiao, Xiaoxian Tang, Xiaowei Zeng

Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells. It is well known that multistability can be lifted from a "subnetwork" (a network with less species and fewer reactions) to large networks. So, we aim to explore the multistability problem of small zero-one networks. In this work, we prove the following main results: 1. any zero-one network with a one-dimensional stoichiometric subspace admits at most one positive steady state (it must be stable), and all the one-dimensional zero-one networks can be classified according to if they indeed admit a stable positive steady state or not; 2. any two-dimensional zero-one network with up to three species either admits only degenerate positive steady states, or admits at most one positive steady state (it must be stable); 3. the smallest zero-one networks (here, by "smallest", we mean these networks contain species as few as possible) that admit nondegenerate multistationarity/multistability contain three species and five/six reactions, and they are three-dimensional. In these proofs, we use the theorems based on the Brouwer degree theory and the theory of real algebraic geometry. Moreover, applying the tools of computational real algebraic geometry, we provide a systematical way for detecting the networks that admit nondegenerate multistationarity/multistability.

零一生化反应网络在细胞信号传导中起着关键作用,如由蛋白磷酸化调节的信号通路。反应网络的多稳定性是细胞决策的关键动力学特征。众所周知,多稳定性可以从“子网络”(具有较少物种和较少反应的网络)提升到大型网络。因此,我们的目的是研究小型零网络的多稳定性问题。在这项工作中,我们证明了以下主要结果:1。任何具有一维化学计量子空间的0 - 1网络最多允许一个正稳态(它必须是稳定的),并且所有的一维0 - 1网络都可以根据是否确实允许一个稳定的正稳态进行分类;2. 任何不超过三个物种的二维零- 1网络要么只承认简并的正稳态,要么最多承认一个正稳态(它必须是稳定的);3. 最小的0 - 1网络(这里的“最小”是指这些网络包含尽可能少的物种)具有非退化多平稳性/多稳定性,包含3种物种和5 / 6个反应,并且它们是三维的。在这些证明中,我们使用了基于browwer次理论和实代数几何理论的定理。此外,应用计算实代数几何的工具,我们提供了一个系统的方法来检测网络承认非退化多平稳/多稳定。
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引用次数: 0
Global dynamics of a reaction-diffusion switching model with multiple stable states and linear harvesting rate. 具有多稳定状态和线性收获速率的反应-扩散切换模型的全局动力学。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-14 DOI: 10.1007/s00285-025-02312-y
Yunfeng Liu, Huaqin Peng, Jianshe Yu, Yuming Chen, Zhiming Guo

The closed fishing season policy plays a crucial role in fishery management by contributing to the restoration and protection of fishery resources, maintaining ecological balance and promoting sustainable development. The population dynamics of fish, particularly marine species, are highly complex. Under the combined effects of ecological mechanisms (such as predation, resource limitations, and competition), fish populations can exhibit multiple stable states. Overfishing increases the vulnerability of fish populations, making them prone to shift from a high-density stable state to a low-density one, and in some cases, leading to the risk of extinction. In this context, developing effective closed fishing season policies to ensure the sustainable development of fishery resources has become a pressing issue. In this paper, we propose a reaction-diffusion model consisting of two sub-equations with multiple stable states and a linear harvesting rate to describe the continuous switching between closed and open fishing seasons. We define a threshold value T ¯ for the duration of the fishing ban T ¯ . When T ¯ T ¯ , the trivial stable state is globally asymptotically stable. Uniqueness of periodic solutions is generally a mathematically challenging problem. However, employing the comparison theorem, we find that conditions on the uniqueness of periodic solutions to the associated ODE system are also applicable to our model. Specifically, under certain conditions, when T ¯ > T ¯ , we provide sufficient conditions on the existence of a globally asymptotically stable periodic solution. Finally, we offer discussion and numerical simulations to illustrate our findings.

休渔期政策对恢复和保护渔业资源、维护生态平衡、促进可持续发展具有重要的渔业管理作用。鱼类,特别是海洋物种的种群动态是非常复杂的。在捕食、资源限制和竞争等生态机制的综合作用下,鱼类种群可以呈现多种稳定状态。过度捕捞增加了鱼类种群的脆弱性,使它们容易从高密度的稳定状态转变为低密度状态,在某些情况下,导致灭绝的危险。在这种情况下,制定有效的休渔期政策以确保渔业资源的可持续发展已成为一个紧迫的问题。本文提出了一个由具有多个稳定状态和线性收获率的两个子方程组成的反应-扩散模型来描述捕捞季节在封闭和开放之间的连续切换。我们为捕鱼禁令的持续时间定义一个阈值T¯∗。当T¯≤T¯∗时,平凡稳定状态是全局渐近稳定的。周期解的唯一性通常是一个具有数学挑战性的问题。然而,利用比较定理,我们发现相关ODE系统周期解的唯一性条件也适用于我们的模型。具体地说,在一定条件下,当T¯> T¯∗,我们给出了全局渐近稳定周期解存在的充分条件。最后,我们提供讨论和数值模拟来说明我们的发现。
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引用次数: 0
A multi-season epidemic model with random genetic drift and transmissibility. 具有随机遗传漂变和可传染性的多季节流行病模型。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-12 DOI: 10.1007/s00285-025-02308-8
Tom Britton, Andrea Pugliese

We consider a model for the spread of an influenza-like disease in which, between seasons, the virus makes a random genetic drift (reducing immunity) and obtains a new random transmissibility (closely related to R 0 ). Given the immunity status at the start of season k, i.e. the community distribution of years since last infection and their associated immunity levels, the outcome of the epidemic season k, characterized by the effective reproduction number R e ( k ) and the fractions infected in the different immunity groups z ( k ) , is determined by the random genetic drift and transmissibility. It is shown that the community immunity status of consecutive seasons, is an ergodic Markov chain, which converges to a stationary distribution. More analytical progress is made for the case where immunity only lasts for one season: we then characterize the stationary distribution of the community fraction having partial immunity (from being infected last season) as well as the stationary distribution of ( R e ( k ) , z ( k ) ) , and the conditional distribution of z ( k ) given R e ( k ) . The effective reproduction number R e ( k ) is closely related to the initial exponential growth rate ρ ( k ) of the outbreak, a quantity which can be estimated early in the epidemic season. As a consequence, this conditional distribution may be used for predicting the final size of the epidemic based on its initial growth and immunity status.

