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Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations 随机基因表达振荡最小混合模型中的精确功率谱
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-06-10 DOI: 10.1137/23m1560914
Chen Jia, Hong Qian, Michael Q. Zhang
{"title":"Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations","authors":"Chen Jia, Hong Qian, Michael Q. Zhang","doi":"10.1137/23m1560914","DOIUrl":"https://doi.org/10.1137/23m1560914","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1204-1226, June 2024. <br/> Abstract. Stochastic oscillations in individual cells are usually characterized by a nonmonotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach to stochastic oscillations in a minimal hybrid model of stochastic gene expression including promoter state switching, protein synthesis and degradation, as well as a genetic feedback loop. The oscillations observed in our model are noise-induced since the deterministic theory predicts stable fixed points. The autocorrelated function, power spectrum, and steady-state distribution of protein concentration fluctuations are computed in closed form. Using the exactly solvable model, we illustrate sustained oscillations as a circular motion along a stochastic hysteresis loop induced by gene state switching. A triphasic stochastic bifurcation upon the increasing strength of negative feedback is observed, which reveals how stochastic bursts evolve into stochastic oscillations. In our model, oscillations tend to occur when the protein is relatively stable and when gene switching is relatively slow. Translational bursting is found to enhance the robustness and broaden the region of stochastic oscillations. These results provide deeper insights into R. Thomas’s two conjectures for single-cell gene expression kinetics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508787","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
Introduction to the SIAP Special Section on the Life Sciences 亚太统计所生命科学专刊简介
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-06-07 DOI: 10.1137/23m1606824
Simone Bianco, Jonathan E. Rubin
{"title":"Introduction to the SIAP Special Section on the Life Sciences","authors":"Simone Bianco, Jonathan E. Rubin","doi":"10.1137/23m1606824","DOIUrl":"https://doi.org/10.1137/23m1606824","url":null,"abstract":"","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141372131","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
Longitudinal Shear Flow over a Superhydrophobic Grating with Partially Invaded Grooves and Curved Menisci 带有部分内陷凹槽和弯曲半月板的超疏水光栅上的纵向剪切流
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-06-05 DOI: 10.1137/23m1616522
Ehud Yariv
{"title":"Longitudinal Shear Flow over a Superhydrophobic Grating with Partially Invaded Grooves and Curved Menisci","authors":"Ehud Yariv","doi":"10.1137/23m1616522","DOIUrl":"https://doi.org/10.1137/23m1616522","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1186-1203, June 2024. <br/> Abstract. We consider longitudinal shear flows over a superhydrophobic grating made up of a periodic array of grooves separated by infinitely thin slats, addressing the case where the liquid partially invades the grooves. We allow for curved menisci, specified via a depression angle at the contact line. We focus on the limit of small solid fractions where the length of the wetted portion of the slat is small compared with the period. Following an earlier analysis of the comparable flow over noninvaded grooves [O. Schnitzer, J. Fluid Mech., 820 (2017), pp. 580–603], this singular limit is treated using matched asymptotic expansions, with an outer region on the scale of a single period and an inner region on the scale of the wetted portion of the slat. The flow problem in both regions is solved using conformal mappings. Asymptotic matching yields a closed-form approximation for the slip length as a function of the solid fraction and depression angle.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552943","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
Realistic Pattern Formations on Surfaces by Adding Arbitrary Roughness 通过添加任意粗糙度在表面形成逼真图案
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-06-03 DOI: 10.1137/22m1518001
Siqing Li, Leevan Ling, Steven J. Ruuth, Xuemeng Wang
{"title":"Realistic Pattern Formations on Surfaces by Adding Arbitrary Roughness","authors":"Siqing Li, Leevan Ling, Steven J. Ruuth, Xuemeng Wang","doi":"10.1137/22m1518001","DOIUrl":"https://doi.org/10.1137/22m1518001","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1163-1185, June 2024. <br/> Abstract. We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies and angles of propagation are used to get periodic rough surfaces with analytic parametric equations. The amplitude of such surfaces is also an important variable in the provided eigenvalue analysis for the Laplace–Beltrami operator and in the generation of pattern formation. Numerical experiments show that the patterns become irregular as the amplitude and frequency of the rough surface increase. For the sake of easy generalization to closed manifolds, we propose a second construction method for rough surfaces, which uses random nodal values and discretized heat filters. We provide numerical evidence that both surface construction methods yield comparable patterns to those observed in real-life animals.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259022","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
Optimal Bacterial Resource Allocation Strategies in Batch Processing 批处理中的最佳细菌资源分配策略
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-31 DOI: 10.1137/22m1506328
Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé
