How do productivity gradient and diffusion shape patterns in a plant-herbivore grazing system?

Natural systems show heterogeneous patchy distributions of vegetation over large landscapes. Reaction-diffusion systems can demonstrate such heterogeneity of species distributions. Here, we analyse a reaction-diffusion model of plant-herbivore interactions in two-dimensional space to illustrate non-homogeneous distributions of plants and herbivores. The non-spatial system shows bottom-up control, where herbivore density is low under low and high primary productivity but increased at intermediate productivity. In addition, the non-spatial system provides bistability between a dense vegetation state devoid of herbivores and a coexisting state of plants and herbivores. In the spatiotemporal model, we give analytical conditions of occurring diffusion-driven (Turing) instability, where a novel point in our model is the relative dispersal of herbivores, which represents the movement of herbivores from a higher to a lower vegetation state in addition to the self-diffusion of both species. It is shown that heterogeneity in the population distribution does not occur if the relative dispersal of herbivores is low, but it appears in the opposite case. Due to bistability in the underlying non-spatial system, the spatiotemporal model produces initial value-dependent patterns. The two initial values make different patterns despite having the same primary productivity and relative dispersal rate. As productivity increases with a given relative herbivore dispersal, pattern transition occurs from a blend of stripes and spots of low vegetation state to a predominantly low-density vegetation state with smaller patches of densely vegetated states with one initial value. On the contrary, a discernible change in vegetation patterns from cold spots in the dense vegetation to hot stripes in the primarily low-vegetated state is noticed under the other initial population value. Furthermore, the population distributions of plants and herbivores in the entire domain after a long period are heterogeneous for both initial values, provided the relative herbivore dispersal is substantial. We estimated mean population densities to observe species fitness in the whole domain under variable productivity. When productivity is high, the mean population density of plants may go up or down, depending on the herbivore's relative dispersal rate. In contrast to the bottom-up control dynamics of the non-spatial system, the system exhibits a top-down control under high relative dispersal, where the herbivore regulates vegetation growth under high productivity. On the other hand, herbivores are extinct under high productivity if the relative dispersal is low.

A mathematical model to study low-dose metronomic scheduling for chemotherapy.

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient's body.

Multimodal distribution of transient time of predator extinction in a three-species food chain.

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.

Demand-induced regime shift in fishery: A mathematical perspective.

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.

Identification of critical autophagy-related proteins in diabetic retinopathy: A multi-dimensional computational study.

Diabetic retinopathy (DR) is a common consequence of diabetes mellitus and a primary cause of visual impairment in middle-aged and elderly individuals. DR is susceptible to cellular degradation facilitated by autophagy. In this study, we have employed a multi-layer relatedness (MLR) approach to uncover novel autophagy-related proteins involved in DR. The objective of MLR is to determine the relatedness of autophagic and DR proteins by incorporating both expression and prior-knowledge-based similarities. We constructed a prior knowledge-based network and identified the topologically significant novel disease-related candidate autophagic proteins (CAPs). Then, we evaluated their significance in a gene co-expression and a differentially-expressed gene (DEG) network. Finally, we investigated the proximity of CAPs to the known disease-related proteins. Leveraging this methodology, we identified three crucial autophagy-related proteins, TP53, HSAP90AA1, and PIK3R1, which can influence the DR interactome in various layers of heterogeneity of clinical manifestations. They are strongly related to multiple detrimental characteristics of DR, such as pericyte loss, angiogenesis, apoptosis, and endothelial cell migration, and hence may be used to prevent or delay the progression and development of DR. We evaluated one of the identified targets, TP53, in a cell-based model and found that its inhibition resulted in reduced angiogenesis in high glucose condition required to control DR.

The effect of noise in an HIV infection model with cytotoxic T-lymphocyte impairment.

