Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to their implications within many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In this work, we investigate the advantages and drawbacks of a single-parameter long-range signalling model across diverse scenarios. By employing linear and multi-scale analyses, we discover that pattern selection is not only partially explained but also depends on nonlinear effects that extend beyond the scope of these analytical techniques.

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

We present a detailed physiological model of the (human) retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system of partial differential equations based on the mathematical framework of the bi-domain equations, which we have generalized to account for multiple cell-types. We discretize in space with non-uniform finite differences and step through time with a custom adaptive time-stepper that employs a backward differentiation formula and an inexact Newton method. A refinement study confirms the accuracy and efficiency of our numerical method. Numerical simulations using the model compare favorably with experimental findings, such as desensitization to light stimuli and calcium buffering in photoreceptors. Other numerical simulations suggest an interplay between photoreceptor gap junctions and inner segment, but not outer segment, calcium concentration. Applications of this model and simulation include analysis of retinal calcium imaging experiments, the design of electroretinograms, the design of visual prosthetics, and studies of ephaptic coupling within the retina.

One mode by which infection-derived immunity fails is when recovery leads to a reduced but nonzero risk of reinfection. This type of partial protection is called leaky immunity with the degree of leakiness quantified by the relative probability a previously infected individual will get infected upon exposure compared to a naively susceptible individual. Previous authors have defined the reinfection threshold, which occurs when the basic reproduction number equals the inverse of the leakiness, however, there has been some debate about whether or not this is a real threshold. Here we show how the reinfection threshold relates to two important occurrences: (1) the point at which the endemic equilibrium changes from being a stable spiral to a stable node, and (2) the point at which the rate of change of the prevalence increases the most relative to leakiness. When the recovery period is short relative to the average lifetime then both occurrences are close to the reinfection threshold. We show how these results are related to the reinfection threshold found in other models of imperfect immunity. To further demonstrate the significance of this threshold in modeling, we conducted a simulation study to evaluate some of the consequences the reinfection threshold might have in parameter estimation and modeling. Using specific parameter values chosen to reflect an acute infection, we found that the basic reproduction number values larger than that of the reinfection threshold value were less identifiable than those below the threshold.

Defending against novel, repeated, or unpredictable attacks, while avoiding attacks on the 'self', are the central problems of both mammalian immune systems and computer systems. Both systems have been studied in great detail, but with little exchange of information across the different disciplines. Here, we present a conceptual framework for structured comparisons across the fields of biological immunity and cybersecurity, by framing the context of defense, considering different (combinations of) defensive strategies, and evaluating defensive performance. Throughout this paper, we pose open questions for further exploration. We hope to spark the interdisciplinary discovery of general principles of optimal defense, which can be understood and applied in biological immunity, cybersecurity, and other defensive realms.

Though overfishing and climate change are the primary reasons for a regime shift in the fishery, we demonstrate here a different reason for the regime shift, not reported earlier to the best of our knowledge. We show that high demand for fish may cause a regime shift in a fishery in a shorter time. For this, a four-dimensional bioeconomic fishery model is considered and analyzed to explore the system's dynamic behavior. The objective is to demonstrate how increasing demand may cause a catastrophic change in the fish and fishery. We provide the local and global stabilities of different equilibrium points, guaranteeing the stable coexistence of ecological and economic states. Our bifurcation analysis revealed that the demand parameter might play positive and negative roles in the system dynamics. Demand can make an unstable fishery stable. It can also help remove the infection from the system. On the flip side, high demand may cause a regime shift from a harvested state to a non-harvested state, making the price unbounded. Using Pontryagin's maximum principle, we further discussed optimal revenue generation.

Dengue disease transmission is a complex vector-borne disease, mainly due to the co-circulation of four serotypes of the virus. Mathematical models have proved to be a useful tool to understand the complexity of this disease. In this work, we extend the model studied by Esteva et al., 2003, originally proposed for two serotypes, to four circulating serotypes. Using epidemic data of dengue fever in Iquitos (Peru) and San Juan (Puerto Rico), we estimate numerically the co-circulation parameter values for selected outbreaks using a bootstrap method, and we also obtained the Basic Reproduction Number, R0, for each serotype, using both analytical calculations and numerical simulations. Our results indicate that the impact of co-circulation of serotypes in population dynamics of dengue infection is such that there is a reduced effect from DENV-3 to DENV-4 in comparison to no-cross effect for epidemics in Iquitos. Concerning San Juan epidemics, also comparing to no-cross effect, we also observed a reduced effect from the predominant serotype DENV-3 to both DENV-2 and DENV-1 epidemics neglecting the very small number of cases of DENV-4.