我们考虑一种流感样疾病的传播模型,在季节之间,病毒进行随机遗传漂变(降低免疫力)并获得新的随机传播力(与r0密切相关)。鉴于k季节开始时的免疫状况,即自上次感染以来的年份群落分布及其相关的免疫水平,以有效繁殖数R e (k)和不同免疫组中感染的分数z (k)为特征的k流行季节的结果由随机遗传漂变和传播性决定。结果表明,连续季节的群体免疫状态是一条遍历马尔可夫链,并收敛于平稳分布。对于免疫仅持续一个季节的情况,我们进行了更多的分析进展:然后我们描述了具有部分免疫(从上一季节感染)的社区分数的平稳分布,以及(R e (k), z (k))的平稳分布,以及给定R e (k)的z (k)的条件分布。有效繁殖数R e (k)与暴发的初始指数增长率ρ (k)密切相关,ρ (k)可在流行季节早期估计。因此,该条件分布可用于根据其初始生长和免疫状态预测该流行病的最终规模。
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引用次数: 0
Competitive exclusion in age-structured populations. 年龄结构人群中的竞争性排斥。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-11 DOI: 10.1007/s00285-025-02311-z
Xi Huo, Hao Kang, Shuang Liu, Shigui Ruan

Competitive exclusion principle, which states that two or more species limited by the same resource cannot coexist indefinitely, is a very common phenomenon in population dynamics. It is well-known that competitive exclusion principle occurs in deterministic competition models, diffusive competition models, and evolutionary competition models. In this paper, we consider an age-structured competition model among N species and obtain an interesting result: under suitable scaled birth and death rates, the species with the smallest maximum age always wins the competition to exclude the other species; that is, the competitive exclusion principle occurs in age-structured competition models.

竞争排斥原则是种群动力学中一个非常普遍的现象,它指出受同一资源限制的两个或两个以上物种不能无限期共存。众所周知,竞争排斥原理存在于确定性竞争模型、扩散竞争模型和进化竞争模型中。本文考虑了N个物种之间的年龄结构竞争模型,得到了一个有趣的结果:在合适的比例生死率下,最大年龄最小的物种总是在竞争中获胜,并将其他物种排除在外;也就是说,竞争排斥原理出现在年龄结构竞争模型中。
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引用次数: 0
Correction: Multi-compartmental staged progression endemic models with fast transitions. 更正:具有快速过渡的多室分阶段进展地方性模型。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-10 DOI: 10.1007/s00285-025-02310-0
Luis Sanz-Lorenzo, Rafael Bravo de la Parra, Jean-Christophe Poggiale, Pierre Auger
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引用次数: 0
Coclique level structure for stochastic chemical reaction networks. 随机化学反应网络的柯立克能级结构。
IF 2.3 4区 数学 Q2 BIOLOGY Pub Date : 2025-11-10 DOI: 10.1007/s00285-025-02261-6
Simone Bruno, Yi Fu, Felipe A Campos, Domitilla Del Vecchio, Ruth J Williams

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding of how chemical reaction rate parameters impact the stochastic behavior of these systems. One property of interest is mean first passage times (MFPTs) between states. However, deriving explicit formulas for MFPTs can be highly complex. In order to address this problem, we first introduce the concept of [Formula: see text] and develop theorems to determine whether certain SCRNs have this feature by studying associated graphs. Additionally, we develop an algorithm to identify, under specific assumptions, all possible coclique level structures associated with a given SCRN. Finally, we demonstrate how the presence of such a structure in a SCRN allows us to derive closed form formulas for both upper and lower bounds for the MFPTs. Our methods can be applied to SCRNs taking values in a generic finite state space and can also be applied to models with non-mass-action kinetics. We illustrate our results with examples from the biological areas of epigenetics, neurobiology and ecology.

连续时间马尔可夫链通常被用作化学反应网络随机行为的模型。更准确地说,这些随机化学反应网络(SCRNs)经常被用来获得化学反应速率参数如何影响这些系统随机行为的机理理解。感兴趣的一个属性是状态之间的平均首次通过时间(MFPTs)。然而,为mfpt推导显式公式可能非常复杂。为了解决这个问题,我们首先引入了[公式:见文本]的概念,并通过研究相关图来开发定理,以确定某些scrn是否具有此特征。此外,我们开发了一种算法,在特定的假设下,识别与给定SCRN相关的所有可能的共团水平结构。最后,我们演示了这种结构在SCRN中的存在如何使我们能够推导出mfpt的上界和下界的封闭形式公式。我们的方法可以应用于在一般有限状态空间中取值的scrn,也可以应用于具有非质量作用动力学的模型。我们用来自表观遗传学、神经生物学和生态学等生物学领域的例子来说明我们的结果。
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引用次数: 0
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