The human endometrium presents a remarkable growth dynamic with an outstanding regenerative capacity. This work aims to develop a phenomenological-based dynamic model to predict the volume changes in the functional layer of the endometrium in each phase of the menstrual cycle. This model considers changes in the endometrial tissue, the blood flow through the spiral arteries, the shedding of the endometrial cells, and the menstrual blood flow. The input variables are estrogen and progesterone; these hormone dynamics are taken from a pre-existing and validated model. Key parameters are modified in order to know their effect on the state variables. The model response was quantitatively assessed using the experimental data of the endometrial cycle reported in the literature. The proposed model provides a better insight into the interactions between ovarian hormones and the endometrial cycle by coupling both physiological processes.

Besides egg fertilization, females of many taxa obtain direct fitness benefits from male mates, such as food, protection or paternal care. But males often increase their own fitness by mating with several females, among which they distribute sperm along with the above-mentioned benefits, reducing the benefits to individual females. These diverging interests lead to a conflict in which each female may try to ensure male fidelity and get exclusive access to male-provided benefits. Here, we use a theoretical model to show how a female of an externally fertilizing species may achieve mate fidelity by soliciting copulations at such a rate that the male has insufficient sperm left to increase his fitness with additional females. We show that three alternative condition-dependent evolutionarily stable mating relationships emerge in this scenario, based on whether one mate's preference for mating rate dominates, or the conflict is resolved by what amounts to negotiation. We demonstrate how these outcomes depend on some features of physiology, ecology, and behavior. In particular, a greater reproductive benefit to a female from exclusive access to a male partner-or the occasional tendency of females to withhold eggs during mating-can increase male fidelity; and continuous sperm regeneration rather than an initially-set stock of sperm allows for multiple within-pair mating across all three mating patterns.

In most taxa of plant and animal kingdoms the initial steps of embryogenesis and the final morphology of an organism are strongly determined. However, these two phenomena do not correlate from phylogenetic point of view, namely, different unrelated taxa can have the same type of early embryogenesis, while there can be different types of cleavage inside one taxon. Here we discuss an approach enabling giving an insight into the understanding of this phenomenon. First, we propose a strategy for constructing developmental graphs (trees) that provide mathematical formalization of a process of embryogenesis. Second, we suggested an algorithm of trees comparison, developed specifically for this type of labeled graphs, which allows calculating a distance between two developmental trees, and thus clustering them into groups. Next we performed the analysis of correspondence between the obtained clusters and the inception of morphological characters in given clustered groups of organisms, which allows describing several particular cases of interrelation between developmental trends and formation of morphological structures. Here we present some illustrations of the suggested methodology on the analysis of plant angiosperm species belonging to different taxa of various ranks.

Many angiosperms have undergone some series of polyploidization events over the course of their evolutionary history. In these genomes, especially those resulting from multiple autopolyploidization, it may be relatively easy to recognize all the ξ sets of n homeologous chromosomes, but it is much harder, if not impossible, to partition these chromosomes into n subgenomes, each representing one distinct genomic component of ξ chromosomes making up the original polyploid. Thus, if we wish to infer the polyploidization history of the genome, we could make use of all the gene trees inferred from the genes in one set of homeologous chromosomes to construct a consensus tree, but there is no evident way of combining the trees from the ξ different sets, because we have no labelling of the chromosomes that is known to be consistent across these sets. We suggest here that lacking a consistent leaf-labelling, the topological structure of the trees may display sufficient resemblance so that a higher level consensus could be revealing of evolutionary history. This would be especially true of the peripheral structures of the tree, likely representing events that occurred more recently and have thus been less obscured by subsequent evolutionary processes. Here, we present a statistical test to assess whether the subgenomes in a polyploid genome could have been added one at a time. The null hypothesis is that the accumulation of chromosomes follows a stochastic process in which transition from one generation to the next is through randomly choosing an edge, and then subdividing this edge in order to link the new internal vertex to a new external vertex. We analyze the probability distributions of a number of peripheral tree substructures, namely leaf- or terminal-pairs, triples and quadruples, arising from this stochastic process, in terms of some exact recurrences. We propose some conjectures regarding the asymptotic behaviours of these distributions. Applying our analysis to a sugarcane genome, we demonstrate that it is unlikely that the accumulation of subgenomes has occurred one at a time.