At active zones of chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotransmission under high-frequency sustained stimulation. In order to investigate this problem, we introduce a non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes the dynamics at a single active zone, the average over many active zones is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate-limiting feature changes over the course of stimulation. Under sustained stimulation, the dynamics given by the ODEs exhibit transient changes leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior and asymptotic periodicity of the ODE-solution.

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may cause abnormal function and sometimes infertility. The inherent complexity in this endocrine system is a challenge to identifying mechanisms of cycle disruption, particularly given the large number of unknown parameters in existing mathematical models. We develop a new endocrine model to limit model complexity and use simulated distributions of unknown parameters for model analysis. By employing a comprehensive model evaluation, we identify a collection of mechanisms that differentiate normal and abnormal phenotypes. We also discover an intermediate phenotype-displaying relatively normal hormone levels and cycle dynamics-that is grouped statistically with the irregular phenotype. Results provide insight into how clinical symptoms associated with ovulatory disruption may not be detected through hormone measurements alone.

We analyse and mutually compare time series of covid-19-related data and mobility data across Belgium's 43 arrondissements (NUTS 3). In this way, we reach three conclusions. First, we could detect a decrease in mobility during high-incidence stages of the pandemic. This is expressed as a sizeable change in the average amount of time spent outside one's home arrondissement, investigated over five distinct periods, and in more detail using an inter-arrondissement "connectivity index" (CI). Second, we analyse spatio-temporal covid-19-related hospitalisation time series, after smoothing them using a generalise additive mixed model (GAMM). We confirm that some arrondissements are ahead of others and morphologically dissimilar to others, in terms of epidemiological progression. The tools used to quantify this are time-lagged cross-correlation (TLCC) and dynamic time warping (DTW), respectively. Third, we demonstrate that an arrondissement's CI with one of the three identified first-outbreak arrondissements is correlated to a substantial local excess mortality some five to six weeks after the first outbreak. More generally, we couple results leading to the first and second conclusion, in order to demonstrate an overall correlation between CI values on the one hand, and TLCC and DTW values on the other. We conclude that there is a strong correlation between physical movement of people and viral spread in the early stage of the sars-cov-2 epidemic in Belgium, though its strength weakens as the virus spreads.

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

The COVID-19 pandemic continues to have a devastating impact on health systems and economies across the globe. Implementing public health measures in tandem with effective vaccination strategies have been instrumental in curtailing the burden of the pandemic. With the three vaccines authorized for use in the U.S. having varying efficacies and waning effects against major COVID-19 strains, understanding the impact of these vaccines on COVID-19 incidence and fatalities is critical. Here, we formulate and use mathematical models to assess the impact of vaccine type, vaccination and booster uptake, and waning of natural and vaccine-induced immunity on the incidence and fatalities of COVID-19 and to predict future trends of the disease in the U.S. when existing control measures are reinforced or relaxed. The results show a 5-fold reduction in the control reproduction number during the initial vaccination period and a 1.8-fold (2-fold) reduction in the control reproduction number during the initial first booster (second booster) uptake period, compared to the respective previous periods. Due to waning of vaccine-induced immunity, vaccinating up to 96% of the U.S. population might be required to attain herd immunity, if booster uptake is low. Additionally, vaccinating and boosting more people from the onset of vaccination and booster uptake, especially with the Pfizer-BioNTech and Moderna vaccines (which confer superior protection than the Johnson & Johnson vaccine) would have led to a significant reduction in COVID-19 cases and deaths in the U.S. Furthermore, adopting natural immunity-boosting measures is important in fighting COVID-19 and transmission rate reduction measures such as mask-use are critical in combating COVID-19. The emergence of a more transmissible COVID-19 variant, or early relaxation of existing control measures can lead to a more devastating wave, especially if transmission rate reduction measures and vaccination are relaxed simultaneously, while chances of containing the pandemic are enhanced if both vaccination and transmission rate reduction measures are reinforced simultaneously. We conclude that maintaining or improving existing control measures, and boosting with mRNA vaccines are critical in curtailing the burden of the pandemic in the U.S.

