Journal of Theoretical Biology最新文献

Terrestrial locomotion is a complex phenomenon that is often linked to the survival of an individual and of an animal species. Mathematical models seek to express in quantitative terms how animals move, but this is challenging because the ways in which the nervous and musculoskeletal systems interact to produce body movement is not completely understood. Models with many variables tend to lack biological interpretability and describe the motion of an animal with too many independent degrees of freedom. Instead, reductionist models aim to describe the essential features of a gait with the smallest number of variables, often concentrating on the center of mass dynamics. In particular, spring–mass models have been successful in extracting and describing important characteristics of running. In this paper, we consider the spring loaded inverted pendulum model under the regime of constant angular velocity, small compression, and small angle swept during stance. We provide conditions for the asymptotic stability of periodic trajectories for the full range of parameters. The hypothesis of linear angular dynamics during stance is successfully tested on publicly available human data of individuals running on a treadmill at different velocities. Our analysis highlights a novel bifurcation phenomenon for varying Froude number: there are periodic trajectories of the spring loaded inverted pendulum model that are stable only in a restricted range of Froude numbers, while they become unstable for smaller or larger Froude numbers.

The advent of rapid and inexpensive sequencing technologies has necessitated the development of computationally efficient methods for analyzing sequence data for many genes simultaneously in a phylogenetic framework. The coalescent process is the most commonly used model for linking the underlying genealogies of individual genes with the global species-level phylogeny, but inference under the coalescent model is computationally daunting in the typical inference frameworks (e.g., the likelihood and Bayesian frameworks) due to the dimensionality of the space of both gene trees and species trees. Here we consider estimation of the branch lengths in fixed species trees with three or four taxa, and show that these branch lengths are identifiable. We also show that for three and four taxa simple estimators for the branch lengths can be derived based on observed site pattern frequencies. Properties of these estimators, such as their asymptotic variances and large-sample distributions, are examined, and performance of the estimators is assessed using simulation. Finally, we use these estimators to develop a hypothesis test that can be used to delimit species under the coalescent model for three or four putative taxa.

Vascular stent intervention is a pivotal treatment for coronary atherosclerosis, though in-stent thrombosis remains a significant postoperative complication with an unclear underlying mechanism. This study utilized dissipated particle dynamics analysis to investigate the impact of stent and its injury on platelet behavior. The findings suggest that thrombus formation upstream of the stent is mainly initiated by upstream arterial injury, which leads to increased platelet accumulation and activation in that area. While thrombosis downstream of the stent is more directly influenced by the stent itself. The morphology and size of in-stent thrombosis can vary significantly due to the different contributions of the stent and underlying injuries. Additionally, the volume of in-stent thrombosis is affected by the extent of the injury and the viscosity of platelets, showing a notable increase in volume with the lengthening of the injury area and rise in platelet viscosity. This study provides a novel theoretical framework for optimizing stent placement strategies and structural designs by examining the effects of stent struts and associated injuries on thrombus formation.

Ecosystems face various emergent uncertainties owing to factors such as climate change and accelerating anthropogenic impacts. Uncertainty is a major challenge and a barrier that ecosystem management faces, because it is difficult to precisely predict a priori risks that can have significant impacts on ecosystems. Hence, management with adaptive capacity is recommended to deal with such uncertainties, and feedback structures are central mechanisms for such flexible management. This study used mathematical models to clarify the specific impacts of feedback structures on ecosystem management, such as resource and wildlife management. In particular, the impact of errors in estimating ecosystem status when providing feedback and the impact of the time lag before feedback effects were implemented into management were examined. Overestimation of ecosystem status or a large time lag led to undesirable temporal oscillations in ecosystem status. However, these scenarios can be avoided when combined with management practices that limit the impact of management on the ecosystem, such as input control. Ecosystem management tends to have a large spatiotemporal scale, and implementing highly accurate monitoring and sophisticated feedback structures is difficult. However, the results suggest that effective ecosystem management with a simple feedback structure can be achieved through such complementary institutional design.

Candida Auris is an emerging fungal pathogen flagged by CDC as a serious global health threat among nosocomial infections in the recent times. As an evolving pathogen that often goes misidentified or unidentified under standard laboratory tests, it has the ability to cause fatal infections among the target population involving patients with serious medical conditions admitted to intensive care facilities, due to its capacity to resist anti-fungal treatment and the ability to persist in the hospital environment for long periods. The subject of this paper is to develop a deterministic model to study the transmission nature of Candida Auris wherein measures like apt admission screening methods with weekly screening follow-ups, transmission prevention, proper treatment protocols and environmental disinfection procedures are introduced as constant mitigating controls into the model initially which are later redefined as variable control functions during the optimal control analysis. The theory of optimal control implemented into the model helps us to understand the sensitivity of each control strategy upon the behaviour of each state variable. Further, cost-effectiveness analysis is rigorously conducted using incremental cost-effectiveness ratio (ICER) to identify and rank the control strategies involved based on their economic efficiency. Numerical simulation for the optimal control analysis is performed in MATLAB using the Forward–Backward Sweep Method and the findings are illustrated graphically.

