As a complement to the experimental work, mathematical models are extensively used to study the functional properties of ionic channels. Even though it is generally assumed that the gating of ionic channels is a Markovian phenomenon, reports based on non-traditional analyses of experimental recordings suggest that non-Markovian processes might be also present. While the stochastic Markov models are by far the most adopted approach for the modeling of ionic channels, a model based on the idea of a deterministic process underlying the gating of ionic channels was proposed by Liebovitch and Toth (Liebovitch, L.S. and Toth, T.I., 1991. Journal of Theoretical Biology, 148(2), pp.243-267.) Here, by using a voltage-dependent K+ channel as a first approximation, we propose a modified version of the deterministic model of Liebovitch and Toth that, in addition to reproducing the single-channel currents simulated by a two-states Markov model, it is capable of reproducing the whole-cell currents produced by a population of K+ channels.

Tuberculosis (TB) is still an important public health issue in Jiangsu province, China. In this study, based on the TB transmission routes and the statistical data of TB cases, we formulate a novel TB epidemic model accounting for the effects of the contaminated environments on TB transmission dynamics. The value of this study lies in two aspects. Mathematically, we define the basic reproduction number, R0, and prove that R0 can be used to govern the threshold dynamics of the model. Epidemiologically, we find that the annual average R0 is 1.13,>1 and TB in Jiangsu is an endemic disease. Therefore, in order to control the TB in Jiangsu efficiently, we must decrease the virus shedding rate or increase the recovery rates, and increase the environmental clearance rate.

The kidneys play an important role in glucose homeostasis in three ways: Via endogenous glucose production from non-carbohydrate precursors (e.g. glutamine, lactate, alanine, glycerol) during both postprandial and post-absorptive states; via glucose filtration and reabsorption by the glomerulus and proximal tubule, respectively; and via glucose utilization and the elimination of its excess in the urine when glucose levels exceed 180mg/dl. The renal release of glucose into the circulation occurs mainly in the renal cortex and results from the glucose phosphorylating capacity of those renal cells, meaning that, cells in the renal cortex can form glucose-6-phosphate. Considering glucose filtration and reabsorption, the kidneys filtrate and reabsorb all circulating glucose, rendering the urine virtually glucose-free in a healthy person. Finally, the kidneys take up glucose from the circulation for energetic self-supply. Besides their role in glucose metabolism, the kidneys are the major site of insulin clearance from the systemic circulation, removing approximately 50% of peripheral insulin. In this regard, insulin clearance by kidneys occurs by degradation in the proximal tubule after being filtered in the glomerulus. All the aforementioned mechanisms affect the glucose concentration levels in the blood, preventing the parametrization of a mathematical model for patients with diabetes mellitus, in the implementation of an artificial pancreas. Aiming for a complete physiological model of the glucose homeostasis, a physiological submodel of the kidneys is presented in a way not described in the literature so far. This submodel is a phenomenological-based semi-physical model with a basic structure rooted in the conservation law and for which the parameters are interpretable. The model's results coincide well with the available clinical data reported for kidney functions associated with glucose and insulin.

Dinosaurs are known for their large body size. Sauropod dinosaurs (Sauropodomorpha) had an especially large body size; some species reached 30 m long and 50 tons. Many hypotheses have been proposed to explain this phenomenon. In this study we examined this question using the life history theory. We constructed a simple model of life history with the following assumptions: the body size of immature individuals increases following a logistic equation. A higher quality and availability of food plants make the initial growth rate faster and the final saturating size larger. The increase in body size stops once reproduction starts. Fertility increases with adult body size and food-plant quality. Mortality due to predation is mitigated by a larger body size. We calculated the optimal body size at maturity that would maximize the lifetime reproductive success or fitness. The analysis showed that adult body size increased with food-plant quality and availability but decreased with higher mortality due to predators and other factors. This conclusion is consistent with geological studies that suggest a high quality and availability of food plants in the Mesozoic era, efficient air-sac breathing, and the lightweight bones of sauropod dinosaurs, allowing rapid growth of small individuals.

Due to the genotoxically challenging environments in which they live in, Mycobacteria have a complex DNA damage repair system that is governed by two major DNA damage responses, namely, the LexA/RecA-dependent response and the newly characterized PafBC-mediated response (Müller et al., 2018). The LexA/RecA-dependent response is a well-known bistable response found in different types of bacteria, and the Mycobacteria-specific PafBC-mediated response interacts with and modifies the LexA/RecA-dependent response (Müller et al., 2018). The interaction between the LexA/RecA-dependent response and the PafBC-mediated response has not been characterized mathematically. Our analysis shows that the addition of the PafBC-mediated response sensitizes the overall DNA damage response, effectively lowering the DNA damage rate threshold for activation.

We propose a model for memory-based movement of an individual. The dynamics are modeled by a stochastic differential equation, coupled with an eikonal equation, whose potential depends on the individual's memory and perception. Under a simple periodic environment, we discover that both long and short-term memory with appropriate time scales are essential for producing expected periodic migrations.