During several epidemics, transmission from deceased people significantly contributed to disease spread, but mathematical analysis of this transmission has not been seen in the literature numerously. Transmission of Ebola during traditional burials was the most well-known example; however, there are several other diseases, such as hepatitis, plague or Nipah virus, that can potentially be transmitted from disease victims. This is especially true in the case of serious epidemics when healthcare is overwhelmed and the operative capacity of the health sector is diminished, such as seen during the COVID-19 pandemic. We present a compartmental model for the spread of a disease with an imperfect vaccine available, also considering transmission from deceased infected in general. The global dynamics of the system are completely described by constructing appropriate Lyapunov functions. To support our analytical results, we perform numerical simulations to assess the importance of transmission from the deceased, considering the data collected from three infectious diseases, Ebola virus disease, COVID-19, and Nipah fever.

The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. Here, based on antibody kinetic data of severe and non-severe COVID-19 patients, topological data analysis (TDA) highlights that severity is not binary. However, there are differences in the shape of antibody responses that further classify COVID-19 patients into non-severe, severe, and intermediate cases of severity. Based on the results of TDA, different mathematical models were developed to represent the dynamics between the different severity groups. The best model was the one with the lowest average value of the Akaike Information Criterion for all groups of patients. Our results suggest that different immune mechanisms drive differences between the severity groups. Further inclusion of different components of the immune system will be central for a holistic way of tackling COVID-19.

During the implementation of strong non-pharmaceutical interventions (NPIs), more than one hundred COVID-19 outbreaks induced by different strains in China were dynamically cleared in about 40 days, which presented the characteristics of small scale clustered outbreaks with low peak levels. To address how did randomness affect the dynamic clearing process, we derived an iterative stochastic difference equation for the number of newly reported cases based on the classical stochastic SIR model and calculate the stochastic control reproduction number (SCRN). Further, by employing the Bayesian technique, the change points of SCRNs have been estimated, which is an important prerequisite for determining the lengths of the exponential growth and decline phases. To reveal the influence of randomness on the dynamic zeroing process, we calculated the explicit expression of the mean first passage time (MFPT) during the decreasing phase using the relevant theory of first passage time (FPT), and the main results indicate that random noise can accelerate the dynamic zeroing process. This demonstrates that powerful NPI measures can rapidly reduce the number of infected people during the exponential decline phase, and enhanced randomness is conducive to dynamic zeroing, i.e. the greater the random noise, the shorter the average clearing time is. To confirm this, we chose 26 COVID-19 outbreaks in various provinces in China and fitted the data by estimating the parameters and change points. We then calculated the MFPTs, which were consistent with the actual duration of dynamic zeroing interventions.

We cover the Warburg effect with a three-component evolutionary model, where each component represents a different metabolic strategy. In this context, a scenario involving cells expressing three different phenotypes is presented. One tumour phenotype exhibits glycolytic metabolism through glucose uptake and lactate secretion. Lactate is used by a second malignant phenotype to proliferate. The third phenotype represents healthy cells, which performs oxidative phosphorylation. The purpose of this model is to gain a better understanding of the metabolic alterations associated with the Warburg effect. It is suitable to reproduce some of the clinical trials obtained in colorectal cancer and other even more aggressive tumours. It shows that lactate is an indicator of poor prognosis, since it favours the setting of polymorphic tumour equilibria that complicates its treatment. This model is also used to train a reinforcement learning algorithm, known as Double Deep Q-networks, in order to provide the first optimal targeted therapy based on experimental tumour growth inhibitors as genistein and AR-C155858. Our in silico solution includes the optimal therapy for all the tumour state space and also ensures the best possible quality of life for the patients, by considering the duration of treatment, the use of low-dose medications and the existence of possible contraindications. Optimal therapies obtained with Double Deep Q-networks are validated with the solutions of the Hamilton-Jacobi-Bellman equation.

We propose a bio-economic model of a fishery describing the variations of the fish stock, the fishing effort and the price of the resource on the market supposed to depend on supply and demand. The originality of this model comes from taking into account the storage of part of the resource for a certain time before being put up for sale on the market. Taking into account the supposedly fast price dynamics compared to the other mechanisms involved and after integration of the stock equation, the system is reduced to a system of two delayed differential equations. The qualitative analysis of the model is carried out with the search for equilibrium points and the study of their stability. The study shows the existence of a catastrophic equilibrium corresponding to the extinction of the resource and one or two sustainable fishery equilibrium points that can coexist under certain conditions. The model shows that storing part of the resource makes it possible to avoid a catastrophic situation with the extinction of the fish stock and to stabilize the fishery in the long term. The study also shows that the price variation of the resource has a stabilizing effect by avoiding the appearance of periodic solutions associated with a stable limit cycle surrounding a sustainable fishery equilibrium point resulting from a Hopf bifurcation, which is contrary to the case without price variation where this is possible.

Pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure above 20 mmHg in the main pulmonary artery, is a cardiovascular disease impacting the pulmonary vasculature. PH is accompanied by chronic vascular remodeling, wherein vessels become stiffer, large vessels dilate, and smaller vessels constrict. Some types of PH, including hypoxia-induced PH (HPH), also lead to microvascular rarefaction. This study analyzes the change in pulmonary arterial morphometry in the presence of HPH using novel methods from topological data analysis (TDA). We employ persistent homology to quantify arterial morphometry for control and HPH mice characterizing normalized arterial trees extracted from micro-computed tomography (micro-CT) images. We normalize generated trees using three pruning algorithms before comparing the topology of control and HPH trees. This proof-of-concept study shows that the pruning method affects the spatial tree statistics and complexity. We find that HPH trees are stiffer than control trees but have more branches and a higher depth. Relative directional complexities are lower in HPH animals in the right, ventral, and posterior directions. For the radius pruned trees, this difference is more significant at lower perfusion pressures enabling analysis of remodeling of larger vessels. At higher pressures, the arterial networks include more distal vessels. Results show that the right, ventral, and posterior relative directional complexities increase in HPH trees, indicating the remodeling of distal vessels in these directions. Strahler order pruning enables us to generate trees of comparable size, and results, at all pressure, show that HPH trees have lower complexity than the control trees. Our analysis is based on data from 6 animals (3 control and 3 HPH mice), and even though our analysis is performed in a small dataset, this study provides a framework and proof-of-concept for analyzing properties of biological trees using tools from Topological Data Analysis (TDA). Findings derived from this study bring us a step closer to extracting relevant information for quantifying remodeling in HPH.

Type I interferons (IFN) are the first line of immune response against infection. In this study, we explore the interaction between Type I IFN and foot-and-mouth disease virus (FMDV), focusing on the effect of this interaction on epithelial cell death. While several mathematical models have explored the interaction between interferon and viruses at a systemic level, with most of the work undertaken on influenza and hepatitis C, these cannot investigate why a virus such as FMDV causes extensive cell death in some epithelial tissues leading to the development of lesions, while other infected epithelial tissues exhibit negligible cell death. Our study shows how a model that includes epithelial tissue structure can explain the development of lesions in some tissues and their absence in others. Furthermore, we show how the site of viral entry in an epithelial tissue, the viral replication rate, IFN production, suppression of viral replication by IFN and IFN release by live cells, all have a major impact on results.

A biologically based computational model was developed to describe the hypothalamic-pituitary-thyroid (HPT) axis in developing Xenopus laevis larvae. The goal of this effort was to develop a tool that can be used to better understand mechanisms of thyroid hormone-mediated metamorphosis in X. laevis and predict organismal outcomes when those mechanisms are perturbed by chemical toxicants. In this report, we describe efforts to simulate the normal biology of control organisms. The structure of the model borrows from established models of HPT axis function in mammals. Additional features specific to X. laevis account for the effects of organism growth, growth of the thyroid gland, and developmental changes in regulation of thyroid stimulating hormone (TSH) by circulating thyroid hormones (THs). Calibration was achieved by simulating observed changes in stored and circulating levels of THs during a critical developmental window (Nieuwkoop and Faber stages 54-57) that encompasses widely used in vivo chemical testing protocols. The resulting model predicts that multiple homeostatic processes, operating in concert, can act to preserve circulating levels of THs despite profound impairments in TH synthesis. Represented in the model are several biochemical processes for which there are high-throughput in vitro chemical screening assays. By linking the HPT axis model to a toxicokinetic model of chemical uptake and distribution, it may be possible to use this in vitro effects information to predict chemical effects in X. laevis larvae resulting from defined chemical exposures.