The human immunodeficiency virus (HIV) interacts with the immune cells within the human body, where the environment is uncertain and noisy. Stochastic models can successfully encapsulate the effect of such a noisy environment compared to their deterministic counterparts. The human immune system is complex but well-coordinated with various immune cells like C D 4T cells, dendritic cells, and cytotoxic T-lymphocyte (CTL) cells, among many others. The CTL can kill the antigenic cells after its recognition. However, the efficacy of CTL in removing the infected C D 4T cells is progressively compromised in HIV-infected individuals. This paper considers a noise-induced HIV-immune cell interaction model with immune impairment. A multiplicative white noise is introduced in the infection rate parameter to represent the fluctuations around the average value of the rate parameter as a causative effect of the noise. We analyzed the deterministic and stochastic models and prescribed sufficient conditions for infection eradication and persistence. It is determined under what parametric restrictions the asymptotic solutions of the noise-induced system will be a limiting case of the deterministic solutions. Simulation results revealed that the solutions of the deterministic system either converge to a CTL-dominated interior equilibrium or a CTL-free immunodeficient equilibrium, depending on the initial values of the system. Stochastic analysis divulged that higher noise might be helpful in the infection removal process. The extinction time of infected C D 4T cells for some fixed immune impairment gradually decreases with increasing noise intensity and follows the power law.

Elucidating the metabolic characteristics of pancreatic ß-cells from patients with type 2 diabetes (T2D) using a genome-scale metabolic modeling.

Diabetes is a global health problem caused primarily by the inability of pancreatic ß-cells to secrete adequate insulin. Despite extensive research, the identity of factors contributing to the dysregulated metabolism-secretion coupling in the ß-cells remains elusive. The present study attempts to capture some of these factors responsible for the impaired ß-cell metabolism-secretion coupling that contributes to diabetes pathogenesis. The metabolic-flux profiles of pancreatic ß-cells were predicted using genome-scale metabolic modeling for ten diabetic patients and ten control subjects. Analysis of these flux states shows reduction in the mitochondrial fatty acid oxidation and mitochondrial oxidative phosphorylation pathways, that leads to decreased insulin secretion in diabetes. We also observed elevated reactive oxygen species (ROS) generation through peroxisomal fatty acid ß-oxidation. In addition, cellular antioxidant defense systems were found to be attenuated in diabetes. Our analysis also uncovered the possible changes in the plasma metabolites in diabetes due to the ß-cells failure. These efforts subsequently led to the identification of seven metabolites associated with cardiovascular disease (CVD) pathogenesis, thus establishing its link as a secondary complication of diabetes.

Diffusive instability in hyperbolic reaction-diffusion equation with different inertia.

This work considers a two-dimensional hyperbolic reaction-diffusion system with different inertia and explores criteria for various instabilities, like a wave, Turing, and Hopf, both theoretically and numerically. It is proven that wave instability may occur in a two-species hyperbolic reaction-diffusion system with identical inertia if the diffusion coefficients of the species are nonidentical but cannot occur if diffusion coefficients are identical. Wave instability may also arise in a two-dimensional hyperbolic reaction-diffusion system if the diffusivities of the species are equal, which is never possible in a parabolic reaction-diffusion system, provided the inertias are different. Interestingly, Turing instability is independent of inertia, but the stability of the corresponding local system depends on the inertia. Theoretical results are demonstrated with an example where the local interaction is represented by the Schnakenberg system.

Mitigating the transmission of infection and death due to SARS-CoV-2 through non-pharmaceutical interventions and repurposing drugs.

The Covid-19 pandemic has put the world under immeasurable stress. There is no specific drug or vaccine till now that can cure the infection or protect people from the infection of coronavirus. It is therefore prudent to use the existing resources and control strategies in an optimal way to contain the virus spread and provide the best possible treatments to the infected individuals. Use of the repurposing drugs along with the non-pharmaceutical intervention strategies may be the right way for fighting against the ongoing pandemic. It is the objective of this work to demonstrate through mathematical modelling and analysis how and to what extent such control strategies can improve the overall Covid-19 epidemic burden. The criteria for disease elimination & persistence were established through the basic reproduction number. A case study with the Indian Covid-19 epidemic data is presented to visualize and illustrate the effects of lockdown, maintaining personal hygiene & safe distancing, and repurposing drugs. It is shown that India can significantly improve the overall Covid-19 epidemic burden through the combined use of NPIs and repurposing drugs though containment of spreading is difficult without serious community participation.

Bistability in a tri-trophic food chain model: Basin stability perspective.