The COVID-19 pandemic has led to widespread attention given to the notions of "flattening the curve" during lockdowns, and successful contact tracing programs suppressing outbreaks. However a more nuanced picture of these interventions' effects on epidemic trajectories is necessary. By mathematical modeling each as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Lockdowns compressed the outbreak in China inversely proportional to population quarantine rates, revealing their critical dependence on timing. Contact tracing had significantly less impact on final outbreak size, but did lead to peak size reduction. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed.

Respiratory viral infections pose a serious public health concern, from mild seasonal influenza to pandemics like those of SARS-CoV-2. Spatiotemporal dynamics of viral infection impact nearly all aspects of the progression of a viral infection, like the dependence of viral replication rates on the type of cell and pathogen, the strength of the immune response and localization of infection. Mathematical modeling is often used to describe respiratory viral infections and the immune response to them using ordinary differential equation (ODE) models. However, ODE models neglect spatially-resolved biophysical mechanisms like lesion shape and the details of viral transport, and so cannot model spatial effects of a viral infection and immune response. In this work, we develop a multiscale, multicellular spatiotemporal model of influenza infection and immune response by combining non-spatial ODE modeling and spatial, cell-based modeling. We employ cellularization, a recently developed method for generating spatial, cell-based, stochastic models from non-spatial ODE models, to generate much of our model from a calibrated ODE model that describes infection, death and recovery of susceptible cells and innate and adaptive responses during influenza infection, and develop models of cell migration and other mechanisms not explicitly described by the ODE model. We determine new model parameters to generate agreement between the spatial and original ODE models under certain conditions, where simulation replicas using our model serve as microconfigurations of the ODE model, and compare results between the models to investigate the nature of viral exposure and impact of heterogeneous infection on the time-evolution of the viral infection. We found that using spatially homogeneous initial exposure conditions consistently with those employed during calibration of the ODE model generates far less severe infection, and that local exposure to virus must be multiple orders of magnitude greater than a uniformly applied exposure to all available susceptible cells. This strongly suggests a prominent role of localization of exposure in influenza A infection. We propose that the particularities of the microenvironment to which a virus is introduced plays a dominant role in disease onset and progression, and that spatially resolved models like ours may be important to better understand and more reliably predict future health states based on susceptibility of potential lesion sites using spatially resolved patient data of the state of an infection. We can readily integrate the immune response components of our model into other modeling and simulation frameworks of viral infection dynamics that do detailed modeling of other mechanisms like viral internalization and intracellular viral replication dynamics, which are not explicitly represented in the ODE model. We can also combine our model with available experimental data and modeling of exposure scenarios and spatiotemporal aspects of mechanisms like mucociliary clearance that are only implicitly described by the ODE model, which would significantly improve the ability of our model to present spatially resolved predictions about the progression of influenza infection and immune response.

Dynamic models of gene expression are urgently required. In this paper, we describe the time evolution of gene expression by learning a jump diffusion process to model the biological process directly. Our algorithm needs aggregate gene expression data as input and outputs the parameters of the jump diffusion process. The learned jump diffusion process can predict population distributions of gene expression at any developmental stage, obtain long-time trajectories for individual cells, and offer a novel approach to computing RNA velocity. Moreover, it studies biological systems from a stochastic dynamic perspective. Gene expression data at a time point, which is a snapshot of a cellular process, is treated as an empirical marginal distribution of a stochastic process. The Wasserstein distance between the empirical distribution and predicted distribution by the jump diffusion process is minimized to learn the dynamics. For the learned jump diffusion process, its trajectories correspond to the development process of cells, the stochasticity determines the heterogeneity of cells, its instantaneous rate of state change can be taken as "RNA velocity", and the changes in scales and orientations of clusters can be noticed too. We demonstrate that our method can recover the underlying nonlinear dynamics better compared to previous parametric models and the diffusion processes driven by Brownian motion for both synthetic and real world datasets. Our method is also robust to perturbations of data because the computation involves only population expectations.