Fibonacci numbers such as 5, 8, and 13 occur in the spiral arrangement of lateral organs at shoot tips in plants. While the cone scales of conifers are normally arranged in 5 and 8 (or 8 and 13) curved rows in opposite directions, other numbers such as 4 and 7 (or 7 and 11) are found anomalously. The observed numbers still obey the Fibonacci rule, with the next number being the sum of the preceding two. Although these observations have been made for centuries, the underlying mechanisms of the numerical relationship have not been investigated. Here, we show that this phenomenon is caused by a two-step mechanism: (1) maintenance of a constant angle between consecutive lateral organs and (2) strong canalization of this angle to a specific value. The first step of the mechanism precedes the second step of the mechanism because the Fibonacci-rule pattern is due to the first step, while the second step distinguishes normal, anomalous and unobserved types. The current dominance of the normal type is a result of the evolutionary process of the second step.

A theoretical model of the pyloric channel, approximated as a two-dimensional tube with sinusoidal corrugation, is developed to estimate the degree of resistance offered by the pylorus to transpyloric flow (gastric emptying and duodenogastric reflux) in the viscous regime. Study indicates that the resistance of the channel depends on pressure gradient, flow behavior index and channel diameter. Flow is majorly determined by the extent of luminal opening; since they scale to fourth power of the diameter for Newtonian flow, with the exponent being higher for pseudoplastic and lesser in case of dilatants relative to Newtonian fluid. At zero pressure difference, across the channel, the closing pylorus drives the aborad propulsion of the contents at the intestinal end, and at the gastric end the flow is driven along the orad direction. While no transfer of contents occur at the centre of pylorus due to zero pressure gradients, it is essential to have a non-zero pressure difference to drive the flow through the channel. The extent of pressure difference is found to linearly relate to the transpyloric flow rate. The resistive function of the pyloric channel is observed at a higher occlusion where there is a development of higher pressure barrier that is sensitive to the flow behavior index, frequency, occlusion, and contraction length.

Flying animals morph and flex their wings during their flight. Their wings morph with the turbulent flow created around them. The wings of modern airplanes do not have this ability. In this study we show that the ability to flex the wings leads to greater stability (higher flutter speed), and that this is due to the more uniform distribution of stresses in the flexing wing. This way the flexing wing becomes the lightest per unit of flapping force, or the strongest per unit of weight.

Human respiratory disease associated with influenza virus infection is of significant public health concern. Macrophages, as part of the front line of host innate cellular defence, have been shown to play an important role in controlling viral replication. However, fatal outcomes of infection, as evidenced in patients infected with highly pathogenic viral strains, are often associated with prompt activation and excessive accumulation of macrophages. Activated macrophages can produce a large amount of pro-inflammatory cytokines, which leads to severe symptoms and at times death. However, the mechanism for rapid activation and excessive accumulation of macrophages during infection remains unclear. It has been suggested that the phenomena may arise from complex interactions between macrophages and influenza virus. In this work, we develop a novel mathematical model to study the relationship between the level of macrophage activation and the level of viral load in influenza infection. Our model combines a dynamic model of viral infection, a dynamic model of macrophages and the essential interactions between the virus and macrophages. Our model predicts that the level of macrophage activation can be negatively correlated with the level of viral load when viral infectivity is sufficiently high. We further identify that temporary depletion of resting macrophages in response to viral infection is a major driver in our model for the negative relationship between the level of macrophage activation and viral load, providing new insight into the mechanisms that regulate macrophage activation. Our model serves as a framework to study the complex dynamics of virus-macrophage interactions and provides a mechanistic explanation for existing experimental observations, contributing to an enhanced understanding of the role of macrophages in influenza viral infection.

Ticks are responsible for spreading harmful diseases including Lyme disease and tick-borne encephalitis. Understanding tick population dynamics and predicting risk of tick-borne disease insurgence helps to design preventive actions against the disease spread. Using a compartmental model describing the pathogen transmission among ticks and hosts, we study the influence of host-targeted tick control strategies with chemical insecticides on tick population and disease transmission dynamics. Our analysis shows that in areas with rapid-growing population of ticks, host-targeted controls using chemical insecticides may enhance disease persistence and even turn a disease-free area to a disease endemic area. Therefore, the complex dynamics of pathogen spread among ticks and hosts should be carefully examined when designing tick control strategies.

