In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of interacting species. Here we explore a model in which predation ability is an independently evolving phenotypic feature, so that even when the relative morphological or physiological traits allow for predation, predation only occurs if the predation ability of individuals has independently evolved to high enough values. In addition to delineating the conditions for the evolutionary emergence of predation, the model reproduces stationary and non-stationary multilevel food webs with the top predators not necessarily having size superiority.

The key role of electro-chemical signals in cellular processes had been known for many years, but more recently the interplay with mechanics has been put in evidence and attracted substantial research interests. Indeed, the sensitivity of cells to mechanical stimuli coming from the microenvironment turns out to be relevant in many biological and physiological circumstances. In particular, experimental evidence demonstrated that cells on elastic planar substrates undergoing periodic stretches, mimicking native cyclic strains in the tissue where they reside, actively reorient their cytoskeletal stress fibres. At the end of the realignment process, the cell axis forms a certain angle with the main stretching direction. Due to the importance of a deeper understanding of mechanotransduction, such a phenomenon was studied both from the experimental and the mathematical modelling point of view. The aim of this review is to collect and discuss both the experimental results on cell reorientation and the fundamental features of the mathematical models that have been proposed in the literature.

Mitochondria are the central hub of ATP production in most eukaryotic cells. Cellular power (energy per unit time), which is primarily generated in these organelles, is crucial to our understanding of cell function in health and disease. We investigated the relation between a mitochondrion's power (metabolic rate) and host cell size by combining metabolic theory with the analysis of two recent databases, one covering 109 protists and the other 63 species including protists, metazoans, microalgae, and vascular plants. We uncovered an interesting statistical regularity: in well-fed protists, relatively elevated values of mitochondrion power cluster around the smallest cell sizes and the medium-large cell sizes. In contrast, in starved protists and metazoans, the relation between mitochondrion power and cell size is inconclusive, and in microalgae and plants, mitochondrion power seems to increase from smaller cells to larger ones (where this investigation includes plant cells of volume up to ca. 2.18 × 105 μm3). Using these results, estimates are provided of the number of active ATP synthase molecules and basal uncouplers.

We revisit a spatial metapopulation model on continuous space as a stochastic point pattern dynamics. In the model, local patches as points are distributed with a certain spatial configuration and status of each patch changes stochastically between occupied and empty: an occupied patch becomes empty by local extinction and an empty patch becomes occupied both by local and global colonization. We carry out simulation analysis and derive an analytical model in terms of singlet, pair and triplet probabilities that describe the stochastic dynamics. Using a simple closure that approximates triplet probabilities by singlet and pair probabilities, we show that equilibrium singlet and pair probabilities can be analytically derived. The derived equilibrium properties successfully describe simulation results under a certain condition where the range of local colonization and the proportion of global colonization play key roles. Our model is an extension of the classical non-spatial Levins model to a spatially explicit metapopulation model. We appeal the advantage of point pattern approach to study spatial dynamics in general ecology and call for the need to deepen our understanding of mathematical tools to explore point pattern dynamics.

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter adif. To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of adif the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For microchamber-grown tumorspheres, there is a threshold in therapy strength below which both subpopulations survive, while high values of adif lead to the complete elimination of the CSC phenotype. For tumorspheres grown on hard and soft agar and in the presence of growth factors, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment.

The mesoderm invagination of the Drosophila embryo is known as an archetypal morphogenic process. To explore the roles of the active cellular forces and the regulation of these forces, we developed an integrated vertex model that combines the regulation of morphogen expression with cell movements and tissue mechanics. Our results suggest that a successful furrow formation requires an apical tension gradient, decreased basal tension, and increased lateral tension, which corresponds to apical constriction, basal expansion, and apicobasal shortening respectively. Our model also considers the mechanical feedback which leads to an ectopic twist expression with external compression as observed in experiments. Our model predicts that ectopic invagination could happen if an external compressive gradient is applied.