p53 protein plays an essential role in protecting the genomic integrity of mammalian cells. A drastic decrease in the amount of p53 protein has been observed in cancerous cells. By using Nutlin-based small molecule drugs, the concentration of p53 can be restored to the desired level. This paper presents the drug-dosage design for p53 pathway, based on a control-oriented nonlinear model. A chattering free sliding mode control (CFSMC) strategy is employed to track the desired trajectory of p53 concentration for both of its dynamic behaviors, i.e., sustained and oscillatory responses. A gain-scheduled modified Utkin observer (GSMUO) is designed for robust state reconstruction and disturbance estimation. The simulation results show that CFSMC and GSMUO exhibit desired robustness and performance properties in the presence of parametric variations, an input disturbance and measurement noise. Moreover, a comprehensive simulation study, along with a detailed quantitative analysis is performed to compare CFSMC-GSMUO with four different techniques: a sliding mode control (SMC) with an equivalent control based sliding mode observer (SMO) and GSMUO, respectively, and a dynamic sliding mode control (DSMC) with SMO and GSMUO, respectively. The analysis demonstrates that the tracking error and utilization of the control energy is the least in the case of CFSMC-GSMUO as compared to its counterparts.

Mycobacterium tuberculosis can exist within a host for lengthy periods, tolerating even antibiotic challenge. This non-heritable, antibiotic tolerant "persister" state, is thought to underlie latent Tuberculosis (TB) infection and a deeper understanding thereof could inform treatment strategies. In addition to experimental studies, mathematical and computational modelling approaches are widely employed to study persistence from both an in vivo and in vitro perspective. However, specialized models (partial differential equations, agent-based, multiscale, etc.) rely on several difficult to determine parameters. In this study, a dynamic mathematical model was developed to predict the response of Mycobacterium smegmatis (a model organism for M. tuberculosis) grown in batch culture and subjected to a range of in vitro environmental stresses. Lag phase dynamics, pH variations and internal nitrogen storage were mechanistically modelled. Experimental results were used to train model parameters using global optimization, with extensive subsequent model validation to ensure extensibility to more complex modelling frameworks. This included an identifiability analysis which indicated that seven of the thirteen model parameters were uniquely identifiable. Non-identifiable parameters were critically evaluated. Model predictions compared to validation data (based on experimental results not used during training) were accurate with less than 16% maximum absolute percentage error, indicating that the model is accurate even when extrapolating to new experimental conditions. The bulk growth model can be extended to spatially heterogeneous simulations such as an agent-based model to simulate in vitro granuloma models or, eventually, in vivo conditions, where distributed environmental conditions are difficult to measure.

Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling.

The Gaia hypothesis considers the life-environment coupled system as a single entity that acts to regulate and maintain habitable conditions on Earth. In this paper we discuss three mechanisms which could potentially lead to Gaia: Selection by Survival, Sequential Selection and Entropic Hierarchy. We use the Tangled Nature Model of co-evolution as a common framework for investigating all three, using an extended version of the standard model to elaborate on Gaia as an example of an entropic hierarchy. This idea, which combines sequential selection together with a reservoir of diversity that acts as a 'memory', implies a tendency towards growth and increasing resilience of the Gaian system over time. We then discuss how Gaian memory could be realised in practice via the microbial seed bank, climate refugia and lateral gene transfer and conclude by discussing testable implications of an entropic hierarchy for the study of Earth history and the search for life in the universe. This paper adds to the existing taxonomy of Gaia hypotheses to suggest an "Entropic Gaia" where we argue that increasing biomass, complexity and enhanced habitability over time is a statistically likely feature of a co-evolving system.

Mechanisms for social learning have rightly been the focus of much work in cultural evolution. But mechanisms for teaching-mechanisms that determine what information is available for learners to learn in the first place-are equally important to cultural evolution, especially in the case of humans. Here, we propose a simple model of teaching in the context of skill transmission. Our model derives the evolutionary cost and benefit of teaching by explicitly representing cognitive aspects of skill transmission as a dual-inheritance process. We then show that teaching cannot evolve when its direct cost is too high. We also show that there is an "explain-exploit" trade-off inherent to teaching: when payoffs from sharing information are not constant, there can be an indirect cost to teaching. This gives rise to an opportunity cost that goes beyond any direct cost that it may also entail. Finally, we show that evolution limits the strength of teaching provided that the direct cost of teaching is an increasing function of teaching effort. We then discuss how these factors might explain why teaching mechanisms are self-limiting, suggesting that such mechanisms may nevertheless play an important role in the evolution of cumulative culture in humans.