{"title":"Optimal Bacterial Resource Allocation Strategies in Batch Processing","authors":"Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé","doi":"10.1137/22m1506328","DOIUrl":"https://doi.org/10.1137/22m1506328","url":null,"abstract":"SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The study of living microorganisms using resource allocation models has been key in elucidating natural behaviors of bacteria, by allowing allocation of microbial resources to be represented through optimal control strategies. The approach can also be applied to research in microbial cell factories, to investigate the optimal production of value-added compounds regulated by an external control. The latter is the subject of this paper, in which we study batch bioprocessing from a resource allocation perspective. Based on previous works, we propose a simple bacterial growth model accounting for the dynamics of the bioreactor and intracellular composition, and we analyze its asymptotic behavior and stability. Using optimization and optimal control theory, we study the production of biomass and metabolites of interest for infinite- and finite-time horizons. The resulting optimal control problems are studied using Pontryagin’s maximum principle and numerical methods, and the solutions found are characterized by the presence of the Fuller phenomenon (producing an infinite set of switching points occurring in a finite-time window) at the junctions with a second-order singular arc. The approach, inspired by biotechnological engineering, aims to shed light upon the role of cellular composition and resource allocation during batch processing and, at the same time, poses very interesting and challenging mathematical problems.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196806","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
First Hitting Time of a One-Dimensional Lévy Flight to Small Targets 一维莱维飞行对小目标的首次命中时间
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-29 DOI: 10.1137/23m1586239
Daniel Gomez, Sean D. Lawley
{"title":"First Hitting Time of a One-Dimensional Lévy Flight to Small Targets","authors":"Daniel Gomez, Sean D. Lawley","doi":"10.1137/23m1586239","DOIUrl":"https://doi.org/10.1137/23m1586239","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1140-1162, June 2024. <br/> Abstract. First hitting times (FHTs) describe the time it takes a random “searcher” to find a “target” and are used to study timescales in many applications. FHTs have been well-studied for diffusive search, especially for small targets, which is called the narrow capture or narrow escape problem. In this paper, we study the FHT to small targets for a one-dimensional superdiffusive search described by a Lévy flight. By applying the method of matched asymptotic expansions to a fractional differential equation we obtain an explicit asymptotic expansion for the mean FHT (MFHT). For fractional order [math] (describing a [math]-stable Lévy flight whose squared displacement scales as [math] in time [math]) and targets of radius [math], we show that the MFHT is order one for [math] and diverges as [math] for [math] and [math] for [math]. We then use our asymptotic results to identify the value of [math] which minimizes the average MFHT and find that (a) this optimal value of [math] vanishes for sparse targets and (b) the value [math] (corresponding to an inverse square Lévy search) is optimal in only very specific circumstances. We confirm our results by comparison to both deterministic numerical solutions of the associated fractional differential equation and stochastic simulations.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259062","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
Generalized Honeycomb-Structured Materials in the Subwavelength Regime 亚波长范围内的广义蜂窝结构材料
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-24 DOI: 10.1137/23m1559786
Borui Miao, Yi Zhu
{"title":"Generalized Honeycomb-Structured Materials in the Subwavelength Regime","authors":"Borui Miao, Yi Zhu","doi":"10.1137/23m1559786","DOIUrl":"https://doi.org/10.1137/23m1559786","url":null,"abstract":"","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102041","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
Inference of Interaction Kernels in Mean-Field Models of Opinion Dynamics 舆情动态均值场模型中的交互核推断
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-22 DOI: 10.1137/22m1544415
Weiqi Chu, Qin Li, M. A. Porter
{"title":"Inference of Interaction Kernels in Mean-Field Models of Opinion Dynamics","authors":"Weiqi Chu, Qin Li, M. A. Porter","doi":"10.1137/22m1544415","DOIUrl":"https://doi.org/10.1137/22m1544415","url":null,"abstract":"","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141111798","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
Asymptotic Analysis and Simulation of Mean First Passage Time for Active Brownian Particles in 1-D 一维活动布朗粒子平均首次通过时间的渐近分析与模拟
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-17 DOI: 10.1137/23m1593917
Sarafa A. Iyaniwura, Zhiwei Peng
{"title":"Asymptotic Analysis and Simulation of Mean First Passage Time for Active Brownian Particles in 1-D","authors":"Sarafa A. Iyaniwura, Zhiwei Peng","doi":"10.1137/23m1593917","DOIUrl":"https://doi.org/10.1137/23m1593917","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1079-1095, June 2024. <br/> Abstract. Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive Brownian particles, the MFPT of ABPs is much less developed. In this paper, we study the MFPT for ABPs in a 1-D domain with absorbing boundary conditions at both ends of the domain. To reveal the effect of swimming on the MFPT, we consider an asymptotic analysis in the weak-swimming or small Péclet ([math]) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to [math]. We explore the effects of the starting positions and starting orientations on the MFPT. Our analysis shows that if the starting orientations are biased towards one side of the domain, the MFPT as a function of the starting position becomes asymmetric about the center of the domain. The analytical results were confirmed by the numerical solutions of the full PDE model.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061644","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
Tick-Borne Pathogen Co-infection by Co-feeding on Incompetent Hosts: Global Convergence and Impact of Developmental Delay 蜱媒病原体通过与无行为能力的宿主同食而共同感染：全球趋同与发育延迟的影响
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-16 DOI: 10.1137/23m1577419
Xue Zhang, Jianhong Wu
{"title":"Tick-Borne Pathogen Co-infection by Co-feeding on Incompetent Hosts: Global Convergence and Impact of Developmental Delay","authors":"Xue Zhang, Jianhong Wu","doi":"10.1137/23m1577419","DOIUrl":"https://doi.org/10.1137/23m1577419","url":null,"abstract":"","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140966626","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
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