Journal of Theoretical Biology最新文献

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Optimisation of gene expression noise for cellular persistence against lethal events 优化基因表达噪音,使细胞持续对抗致死事件。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-25 DOI: 10.1016/j.jtbi.2024.111996
Pavol Bokes , Abhyudai Singh
{"title":"Optimisation of gene expression noise for cellular persistence against lethal events","authors":"Pavol Bokes ,&nbsp;Abhyudai Singh","doi":"10.1016/j.jtbi.2024.111996","DOIUrl":"10.1016/j.jtbi.2024.111996","url":null,"abstract":"<div><div>Bacterial cell persistence, crucial for survival under adverse conditions like antibiotic exposure, is intrinsically linked to stochastic fluctuations in gene expression. Certain genes, while inhibiting growth under normal circumstances, confer tolerance to antibiotics at elevated expression levels. The occurrence of antibiotic events lead to instantaneous cellular responses with varied survival probabilities correlated with gene expression levels. Notably, cells with lower protein concentrations face higher mortality rates. This study aims to elucidate an optimal strategy for protein expression conducive to cellular survival. Through comprehensive mathematical analysis, we determine the optimal burst size and frequency that maximise cell proliferation. Furthermore, we explore how the optimal expression distribution changes as the cost of protein expression to growth escalates. Our model reveals a hysteresis phenomenon, characterised by discontinuous transitions between deterministic and stochastic optima. Intriguingly, stochastic optima possess a noise floor, representing the minimal level of fluctuations essential for optimal cellular resilience.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"598 ","pages":"Article 111996"},"PeriodicalIF":1.9,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142741485","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
An analytical, numerical and experimental study of in-vitro SARS-CoV-2 evolution in Vero B4 cells 体外 SARS-CoV-2 在 Vero B4 细胞中演变的分析、数值和实验研究。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-23 DOI: 10.1016/j.jtbi.2024.112000
Matthew Nicol , Julian D.J. Sng , Yanshan Zhu , Sissy Therese Sonnleitner , Kirsty R. Short , Meagan Carney
{"title":"An analytical, numerical and experimental study of in-vitro SARS-CoV-2 evolution in Vero B4 cells","authors":"Matthew Nicol ,&nbsp;Julian D.J. Sng ,&nbsp;Yanshan Zhu ,&nbsp;Sissy Therese Sonnleitner ,&nbsp;Kirsty R. Short ,&nbsp;Meagan Carney","doi":"10.1016/j.jtbi.2024.112000","DOIUrl":"10.1016/j.jtbi.2024.112000","url":null,"abstract":"<div><div>We derive a numerical model representing the emergence and evolution of SARS-CoV-2 variants, informed by data from in-vitro passaging experiments in Vero B4 cells. We compare our numerical simulation results against probabilistic derivations of the expected probability of and time until the fittest variant becomes fixed in the population. Contrary to literature surrounding DNA viruses and eukaryotes where probabilities of fitness extremes are often modelled by exponential decaying tail, we show that above wildtype fitness differences for SARS-CoV-2 are actually best modelled by a heavy-tailed Fréchet distribution. Furthermore, we find that SARS-CoV-2 variants evolve through an essentially deterministic process rather than a diffusional one, with the dynamics driven by the fitness difference between the top variants rather than by the sampling/dilution process. An interesting consequence of this setting is that the number of variant virions, rather than their proportion, is a better predictor of the probability of fixation for a given variant.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"598 ","pages":"Article 112000"},"PeriodicalIF":1.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142717695","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
Noise-induced entrainment of the circadian clock by thermoperiods in tomato: A computational approach 番茄昼夜节律时钟在噪声诱导下受恒温周期影响:计算方法
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-22 DOI: 10.1016/j.jtbi.2024.111999
Ting Huang , Hengmin Lv , Yiting Shu , Jian Luo , Linxuan Yu , Bing Chen , Xin Sun , Xilin Hou , Xiong You , Tonghua Zhang
{"title":"Noise-induced entrainment of the circadian clock by thermoperiods in tomato: A computational approach","authors":"Ting Huang ,&nbsp;Hengmin Lv ,&nbsp;Yiting Shu ,&nbsp;Jian Luo ,&nbsp;Linxuan Yu ,&nbsp;Bing Chen ,&nbsp;Xin Sun ,&nbsp;Xilin Hou ,&nbsp;Xiong You ,&nbsp;Tonghua Zhang","doi":"10.1016/j.jtbi.2024.111999","DOIUrl":"10.1016/j.jtbi.2024.111999","url":null,"abstract":"<div><div>The endogenous circadian rhythm (approximately 24 h) allows plants to adapt to daily light and temperature variations. Although the mechanism of photoperiod entrainment has been studied extensively, entrainment to diurnal temperature rhythms remains poorly understood. Here we investigate the stochastic entrainment of the circadian clock in the model crop tomato, subject to different thermoperiods. We first proposed the deterministic model of the thermoresponsive circadian clock. The expressions of the circadian clock genes under constant warm temperature (29 ℃) were quantified by RT-qPCR for basal parameters estimation through minimizing the cost function. Model simulations by the stochastic simulation algorithm showed warm temperatures resulting in an advanced phase for approximately 3–4 h. A few hundred molecules for the system size of the stochastic model were sufficient to engage the robust oscillations. Multiple temperature inputs and abnormal temperature cycles similarly showed the invariant robustness of the oscillations. In addition, phases of the core circadian elements were remarkably correlated linearly with periods under temperature cycles. Whereas, the phases were correlated with the duration of daily warm temperature stimuli in a polynomial mode.