Exposure to pathogens elicits a complex immune response involving multiple interdependent pathways. This response may mitigate detrimental effects and restore health but, if imbalanced, can lead to negative outcomes including sepsis. This complexity and need for balance pose a challenge for clinicians and have attracted attention from modelers seeking to apply computational tools to guide therapeutic approaches. In this work, we address a shortcoming of such past efforts by incorporating the dynamics of energy production and consumption into a computational model of the acute immune response. With this addition, we performed fits of model dynamics to data obtained from non-human primates exposed to Escherichia coli. Our analysis identifies parameters that may be crucial in determining survival outcomes and also highlights energy-related factors that modulate the immune response across baseline and altered glucose conditions.

The spread of infectious diseases is a world-wide problem that has a greater impact on low-income countries. Mathematical modelling is a useful tool to better understand these diseases and to plan prevention and interventions. In this article, discrete-time binomial chain models, which are used for modelling the transmission of infectious diseases, have been extended by the addition of a spatial component. The spatial component is included in the function which represents the number of contacts that an individual makes. The spatio-stochastic model is derived to form three cases to match different modelling scenarios, namely: a model with only local transmission, a model with interaction between spatial units but no migration, and a model with interaction and migration between spatial units. Simulations are then used to compare the different models. The spatio-stochastic model is also demonstrated with an application to measles data. From this study, it can be seen that the type of model and inclusion of a spatial component plays an important role in the transmission of infectious diseases. The importance of choosing a model which best represents the dynamics and circumstances of an infectious disease is highlighted. The models presented in this paper allows flexibility which accommodate for a wide range of modelling cases.

Network modeling is an effective tool for understanding the properties of complex systems. Networks are widely used to help us gain insight into biological systems. In this way, the cell, gene, and protein are denoted as nodes, and the connection elements are regarded as links or edges. In this paper, a novel stochastic strategy is developed for identifying the most influential edges on the stability of biological networks. Regarding the principles of networks and control-theory basics like Jacobian and eigenvalue sensitivity-based analysis, a new criterion is proposed, called "random sensitivity index matrix" (RSIM). RSIM evaluates the eigenvalue sensitivity of all edges in a network in the presents of stochastic disturbances based on the Monte Carlo algorithm. Through the values of RSIM elements, the sensitive edges are identifiable. In addition, the contribution of each edge in network instability has been compared through different percentages of disturbances. Different percentages of disturbances did not change the results. The performance of the proposed method was verified by simulation results for Lac (lactose) operon and MAPK (Mitogen-activated protein kinases) as two sample biological networks.

Scaling of nuclear size with cell size has been observed in many species and cell types. In this work we formulate a modeling framework based on the limiting component hypothesis. We derive a family of spatio-temporal mathematical models for nuclear size determination based on different transport and growth mechanisms. We analyse model properties and use in vitro experimental data to identify the most probable mechanism. This suggests that nuclear volume scales with cell volume and that a nucleus controls its import rate as it grows. We further test the model by comparing to data of early frog development, where rapid cell divisions set the relevant time scales.

We study the adaptive dynamics of the colonization rate of species living in a patchy habitat when there is a trade-off with the competitive strength for individual patches. To that end, we formulate a continuous-time competition-colonization model that also includes ownership effects as well as random disturbance affecting the mortality rate. We find that intermediate disturbance (as measured by the fluctuation intensity of the mortality rate), a strong competition-colonization trade-off, and a weak ownership effect are necessary conditions for evolutionary branching and hence for the emergence of polymorphisms (i.e., coexistence) by small evolutionary steps. Specifically, concerning ownership we find that with low-intermediate disturbance, a weak ownership advantage favours evolutionary branching while ownership disadvantage does not. This asymmetry disappears at the higher-intermediate disturbance. Moreover, at a low-intermediate disturbance, the effect of the strength of the competition-colonization trade-off on evolutionary branching is non-monotonic disappears because the possibility of branching disappears again when the trade-off is too strong. We also find that there can be multiple evolutionary attractors for polymorphic populations, each with its own basin of attraction. With small but non-zero random evolutionary steps and depending on the initial polymorphic condition just after branching, a coevolutionary trajectory may come arbitrarily close to the shared boundary of two such basins and may even jump from one side to the other, which can lead to various kinds of long-term evolutionary dynamics, including evolutionary branching-extinction cycles.