The time a red blood cell (RBC) spends in the microvasculature is of prime importance for a number of physiological processes. In this work, we present a methodology for computing an approximation of the so-called transit time distribution (TTD), i.e., the probabilistic description of how long a RBC will reside within the network. As a proof of concept, we apply this methodology to three flavors of the mesh networks. We show that each network type supports multiple distinct steady-state configurations and we present tools for analyzing the associated collection of TTDs, ranging from standard measures like mean capillary transit time (MCTT) and capillary transit time heterogeneity (CTTH) to novel metrics.

We study the effects of the immune system on multiple cancer colonies. When cancer cells proliferate, cytotoxic T lymphocytes (CTLs) reactive to the cancer-specific antigens are activated, suppressing the growth of cancer colonies. The immune reaction activated by a large cancer colony may suppress and eliminate smaller colonies. However, cancer cells mitigate immune reactions by slowing down the activation of CTLs in dendritic cells with regulatory T cells and by inactivating CTLs attacking cancer cells with immune checkpoints. If cancer cells strongly suppress the immune reaction, the system may become bistable, where both the cancer-dominated and immunity-dominated states are locally stable. We study several models differing in the distance between colonies and the migration speeds of CTLs and regulatory T cells. We examine how the domains of attraction for multiple equilibria change with parameters. Nonlinear cancer-immunity dynamics may produce a sharp transition from a state with a small number of colonies and strong immunity to one with many colonies and weak immunity, resulting in the rapid emergence of many cancer colonies in the same organ or metastatic sites.

The renin-angiotensin systems play pivotal role in cardiovascular physiology through its effects on regulating blood pressure and electrolyte homeostasis. Components of circulating RAS (cRAS) that include precursor angiotensinogen, two critical enzymes (renin and angiotensin-converting enzyme, ACE), their bioactive products, angiotensin- I, II together with its receptors (AT1R and AT2R) essentially determine this homeostasis. Most classical studies, however, showed the deleterious role of cRAS in elevating the blood pressure. Contemporary discovery of non-canonical components of the RAS has challenged this classic hypothesis that it can only exert deleterious effects on the cardiovascular systems. Using the classic cRAS model, we have designed in-silico experiments to test the hypothesis that AT2R-mediated feedback effects play pivotal role for maintaining the normal variation of the mean-arterial pressure (MAP).Beside the AT2R-mediation of downstream singling pathways consisting of several non-canonical RAS components, this study first time illustrated AT2R mediated feedback controls over the blood pressure regulation: one that impedes AT1R activity, and the other that downregulates renin. It has been shown that relatively stronger suppression of renin activity significantly contributes in maintaining the normal MAP and that tight AT2R-mediated regulation is relaxed in hyper-and hypotension. This control mechanism is noted to be robustly maintained with the MAP variations through an established linear steady-state relationship among renin, angiotensin I and angiotensin II. This examination suggests that AT2R-mediated downregulation of renin activities potentially counteracts the AT1R-mediated deleterious actions of Ang II. This study, therefore, provides a solid ground for considering different AT2 receptor adaptor protein and direct agonism at AT2R that can cause greater effects along with contemporary approaches of blocking AT1R mediation to attenuate hypertension or other cardiovascular disorders.

The classic Rosenzweig-MacArthur predator-prey model has been shown to exhibit, like other coupled nonlinear ordinary differential equations (ODEs) from ecology, worrying sensitivity to model structure. This sensitivity manifests as markedly different community dynamics arising from saturating functional responses with nearly identical shapes but different mathematical expressions. Using a stochastic differential equation (SDE) version of the Rosenzweig-MacArthur model with the three functional responses considered by Fussmann & Blasius (2005), I show that such sensitivity seems to be solely a property of ODEs or stochastic systems with weak noise. SDEs with strong environmental noise have by contrast very similar fluctuations patterns, irrespective of the mathematical formula used. Although eigenvalues of linearized predator-prey models have been used as an argument for structural sensitivity, they can also be an argument against structural sensitivity. While the sign of the eigenvalues' real part is sensitive to model structure, its magnitude and the presence of imaginary parts are not, which suggests noise-driven oscillations for a broad range of carrying capacities. I then discuss multiple other ways to evaluate structural sensitivity in a stochastic setting, for predator-prey or other ecological systems.