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"598 ","pages":"Article 111999"},"PeriodicalIF":1.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142712030","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
Phase synchronization analysis of EEG functional connectivity in Parkinson’s disease 帕金森病脑电图功能连接的相位同步分析。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-20 DOI: 10.1016/j.jtbi.2024.111997
Karthikeyan Rajagopal , Nafise Naseri , Fatemeh Parastesh , Farnaz Ghassemi , Sajad Jafari
{"title":"Phase synchronization analysis of EEG functional connectivity in Parkinson’s disease","authors":"Karthikeyan Rajagopal ,&nbsp;Nafise Naseri ,&nbsp;Fatemeh Parastesh ,&nbsp;Farnaz Ghassemi ,&nbsp;Sajad Jafari","doi":"10.1016/j.jtbi.2024.111997","DOIUrl":"10.1016/j.jtbi.2024.111997","url":null,"abstract":"<div><div>There is a growing need for research on Parkinson’s disease (PD), a neurological condition that often affects the elderly. By examining brain network connectivity, researchers are able to discover how different brain regions interact during various cognitive and behavioral tasks. They can also understand how changes in nonlinear connections may be linked to neurological and mental illnesses. In this paper, the synchrony levels of 59 EEG channels from 26 Parkinson’s patients and 13 healthy subjects is examined by utilizing Phase-Lag Index (PLI) during a motor task and resting-state conditions. Examining different EEG frequency bands shows that whole-brain synchronization in the delta band is significantly lower in PD patients compared to healthy subjects during the task. PD patients also exhibit a lower clustering coefficient and a higher shortest path length in this band during the task, which shows the higher small-worldness in Parkinson’s patients compared to healthy individuals. Moreover, the global efficiency in the delta band is significantly reduced in PD patients during the task. An analysis of local efficiency shows that PD and control groups differ in 57 channels. These results reveal that Parkinson’s patients appear to have considerable pathological abnormalities in their delta band connectivity and its characteristic features.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"598 ","pages":"Article 111997"},"PeriodicalIF":1.9,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142689767","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
A stochastic population model for the impact of cancer cell dormancy on therapy success 癌细胞休眠对治疗成功率影响的随机群体模型。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-19 DOI: 10.1016/j.jtbi.2024.111995
Jochen Blath , Anna Kraut , Tobias Paul , András Tóbiás
{"title":"A stochastic population model for the impact of cancer cell dormancy on therapy success","authors":"Jochen Blath ,&nbsp;Anna Kraut ,&nbsp;Tobias Paul ,&nbsp;András Tóbiás","doi":"10.1016/j.jtbi.2024.111995","DOIUrl":"10.1016/j.jtbi.2024.111995","url":null,"abstract":"<div><div>Therapy evasion – and subsequent disease progression – is a major challenge in current oncology. An important role in this context seems to be played by various forms of cancer cell dormancy. For example, therapy-induced dormancy, over short timescales, can create serious obstacles to aggressive treatment approaches such as chemotherapy, and long-term dormancy may lead to relapses and metastases even many years after an initially successful treatment.</div><div>In this paper, we focus on individual cancer cells switching into and out of a dormant state both spontaneously as well as in response to treatment. We introduce an idealized mathematical model, based on stochastic agent-based interactions, for the dynamics of cancer cell populations involving individual short-term dormancy, and allow for a range of (multi-drug) therapy protocols. Our analysis – based on simulations of the many-particle limit – shows that in our model, depending on the specific underlying dormancy mechanism, even a small initial population (of explicitly quantifiable size) of dormant cells can lead to therapy failure under classical single-drug treatments that would successfully eradicate the tumour in the absence of dormancy. We further investigate and quantify the effectiveness of several multi-drug regimes (manipulating dormant cancer cells in specific ways, including increasing or decreasing resuscitation rates or targeting dormant cells directly). Relying on quantitative results for concrete simulation parameters, we provide some general basic rules for the design of (multi-)drug treatment protocols depending on the types and processes of dormancy mechanisms present in the population.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"597 ","pages":"Article 111995"},"PeriodicalIF":1.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142683610","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