Combination therapies have shown remarkable success in preventing the evolution of resistance to multiple drugs, including HIV, tuberculosis, and cancer. Nevertheless, the rise in drug resistance still remains an important challenge. The capability to accurately predict the emergence of resistance, either to one or multiple drugs, may help to improve treatment options. Existing theoretical approaches often focus on exponential growth laws, which may not be realistic when scarce resources and competition limit growth. In this work, we study the emergence of single and double drug resistance in a model of combination therapy of two drugs. The model describes a sensitive strain, two types of single-resistant strains, and a double-resistant strain. We compare the probability that resistance emerges for three growth laws: exponential growth, logistic growth without competition between strains, and logistic growth with competition between strains. Using mathematical estimates and numerical simulations, we show that between-strain competition only affects the emergence of single resistance when resources are scarce. In contrast, the probability of double resistance is affected by between-strain competition over a wider space of resource availability. This indicates that competition between different resistant strains may be pertinent to identifying strategies for suppressing drug resistance, and that exponential models may overestimate the emergence of resistance to multiple drugs. A by-product of our work is an efficient strategy to evaluate probabilities of single and double resistance in models with multiple sequential mutations. This may be useful for a range of other problems in which the probability of resistance is of interest.

In this paper we analyze the potential effect of immunotherapies on castration-resistant form of human Prostate Cancer (PCa). In particular, we examine the potential effect of the dendritic vaccine sipuleucel-T, the only currently available immunotherapy option for advanced PCa, and of ipilimumab, a drug targeting the Cytotoxic T-Lymphocyte Antigen 4 (CTLA4), exposed on the CTLs membrane, currently under Phase II clinical trial. The model, building on the one by Rutter and Kuang, includes different types of immune cells and interactions and is parameterized on available data. Our results show that the vaccine has only a very limited effect on PCa, while repeated treatments with ipilimumab appear potentially capable of controlling and even eradicating an androgen-independent prostate cancer. From a mathematical analysis of a simplified model, it seems likely that, under continuous administration of ipilimumab, the system lies in a bistable situation where both the no-tumor equilibrium and the high-tumor equilibrium are attractive. The schedule of periodic treatments could then determine the outcome, and mathematical models could help determine an optimal schedule.

We mathematically model the uptake of phosphorus by a soil community consisting of a plant and two bacterial groups: copiotrophs and oligotrophs. Four equilibrium states emerge, one for each of the species monopolising the resource and dominating the community and one with coexistence of all species. We show that the dynamics are controlled by the ratio of chemical adsorption to bacterial death permitting either oscillatory states or quasi-steady uptake. We show how a steady state can emerge which has soil and plant nutrient content unresponsive to increased fertilization. However, the additional fertilization supports the copiotrophs leading to community reassembly. Our results demonstrate the importance of time-series measurements in nutrient uptake experiments.

The interplay between the dengue virus and the innate immune response is not fully understood. Here, we use deterministic and stochastic approaches to investigate the dynamics of the interaction between the interferon-mediated innate immune response and the dengue virus. We aim to develop a quantitative representation of these complex interactions and predict their system-level dynamics. Our simulation results predict bimodal and bistable dynamics that represent viral clearance and virus-producing states. Under normal conditions, we determined that the viral infection outcome is modulated by the innate immune response and the positive-strand viral RNA concentration. Additionally, we tested system perturbations by external stimulation, such as the direct induction of the innate immune response by interferon, and a therapeutic intervention consisting of the direct application of mRNA encoding for several interferon-stimulated genes. Our simulation results suggest optimal regimes for the studied intervention approaches.

In this article, the stability of equilibrium solutions of a recently formulated mathematical model of Savanna ecosystem is analytically and numerically analyzed. The mathematical model is formulated by generalizing all plant life into three components; trees, tree saplings, and grass under ecologically valid effects of fire, rainfall and competition for space. Fire has a considerable effect on trees by delaying the recruitment of saplings to trees and the recruitment rate is a piecewise linear decreasing function of grass with a sigmoidal shape. This leads to there existing different equilibria in the plant community of a Savanna ecosystem. It is rigorously demonstrated that the local stability of equilibria depends on the slope and value of the recruitment function. Moreover, it is found that the composition of high grass cover and low tree cover or low grass cover and high tree cover are the stable equilibria, while intermediate cover results in unstable equilibria. In analyzing the global stability of solutions, it is found that the limit set is an equilibrium solution. Several numerical simulations are provided to validate the analytical studies of the behavior of the equilibrium solutions. The numerical solutions are generated using a Python ordinary differential equation(ODE) solver. The analytical and numerical solutions presented in this work are very important for further developments in the area of mathematical ecology.

INTRODUCTION: Strains and sprains of soft tissues, including tendons and ligaments, are frequently occurring injuries. Musculoskeletal models show great promise in prediction and prevention of these injuries. However, these models rarely account for the viscoelastic properties of ligaments and tendons, much less their failure properties. The purpose of this project was to develop, simplify, and analyze a collagen-distribution model to address these limitations. MODEL DEVELOPMENT: A distribution-moment approximation was applied to an existing partial differential equation model to reduce its computational complexity. The resulting model was equipped with a Voigt model in series, which endowed it with viscoelastic properties in addition to failure properties. RESULTS: The model was able to reproduce the characteristic toe, linear, and failure regions ubiquitous throughout in-vitro tests on tissue specimens. In addition, it was able to reproduce a tri-phasic creep test consisting of an initial deformation, a steady-state, and failure. Stress-relaxation and hysteresis were also reproducible by the model. DISCUSSION AND CONCLUSION: The ability to reproduce so many characteristics of biological tissues suggests more bio-fidelity was achieved by the reduced model was other currently available models. Future work to further improve its bio-fidelity is proposed for specific tendons and ligaments.

