Bulletin of Mathematical Biology最新文献

Dynamics of Antibody Binding and Neutralization during Viral Infection.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-28 DOI: 10.1007/s11538-024-01373-2

Zhenying Chen, Hasan Ahmed, Cora Hirst, Rustom Antia

{"title":"Dynamics of Antibody Binding and Neutralization during Viral Infection.","authors":"Zhenying Chen, Hasan Ahmed, Cora Hirst, Rustom Antia","doi":"10.1007/s11538-024-01373-2","DOIUrl":"https://doi.org/10.1007/s11538-024-01373-2","url":null,"abstract":"In vivo in infection, virions are constantly produced and die rapidly. In contrast, most antibody binding assays do not include such features. Motivated by this, we considered virions with n = 100 binding sites in simple mathematical models with and without the production of virions. In the absence of viral production, at steady state, the distribution of virions by the number of sites bound is given by a binomial distribution, with the proportion being a simple function of antibody affinity (Kon/Koff) and concentration; this generalizes to a multinomial distribution in the case of two or more kinds of antibodies. In the presence of viral production, the role of affinity is replaced by an infection analog of affinity (IAA), with IAA = Kon/(Koff + dv + r), where dv is the virus decay rate and r is the infection growth rate. Because in vivo dv can be large, the amount of binding as well as the effect of Koff on binding are substantially reduced. When neutralization is added, the effect of Koff is similarly small which may help explain the relatively high Koff reported for many antibodies. We next show that the n+2-dimensional model used for neutralization can be simplified to a 2-dimensional model. This provides some justification for the simple models that have been used in practice. A corollary of our results is that an unexpectedly large effect of Koff in vivo may point to mechanisms of neutralization beyond stoichiometry. Our results suggest reporting Kon and Koff separately, rather than focusing on affinity, until the situation is better resolved both experimentally and theoretically.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"8"},"PeriodicalIF":2.0,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142750116","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

Multi-Grid Reaction-Diffusion Master Equation: Applications to Morphogen Gradient Modelling. 多网格反应-扩散主方程：形态发生梯度模型的应用

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-27 DOI: 10.1007/s11538-024-01377-y

Radek Erban, Stefanie Winkelmann

引用次数: 0

Parameter Estimation and Identifiability in Kinetic Flux Profiling Models of Metabolism. 代谢动力学通量剖析模型中的参数估计和可识别性。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-27 DOI: 10.1007/s11538-024-01386-x

Breanna Guppy, Colleen Mitchell, Eric B Taylor

{"title":"Parameter Estimation and Identifiability in Kinetic Flux Profiling Models of Metabolism.","authors":"Breanna Guppy, Colleen Mitchell, Eric B Taylor","doi":"10.1007/s11538-024-01386-x","DOIUrl":"10.1007/s11538-024-01386-x","url":null,"abstract":"Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"7"},"PeriodicalIF":2.0,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11602815/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142726209","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}

引用次数: 0

Genome Galaxy Identified by the Circular Code Theory. 用循环密码理论识别基因组星系

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-26 DOI: 10.1007/s11538-024-01366-1

Christian J Michel, Jean-Sébastien Sereni

{"title":"Genome Galaxy Identified by the Circular Code Theory.","authors":"Christian J Michel, Jean-Sébastien Sereni","doi":"10.1007/s11538-024-01366-1","DOIUrl":"https://doi.org/10.1007/s11538-024-01366-1","url":null,"abstract":"The genome galaxy identified in bacteria is studied by expressing the reading frame retrieval (RFR) function according to the YZ-content (GC-, AG- and GT-content) of bacterial codons. We have developed a simple probabilistic model for ambiguous sequences in order to show that the RFR function is a measure of the gene reading frame retrieval. Indeed, the RFR function increases with the ratio of ambiguous sequences and the ratio of ambiguous sequences decreases when the codon usage dispersion increases. The classical GC-content is the best parameter for characterizing the upper arm, which is related to bacterial genes with a low GC-content, and the lower arm, which is related to bacterial genes with a high GC-content. The galaxy center has a GC-content around 0.5. Then, these results are confirmed by expressing the GC-content of bacterial codons as a function of the codon usage dispersion. Finally, the bacterial genome galaxy is better described with the GC3-content in the 3rd codon site compared to the GC1-content and GC2-content in the 1st and 2nd codons sites, respectively. Whereas the codon usage is used extensively by biologists, its dispersion, which is an important parameter to reveal this genome galaxy, is surprisingly little known and unused. Therefore, we have developed a mathematical theory of codon usage dispersion by deriving several formulæ. It shows three important parameters in codon usage: the minimum and maximum codon probabilities and the number of codons with high frequency, i.e. with a probability at least 1/64. By applying this theory to the evolution of the genetic code, we see that bacteria have optimised the number of codons with high frequency to maximise the codon dispersion, thus maximising the capacity to retrieve the reading frame in genes. The derived formulæ of dispersion can be easily extended to any weighted code over a finite alphabet.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"5"},"PeriodicalIF":2.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142715477","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

Analysis of a Single Cell RNA-seq Workflow by Random Matrix Theory Methods. 用随机矩阵理论方法分析单细胞 RNA-seq 工作流程。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-25 DOI: 10.1007/s11538-024-01376-z