The most important issue of concern in a food chain is the stability of species and their nature of persistence against system parameter changes. For understanding the stable dynamics and their response against parameter perturbation, the local stability analysis is an insufficient tool. A global stability analysis by the conventional techniques seems to supplement some of the shortcomings, however, it becomes more challenging for multistable ecosystems. Either of the techniques fails to provide a complete description of the complexity in dynamics that may evolve in the system, especially, when there is any transition between the stable states. A tri-trophic resource-consumer-predator food chain model has been revisited here that shows bistability and transition to monostability via a border collision that leads to a state of predator extinction. Although earlier studies have partially revealed the dynamics of such transitions, we would like to present additional and precise information by analyzing the system from the perspective of basin stability. By drawing different bifurcation diagrams against three important parameters, using different initial conditions, we identify the range of parameter values within which the stability of the states persists and changes to various complex dynamics. We emphasize the changes in the geometry of the basins of attraction and get a quantitative estimate of the nature of relative changes in the area of the basins (basin stability) during the transitions. Furthermore, we demonstrate the presence of a down-up control, in addition to the conventional bottom-up and top-down control phenomena in the food chain. The application of basin stability in food networks will go a long way for accurate analysis of their dynamics.

The interplay between DNA damage and autophagy in lung cancer: A mathematical study.

The rising mortality in lung cancer, as well as the constraints of the existing drugs, have made it a major research topic. DNA damage marks the early onset of cancer as it often results from vulnerabilities due to UV rays, oxidative stress, ionizing radiation, and various types of genotoxic attacks. p53 plays an unequivocal role in the DNA repair process and has an abiding presence at the crossroads of the pathways linking DNA damage and cancer. p53 also regulates autophagy in a dual manner based on its cellular localization. The plexus of autophagy regulated by p53 includes AMPK and BCL2, which are positive and negative regulators of prime autophagy inducer beclin1, respectively. Although autophagy is a quintessential process, its levels need to be monitored as uncontrolled autophagy may lead to cell death. The association of p53 and autophagic cell death is very vital as the former acts whenever any threat comes to DNA while the latter may play a role in getting rid of the culprit cell. Therefore, in this paper, we have formulated a seven-dimensional mathematical model connecting p53, DNA damage, and autophagy in lung cancer. We performed both local and global sensitivity analysis along with parameter recalibration analysis to understand the system dynamics. We hypothesized that, by the modulation of beclin1 level, the regulation of AMPK and BCL2 could be a possible strategy to mitigate the progression of lung cancer.

Persistence and extinction of species in a disease-induced ecological system under environmental stochasticity.

Population extinction is a serious issue both from the theoretical and practical points of view. We explore here how environmental noise influences persistence and extinction of interacting species in presence of a pathogen even when the populations remain stable in its deterministic counterpart. Multiplicative white noise is introduced in a deterministic predator-prey-parasite system by randomly perturbing three biologically important parameters. It is revealed that the extinction criterion of species may be satisfied in multiple ways, indicating various routes to extinction, and disease eradication may be possible with the right environmental noise. Predator population cannot survive, even when its focal prey strongly persists if its growth rate is lower than some critical value, measured by half of the corresponding noise intensity. It is shown that the average extinction time of population decreases with increasing noise intensity and the probability distribution of the extinction time follows the log-normal density curve. A case study on red grouse (prey) and fox (predator) interaction in presence of the parasites trichostrongylus tenuis of grouse is presented to demonstrate that the model well fits the field data.

Diffusion-induced regular and chaotic patterns in a ratio-dependent predator-prey model with fear factor and prey refuge.

Population distribution of interacting species in a large scale natural system is heterogeneous and subject to change for various reasons. Here, we explore how behavioral modification in prey species due to fear of predator and mutual interference between predators can create different spatiotemporal patterns in population distribution. We show that the fear factor and diffusion in a ratio-dependent predator-prey model may show more complex dynamics than observed earlier. It is shown that when prey diffusivity is low, prey remains concentrated at different patches throughout the domain. However, prey density becomes low at the patches as they disperse at a higher rate. Mixed and stripe patterns are observed during the transition from a hot spot pattern at the lower prey diffusivity to a cold spot pattern at its higher value. Pattern transition is, however, completely opposite if the antipredator behavior is gradually increased. Our simulation results reveal that the spatiotemporal chaotic pattern may also be observed in the Hopf-Turing region of instability provided prey shows a higher level of antipredator behavior. The chaotic pattern of the Hopf-Turing region may be shifted to a spot type pattern of the Turing region depending on the refuge level of the habitat.

