Bulletin of Mathematical Biology最新文献

{"title":"Whole-Colony Dynamic Energy Budget Model for Bumble Bees: Assessing the Impact of Wildflower Patches on Crop Pollination.","authors":"Pau Capera-Aragones, Joany Mariño, Amy Hurford, Rebecca C Tyson, Eric Foxall","doi":"10.1007/s11538-025-01448-8","DOIUrl":"10.1007/s11538-025-01448-8","url":null,"abstract":"<p><p>Bumble bees are important pollinators of many crops around the world. In recent decades, agricultural intensification has resulted in significant declines in bumble bee populations and the pollination services they provide. Empirical studies have shown that this trend can be reversed by enhancing the agricultural landscape, for example, by placing wildflower patches adjacent to crops. Despite the empirical evidence, the mechanisms behind these positive effects are not fully understood. Theoretical studies, in the form of mathematical or computational models, have proven useful in providing insights, but the complexity of the underlying system means that certain factors remain unexplored. In this work, we build a unique model coupling a whole-colony Dynamic Energy Budget (DEB) approach for population dynamics to a Maximum Entropy (MaxEnt) principle formulation for the spatial distribution of foraging bees. The use of a DEB to asses whole-colony energy budgets, and its coupling to a spacial model is novel. The use of MaxEnt to predict foraging spatial distributions is still in its early stages, and our work highlights its potential to advance and expand upon the traditional assumptions of the Ideal Free Distribution. We use the developed model to asses the possible benefits and drawbacks of planting wildflower nearby crops for crop pollination services. We answer questions of when should wildflowers bloom, how many should we plant, which type of wildflowers, and where should we place them.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"83"},"PeriodicalIF":2.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12095363/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109668","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":"Inference of Pairwise Interactions from Strain Frequency Data Across Settings and Context-Dependent Mutual Invasibilities.","authors":"Thi Minh Thao Le, Sten Madec, Erida Gjini","doi":"10.1007/s11538-025-01450-0","DOIUrl":"10.1007/s11538-025-01450-0","url":null,"abstract":"<p><p>We propose a method to estimate pairwise strain interactions from population-level frequencies across different endemic settings. We apply the framework of replicator dynamics, derived from a multi-strain SIS model with co-colonization, to extract from 5 datasets the fundamental backbone of strain interactions. In our replicator, each pairwise invasion fitness explicitly arises from local environmental context and trait variations between strains. We adopt the simplest formulation for multi-strain coexistence, where context is encoded in basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and mean global susceptibility to co-colonization k, and trait variations <math><msub><mi>α</mi> <mrow><mi>ij</mi></mrow> </msub> </math> capture pairwise deviations from k. We integrate Streptococcus pneumoniae serotype frequencies and serotype identities collected from 5 environments: epidemiological surveys in Denmark, Nepal, Iran, Brazil and Mozambique, and mechanistically link their distributions. Our results have twofold implications. First, we offer a new proof-of-concept in the inference of multi-species interactions based on cross-sectional data. We also discuss 2 key aspects of the method: the site ordering for sequential fitting, and stability constraints on the dynamics. Secondly, we effectively estimate at high-resolution more than 70% of the <math><mrow><mn>92</mn> <mo>×</mo> <mn>92</mn></mrow> </math> pneumococcus serotype interaction matrix in co-colonization, allowing for further projections and hypotheses testing. We show that, in these bacteria, both within- and between- serotype interaction coefficients' distribution emerge to be unimodal, their difference in mean broadly reflecting stability assumptions on serotype coexistence. This framework enables further model calibration to global data: cross-sectional across sites, or longitudinal in one site over time, - and should allow a more robust and integrated investigation of intervention effects in such biodiverse ecosystems.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"82"},"PeriodicalIF":2.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12095429/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109662","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":"Impacts of Tempo and Mode of Environmental Fluctuations on Population Growth: Slow- and Fast-Limit Approximations of Lyapunov Exponents for Periodic and Random Environments.","authors":"Pierre Monmarché, Sebastian J Schreiber, Édouard Strickler","doi":"10.1007/s11538-025-01443-z","DOIUrl":"10.1007/s11538-025-01443-z","url":null,"abstract":"&lt;p&gt;&lt;p&gt;Populations consist of individuals living in different states and experiencing temporally varying environmental conditions. Individuals may differ in their geographic location, stage of development (e.g., juvenile versus adult), or physiological state (infected