Cortical spreading depolarization (CSD) is a neuropathological condition involving propagating waves of neuronal silence, and is related to multiple diseases, such as migraine aura, traumatic brain injury (TBI), stroke, and cardiac arrest, as well as poor outcome of patients. While CSDs of different severity share similar roots on the ion exchange level, they can lead to different vascular responses (namely spreading hyperemia and spreading ischemia). In this paper, we propose a mathematical model relating neuronal activities to predict vascular changes as measured with near-infrared spectroscopy (NIRS) and fMRI recordings, and apply it to the extreme case of CSD, where sustained near-complete neuronal depolarization is seen. We utilize three serially connected models (namely, ion exchange, neurovascular coupling, and hemodynamic model) which are described by differential equations. Propagating waves of ion concentrations, as well as the associated vasodynamics and hemodynamics, are simulated by solving these equations. Our proposed model predicts vasodynamics and hemodynamics that agree both qualitatively and quantitatively with experimental literature. Mathematical modeling and simulation offer a powerful tool to help understand the underlying mechanisms of CSD and help interpret the data. In addition, it helps develop novel monitoring techniques prior to data collection. Our simulated results strongly suggest that fMRI is unable to reliably distinguish between spreading hyperemia and spreading ischemia, while NIRS signals are substantially distinct in the two cases.

The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria. We apply the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.

The continual distress of COVID-19 cannot be overemphasized. The pandemic economic and social costs are alarming, with recent attributed economic loss amounting to billions of dollars globally. This economic loss is partly driven by workplace absenteeism due to the disease. Influenza is believed to be a culprit in reinforcing this phenomenon as it may exist in the population concurrently with COVID-19 during the influenza season. Furthermore, their joint infection may increase workplace absenteeism leading to additional economic loss. The objective of this project will aim to quantify the collective impact of COVID-19 and influenza on workplace absenteeism via a mathematical compartmental disease model incorporating population screening and vaccination. Our results indicate that appropriate PCR testing and vaccination of both COVID-19 and seasonal influenza may significantly alleviate workplace absenteeism. However, with COVID-19 PCR testing, there may be a critical threshold where additional tests may result in diminishing returns. Regardless, we recommend on-going PCR testing as a public health intervention accompanying concurrent COVID-19 and influenza vaccination with the added caveat that sensitivity analyses will be necessary to determine the optimal thresholds for both testing and vaccine coverage. Overall, our results suggest that rates of COVID-19 vaccination and PCR testing capacity are important factors for reducing absenteeism, while the influenza vaccination rate and the transmission rates for both COVID-19 and influenza have lower and almost equal affect on absenteeism. We also use the model to estimate and quantify the (indirect) benefit that influenza immunization confers against COVID-19 transmission.

Metastatic cascade is a multi-stage process that starts with separation of a cancer cell from the primary tumor and ends with the emergence of a detectable metastasis. In the process the initiator cancer cell enters the circulatory system (intravasates), flows with the blood, and exits the circulation (extravasates) into an organ or tissue. The time period between intravasation and extravasation constitutes the circulation stage of the metastatic cascade. This stage is unique in that it lends itself naturally to various non-invasive observations and measurements in an individual cancer patient. This creates an opportunity for gaining insight into metastasis, its mathematical modeling, and designing diagnostic/prognostic tools and new cancer therapies. Although mechanisms of intravasation, survival and extravasation of circulating tumor cells (CTCs) are very complex and largely unknown, mathematical modeling of the circulation stage of the metastatic cascade is facilitated by two inter-related factors: a relative simplicity of the circulatory network and the cyclic nature of blood flow. The article presents a single-subject stochastic model of CTC dynamics that leads to simple formulas, applicable to any homogeneous CTC population, for organ-specific extravasation probabilities, the distribution and expected value of the number, X, of circulation cycles completed by a CTC prior to extravasation, and the average circulation time. In particular, we found that the distribution of random variable X is geometric G(x), where parameter x is measurable, at least in principle, in an individual subject. We also discuss implications of our results for cancer research and treatment.