Cooperative SIR dynamics as a model for spontaneous blood clot initiation 作为自发血凝块形成模型的合作 SIR 动力学。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-17 DOI: 10.1016/j.jtbi.2024.111991
Philip Greulich
{"title":"Cooperative SIR dynamics as a model for spontaneous blood clot initiation","authors":"Philip Greulich","doi":"10.1016/j.jtbi.2024.111991","DOIUrl":"10.1016/j.jtbi.2024.111991","url":null,"abstract":"<div><div>Blood clotting is an important physiological process to suppress bleeding upon injury, but when it occurs inadvertently, it can cause thrombosis, which can lead to life threatening conditions. Hence, understanding the microscopic mechanistic factors for inadvertent, spontaneous blood clotting, in absence of a vessel breach, can help in predicting and averting such conditions. Here, we present a minimal model – reminiscent of the SIR model – for the initiating stage of spontaneous blood clotting, the collective activation of blood platelets. This model predicts that in the presence of very small initial activation signals, collective activation of the platelet population is possible, but requires a sufficient degree of heterogeneity of platelet sensitivity. To propagate the activation signal and achieve collective activation of the bulk platelet population, it requires the presence of, possibly only few, hyper-sensitive platelets, but also a sufficient proportion of platelets with intermediate, yet higher-than-average sensitivity. A comparison with experimental results demonstrates a qualitative agreement for high platelet signalling activity.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"598 ","pages":"Article 111991"},"PeriodicalIF":1.9,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142676877","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
Enlightening the blind spot of the Michaelis–Menten rate law: The role of relaxation dynamics in molecular complex formation 揭示迈克尔-门顿速率定律的盲点:弛豫动力学在分子复合物形成中的作用。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-16 DOI: 10.1016/j.jtbi.2024.111989
Junghun Chae , Roktaek Lim , Thomas L.P. Martin , Cheol-Min Ghim , Pan-Jun Kim
{"title":"Enlightening the blind spot of the Michaelis–Menten rate law: The role of relaxation dynamics in molecular complex formation","authors":"Junghun Chae ,&nbsp;Roktaek Lim ,&nbsp;Thomas L.P. Martin ,&nbsp;Cheol-Min Ghim ,&nbsp;Pan-Jun Kim","doi":"10.1016/j.jtbi.2024.111989","DOIUrl":"10.1016/j.jtbi.2024.111989","url":null,"abstract":"<div><div>The century-long Michaelis–Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an equilibrium (quasi-steady state) compared to the pace of molecular concentration changes. Yet, in the case of actively time-varying molecular concentrations with transient or oscillatory dynamics, the deviation of the complex profile from the quasi-steady state becomes relevant. A recent theoretical approach, known as the effective time-delay scheme (ETS), suggests that the delay from the relaxation time of molecular complex formation contributes to the substantial breakdown of the quasi-steady state assumption. Here, we systematically expand this ETS and inquire into the comprehensive roles of relaxation dynamics in complex formation. Through the modeling of rhythmic protein–protein and protein–DNA interactions and the mammalian circadian clock, our analysis reveals the effect of the relaxation dynamics beyond the time delay, which extends to the dampening of changes in the complex concentration with a reduction in the oscillation amplitude compared to the quasi-steady state. Interestingly, the combined effect of the time delay and amplitude reduction shapes both qualitative and quantitative oscillatory patterns such as the emergence and variability of the mammalian circadian rhythms. These findings highlight the downside of the routine assumption of quasi-steady states and enhance the mechanistic understanding of rich time-varying biomolecular processes.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"597 ","pages":"Article 111989"},"PeriodicalIF":1.9,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142668951","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
Vaccination strategies in a pair formation model for human papillomavirus infection: An optimal control approach 人类乳头瘤病毒感染配对形成模型中的疫苗接种策略:最佳控制方法。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-16 DOI: 10.1016/j.jtbi.2024.111994
Fernando Saldaña