Chimeric simian and human immunodeficiency viruses (SHIVs) are appropriate animal models for the human immunodeficiency virus (HIV) because HIV has quite a narrow host range. Additionally, SHIVs that encode the HIV-1 Env protein and are infectious to macaques have many strains that show different pathogenesis, such as the highly pathogenic SHIV-KS661 and the less pathogenic SHIV-#64. Therefore, we used SHIVs to understand different aspects of AIDS pathogenesis. In a previous study, we established a mathematical model of in vivo early SHIV infection dynamics, which revealed the expected uninfected and infected dynamics in Rhesus macaques. In concrete, the number of uninfected CD4+ T cells in SHIV-KS661-infected Rhesus macaques decreased more significantly and rapidly than that of SHIV-#64 Rhesus macaques, and these Rhesus macaques did not any induce host immune response. In contrast, the number of uninfected CD4+ T cells in SHIV-#64-infected Rhesus macaques is maintained, and host immune response developed. Although we considered that the peak viral load might determine whether systemic CD4+ T cell depletion occurs or host immune responses develop, we could not investigate this because our model quantified only SHIV infection prior to the development of the pathogenicity or host immune responses. Therefore, we developed a new mathematical model to investigate why SHIV-#64 and SHIV-KS661 showed different long-term viral dynamics. We fitted our new model considering antibody responses to our experimental datasets that included antibody titers, CD4+ T cells, and viral load data. We performed a maximum likelihood estimation using a non-linear mixed effect model. From the results, we derived the basic reproduction numbers of SHIV-#64 and SHIV-KS661 from intravenous infection (IV) and SHIV-KS661 from intrarectal infection (IR), as well as the antiviral effects of antibodies against SHIV-#64(IV) and SHIV-KS661(IR). We found significant differences between the basic reproduction number of SHIV-#64(IV) or -KS661(IR) and that of SHIV-KS661(IV). We found no clear difference between the antiviral effects of SHIV-#64(IV) and SHIV-KS661(IR), and revealed that an antiviral effect more than 90% of that of maximum antibody responses was induced from initial antibody responses (i.e., antibody response just after its inducement). In conclusion, we found that the basic reproduction number, rather than SHIV strains determines whether systemic CD4+ T cell depletion develops, and the subsequent antibody responses occurs.

As protection against infectious disease, immunity is conferred by one of two main defense mechanisms, namely (i) resistance generated by previous infection (known as natural immunity) or (ii) by being vaccinated (known as artificial immunity). To analyze, a modified SVIRS epidemic model is established that integrates the effects of the durability of protection and imperfectness in the framework of the human decision-making process as a vaccination game. It is supposed that immunized people become susceptible again when their immunity expires, which depends on the duration of immunity. The current theory for most voluntary vaccination games assumes that seasonal diseases such as influenza are controlled by a temporal vaccine, the immunity of which lasts for only one season. Also, a novel perspective is established involving an individual's immune system combined with self-interest to take the vaccine and natural immunity obtained from infection by coupling a disease-spreading model with an evolutionary game approach over a long period. Numerical simulations show that the longer attenuation helps significantly to control the spread of disease. Also discovered is the entire mechanism of active and passive immunities, in the sense of how they coexist with natural and artificial immunity. Thus, the prospect of finding the optimal strategy for eradicating a disease could help in the design of effective vaccination campaigns and policies.

We model the COVID-19 coronavirus epidemics in China, South Korea, Italy, France, Germany and the United Kingdom. We identify the early phase of the epidemics, when the number of cases grows exponentially, before government implementation of major control measures. We identify the next phase of the epidemics, when these social measures result in a time-dependent exponentially decreasing number of cases. We use reported case data, both asymptomatic and symptomatic, to model the transmission dynamics. We also incorporate into the transmission dynamics unreported cases. We construct our models with comprehensive consideration of the identification of model parameters. A key feature of our model is the evaluation of the timing and magnitude of implementation of major public policies restricting social movement. We project forward in time the development of the epidemics in these countries based on our model analysis.

While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.

Reinforcing the high-dose/refuge strategy with releases of transgenic insects has been suggested as a method for simultaneously managing agricultural pest populations and resistance to transgenic crops. Theoretical and empirical studies have shown that these approaches can work when deployed against closed populations and the assumptions of the HDR strategy are met. However, field-evolved resistance is often linked to non-recessive resistance or refuge non-compliance, and pest management regimes are likely to take place at the landscape-level. It is therefore important to understand how effective such strategies are when resistance is non-recessive, and how they could be employed in agricultural landscapes. We developed a spatially-explicit model to investigate the efficacy of strategies combining refuges with transgenic insect releases to manage a pest with non-recessive resistance in agricultural landscapes. We compared two release strategies, area-wide releases and localised releases targeted at population hotspots, and analysed the effects of refuge and release parameters on population and resistance dynamics. Area-wide releases reliably achieved landscape-level pest eradication. Localised releases also eradicated the pest when low release thresholds were combined with high release ratios, and maintained the pest at low densities when insufficient to achieve extinction. Reinforcing refuges with localised releases also greatly enhanced the probability of resistance extinction. However, when resistance remained in the population, localised releases prevented resistance from reaching fixation rather than greatly delaying or reversing resistance evolution. Our work indicates that combining refuges with simple release policies is effective for landscape-level pest suppression when the HDR assumptions are violated, but more nuanced release strategies may be required to enhance the benefits to resistance management.