Chemotherapeutic drugs are used to treat almost all types of cancer, but the intended response, i.e., elimination, is often incomplete, with a subset of cancer cells resisting treatment. Two critical factors play a role in chemoresistance: the p53 tumour suppressor gene and the X-linked inhibitor of apoptosis (XIAP). These proteins have been shown to act synergistically to elicit cellular responses upon DNA damage induced by chemotherapy, yet, the mechanism is poorly understood. This study introduces a mathematical model characterising the apoptosis pathway activation by p53 before and after mitochondrial outer membrane permeabilisation upon treatment with the chemotherapy Doxorubicin (Dox). "In-silico" simulations show that the p53 dynamics change dose-dependently. Under medium to high doses of Dox, p53 concentration ultimately stabilises to a high level regardless of XIAP concentrations. However, caspase-3 activation may be triggered or not depending on the XIAP induction rate, ultimately determining whether the cell will perish or resist. Consequently, the model predicts that failure to activate apoptosis in some cancer cells expressing wild-type p53 might be due to heterogeneity between cells in upregulating the XIAP protein, rather than due to the p53 protein concentration. Our model suggests that the interplay of the p53 dynamics and the XIAP induction rate is critical to determine the cancer cells' therapeutic response.

The evolution of altruism and spite is facilitated by positive and negative assortments, respectively. Animals repeatedly meet the same opponents and can choose to keep or terminate the interaction. Previous studies have showed that if the probability that the interaction stops depends on how the pairs are, then a positive assortment can emerge, encouraging the evolution of altruism in dyadic interactions and in interactions involving more than two individuals. In contrast, according to another previous study if the probability that the interaction stops depends on how the pairs are, then a negative assortment can emerge, encouraging the evolution of spite in dyadic interactions. Is the evolution of spite facilitated by interactions involving more than two individuals, in addition to dyadic interactions? The present study shows that the evolution of spite in interactions involving many individuals is possible by studying the repeated n-player game played using spiteful and nonspiteful strategies with opting-out options. These results suggest that spite in large groups may evolve through an opt-out mechanism. It also promotes the investigation about whether there are any examples of spiteful behavior in large groups that have evolved through negative assortment in opt-out options in nature.

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We look at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.

Calcium plays a vital role in various biological processes, including muscle contractions, blood clotting, skeletal mineralization, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low extracellular calcium concentration can have dangerous effects on the body. Mathematical modeling is a well-suited approach to investigate the complex physiological processes involved in calcium regulation. While mathematical models have been developed to study calcium homeostasis in male rats, none have been used to investigate known sex differences in hormone levels nor the unique physiological states of pregnancy and lactation. Calcitriol, the active form of vitamin D, plays a key role in intestinal calcium absorption, renal calcium reabsorption, and bone remodeling. It has been shown that, when compared to age-matched male rats, females have significantly lower calcitriol levels. In this study we first seek to investigate the impact of this difference as well as other known sex differences on calcium homeostasis using mathematical modeling. Female bodies differ from male bodies in that during their lifetime they may undergo massive adaptations during pregnancy and lactation. Indeed, maternal adaptations impact calcium regulation in all mammals. In pregnant rodents, intestinal absorption of calcium is massively increased in the mother's body to meet the needs of the developing fetus. In a lactating rodent, much of the calcium needs of milk are met by bone resorption, intestinal absorption, and renal calcium reabsorption. Given these observations, the goal of this project is to develop multi-scale whole-body models of calcium homeostasis that represents (1) how sex differences impact calcium homeostasis in female vs. male rats and (2) how a female body adapts to support the excess demands brought on by pregnancy and lactation. We used these models to quantify the impact of individual sex differences as well as maternal adaptations during pregnancy and lactation. Additionally, we conducted "what if" simulations to test whether sex differences in calcium regulation may enable females to better undergo maternal adaptations required in pregnancy and lactation than males.

To demonstrate their commitment, for instance during wartime, members of a group will sometimes all engage in the same ruinous display. Such uniform, high-cost signals are hard to reconcile with standard models of signaling. For signals to be stable, they should honestly inform their audience; yet, uniform signals are trivially uninformative. To explain this phenomenon, we design a simple model, which we call the signal runaway game. In this game, senders can express outrage at non-senders. Outrage functions as a second-order signal. By expressing outrage at non-senders, senders draw attention to their own signal, and benefit from its increased visibility. Using our model and a simulation, we show that outrage can stabilize uniform signals, and can lead signal costs to run away. Second-order signaling may explain why groups sometimes demand displays of commitment from all their members, and why these displays can entail extreme costs.