Predicting and preparing for the trajectory of disease epidemics relies on a knowledge of environmental and socioeconomic factors that affect transmission rates on local and global spatial scales. This article discusses the simulation of epidemic outbreaks on human metapopulation networks with community structure, such as cities within national boundaries, for which infection rates vary both within and between communities. We demonstrate mathematically, through next-generation matrices, that the structures of these communities, setting aside all other considerations such as disease virulence and human decision-making, have a profound effect on the reproduction rate of the disease throughout the network. In high modularity networks, with high levels of separation between neighboring communities, disease epidemics tend to spread rapidly in high-risk communities and very slowly in others, whereas in low modularity networks, the epidemic spreads throughout the entire network as a steady pace, with little regard for variations in infection rate. The correlation between network modularity and effective reproduction number is stronger in population with high rates of human movement. This implies that the community structure, human diffusion rate, and disease reproduction number are all intertwined, and the relationships between them can be affected by mitigation strategies such as restricting movement between and within high-risk communities. We then test through numerical simulation the effectiveness of movement restriction and vaccination strategies in reducing the peak prevalence and spread area of outbreaks. Our results show that the effectiveness of these strategies depends on the structure of the network and the properties of the disease. For example, vaccination strategies are most effective in networks with high rates of diffusion, whereas movement restriction strategies are most effective in networks with high modularity and high infection rates. Finally, we offer guidance to epidemic modelers as to the ideal spatial resolution to balance accuracy and data collection costs.

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external and parametric disturbances and (2) in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP or opposer modules), the modules containing negative feedback with buffer action (NFBLB or balancer modules) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

Within-host models of infection can provide important insights into the processes that affect parasite spread and persistence in host populations. However, modeling can be limited by the availability of empirical data, a problem commonly encountered in natural systems. Here, we used six years of immune-infection observations of two gastrointestinal helminths (Trichostrongylus retortaeformis and Graphidium strigosum) from a population of European rabbits (Oryctolagus cuniculus) to develop an age-dependent, mathematical model that explicitly included species-specific and cross-reacting antibody (IgA and IgG) responses to each helminth in hosts with single or dual infections. Different models of single infection were formally compared to test alternative mechanisms of parasite regulation. The two models that best described single infections of each helminth species were then coupled through antibody cross-immunity to examine how the presence of one species could alter the host immune response to, and the within-host dynamics of, the other species. For both single infections, model selection suggested that either IgA or IgG responses could equally explain the observed parasite intensities by host age. However, the antibody attack rate and affinity level changed between the two helminths, it was stronger against T. retortaeformis than against G. strigosum and caused contrasting age-intensity profiles. When the two helminths coinfect the same host, we found variation of the species-specific antibody response to both species together with an asymmetric cross-immune response driven by IgG. Lower attack rate and affinity of antibodies in dual than single infections contributed to the significant increase of both helminth intensities. By combining mathematical modeling with immuno-infection data, our work provides a tractable model framework for disentangling some of the complexities generated by host-parasite and parasite-parasite interactions in natural systems.

Dysregulated inflammation underlies various diseases. Specialized pro-resolving mediators (SPMs) like Resolvin D1 (RvD1) have been shown to resolve inflammation and halt disease progression. Macrophages, key immune cells that drive inflammation, respond to the presence of RvD1 by polarizing to an anti-inflammatory type (M2). However, RvD1's mechanisms, roles, and utility are not fully understood. This paper introduces a gene-regulatory network (GRN) model that contains pathways for RvD1 and other SPMs and proinflammatory molecules like lipopolysaccharides. We couple this GRN model to a partial differential equation-agent-based hybrid model using a multiscale framework to simulate an acute inflammatory response with and without the presence of RvD1. We calibrate and validate the model using experimental data from two animal models. The model reproduces the dynamics of key immune components and the effects of RvD1 during acute inflammation. Our results suggest RvD1 can drive macrophage polarization through the G protein-coupled receptor 32 (GRP32) pathway. The presence of RvD1 leads to an earlier and increased M2 polarization, reduced neutrophil recruitment, and faster apoptotic neutrophil clearance. These results support a body of literature that suggests that RvD1 is a promising candidate for promoting the resolution of acute inflammation. We conclude that once calibrated and validated on human data, the model can identify critical sources of uncertainty, which could be further elucidated in biological experiments and assessed for clinical use.