Odors emanating from a biologically relevant source are rapidly embedded within a windy, turbuluent medium that folds and spins filaments into fragmented strands of varying sizes. Environmental odor plumes therefore exhibit complex spatiotemporal dynamics, and rarely yield an easily discernible concentration gradient marking an unambiguous trail to an odor source. Thus, sensory integration of chemical input, encoding odor identity or concentration, and mechanosensory input, encoding wind speed, is a critical task that animals face in resolving the complex dynamics of odor plumes and tracking an odor source. In insects, who employ olfactory navigation as their primary means of foraging for food and finding mates, the antennal lobe (AL) is the first brain structure that processes sensory odor information. Although the importance of chemosensory and mechanosensory integration is widely recognized, the AL itself has traditionally been viewed purely from the perspective of odor encoding, with little attention given to its role as a bimodal integrator. In this work, we seek to explore the AL as a model for studying sensory integration - it boasts well-understood architecture, well-studied olfactory responses, and easily measurable cells. Using a moth model, we present experimental data that clearly demonstrates that AL neurons respond, in dynamically distinct ways, to both chemosensory and mechanosensory input; mechanosensory responses are transient and temporally precise, while olfactory responses are long-lasting but lack temporal precision. We further develop a computational model of the AL, show that our model captures odor response dynamics reported in the literature, and examine the dynamics of our model with the inclusion of mechanosensory input; we then use our model to pinpoint dynamical mechanisms underlying the bimodal AL responses revealed in our experimental work. Finally, we propose a novel hypothesis about the role of mechanosensory input in sculpting AL dynamics and the implications for biological odor tracking.

Infamously, the presence of honest communication in a signaling environment may be difficult to reconcile with small (relative) signaling costs or a low degree of common interest between sender (beneficiary) and receiver (donor). This paper posits that one mechanism through which such communication can arise is through inattention on the part of the receiver, which allows for honest communication in settings where-should the receiver be fully attentive-honest communication would be impossible. We explore this idea through the Sir Philip Sidney game in detail and show that some degree of inattention is always weakly better for the receiver and may be strictly better. We compare limited attention to Lachmann and Bergstrom's (1998) notion of a signaling medium and show that the receiver-optimal degree of inattention is equivalent to the receiver-optimal choice of medium.

It is essential to understand the failure modes and the failure moments of curved stems since trees could be damaged and may cause severe loss of life and property in urban. In our previous papers, the cracking failure mechanism of hollow erect and curved trunks under bending moment was clarified and we also found that the mechanism of cracking failure of solid trunk is different from the hollow one. While the existing equation to calculate the transverse stress of a solid curved stem under a bending moment is approximate and may cause considerable errors when the initial curvature of stem is small. To solve this problem, a series of novel equations were derived in this study. Among these newly derived equations, 3 of them are especially practical in the assessment of the risk of urban tree for both safety and environment management which are Mc, cminR and ccriR. The equation of Mc is to calculate the bending moment for a solid curved trunk at which the cracking failure is initiated and this equation is more accurate than the existing equation. The equation of cminR is to calculate the minimum cR (c: curvature, R: radius of trunk) below which cracking failure will not occur, and the equation of ccriR is to calculate the critical cR which represents equal opportunities for cracking and bending failure of the stem to occur. To exert our model to practice, the equations derived in this paper were applied to literature data (Wood handbook, 1999). From the data of 41 species of softwood and 48 species of hardwood, statistically, hardwoods have larger average values of cminR and ccriR than softwoods which means that hardwoods are more resistant to cracking failure than softwoods.

Plants can adjust their competitive traits for acquiring resources in response to the relatedness of their neighbours. Recently, it has been found that plants can alter their investment in traits of attracting pollinators based on kin-interaction. We build a mathematical model to study the optimal floral display to attract pollinators in a patch with kin structure. We show that when plants can attract pollinators to a whole patch through the magnet effect, the floral display should increase with the increasing relatedness of the plants in the patch. Our model also indicates that increasing investment into attracting pollinators is a form of altruism, reducing a plant's own seed production but increasing the contribution of other plants to its fitness. We also predict that seed production should increase with increasing relatedness in the patch. Our model provides the explicit conditions when resource allocation to attract pollinators in response to neighbour relatedness can be favoured by kin selection, and a possible mechanism for the plants to deal with the consequent loss of pollinator diversity and abundance.