In this paper, we present a multi-layer, activity-dependent model for the joint development of ocular dominance (OD) columns and cytochrome oxidase (CO) blobs in primate V1. For simplicity, we focus on layers 4C and 2/3 with both layers receiving direct thalamic inputs and layer 4C sending vertical projections to layer 2/3. Both the thalamic and the vertical connections are taken to be modifiable by activity. Using a correlation-based Hebbian learning rule with subtractive normalization, we show how the formation of an OD map in layer 4C is inherited by layer 2/3 via the vertical projections. Competition between these feedforward projections and the direct thalamic input to layer 2/3 then results in the formation of CO blobs superimposed upon the ocular dominance map. The spacing of the OD columns is determined by the spatial profile of the intralaminar connections within layer 4, while the spacing of CO blobs depends both on the width of the OD columns inherited from layer 4 and the spatial distribution of intralaminar connections within the superficial layer. The resulting CO blob distribution is shown to be consistent with experimental data. In addition, we numerically simulate monocular deprivation and find that while the CO blob distribution is unaltered, the OD pattern undergoes modification. The OD stripes of the deprived eye narrow, whereas the OD stripes for the remaining open eye widen.

Cross-immunity, as an evolutionary driver, can contribute to pathogen evolution, particularly pathogen diversity. Healthcare interventions aimed at reducing disease severity or transmission are commonly used to control diseases and can also induce pathogen evolution. Understanding pathogen evolution in the context of cross-immunity and healthcare interventions is crucial for infection control. This study starts by modelling cross-immunity, the extent of which is determined by strain traits and host characteristics. Given that all hosts have the same characteristics, full cross-immunity between residents and mutants occurs when mutation step sizes are small enough. Cross-immunity can be partial when the step size is large. The presence of partial cross-immunity reduces pathogen load and shortens the infectious period inside hosts, reducing transmission between hosts and improving host population survival and recovery. This study focuses on how pathogens evolve through small and large mutational steps and how healthcare interventions affect pathogen evolution. Using the theory of adaptive dynamics, we found that when mutational steps are small (only full cross-immunity is present), pathogen diversity cannot occur because it maximises the basic reproduction number. This results in intermediate values for both pathogen growth and clearance rates. However, when large mutational steps are allowed (with full and partial cross-immunity present), pathogens can evolve into multiple strains and induce pathogen diversity. The study also shows that different healthcare interventions can have varying effects on pathogen evolution. Generally, low levels of intervention are more likely to induce strain diversity, while high levels are more likely to result in strain reduction.

The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms.

Synchronization of interconnecting units is one of the hottest topics many researchers are interested in. In addition, this emerging phenomenon is responsible for many biological processes, and thus, the synchronization of interacting neurons is an important field of study in neuroscience. Employing the memristive Chialvo (mChialvo) neuron map, this paper investigates the effect of electrical, inner-linking, chemical, and hybrid coupling functions on the synchronization state of a neuronal network with regular structure. Master stability function (MSF) analysis is performed to obtain the necessary conditions for synchronizing the built networks. Afterward, the MSF-based results are confirmed by calculating the synchronization error. Besides, the dynamics of the synchronous neurons are discussed based on the bifurcation analysis. Our results suggest that, compared to the electrical and inner-linking functions, chemical synapses facilitate mChialvo neurons' synchronization since the neurons can achieve synchrony with a negligible chemical coupling strength. Further studies reveal that based on the active synapses, coupled mChialvo neurons can reach cluster synchronization, chimera state, sine-like synchronization, phase synchronization, and cluster phase synchronization.