Genome scale metabolic model driven strategy to delineate host response to Mycobacterium tuberculosis infection.

We analyze high throughput proteomics data reflecting the response of the Mφ-like THP1 cell line to Mycobacterium tuberculosis (M. tuberculosis) infection. M. tuberculosis's engagement with the host's metabolic pathways is a known strategy employed by the pathogen to shift the balance in its favour. Our study revisits this strategy through the integration of the temporal proteomics data in the genome-scale metabolic model (GSMM) giving context-specific GSMMs. THP1 cells were infected with H37Ra, H37Rv, BND433 and JAL2287 strains of M. tuberculosis and the host response was studied at 6, 18, 30 and 42 hours after infection. We have developed a modified flux balance analysis (FBA), which does not use an objective function, to find the fluxes of metabolic reactions in different strains and stages of infection and have revealed different functional modules. Hence, we have established a method of rewiring using GSMMs to explore potential strategies to change the flux state of virulent M. tuberculosis infected macrophages as against their avirulent counterparts. Our methodology gives a correlation between different flux states, the extent of which was interpreted as the extent of rewiring. The accuracy of the results from the proposed methodology was validated with gene knockout experimental data. We found that more than one reaction has to be rewired simultaneously to alter virulent to an avirulent response. The identified modules showed influence across the investigated strains and time points suggesting that these reactions could be therapeutically targeted. This novel methodology is now available for use in other systems.

Exploring gene knockout strategies to identify potential drug targets using genome-scale metabolic models.

Research on new cancer drugs is performed either through gene knockout studies or phenotypic screening of drugs in cancer cell-lines. Both of these approaches are costly and time-consuming. Computational framework, e.g., genome-scale metabolic models (GSMMs), could be a good alternative to find potential drug targets. The present study aims to investigate the applicability of gene knockout strategies to be used as the finding of drug targets using GSMMs. We performed single-gene knockout studies on existing GSMMs of the NCI-60 cell-lines obtained from 9 tissue types. The metabolic genes responsible for the growth of cancerous cells were identified and then ranked based on their cellular growth reduction. The possible growth reduction mechanisms, which matches with the gene knockout results, were described. Gene ranking was used to identify potential drug targets, which reduce the growth rate of cancer cells but not of the normal cells. The gene ranking results were also compared with existing shRNA screening data. The rank-correlation results for most of the cell-lines were not satisfactory for a single-gene knockout, but it played a significant role in deciding the activity of drug against cell proliferation, whereas multiple gene knockout analysis gave better correlation results. We validated our theoretical results experimentally and showed that the drugs mitotane and myxothiazol can inhibit the growth of at least four cell-lines of NCI-60 database.

Mathematical perspective of Covid-19 pandemic: Disease extinction criteria in deterministic and stochastic models.

The world has been facing the biggest virological invasion in the form of Covid-19 pandemic since the beginning of the year 2020. In this paper, we consider a deterministic epidemic model of four compartments based on the health status of the populations of a given country to capture the disease progression. A stochastic extension of the deterministic model is further considered to capture the uncertainty or variation observed in the disease transmissibility. In the case of a deterministic system, the disease-free equilibrium will be globally asymptotically stable if the basic reproduction number is less than unity, otherwise, the disease persists. Using Lyapunov functional methods, we prove that the infected population of the stochastic system tends to zero exponentially almost surely if the basic reproduction number is less than unity. The stochastic system has no interior equilibrium, however, its asymptotic solution is shown to fluctuate around the endemic equilibrium of the deterministic system under some parametric restrictions, implying that the infection persists. A case study with the Covid-19 epidemic data of Spain is presented and various analytical results have been demonstrated. The epidemic curve in Spain clearly shows two waves of infection. The first wave was observed during March-April and the second wave started in the middle of July and not completed yet. A real-time reproduction number has been given to illustrate the epidemiological status of Spain throughout the study period. Estimated cumulative numbers of confirmed and death cases are 1,613,626 and 42,899, respectively, with case fatality rate 2.66% till the deadly virus is eliminated from Spain.