or susceptible). Environmental conditions may vary due to abiotic (e.g. temperature) or biotic (e.g. resource availability) factors. As the survival, growth, and reproduction of individuals depend on their state and environmental conditions, environmental fluctuations often impact population growth. Here, we examine to what extent the tempo and mode of these fluctuations matter for population growth. We model population growth for a population with d individual states and experiencing N different environmental states. The models are switching, linear ordinary differential equations &lt;math&gt; &lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;'&lt;/mo&gt;&lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mi&gt;A&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;σ&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;ω&lt;/mi&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; where &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mi&gt;d&lt;/mi&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; corresponds to the population densities in the d individual states, &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; is a piece-wise constant function representing the fluctuations in the environmental states &lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; , &lt;math&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt; is the frequency of the environmental fluctuations, and &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;)&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;A&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; are Metzler matrices representing the population dynamics in the environmental states &lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; . &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; can either be a periodic function or correspond to a continuous-time Markov chain. Under suitable conditions, there exists a Lyapunov exponent &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Λ&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;ω&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; such that &lt;math&gt; &lt;mrow&gt;&lt;msub&gt;&lt;mo&gt;lim&lt;/mo&gt; &lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;→&lt;/mo&gt; &lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt; &lt;/msub&gt; &lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mi&gt;t&lt;/mi&gt;&lt;/mfrac&gt; &lt;mo&gt;log&lt;/mo&gt; &lt;msub&gt;&lt;mo&gt;∑&lt;/mo&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt; &lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;t&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mi&gt;Λ&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;ω&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; for all non-negative, non-zero initial conditions x(0) (with probability one in the random case). For both random and periodic switching, we derive analytical first-order and second-order a","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"81"},"PeriodicalIF":2.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109656","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":"Estimating Hidden Cholera Burden and Intervention Effectiveness.","authors":"Murshed Ahmed Ovi, Andrei Afilipoaei, Hao Wang","doi":"10.1007/s11538-025-01460-y","DOIUrl":"10.1007/s11538-025-01460-y","url":null,"abstract":"<p><p>Cholera remains a significant public health threat in many parts of the world, with differing levels of compliance to intervention strategies and undocumented cases contributing to reservoir contamination with Vibrio cholerae at varying rates alongside reported cases. To address this, we incorporate an inapparent cholera-infected compartment into the iSIR model and equip it with parameters depicting vaccination and compliance levels for water and food sanitation, handwashing, and safe fecal disposal. Our model shows that the bacteria shedding from the inapparent infection can significantly affect the spread of cholera. Also, we identify that lowering the bacteria ingestion rate among the susceptible and controlling the bacteria shedding from reported infected are two key components for obtaining a disease-free state in the long run. The model fitting to cholera outbreaks in Haiti, Kenya, Malawi, and Zimbabwe implies that at least 88.5% of cases are inapparent, with the first reporting appearing up to 11 weeks after the start of the outbreak. Additionally, we find that the combination of water and food sanitation and handwashing is the most effective intervention strategy for reducing the cholera outbreak peak if compliance with these measures remains at moderate or high levels. However, with low compliance, safe fecal disposal of the reported infected individuals combined with vaccination coverage of the susceptible population is suggested to obtain the lowest outbreak peak.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"80"},"PeriodicalIF":2.