Sleep loss causes decrements in cognitive performance, which increases risks to those in safety-sensitive fields, including medicine and aviation. Mathematical models can be formulated to predict performance decrement in response to sleep loss, with the goal of identifying when an individual may be at highest risk for an accident. This work produces an Ensemble Mixed Effects Model that combines a traditional Linear Mixed Effects (LME) model with a semi-parametric, nonlinear model called Mixed Effects Random Forest (MERF). Using this model, we predict performance on the Psychomotor Vigilance Task (PVT), a test of sustained attention, using biologically motivated features extracted from a dataset containing demographic, sleep, and cognitive test data from 44 healthy participants studied during inpatient sleep loss laboratory experiments. Our Ensemble Mixed Effects Model accurately predicts an individual's trend in PVT performance, and fits the data better than prior published models. The ensemble successfully combines MERF's high rate of peak identification with LME's conservative predictions. We investigate two questions relevant to this model's potential use in operational settings: the tradeoff between additional model features versus ease of collecting these features in real-world settings, and how recent a cognitive task must have been administered to produce strong predictions. This work addresses limitations of previous approaches by developing a predictive model that accounts for interindividual differences and utilizes a nonlinear, semi-parametric method called MERF. We methodologically address the modeling decisions required for this prediction problem, including the choice of cross-validation method. This work is novel in its use of data from a highly-controlled inpatient study protocol that uncouples the influence of the sleep-wake cycle from the endogenous circadian rhythm on the cognitive task being modeled. This uncoupling provides a clearer picture of the model's real-world predictive ability for situations in which people work at different circadian times (e.g., night- or shift-work).

The surface shape is an important aspect to take into account to ensure the success of an implant. At the cellular scale level, the cell behaviour, especially its migration, is affected by the specificities of the surface of the substrate, such as the stiffness of the surface and its roughness topography. The latter has been shown to have a great impact on various cell mechanisms, such as the cell adhesion, migration, or proliferation. In fact, the mere presence of micro roughness leads to an improvement of those mechanisms, with a better integration of the implants. However, the phenomena behind those improvements are still not clear. In this paper, we propose a three-dimensional (3D) model of a single cell migration using a Cellular Potts (CP) model to study the influence of the surface topography on cell motility. To do so, various configurations were tested, such as: (i) a substrate with a random roughness, (ii) a substrate with a rectangular groove pattern (parallel and perpendicular to the direction of motion), (ii) a substrate with a sinusoidal groove pattern. To evaluate the influence of the surface topography on cell motility, for each configuration, the cell speed and shape as well as the contact surface between the cell and the substrate have been quantified. Our numerical results demonstrate that, in agreement with the experimental observations of the literature, the substrate topography has an influence on the cell efficiency (i.e. cell speed), orientation and shape. Besides, we also show that the increase of the contact surface alone in presence of roughness is not enough to explain the improvement of cell migration on the various rough surfaces. Finally, we highlight the importance of the roughness dimension on cell motility. This could be a critical aspect to consider for further analyses and applications, such as surface treatments for medical applications.

A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (gK-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing gK-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1-8 Hz) are lower than the input frequencies (15-35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

A deeper understanding of the processes underlying the distribution of animals in space is crucial for both basic and applied ecology. The Common buzzard (Buteo buteo) is a highly aggressive, territorial bird of prey that interacts strongly with its intra- and interspecific competitors. We propose and use random matrix theory to quantify the strength and range of repulsion as a function of the buzzard population density, thus providing a novel approach to model density dependence. As an indicator of territorial behaviour, we perform a large-scale analysis of the distribution of buzzard nests in an area of 300 square kilometres around the Teutoburger Wald, Germany, as gathered over a period of 20 years. The nearest and next-to-nearest neighbour spacing distribution between nests is compared to the two-dimensional Poisson distribution, originating from uncorrelated random variables, to the complex eigenvalues of random matrices, which are strongly correlated, and to a two-dimensional Coulomb gas interpolating between these two. A one-parameter fit to a time-moving average reveals a significant increase of repulsion between neighbouring nests, as a function of the observed increase in absolute population density over the monitored period of time, thereby proving an unexpected yet simple model for density-dependent spacing of predator territories. A similar effect is obtained for next-to-nearest neighbours, albeit with weaker repulsion, indicating a short-range interaction. Our results show that random matrix theory might be useful in the context of population ecology.

A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations.

Multiple infection of target cells by human immunodeficiency virus (HIV) may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy, bringing more challenges to the control of infection. The mechanisms underlying HIV multiple infection and their relative contributions are not fully understood. In this paper, we develop and analyze a mathematical model that includes sequential cell-free virus infection (i.e.one virus is transmitted each time in a sequential infection of target cells by virus) and cell-to-cell transmission (i.e.multiple viral genomes are transmitted simultaneously from infected to uninfected cells). By comparing model prediction with the distribution data of proviral genomes in HIV-infected spleen cells, we find that multiple infection can be well explained when the two modes of viral transmission are both included. Numerical simulation using the parameter estimates from data fitting shows that the majority of T cell infections are attributed to cell-to-cell transmission and this transmission mode also accounts for more than half of cell's multiple infections. These results suggest that cell-to-cell transmission plays a critical role in forming HIV multiple infection and thus has important implications for HIV evolution and pathogenesis.

