Bulletin of Mathematical Biology最新文献

{"title":"An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions.","authors":"Samuel A Isaacson, Ying Zhang","doi":"10.1007/s11538-024-01392-z","DOIUrl":"10.1007/s11538-024-01392-z","url":null,"abstract":"<p><p>We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form <math><mrow><mtext>A</mtext> <mo>+</mo> <mtext>B</mtext> <mo>↔</mo> <mtext>C</mtext></mrow> </math> . A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"13"},"PeriodicalIF":2.0,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142799410","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":"[PSI]-CIC: A Deep-Learning Pipeline for the Annotation of Sectored Saccharomyces cerevisiae Colonies.","authors":"Jordan Collignon, Wesley Naeimi, Tricia R Serio, Suzanne Sindi","doi":"10.1007/s11538-024-01379-w","DOIUrl":"10.1007/s11538-024-01379-w","url":null,"abstract":"<p><p>The <math><mrow><mo>[</mo> <mi>P</mi> <mi>S</mi> <msup><mi>I</mi> <mo>+</mo></msup> <mo>]</mo></mrow> </math> prion phenotype in yeast manifests as a white, pink, or red color pigment. Experimental manipulations destabilize prion phenotypes, and allow colonies to exhibit <math><mrow><mo>[</mo> <mi>p</mi> <mi>s</mi> <msup><mi>i</mi> <mo>-</mo></msup> <mo>]</mo></mrow> </math> (red) sectored phenotypes within otherwise completely white colonies. Further investigation of the size and frequency of sectors that emerge as a result of experimental manipulation is capable of providing critical information on mechanisms of prion curing, but we lack a way to reliably extract this information. Images of experimental colonies exhibiting sectored phenotypes offer an abundance of data to help uncover molecular mechanisms of sectoring, yet the structure of sectored colonies is ignored in traditional biological pipelines. In this study, we present [PSI]-CIC, the first computational pipeline designed to identify and characterize features of sectored yeast colonies. To overcome the barrier of a lack of manually annotated data of colonies, we develop a neural network architecture that we train on synthetic images of colonies and apply to real images of <math><mrow><mo>[</mo> <mi>P</mi> <mi>S</mi> <msup><mi>I</mi> <mo>+</mo></msup> <mo>]</mo></mrow> </math> , <math><mrow><mo>[</mo> <mi>p</mi> <mi>s</mi> <msup><mi>i</mi> <mo>-</mo></msup> <mo>]</mo></mrow> </math> , and sectored colonies. In hand-annotated experimental images, our pipeline correctly predicts the state of approximately 95% of colonies detected and frequency of sectors in approximately 89.5% of colonies detected. The scope of our pipeline could be extended to categorizing colonies grown under different experimental conditions, allowing for more meaningful and detailed comparisons between experiments. Our approach streamlines the analysis of sectored yeast colonies providing a rich set of quantitative metrics and provides insight into mechanisms driving the curing of prion phenotypes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"12"},"PeriodicalIF":2.0,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11624247/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142784208","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":"Identifying Markov Chain Models from Time-to-Event Data: An Algebraic Approach.","authors":"Ovidiu Radulescu, Dima Grigoriev, Matthias Seiss, Maria Douaihy, Mounia Lagha, Edouard Bertrand","doi":"10.1007/s11538-024-01385-y","DOIUrl":"10.1007/s11538-024-01385-y","url":null,"abstract":"<p><p>Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"11"},"PeriodicalIF":2.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766486","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":"Targeting CD4+ T cell Exhaustion to Improve Future Immunotherapy Strategies.","authors":"Tyler Simmons, Doron Levy","doi":"10.1007/s11538-024-01389-8","DOIUrl":"10.1007/s11538-024-01389-8","url":null,"abstract":"<p><p>As of late, reinvigoration of exhausted T cells as a form of immunotherapy against cancer has been a promising strategy. However, inconsistent results highlight the uncertainties in the current understanding of cellular exhaustion and the need for research and better treatment design. In our previous work, we utilized mathematical modeling and analysis to recapitulate and complement the biological understanding of exhaustion in response to growing tumors. The results of this work recognized that the population size of progenitor exhausted CD8+ T cells played a larger factor in tumor control compared to cytotoxic abilities. From this notion, it was theorized that exhaustion in CD4+ T cells, which are known to help coordinate and promote the size of the CD8+ T cell response, would be a significant component of tumor control. To test this theory, this paper expands on the previous mathematical framework by incorporating CD4+ T cells and the exhaustion they face in response to tumoral settings. Analysis of this model supports our theory, indicating that targeting CD4+ T cell exhaustion would have a potentially large impact on tumor burden and should be investigated along with current immunotherapy strategies of exhausted CD8+ T cell reinvigoration. Ultimately, this work narrows the scope of future research, providing a potential target for improved therapeutic efforts.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"10"},"PeriodicalIF":2.0,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766489","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":"A Simplified Mathematical Model for Cell Proliferation in a Tissue-Engineering Scaffold.","authors":"Amy María Sims, Mona James, Sai Kunnatha, Shreya Srinivasan, Haniyeh Fattahpour, Ashok Joseph, Paul Joseph, Pejman Sanaei","doi":"10.1007/s11538-024-01390-1","DOIUrl":"10.1007/s11538-024-01390-1","url":null,"abstract":"<p><p>While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior-particularly nutrient consumption and depletion within the scaffold-has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. This work presents a comprehensive continuum model for cell proliferation within two-dimensional tissue-engineering scaffolds. Through mathematical modeling and asymptotic analysis based on the small aspect ratio of the scaffolds, the study aims to reduce computational burdens and solve mathematical models for tissue growth within porous scaffolds. The model incorporates fluid dynamics of nutrient feed flow, nutrient transport, cell concentration, and tissue growth, considering the evolving scaffold porosity due to cell proliferation, with the crux of the work establishing the ideal pore shape for channels within the tissue-engineering scaffold to obtain the maximum tissue growth. We investigate scaffolds with specific two-dimensional initial porosity profiles, and our results show that scaffolds which are uniformly graded in porosity throughout their depth promote more tissue growth.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"9"},"PeriodicalIF":2.0,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142766483","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":"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":"10.1007/s11538-024-01373-2","url":null,"abstract":"<p><p>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 (K_on/K_off) 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 = K_on/(K_off + d_v + r), where d_v is the virus decay rate and r is the infection growth rate. Because in vivo d_v can be large, the amount of binding as well as the effect of K_off on binding are substantially reduced. When neutralization is added, the effect of K_off is similarly small which may help explain the relatively high K_off 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 K_off in vivo may point to mechanisms of neutralization beyond stoichiometry. Our results suggest reporting K_on and K_off separately, rather than focusing on affinity, until the situation is better resolved both experimentally and theoretically.</p>","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}

{"title":"Multi-Grid Reaction-Diffusion Master Equation: Applications to Morphogen Gradient Modelling.","authors":"Radek Erban, Stefanie Winkelmann","doi":"10.1007/s11538-024-01377-y","DOIUrl":"10.1007/s11538-024-01377-y","url":null,"abstract":"<p><p>The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"6"},"PeriodicalIF":2.0,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11602816/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142726205","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":"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":"<p><p>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.</p>","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}

{"title":"Genome Galaxy Identified by the Circular Code Theory.","authors":"Christian J Michel, Jean-Sébastien Sereni","doi":"10.1007/s11538-024-01366-1","DOIUrl":"10.1007/s11538-024-01366-1","url":null,"abstract":"<p><p>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.</p>","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}

{"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":"<p><p>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.</p>","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}