Many researchers have studied the population dynamics of microbe of microbes as a typical example of population dynamics. The Monod equation, which mainly focuses on the growth and stationary phases, is used when plotting a growth curve. However, the growth potential in the late stage of culture has been overlooked. Previous studies considered the direct degradation of products to the limiting substrate. In this study, we considered microbial growth during the stationary phase, which enables us to describe the dynamics precisely. The microbes were divided into two populations: one grew by consuming the limiting substrate and the other degraded the products by metabolism. According to the numerical analysis of our model, microbes may choose one of two strategies: one consumes substrates and expands quickly, and the other grows slowly while cleaning up the environment in which they thrive. Furthermore, we found three types of microbial growth depending on their ability to detect metabolite accumulation. Using experimentally measured data, this model can estimate the dynamics of cell density, the substrates, and the metabolites used. The model's disentangling of growth curves offers novel interpretive possibilities for culture system dynamics.

The cost of germline maintenance gives rise to a trade-off between lowering the deleterious mutation rate and investing in life history functions. Therefore, life history and the mutation rate coevolve, but this coevolution is not well understood. We develop a mathematical model to analyse the evolution of resource allocation traits, which simultaneously affect life history and the deleterious mutation rate. First, we show that the invasion fitness of such resource allocation traits can be approximated by the basic reproductive number of the least-loaded class; the expected lifetime production of offspring without deleterious mutations born to individuals without deleterious mutations. Second, we apply the model to investigate (i) the coevolution of reproductive effort and germline maintenance and (ii) the coevolution of age-at-maturity and germline maintenance. This analysis provides two resource allocation predictions when exposure to environmental mutagens is higher. First, selection favours higher allocation to germline maintenance, even if it comes at the expense of life history functions, and leads to a shift in allocation towards reproduction rather than survival. Second, life histories tend to be faster, characterised by individuals with shorter lifespans and smaller body sizes at maturity. Our results suggest that mutation accumulation via the cost of germline maintenance can be a major force shaping life-history traits.

Excessive accumulation of β-catenin proteins is a vital driver in the development of breast cancer. Many clinical assessments incorporating immunotherapy with targeted mRNA of β-catenin are costly endeavor. This paper develops novel mathematical models for different treatments by invoking available clinical data to calibrate models, along with the selection and evaluation of therapy strategies in a faster manner with lower cost. Firstly, in order to explore the interactions between cancer cells and the immune system within the tumor microenvironment, we construct different types of breast cancer treatment models based on RNA interference technique and immune checkpoint inhibitors, which have been proved to be an effective combined therapy in pre-clinical trials associated with the inhibition of β-catenin proteins to enhance intrinsic anti-tumor immune response. Secondly, various techniques including MCMC are adopted to estimate multiple parameters and thus simulations in agreement with experimental results sustain the validity of our models. Furthermore, the gradient descent method and particle swarm algorithm are designed to optimize therapy schemes to inhibit the growth of tumor and lower the treatment cost. Considering the mechanisms of drug resistance in vivo, simulations exhibit that therapies are ineffective resulting in cancer relapse in the prolonged time. For this reason, parametric sensitivity analysis sheds light on the choice of new treatments which indicate that, in addition to inhibiting β-catenin proteins and improving self-immunity, the injection of dendritic cells promoting immunity may provide a novel vision for the future of cancer treatment. Overall, our study provides witness of principle from a mathematical perspective to guide clinical trials and the selection of treatment regimens.