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109714","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":"Noise-Driven Transitions in Collective Foraging of Ant Colonies.","authors":"Tao Feng, Chenbo Liu, Russell Milne","doi":"10.1007/s11538-025-01461-x","DOIUrl":"10.1007/s11538-025-01461-x","url":null,"abstract":"<p><p>Understanding the collective foraging strategies of ant colonies is essential for studying self-organization and collective behavior in biological systems. This study introduces a simplified foraging model that classifies worker roles into two functional groups-available workers and active foragers-providing a concise yet effective framework for analyzing foraging dynamics. Our model effectively reproduces the foraging dynamics observed in more complex three-dimensional models, while taking a more tractable form that is more conducive to mathematical analysis. We examine the effects of stochasticity in mortality rates of foragers and workers on foraging state transitions, with a particular emphasis on the critical noise threshold, transition probability, and transition time. While the critical noise threshold is reduced by stochasticity in either of the two mortality rates, that of active foragers has the greatest effect. We find that slight increases in the arrival rate of available workers and the recruitment rate of active foragers enhance the colony's resilience to environmental stochasticity, suggesting that colonies can self-regulate via a feedback loop of foraging and recruitment to maintain their foraging while their environment changes around them. In contrast, varying the mortality rate of available workers had little effect on this resilience, analogously to experimental observations that older or unhealthy worker ants disproportionately transition into foraging roles. This study not only advances our understanding of ant foraging dynamics by simplifying complex models but also provides valuable insights into the robustness of foraging activities under varying environmental conditions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"78"},"PeriodicalIF":2.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109620","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":"Homogenization Reveals Large-Scale Dynamics in the Spread of Chronic Wasting Disease.","authors":"Jen McClure, James Powell","doi":"10.1007/s11538-025-01456-8","DOIUrl":"10.1007/s11538-025-01456-8","url":null,"abstract":"<p><p>Thresholds in environmental transmission can significantly alter the dynamics of disease spread in wildlife. However, the impact of thresholds in landscapes with high spatial variability is not well understood. We investigate this phenomenon in chronic wasting disease (CWD), a degenerative cervid illness exhibiting direct transmission between individuals and indirect transmission through environmental hazard. The indirect pathway exhibits threshold behavior analogous to a strong Allee effect. We derive a partial differential equation (PDE) model for CWD on the scale of hours and tens of meters. Leveraging highly variable landscape structure, we homogenize this model to yield an asymptotically accurate approximal model on the scale of years and kilometers. Our homogenized model describes the aggregate effect of thresholded transmission on large scales - to our knowledge, the first time such a description has been identified. The model predicts that direct transmission in CWD will lead to pulled fronts, whereas indirect transmission generates pushed fronts. Pushed fronts allow CWD to spread even when infectives infect less than one susceptible on average. We use a hypothetical binary distribution of habitat types to showcase the homogenized model's ability to predict how distribution of cover in a landscape can influence CWD spread and potential mitigation efforts.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"79"},"PeriodicalIF":2.0,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12092501/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144109654","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":"Spatial Segregation Across Travelling Fronts in Individual-Based and Continuum Models for the Growth of Heterogeneous Cell Populations.","authors":"José A Carrillo, Tommaso Lorenzi, Fiona R Macfarlane","doi":"10.1007/s11538-025-01452-y","DOIUrl":"10.1007/s11538-025-01452-y","url":null,"abstract":"<p><p>We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they are less compressed, and thus their movement occurs down the gradient of the cellular pressure. The cellular pressure is defined as a weighted sum of the densities (i.e. the volume fractions) of cells with different phenotypes. To translate into mathematical terms the idea that cells with distinct phenotypes have different morphological and mechanical properties, both the cell mobility and the weighted amount the cells contribute to the cellular pressure vary with their phenotype. We formally derive this model as the continuum limit of an on-lattice individual-based model, where cells are represented as single agents undergoing a branching biased random walk corresponding to phenotype-dependent and pressure-regulated cell division, death, and movement. Then, we study travelling wave solutions whereby cells with different phenotypes are spatially segregated across the invading front. Finally, we report on numerical simulations of the two models, demonstrating excellent agreement between them and the travelling wave analysis. The results presented here indicate that inter-cellular variability in mobility can support the maintenance of spatial segregation across invading fronts, whereby cells with a higher mobility drive invasion by occupying regions closer to the front edge.