{"title":"Vaccination strategies in a pair formation model for human papillomavirus infection: An optimal control approach","authors":"Fernando Saldaña","doi":"10.1016/j.jtbi.2024.111994","DOIUrl":"10.1016/j.jtbi.2024.111994","url":null,"abstract":"<div><div>Human papillomavirus (HPV) infection is a widespread sexually transmitted infection responsible for several cancers including anal, oropharyngeal, penile, vaginal, and cervical cancer. Despite HPV vaccines have been available for almost 20 years and are incredibly effective in preventing infection, the scale-up of vaccination has been slow in many low and middle-income countries. This analysis uses a pair model that explicitly accounts for sexual partnership formation to investigate HPV immunization programs. The optimality of vaccine interventions is analyzed using optimal control theory. We give formal proof of the existence of optimal control solutions and obtain first-order optimality conditions via Pontryagin’s Maximum Principle. Extensive numerical simulations are used to investigate plausible what-if scenarios to understand under which conditions the inclusion of males should be recommended in addition to female vaccination. The results suggest that a gender-neutral vaccination program should be recommended in regions where vaccination uptake in women is still low whereas for an already existing female-only program with high uptake, it is more effective to keep increasing coverage in females.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"597 ","pages":"Article 111994"},"PeriodicalIF":1.9,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142669413","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
Peripheral straightness leads to shape diversification during formations of entire leaves 外围平直度导致整个叶片形成过程中的形状多样化。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-15 DOI: 10.1016/j.jtbi.2024.111990
Akiko M. Nakamasu
{"title":"Peripheral straightness leads to shape diversification during formations of entire leaves","authors":"Akiko M. Nakamasu","doi":"10.1016/j.jtbi.2024.111990","DOIUrl":"10.1016/j.jtbi.2024.111990","url":null,"abstract":"<div><div>The ways to read out positional information are essential to determine final shapes in developmental processes. Relative shaping to different sizes of positional information enables robust morphogenesis; however, the same difference sometimes causes diversity. Different responses to a positional information will enable such switching of identical/diverse shapes, though detail mechanisms remain unknown.</div><div>In this paper, we describe growing forms by constructing the contour of a two-dimensional object using propagating points and segments connecting them. In plant morphogenesis that lacks almost cell movements, tissue growth accompanied by cell divisions is central. We focused on peripheral cell composition in leaf formation as a frame. The growth with or without cell division on the periphery was analyzed with simple algorithms. We calculated the shapes of entire leaves with different ovality using combined growth algorithms as a model. Responces of the respective algorithms to simple positional information were explored to seek the origin of the shape diversification.</div><div>The algorithm for “growth with cell divisions” maintained identical shapes; however, diverse shapes were generated by the algorithm “growth without cell division” with gradients. The simplified model allowed us to interpret the oval shape diversity due to slants on edges. We concluded that peripheral straightness can generate shape diversity, at least in leaf morphogenesis.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"597 ","pages":"Article 111990"},"PeriodicalIF":1.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645137","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
A comprehensive study on tuberculosis prediction models: Integrating machine learning into epidemiological analysis 结核病预测模型综合研究:将机器学习融入流行病学分析。
IF 1.9 4区 数学
Journal of Theoretical Biology Pub Date : 2024-11-13 DOI: 10.1016/j.jtbi.2024.111988
Hamna Mariyam K.B. , Sayooj Aby Jose , Anuwat Jirawattanapanit , Karuna Mathew
{"title":"A comprehensive study on tuberculosis prediction models: Integrating machine learning into epidemiological analysis","authors":"Hamna Mariyam K.B. ,&nbsp;Sayooj Aby Jose ,&nbsp;Anuwat Jirawattanapanit ,&nbsp;Karuna Mathew","doi":"10.1016/j.jtbi.2024.111988","DOIUrl":"10.1016/j.jtbi.2024.111988","url":null,"abstract":"<div><div>Tuberculosis (TB), the second leading infectious killer globally, claimed the lives of 1.3 million individuals in 2022, after COVID-19, surpassing the toll of HIV and AIDS. With an estimated 10.6 million new TB cases worldwide in 2022, the gravity of the disease persists, necessitating urgent attention. Tuberculosis remains a critical public health crisis, and efforts to combat this infectious disease demand intensified global commitment and resources. This study utilizes predictive modeling techniques to forecast the incidence of Tuberculosis (TB), employing a range of machine learning models. Additionally, the research incorporates impactful visualizations for comprehensive data exploration, analysis and comparison. Various machine learning models are developed to anticipate TB incidence, with the optimal performing model to customize a user-defined function. This research provides valuable insights into the potential determinants influencing TB incidence, contributing to the identification of strategies for preventing the spread of Tuberculosis.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"597 ","pages":"Article 111988"},"PeriodicalIF":1.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142632802","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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