Nanoparticles (NPs) coated with peptide-major histocompatibility complexes (pMHCs) can be used as a therapy to treat autoimmune diseases. They do so by inducing the differentiation and expansion of disease-suppressing T regulatory type 1 (Tr1) cells by binding to their T cell receptors (TCRs) expressed as TCR-nanoclusters (TCRnc). Their efficacy can be controlled by adjusting NP size and number of pMHCs coated on them (referred to as valence). The binding of these NPs to TCRnc on T cells is thus polyvalent and occurs at three levels: the TCR-pMHC, NP-TCRnc and T cell levels. In this study, we explore how this polyvalent interaction is manifested and examine if it can facilitate T cell activation downstream. This is done by developing a multiscale biophysical model that takes into account the three levels of interactions and the geometrical complexity of the binding. Using the model, we quantify several key parameters associated with this interaction analytically and numerically, including the insertion probability that specifies the number of remaining pMHC binding sites in the contact area between T cells and NPs, the dwell time of interaction between NPs and TCRnc, carrying capacity of TCRnc, the distribution of covered and bound TCRs, and cooperativity in the binding of pMHCs within the contact area. The model was fit to previously published dose-response curves of interferon-γ obtained experimentally by stimulating a population of T cells with increasing concentrations of NPs at various valences and NP sizes. Exploring the parameter space of the model revealed that for an appropriate choice of the contact area angle, the model can produce moderate jumps between dose-response curves at low valences. This suggests that the geometry and kinetics of NP binding to TCRnc can act in synergy to facilitate T cell activation.

In this study, we developed a mechanistic model formulated as a system of reaction-diffusion equations (RDE) to explore the spatiotemporal dynamics of a theoretical pest with a tillering host plant in a controlled rectangular plant field. Local perturbation analysis, a recently developed method of analysis for wave propagation, was utilized to determine patterning regimes resulting from the local and global behaviors of the slow and fast diffusing components of the RDE system, respectively. Turing analysis was done to show that the RDE system does not exhibit Turing patterns. With bug mortality as the bifurcation parameter, regions with oscillations and stable coexistence of the pest and tillers were identified. Numerical simulations illustrate the patterning regimes in 1D and 2D settings. The oscillations suggest that recurrences in pest infestation is possible. Moreover, simulations showed that patterns produced in the model are strongly influenced by the pests' homogeneous dynamics inside the controlled environment.

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two classes. We address this problem by developing a multiclass classification based on probabilistic modeling and optimal decision theory that minimizes the convex combination of false classification rates. The classification process is challenging when the relative fraction of the population in each class, or generalized prevalence, is unknown. Thus, we also develop a method for estimating the generalized prevalence of test data that is independent of classification of the test data. We validate our approach on serological data with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) naïve, previously infected, and vaccinated classes. Synthetic data are used to demonstrate that (i) prevalence estimates are unbiased and converge to true values and (ii) our procedure applies to arbitrary measurement dimensions. In contrast to the binary problem, the multiclass setting offers wide-reaching utility as the most general framework and provides new insight into prevalence estimation best practices.

A discrete model is proposed for the temporal evolution of a population of cells sorted according to their telomeric length. This model assumes that, during cell division, the distribution of the genetic material to daughter cells is asymmetric, i.e. chromosomes of one daughter cell have the same telomere length as the mother, while in the other daughter cell telomeres are shorter. Telomerase activity and cell death are also taken into account. The continuous model is derived from the discrete model by introducing the generational age as a continuous variable in [0,h], being h the Hayflick limit, i.e. the number of times that a cell can divide before reaching the senescent state. A partial differential equation with boundary conditions is obtained. The solution to this equation depends on the initial telomere length distribution. The initial and boundary value problem is solved exactly when the initial distribution is of exponential type. For other types of initial distributions, a numerical solution is proposed. The model is applied to the human follicular growth from preantral to preovulatory follicle as a case study and the aging rate is studied as a function of telomerase activity, the initial distribution and the Hayflick limit. Young, middle and old cell-aged initial normal distributions are considered. In all cases, when telomerase activity decreases, the population ages and the smaller the h value, the higher the aging rate becomes. However, the influence of these two parameters is different depending on the initial distribution. In conclusion, the worst-case scenario corresponds to an aged initial telomere distribution.