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"77"},"PeriodicalIF":2.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12089248/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144092833","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":"The Effect of Antibodies in the Presence of Syncytia During Viral Infections.","authors":"Isabelle Beach, Hana M Dobrovolny","doi":"10.1007/s11538-025-01463-9","DOIUrl":"10.1007/s11538-025-01463-9","url":null,"abstract":"<p><p>Syncytia formation occurs when viruses fuse cells together, creating multinucleated cells. By spreading through fusion, the virus avoids the extracellular environment, protecting it from antibodies that can neutralize the virus. To investigate the effect of this protection, we used a mathematical model to simulate viral infections that spread via both cell-free transmission and syncytia formation and included the effect of antibodies. We compared infections with high, low, and no syncytia fusion, finding that even a low rate of syncytia formation affects infection dynamics and can hinder antibody effectiveness. Specifically, we find that the presence of syncytia increases the viral load, delays the time of peak, and increases the number of cells infected by the virus as compared to infections without syncytia formation. This mathematical model sheds light on how syncytia formation shields viruses from antibodies, aiding in spread of the virus in spite of a robust immune response.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"76"},"PeriodicalIF":2.0,"publicationDate":"2025-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144092834","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":"Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation.","authors":"Kashvi Srivastava, Justin Eilertsen, Victoria Booth, Santiago Schnell","doi":"10.1007/s11538-025-01451-z","DOIUrl":"10.1007/s11538-025-01451-z","url":null,"abstract":"<p><p>The application of the standard quasi-steady-state approximation to the Michaelis-Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, <math><msub><mi>e</mi> <mn>0</mn></msub> </math> , to the Michaelis constant, <math><msub><mi>K</mi> <mi>M</mi></msub> </math> , decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation as compared to other quasi-steady-state reductions in its proximity. Using standard tools from the analysis of ordinary differential equations, we show that while <math> <mrow><msub><mi>e</mi> <mn>0</mn></msub> <mo>/</mo> <msub><mi>K</mi> <mi>M</mi></msub> </mrow> </math> provides an indication of the standard quasi-steady-state approximation's asymptotic accuracy, the standard quasi-steady-state approximation's predominance relies on a small ratio of <math><msub><mi>e</mi> <mn>0</mn></msub> </math> to the Van Slyke-Cullen constant, K. Here, we define the predominance of a quasi-steady-state reduction when it offers the highest approximation accuracy among other well-known reductions with overlapping validity conditions. We conclude that the magnitude of <math> <mrow><msub><mi>e</mi> <mn>0</mn></msub> <mo>/</mo> <mi>K</mi></mrow> </math> offers the most accurate measure of the validity of the standard quasi-steady-state approximation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"73"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084256/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085996","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":"Modelling Population-Level Hes1 Dynamics: Insights from a Multi-framework Approach.","authors":"Gesina Menz, Stefan Engblom","doi":"10.1007/s11538-025-01447-9","DOIUrl":"10.1007/s11538-025-01447-9","url":null,"abstract":"<p><p>Mathematical models of living cells have been successively refined with advancements in experimental techniques. A main concern is striking a balance between modelling power and the tractability of the associated mathematical analysis. In this work we model the dynamics for the transcription factor Hairy and enhancer of split-1 (Hes1), whose expression oscillates during neural development, and which critically enables stable fate decision in the embryonic brain. We design, parametrise, and analyse a detailed spatial model using ordinary differential equations (ODEs) over a grid capturing both transient oscillatory behaviour and fate decision on a population-level. We also investigate the relationship between this ODE model and a more realistic grid-based model involving intrinsic noise using mostly directly biologically motivated parameters. While we focus specifically on Hes1 in neural development, the approach of linking deterministic and stochastic grid-based models shows promise in modelling various biological processes taking place in a cell population. In this context, our work stresses the importance of the interpretability of complex computational models into a framework which is amenable to mathematical analysis.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 6","pages":"74"},"PeriodicalIF":2.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084287/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144086005","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}