What conditions select flowering patterns within inflorescences, or variation in the anthesis interval within inflorescences among plants? Under what conditions are gradual blooming and simultaneous blooming, both traits related to floral display size, advantageous? We constructed a simulation model in which the opening times and longevities of individual flowers within inflorescences, the sizes of attractive structures of individual flowers, and the numbers of ovules and pollen grains produced by individual flowers evolve. Individual plants in the population compete for pollinators, and plants are selected by pollinators according to their floral display sizes and amounts of resources allocated to attractive structures. We found that, if the proportion of pollen on a pollinator deposited on a stigma was low, gradual blooming did not evolve even if inbreeding depression was greater than 0.5. This is because the amount of outcross-pollen on pollinators decreased at a low rate during flower visits within a single inflorescence, and the selfing rate was suppressed to a low level even if the floral display size was large. On the other hand, if the proportion of pollen deposition was high, gradual blooming evolved even if inbreeding depression was smaller than 0.5. This may be because gradual blooming can enhance pollen delivery to other plants by reducing the loss of self-pollen by geitonogamy. On the other hand, allocation ratios among floral organs (female and male organs and attractive structures) were independent of the degree of simultaneous and gradual blooming within inflorescences. We concluded that the evolution of gradual blooming is more strongly affected by the proportion of pollen on a pollinator deposited on a stigma than by inbreeding depression.

Viral coinfections are responsible for a significant portion of cases of patients hospitalized with influenza-like illness. As our awareness of viral coinfections has increased, researchers have started to experimentally examine some of the virus–virus interactions underlying these infections. One mechanism of interaction between viruses is through the innate immune response. This seems to occur primarily through the interferon response, which generates an antiviral state in nearby uninfected cells, a phenomenon know as the bystander effect. Here, we develop a mathematical model of two viruses interacting through the bystander effect. We find that when the rate of removal of cells to the protected state is high, growth of the first virus is suppressed, while the second virus enjoys sole access to the protected cells, enhancing its growth. Conversely, growth of the second virus can be fully suppressed if its ability to infect the protected cells is limited.

Prothrombinase complex, composed of coagulation factors Xa (FXa) and Va (FVa) is a major enzyme of the blood coagulation network that produces thrombin via activation of its inactive precursor prothrombin (FII) on the surface of phospholipid membranes. However, pathways and mechanisms of prothrombinase formation and substrate delivery are still discussed. Here we designed a novel mathematical model that considered different potential pathways of FXa or FII binding (from the membrane or from solution) and analyzed the kinetics of thrombin formation in the presence of a wide range of reactants concentrations. We observed the inhibitory effect of large FVa concentrations and this effect was phospholipid concentration-dependent. We predicted that efficient FII activation occurred via formation of the ternary complex, in which FVa, FXa and FII were in the membrane-bound state. Prothrombin delivery was mostly membrane-dependent, but delivery from solution was predominant under conditions of phospholipid deficiency or FXa/FVa excess. Likewise, FXa delivery from solution was predominant in the case of FVa excess, but high FII did not switch the FXa delivery to the solution-dependent one. Additionally, the FXa delivery pathway did not depend on the phospholipid concentration, being the membrane-dependent one even in case of the phospholipid deficiency. These results suggest a flexible mechanism of prothrombinase functioning which utilizes different complex formation and even inhibitory mechanisms depending on conditions.

We investigate an efficient computational tool to suggest useful treatment regimens for people infected with the human immunodeficiency virus (HIV). Structured treatment interruption (STI) is a regimen in which therapeutic drugs are periodically administered and withdrawn to give patients relief from an arduous drug therapy. Numerous studies have been conducted to find better STI treatment strategies using various computational tools with mathematical models of HIV infection. In this paper, we leverage a modified version of the double deep Q network with prioritized experience replay to improve the performance of classic deep learning algorithms. Numerical simulation results show that our methodology produces significantly more optimal cost values for shorter treatment periods compared to other recent studies. Furthermore, our proposed algorithm performs well in one-day segment scenarios, whereas previous studies only reported results for five-day segment scenarios.

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it’s efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge–Kutta 4 and multi-step methods like Adams–Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between $L_{\infty }$ error and run-time is to use Runge–Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10–60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.