Vascular endothelial cells (ECs) residing in the innermost layer of blood vessels are exposed to dynamic wall shear stress (WSS) induced by blood flow. The intracellular nitric oxide (NO) and reactive oxygen species (ROS) in ECs modulated by the dynamic WSS play important roles in endothelial functions. Mathematical modeling is a popular methodology for biophysical studies. It can not only explain existing cell experiments, but also reveal the underlying mechanism. However, the previous mathematical models of NO dynamics in ECs are limited to the static WSS induced by constant flow, while arterial blood flow is a periodic pulsatile flow with varying amplitude and frequency at different exercise intensities. In this study, a mathematical model of intracellular NO and ROS dynamics activated by dynamic WSS based on the in vitro cell experiments is developed. With the hypothesis of the viscoelastic body, the Kelvin model is adopted to simulate the mechanosensors on EC. Thus, the NO dynamics activated by dynamic shear stresses induced by constant flow, pulsatile flow, and oscillatory flow are analyzed and compared. Moreover, the roles of ROS have been considered for the first time in the modeling of NO dynamics in ECs based on the analysis of cell experiments. The predictions of the proposed model coincide fairly well with the experimental data when ECs are subjected to exercise-induced WSS. The mechanism is elucidated that WSS induced by moderate-intensity exercise is most favorable to NO production in ECs. This study can provide valuable insights for further study of NO and ROS dynamics in ECs and help develop appropriate exercise regimens for improving endothelial functions.

The central challenge of mathematical modeling of real-world systems is to strike an appropriate balance between insightful abstraction and detailed accuracy. Models in mathematical epidemiology frequently tend to either extreme, focusing on analytically provable boundaries in simplified, mass-action approximations, or else relying on calculated numerical solutions and computational simulation experiments to capture nuance and details specific to a particular host-disease system. We propose that there is value in an approach striking a slightly different compromise in which a detailed but analytically difficult system is modeled with careful detail, but then abstraction is applied to the results of numerical solutions to that system, rather than to the biological system itself. In this 'Portfolio of Model Approximations' approach, multiple levels of approximation are used to analyze the model at different scales of complexity. While this method has the potential to introduce error in the translation from model to model, it also has the potential to produce generalizable insight for the set of all similar systems, rather than isolated, tailored results that must be started anew for each next question. In this paper, we demonstrate this process and its value with a case study from evolutionary epidemiology. We consider a modified Susceptible-Infected-Recovered model for a vector-borne pathogen affecting two annually reproducing hosts. From observing patterns in simulations of the system and exploiting basic epidemiological properties, we construct two approximations of the model at different levels of complexity that can be treated as hypotheses about the behavior of the model. We compare the predictions of the approximations to the simulated results and discuss the trade-offs between accuracy and abstraction. We discuss the implications for this particular model, and in the context of mathematical biology in general.

Computational methods are becoming commonly used in many areas of medical research. Recently, the modeling of biological mechanisms associated with disease pathophysiology have benefited from approaches such as Quantitative Systems Pharmacology (briefly QSP) and Physiologically Based Pharmacokinetics (briefly PBPK). These methodologies show the potential to enhance, if not substitute animal models. The main reasons for this success are the high accuracy and low cost. Solid mathematical foundations of such methods, such as compartmental systems and flux balance analysis, provide a good base on which to build computational tools. However, there are many choices to be made in model design, that will have a large impact on how these methods perform as we scale up the network or perturb the system to uncover the mechanisms of action of new compounds or therapy combinations. A computational pipeline is presented here that starts with available-omic data and utilizes advanced mathematical simulations to inform the modeling of a biochemical system. Specific attention is devoted to creating a modular workflow, including the mathematical rigorous tools to represent complex chemical reactions, and modeling drug action in terms of its impact on multiple pathways. An application to optimizing combination therapy for tuberculosis shows the potential of the approach.

Gut microbiota plays a key role in host health under normal conditions. However, bacterial composition can be altered by external factors such as antibiotic (AB) intake. While there are many descriptive publications about the effects of AB on gut microbiota composition after treatment, the dynamics and interactions among the bacterial taxa are still poorly understood. In this work, we performed a longitudinal study of gut microbiome dynamics in B. germanica treated with kanamycin. The AB was supplied in three separate periods, giving the microbiota time to recover between each antibiotic intake. We applied two new statistical models, not focusing on pair-wise interactions, to more realistically study the interactions between groups of bacterial taxa and how some groups affect a single taxon. The first model provides information on the importance of a given genus, and the rest of the community, to define the abundance of that genus. The second model, on the other hand, provides details about the relationship between groups of bacteria, focusing on which community groups affect the taxa. These models help us to identify which bacteria are community-dependent in stress conditions, which taxa might be better adapted than the rest of the community, and which bacteria might be working together within the community to overcome the antibiotic. In addition, these models enable us to identify different bacterial groups that were separated in control conditions but were found together in treated conditions, suggesting that when the environment is more hostile (as it is under antibiotic treatment), the whole community tends to work together.