In some species of separate sexes, males present a nuptial gift containing nutrition to their mate. Producing a large nuptial gift is a considerable cost to the male, but it may improve his siring success if the female reduces the likelihood to accept another male after receiving a large gift. The female may receive a direct benefit by accepting another male who provides an additional nuptial gift. Additionally, the female may receive an indirect fitness benefit via laying offspring sired by a male who is able to produce a large nuptial gift. We formalized the multivariate quantitative genetics model describing the coevolution of the size of nuptial gift produced by the male (x) and the female's propensity to engage in remating (y). We analyzed the model focusing two cases: [1] remating females receive no indirect fitness benefit, but enjoy direct benefit of nutrition; and [2] remating females receive no direct benefit, but enjoy an indirect fitness benefit due to a positive genetic correlation of x and y, which is possible if random mutations tend to make males produce small nuptial gifts. In both cases, the stable evolutionary equilibrium with neither nuptial gift nor remating (x-=y-=0) always exists. Another stable equilibrium may exist in which male produces nuptial gifts (x->0) and female engage in multiple mating (y->0). We discussed implications to the sexual conflict.

Understanding under which conditions conjugative plasmids encoding antibiotic resistance can invade bacterial communities in the gut is of particular interest to combat the spread of antibiotic resistance within and between animals and humans. We extended a one-compartment model of conjugation to a two-compartment model, to analyse how differences in plasmid dynamics in the gut lumen and at the gut wall affect the invasion of plasmids. We compared scenarios with one and two compartments, different migration rates between the lumen and wall compartments, and different population dynamics. We focused on the effect of attachment and detachment rates on plasmid dynamics, explicitly describing pair formation followed by plasmid transfer in the pairs. The parameter space allowing plasmid invasion in the one-compartment model is affected by plasmid costs and intrinsic conjugation rates of the transconjugant, but not by these characteristics of the donor. The parameter space allowing plasmid invasion in the two-compartment model is affected by attachment and detachment rates in the lumen and wall compartment, and by the bacterial density at the wall. The one- and two-compartment models predict the same parameter space for plasmid invasion if the conditions in both compartments are equal to the conditions in the one-compartment model. In contrast, the addition of the wall compartment widens the parameter space allowing invasion compared with the one-compartment model, if the density at the wall is higher than in the lumen, or if the attachment rate at the wall is high and the detachment rate at the wall is low. We also compared the pair-formation models with bulk-conjugation models that describe conjugation by instantaneous transfer of the plasmid at contact between cells, without explicitly describing pair formation. Our results show that pair-formation and bulk-conjugation models predict the same parameter space for plasmid invasion. From our simulations, we conclude that conditions at the gut wall should be taken into account to describe plasmid dynamics in the gut and that transconjugant characteristics rather than donor characteristics should be used to parameterize the models.

Frequencies of deleterious mutations are higher than expected in many plants. Here, by developing a two-locus two-allele model, I examine the effects of differential timing of the expression of deleterious mutations (two-stage effects) on the maintenance of mutations. I assume early- and late-acting loci to distinguish whether maintenance of mutations in populations with high selfing rates is explained better by two-stage effects of single mutations, or by separate mutations in both early- and late-acting loci. I found that, when ovules are overproduced, the stable frequency of early-acting mutations is higher if mutations also occur in a late-acting locus than if a late-acting mutation is lacking. The stable frequency of late-acting mutations is higher if mutations also occur in an early-acting locus than if an early-acting mutation is lacking. Selective interference does not account for these results because analyses in which the number of loci subject to mutations is equalized are included. Overproduction of ovules has little effect on maintenance if either early- or late-acting mutations are lacking, whereas when ovules are not overproduced, the two-stage effect does not enhance the maintenance of mutations. Hence, mutations occurring in both loci coupled with overproduction of ovules enhances the maintenance of mutations in populations with high selfing rates. The detailed mechanisms underlying the two-stage effect were also analyzed.