Sivan Leviyang

{"title":"Analysis of a Single Cell RNA-seq Workflow by Random Matrix Theory Methods.","authors":"Sivan Leviyang","doi":"10.1007/s11538-024-01376-z","DOIUrl":"10.1007/s11538-024-01376-z","url":null,"abstract":"Single cell RNA-seq (scRNAseq) workflows typically start with a count matrix and end with the clustering of sampled cells. While a range of methods have been developed to cluster scRNAseq datasets, no theoretical tools exist to explain why a particular cluster exists or why a hypothesized cluster is missing. Recently, several authors have shown that eigenvalues of scRNAseq count matrices can be approximated using random matrix models. In this work, we extend these previous works to the study of a scRNAseq workflow. We model scaled count matrices using random matrices with normally distributed entries. Using these random matrix models, we quantify the differential expression of a cluster and develop predictions for the workflow, and in particular clustering, as a function of the differential expression. We also use results from random matrix theory (RMT) to develop predictive formulas for portions of the scRNAseq workflow. Using simulated and real datasets, we show that our predictions are accurate if certain conditions hold on differential expression, with our RMT based predictions requiring particularly stringent condition. We find that real datasets violate these conditions, leading to bias in our predictions, but our predictions are better than a naive estimator and we point out future work that can improve the predictions. To our knowledge, our formulas represents the first predictive results for scRNAseq workflows.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"4"},"PeriodicalIF":2.0,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142709114","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

The Post-Kelly Strategy: A Negative Feedback Model of Reallocating Ant Foragers. 后凯利战略：重新分配蚂蚁觅食者的负反馈模型

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-23 DOI: 10.1007/s11538-024-01383-0

Kun Wei, Jiecong Wang

{"title":"The Post-Kelly Strategy: A Negative Feedback Model of Reallocating Ant Foragers.","authors":"Kun Wei, Jiecong Wang","doi":"10.1007/s11538-024-01383-0","DOIUrl":"https://doi.org/10.1007/s11538-024-01383-0","url":null,"abstract":"In ant foraging, the manner of group-mass recruitment demonstrates remarkable adaptability between tandem running and mass recruitment. In contrast to tandem running, where a leader recruits only one worker, the first phase of group-mass recruitment is characterized by strong invitations from leaders that result in a large group of recruits leaving the nest together in a rush, thereby accelerating the process of recruiting towards discovered resources. Furthermore, unlike sole mass recruitment, the influence of leaders during this first phase enhances the accuracy of information about food qualities and ensures a more rational allocation of recruits compared to simply following a dominant pheromone trail. In this study, we propose a model that integrates the Kelly criterion for the first phase of group-mass recruitment, followed by a post-Kelly strategy incorporating a delayed Pólya urn with two stages for the second phase of group-mass recruitment. The analytical process and simulation demonstrate that the Kelly criterion aims to maximize recruitment intensity during the initial foraging phase, employing crowd tactics to capture all available food sources and enhance competitiveness with other food-exploiting species. On the other hand, the post-Kelly strategy elucidates how the crowding negative feedback mitigates congestion resulting from overexploitation and improves overall efficiency in food exploitation.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"3"},"PeriodicalIF":2.0,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142695233","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

Discontinuity-Induced Dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model. 基于电导的自适应指数积分与火焰模型中的间断性诱导动力学

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-14 DOI: 10.1007/s11538-024-01384-z

Mathieu Desroches, Piotr Kowalczyk, Serafim Rodrigues

引用次数: 0

Pathophysiological Mechanisms of the Onset, Development, and Disappearance Phases of Skin Eruptions in Chronic Spontaneous Urticaria. 慢性自发性荨麻疹发病、发展和消退阶段的病理生理机制

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-14 DOI: 10.1007/s11538-024-01380-3

Sungrim Seirin-Lee, Shunsuke Takahagi, Michihiro Hide

{"title":"Pathophysiological Mechanisms of the Onset, Development, and Disappearance Phases of Skin Eruptions in Chronic Spontaneous Urticaria.","authors":"Sungrim Seirin-Lee, Shunsuke Takahagi, Michihiro Hide","doi":"10.1007/s11538-024-01380-3","DOIUrl":"10.1007/s11538-024-01380-3","url":null,"abstract":"Chronic spontaneous urticaria (CSU) is a typical example of an intractable skin disease with no clear cause and significantly affects daily life of patients. Because CSU is a human-specific disease and lacks proper animal model, there are many questions regarding its pathophysiological dynamics. On the other hand, most clinical symptoms of urticaria are notable as dynamic appearance of skin eruptions called wheals. In this study, we explored dynamics of wheal by dividing it into three phases using a mathematical model: onset, development, and disappearance. Our results suggest that CSU onset is critically associated with endovascular dynamics triggered by basophils positive feedback. In contrast, the development phase is regulated by mast cell dynamics via vascular gap formation. We also suggest a disappearance mechanism of skin eruptions in CSU through an extension of the mathematical model using qualitative and quantitative comparisons of wheal expansion data of real patients with urticaria. Our results suggest that the wheal dynamics of the three phases and CSU development are hierarchically related to endovascular and extravascular pathophysiological networks.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"1"},"PeriodicalIF":2.0,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11564288/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142615295","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}

引用次数: 0

Counting Cherry Reduction Sequences in Phylogenetic Tree-Child Networks is Counting Linear Extensions. 计算系统发育树-子网络中的樱桃还原序列就是计算线性延伸。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-09 DOI: 10.1007/s11538-024-01374-1

Tomás M Coronado, Joan Carles Pons, Gabriel Riera

引用次数: 0

Speed and Shape of Population Fronts with Density-Dependent Diffusion. 依赖密度扩散的种群前沿的速度和形状

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2024-11-09 DOI: 10.1007/s11538-024-01381-2

Beth M Stokes, Tim Rogers, Richard James

引用次数: 0