Tracing the footsteps of autophagy in computational biology.

Autophagy plays a crucial role in maintaining cellular homeostasis through the degradation of unwanted materials like damaged mitochondria and misfolded proteins. However, the contribution of autophagy toward a healthy cell environment is not only limited to the cleaning process. It also assists in protein synthesis when the system lacks the amino acids' inflow from the extracellular environment due to diet consumptions. Reduction in the autophagy process is associated with diseases like cancer, diabetes, non-alcoholic steatohepatitis, etc., while uncontrolled autophagy may facilitate cell death. We need a better understanding of the autophagy processes and their regulatory mechanisms at various levels (molecules, cells, tissues). This demands a thorough understanding of the system with the help of mathematical and computational tools. The present review illuminates how systems biology approaches are being used for the study of the autophagy process. A comprehensive insight is provided on the application of computational methods involving mathematical modeling and network analysis in the autophagy process. Various mathematical models based on the system of differential equations for studying autophagy are covered here. We have also highlighted the significance of network analysis and machine learning in capturing the core regulatory machinery governing the autophagy process. We explored the available autophagic databases and related resources along with their attributes that are useful in investigating autophagy through computational methods. We conclude the article addressing the potential future perspective in this area, which might provide a more in-depth insight into the dynamics of autophagy.

Infection spreading and recovery in a square lattice.

We investigate spreading and recovery of disease in a square lattice, and, in particular, emphasize the role of the initial distribution of infected patches in the network on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, viz., infected core patches (ICP), infected peripheral patches (IPP), and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration; however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue-based semianalytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.

Effect of delay in transportation of extracellular glucose into cardiomyocytes under diabetic condition: a study through mathematical model.

A four-dimensional model was built to mimic the cross-talk among plasma glucose, plasma insulin, intracellular glucose and cytoplasmic calcium of a cardiomyocyte. A time delay was considered to represent the time required for performing various cellular mechanisms between activation of insulin receptor and subsequent glucose entry from extracellular region into intracellular region of a cardiac cell. We analysed the delay-induced model and deciphered conditions for stability and bifurcation. Extensive numerical computations were performed to validate the analytical results and give further insights. Sensitivity study of the system parameters using LHS-PRCC method reveals that some rate parameters, which represent the input of plasma glucose, absorption of glucose by noncardiac cells and insulin production, are sensitive and may cause significant change in the system dynamics. It was observed that the time taken for transportation of extracellular glucose into the cell through GLUT4 plays an important role in maintaining physiological oscillations of the state variables. Parameter recalibration exercise showed that reduced input rate of glucose in the blood plasma or an alteration in transportation delay may be used for therapeutic targets in diabetic-like condition for maintaining normal cardiac function.

Restoration of cytosolic calcium inhibits Mycobacterium tuberculosis intracellular growth: Theoretical evidence and experimental observation.

Mycobacterium tuberculosis (Mtb) is a highly successful intracellular pathogen because of its ability to modulate host's anti-microbial pathways. Phagocytosis acts as the first line of defence against microbial infection. However, Mtb inhibits Phosphatidylinositol 3-phosphate (PI3P) oscillations which is required for phagolysosomal fusion. Here we attempted to understand the mechanisms by which Mtb eliminates phagosome-lysosome fusion. To address this, we built a four dimensional ordinary differential equation model and explored the contribution of PI3P during Mtb phagocytosis. Using this model, we identified some sensitive parameters that influence the dynamics of host-pathogen interactions. We observed that PI3P dynamics can be controlled by regulating the intracellular calcium oscillations. Some plausible methods to restore PI3P oscillations are ER flux rate, recruitment rate of proteins, like Rab GTPase, and cooperativity coefficient of calcium dependent consumption of calmodulin. Further, we investigated whether modulation of these pathways is a potential therapeutic intervention strategy. Here we showed that RyR2 agonist caffeine stimulated calcium influx and inhibited growth of intracellular Mtb in macrophages. Taken together, we demonstrate that modulation of host calcium level is a plausible strategy for killing of intracellular Mtb.