The tumor control probability (TCP) is a metric used to calculate the probability of controlling or eradicating tumors through radiotherapy. Cancer cells vary in their response to radiation, and although many factors are involved, the tumor microenvironment is a crucial one that determines radiation efficacy. The tumor microenvironment plays a significant role in cancer initiation and propagation, as well as in treatment outcome. We have developed stochastic formulations to study the impact of arbitrary microenvironmental fluctuations on TCP and extinction probability (EP), which is defined as the probability of cancer cells removal in the absence of treatment. Since the derivation of analytical solutions are not possible for complicated cases, we employ a modified Gillespie algorithm to analyze TCP and EP, considering the random variations in cellular proliferation and death rates. Our results show that increasing the standard deviation in kinetic rates initially enhances the probability of tumor eradication. However, if the EP does not reach a probability of 1, the increase in the standard deviation subsequently has a negative impact on probability of cancer cells removal, decreasing the EP over time. The greatest effect on EP has been observed when both birth and death rates are being randomly modified and are anticorrelated. In addition, similar results are observed for TCP, where radiotherapy is included, indicating that increasing the standard deviation in kinetic rates at first enhances the probability of tumor eradication. But, it has a negative impact on treatment effectiveness if the TCP does not reach a probability of 1.

The biological interactions underpinning the Arabidopsis circadian clock have been systematically uncovered and explored by biological experiments and mathematical models. This is captured by a series of published ordinary differential equation (ODE) models, which describe plant clock dynamics in response to light/dark conditions. However, understanding the role of temperature in resetting the clock (entrainment) and the mechanisms by which circadian rhythms maintain a near-24 h period over a range of temperatures (temperature compensation) is still unclear. Understanding entrainment and temperature compensation may elucidate the principles governing the structure of the circadian clock network. Here we explore the design principles of the Arabidopsis clock and its responses to changes in temperature. We analyse published clock models of Arabidopsis, spanning a range of complexity, and incorporate temperature-dependent dynamics into the parameters of translation rates in these models, to discern which regulatory patterns may best explain clock function and temperature compensation. We additionally construct three minimal clock models and explore what key features govern their rhythmicity and temperature robustness via a series of random parameterisations. Results show that the highly repressive interactions between the components of the plant clock, together with autoregulation patterns and three-node feedback loops, are associated with circadian function of the clock in general, and enhance its robustness to temperature variation in particular. However, because the networks governing clock function vary with time due to light and temperature conditions, we emphasise the importance of studying plant clock functionality in its entirety rather than as a set of discrete regulation patterns.

Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.

Being the primary mean of translating the chemical signal into the electric signal in neuromuscular junction, the nACh receptor is the first kind of ligand-gated channel that its kinetic structure has been known clearly. The next problem is to know quantitatively how it works in a living system. In this paper, we construct a piece-wise deterministic process to mimic the membrane voltage fluctuation driven by a single nACh receptor. The power spectrum of the voltage fluctuation is solved analytically, which reveals the 1/ω4-type noise.

Reperfusion of the blood flow to ischemic myocardium is the standard treatment for patients suffering myocardial infarction. However, the reperfusion itself can also induce myocardial injury, in which the actual mechanism and its risk factors remain unclear. This work aims to study the mechanism of ischemia-reperfusion treatment using a three-dimensional (3D) oxygen diffusion model. An electrical model is then coupled to an oxygen model to identify the possible region of myocardial damage. Our findings show that the value of oxygen exceeds its optimum (>1.0) at the ischemic area during early reperfusion period. This complication was exacerbated in a longer ischemic period. While a longer reperfusion time causes a continuous excessive oxygen supply to the ischemic area throughout the reperfusion time. This work also suggests the use of less than 0.8 of initial oxygen concentration in the reperfusion treatment to prevent undesired upsurge at the early reperfusion period and further myocardial injury. We also found the region at risk for myocardial injury is confined in the ischemic vicinity revealed by its electrical conductivity impairment. Although there is a risk that reperfusion leads to myocardial injury for excessive oxygen accumulation, the reperfusion treatment is helpful in reducing the infarct size.