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

Double strand break (DSB) repair is critical to maintaining the integrity of the genome. DSB repair deficiency underlies multiple pathologies, including cancer, chromosome instability syndromes, and, potentially, neurodevelopmental defects. DSB repair is mainly handled by two pathways: highly accurate homologous recombination (HR), which requires a sister chromatid for template-based repair, limited to S/G2 phases of the cell cycle, and canonical non-homologous end joining (c-NHEJ), available throughout the cell cycle in which minimum homology is sufficient for highly efficient yet error-prone repair. Some circumstances, such as cancer, require alternative highly mutagenic DSB repair pathways like microhomology-mediated end-joining (MMEJ) and single-strand annealing (SSA), which are triggered to attend to DNA damage. These non-canonical repair alternatives are emerging as prominent drivers of resistance in drug-based tumor therapies. Multiple DSB repair options require tight inter-pathway regulation to prevent unscheduled activities. In addition to this complexity, epigenetic modifications of the histones surrounding the DSB region are emerging as critical regulators of the DSB repair pathway choice. Modeling approaches to understanding DSBs repair pathway choice are advantageous to perform simulations and generate predictions on previously uncharacterized aspects of DSBs response. In this work, we present a Boolean network model of the DSB repair pathway choice that incorporates the knowledge, into a dynamic system, of the inter-pathways regulation involved in DSB repair, i.e., HR, c-NHEJ, SSA, and MMEJ. Our model recapitulates the well-characterized HR activity observed in wild-type cells in response to DSBs. It also recovers clinically relevant behaviors of BRCA1/FANCS mutants, and their corresponding drug resistance mechanisms ascribed to DNA repair gain-of-function pathogenic variants. Since epigenetic modifiers are dynamic and possible druggable targets, we incorporated them into our model to better characterize their involvement in DSB repair. Our model predicted that loss of the TIP60 complex and its corresponding histone acetylation activity leads to activation of SSA in response to DSBs. Our experimental validation showed that TIP60 effectively prevents activation of RAD52, a key SSA executor, and confirms the suitable use of Boolean network modeling for understanding DNA DSB repair.

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we take into account the nonlinear interaction between oxygen and carbon dioxide in the blood volume, referred to as the Bohr and Haldane effects. We also propose a definition of the physiological dead space volume (the lung volume that does not contribute to gas exchange) which depends on the pathological state and the breathing scenario. This coupled ventilation-gas diffusion model is driven by the sole action of the respiratory muscles. We analyse its sensitivity with respect to characteristic parameters: the resistance of the bronchial tree, the elastance of the lung tissue and the oxygen and carbon dioxide diffusion coefficients of the alveolo-capillary membrane. Idealized pathological situations are also numerically investigated. We obtain realistic qualitative tendencies, which represent a first step towards classification of the pathological behaviours with respect to the considered input parameters.

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.

In his famous two-part paper, published in Journal of Theoretical Biology in 1964, W. D. Hamilton predicted that natural selection acting in male-haploid populations favours a ratio of males to females that is in accordance with the golden ratio. This prediction has found its way into the pages of one of the best-selling books of all time, Dan Brown's 2003 novel The da Vinci Code, and is therefore in the running for the most widely known quantitative result in the history of evolutionary biology. Unfortunately, this golden-ratio result is wrong, and was later corrected by Hamilton, who showed that natural selection actually favours an unbiased sex ratio in this setting. But it has been unclear exactly how Hamilton arrived at the golden-ratio result in the first place. Here I show that the solution to this puzzle is found in unpublished work held in the British Library's W. D. Hamilton Archive. Specifically, in addition to employing a faulty method for calculating relatedness, Hamilton had also employed a faulty method for calculating reproductive value, considering only genetic contributions to the next generation rather than to the distant future. Repeating both mistakes recovers his erroneous golden-ratio result.

A key characteristic of acute communicable diseases is the infectiousness that varies over time as the infection dynamics evolve within a host, which influences the risk of transmission in different stages of the disease. Despite the evidence of time-varying transmission risk, most dynamic models of epidemics assume a constant transmission rate during the infectious period. Recent work has shown the difference in epidemic dynamics when this assumption is relaxed and different transmission rates are used by discretizing the infectious period into multiple sub-periods. Here, we develop an age-structured model to integrate a continuous time-varying transmission risk, based on an established correlation between the viral dynamics and infectiousness profile. Taking into account the natural history and parameter estimates of COVID-19 caused by the original strain of SARS-CoV-2, we demonstrate the difference in temporal epidemic dynamics when a continuous time-varying transmission probability is used as compared to multiple constant transmission probabilities. Our results show a significant difference between the incidence curves in terms of the magnitude and peak time, even when the reproduction number and total number of infections are the same for continuous and discrete transmission probabilities. Finally, we demonstrate the spurious outcome of preventing an epidemic through the isolation of infectious individuals when constant transmission probabilities are used, highlighting the importance of integrating a continuous time-dependent transmission parameter in dynamic models. These findings suggest a more cautious interpretation of model outcomes, especially those that are intended to evaluate the effectiveness of interventions and inform policy decisions for disease mitigation strategies.