Shared resource extraction among profit-seeking individuals involves a tension between individual benefit and the collective well-being represented by the persistence of the resource. Many game theoretic models explore this scenario, but these models tend to assume either best response dynamics (where individuals instantly switch to better paying strategies) or imitation dynamics (where individuals copy successful strategies from neighbours), and do not systematically compare predictions under the two assumptions. Here we propose an iterated game on a social network with payoff functions that depend on the state of the resource. Agents harvest the resource, and the strategy composition of the population evolves until an equilibrium is reached. The system is then repeatedly perturbed and allowed to re-equilibrate. We compare model predictions under best response and imitation dynamics. Compared to imitation dynamics, best response dynamics increase sustainability of the system, the persistence of cooperation while decreasing inequality and debt corresponding to the Gini index in the agents' cumulative payoffs. Additionally, for best response dynamics, the number of strategy switches before equilibrium fits a power-law distribution under a subset of the parameter space, suggesting the system is in a state of self-organized criticality. We find little variation in most mean results over different network topologies; however, there is significant variation in the distributions of the raw data, equality of payoff, clustering of like strategies and power-law fit. We suggest the primary mechanisms driving the difference in sustainability between the two strategy update rules to be the clustering of like strategies as well as the time delay imposed by an imitation processes. Given the strikingly different outcomes for best response versus imitation dynamics for common-pool resource systems, our results suggest that modellers should choose strategy update rules that best represent decision-making in their study systems.

In this paper, we present and analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

Alternate bearing, seen in many types of plants, is the variable yield with a strongly biennial pattern. In this paper, we introduce a new model for alternate bearing behavior. Similar to the well-known Resource Budget Model, our model is based on the balance between photosynthesis or other limiting resource accumulation and reproduction processes. We consider two novel features with our model, 1) the existence of a finite capacity in the tree's resource reservoir and 2) the possibility of having low (but non-zero) yield when the tree's resource level is low. We achieve the former using a density dependent resource accumulation function, and the latter by removing the concept of the well-defined threshold used in the Resource Budget Model. At the level of an individual tree, our model has a stable two-cycle solution, which is suitable to model plants in which the alternate bearing behavior is pronounced. We incorporate environmental stochasticity by adding two uncorrelated noise terms to the parameters of the model associated with the nutrient accumulation and reproduction processes. Furthermore, we examine the model's behavior on a system of two coupled trees with direct coupling. Unlike the coupled Resource Budget Model, for which the only stable solution is the out-of-phase solution, our model with direct coupling has stable in-phase period-2 solutions. This suggests that our model might serve to explain spatial synchrony on a larger scale.

In this paper, the interest is in a structured Markov chain model to describe the transmission dynamics of tuberculosis (TB) in the setting of small communities of hosts sharing confined spaces, and to explore the potential impact of new pre-exposure vaccines on reducing the number of new TB cases during an outbreak of the disease. The model under consideration incorporates endogenous reactivation of latent tubercle bacilli, exogenous reinfection of latently infected TB hosts, loss of effectiveness of the vaccine protection, and death of hosts due to tubercle bacilli and from causes beyond TB. Various probabilistic measures are defined and analytically studied to describe extreme values and the number of vaccinations during an outbreak, and a random version of the basic reproduction number is used to measure the transmission potential during the initial phase of the epidemic. Our numerical experiments allow us to compare different pre-exposure vaccines versus the level of coverage in terms of these probabilistic measures.

Adult neurogenesis - the generation of neurons during adulthood - is intensively studied, yet little is known about its consequences at the tissue level. In the teleost fish Apteronotus leptorhynchus, morphometric analysis has revealed that the total number of cells in the spinal cord increases continuously throughout adulthood, driven by the activity of neurogenic stem/progenitor cells in both the ependymal layer at the central canal and in the radially located parenchyma. This net increase in cell numbers demonstrates cellular addition, as opposed to cellular turnover which appears to be the common outcome of adult neurogenesis in mammals. Grounded on a comprehensive set of quantitative data generated through high-resolution mapping of stem cells and their progeny, we constructed a cellular automata model of the stem-cell-driven growth of the spinal cord. Simulations based on this model suggest that three cellular mechanisms play a critical role for promoting sustained tissue growth and acquisition of correct form of the spinal cord, including the development of the ependymal layer and the parenchyma: the number of symmetric stem-cell divisions versus asymmetric divisions; the probability of the progeny of progenitor cells to undergo cell death; and the radial drifting of cells.

We consider a homogeneous birth-death process with three different sampling schemes. First, individuals can be sampled through time and included in a reconstructed phylogenetic tree. Second, they can be sampled through time and only recorded as a point 'occurrence' along a timeline. Third, extant individuals can be sampled and included in the reconstructed phylogenetic tree with a fixed probability. We further consider that sampled individuals can be removed or not from the process, upon sampling, with fixed probability. We derive the probability distribution of the population size at any time in the past conditional on the joint observation of a reconstructed phylogenetic tree and a record of occurrences not included in the tree. We also provide an algorithm to simulate ancestral population size trajectories given the observation of a reconstructed phylogenetic tree and occurrences. This distribution can be readily used to draw inferences about the ancestral population size in the field of epidemiology and macroevolution. In epidemiology, these results will allow data from epidemiological case count studies to be used in conjunction with molecular sequencing data (yielding reconstructed phylogenetic trees) to coherently estimate prevalence through time. In macroevolution, it will foster the joint examination of the fossil record and extant taxa to reconstruct past biodiversity.