A common side effect of pharmaceutical drugs is an increased propensity for cardiac arrhythmias. Many drugs bind to cardiac ion-channels in a state-specific manner, which alters the ionic conductances in complicated ways, making it difficult to identify the mechanisms underlying pro-arrhythmic drug effects. To better understand the fundamental mechanisms underlying the diverse effects of state-dependent sodium (Na+) channel blockers on cellular excitability, we consider two canonical motifs of drug-ion-channel interactions and compare the effects of Na+ channel blockers on the rate-dependence of peak upstroke velocity, conduction velocity, and vulnerable window size. In the literature, both motifs are referred to as "guarded receptor," but here we distinguish between state-specific binding that does not alter channel gating (referred to here as "guarded receptor") and state-specific binding that blocks certain gating transitions ("gate immobilization"). For each drug binding motif, we consider drugs that bind to the inactivated state and drugs that bind to the non-inactivated state of the Na+ channel. Exploiting the idealized nature of the canonical binding motifs, we identify the fundamental mechanisms underlying the effects on excitability of the various binding interactions. Specifically, we derive the voltage-dependence of the drug binding time constants and the equilibrium fractions of channels bound to drug, and we then derive a formula that incorporates these time constants and equilibrium fractions to elucidate the fundamental mechanisms. In the case of charged drug, we find that drugs that bind to inactivated channels exhibit greater rate-dependence than drugs that bind to non-inactivated channels. For neutral drugs, the effects of guarded receptor interactions are rate-independent, and we describe a novel mechanism for reverse rate-dependence resulting from neutral drug binding to non-inactivated channels via the gate immobilization motif.

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker-Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions.

Floral food deception is a well-known phenomenon which is not thoroughly understood. Particularly, it is unclear what drives a plant towards Batesian mimicry or towards generalized food deception. We analysed the evolutionary game between a Model species with nectar-secreting flowers and a Deceiver species that provides no nectar who share pollinators for reproduction. We focused our analysis on the effect of similarity of floral signals between participating plants and on costs of nectar production. We defined payoffs in the game between Models and Deceivers as the stationary visitation frequencies to participating species with different signal similarities and nectar costs. Therefore, fitness payoff of each strategy was a product of complex interactions between plant species composing the community and the pollinators visiting them. Our model provides a unified framework in which consequences of Model species interaction with different deception modes can be compared. Our findings suggest that plant-pollinator systems, like other mutualistic systems, are prone to exploitation, and that exploitation may persist at a large range of conditions. We showed that floral similarity, and thus, pollinators' ability to discriminate between Model and deceptive species, governs the stability of Batesian mimicry, while pollinator switching and sampling behaviour enables the persistence of general food deception.

Theoretical studies over the past decades have revealed various factors that favor or disfavor the evolution of dispersal. Among these, environmental heterogeneity is one driving force that can impact dispersal traits, because dispersing individuals can obtain a fitness benefit through finding better environments. Despite this potential benefit, some previous works have shown that the existence of spatial heterogeneity hinders evolution of dispersal. On the other hand, temporal heterogeneity has been shown to promote dispersal through a bet-hedging mechanism. When they are combined in a patch-structured population in which the quality of each patch varies over time independently of the others, it has been shown that spatiotemporal heterogeneity can favor evolution of dispersal. When individuals can use patch quality information so that dispersal decision is conditional, the evolutionary outcome can be different since individuals have options to disperse more/less offspring from bad/good patches. In this paper, we generalize the model and results of previous studies. We find richer dynamics including bistable evolutionary dynamics when there is arrival bias towards high-productivity patches. Then we study the evolution of conditional dispersal strategy in this generalized model. We find a surprising result that no offspring will disperse from a patch whose productivity was low when these offspring were born. In addition to mathematical proofs, we also provide intuition behind this initially counter-intuitive result based on reproductive-value arguments. Dispersal from high-productivity patches can evolve, and its parameter dependence behaves similarly, but not identically, to the case of unconditional dispersal. Our results unveil an importance of whether or not individuals can use patch quality information in dispersal evolution.