We review studies on tissue transplantation experiments for various species: one piece of the donor tissue is excised and transplanted into a slit in the host tissue, then observe the behavior of this grafted tissue. Although we have known the results of some transplantation experiments, there are many more possible experiments with unknown results. We develop a penalty function-based method that uses the known experimental results to infer the unknown experimental results. Similar experiments without similar results get penalized and correspond to smaller probability. This method can provide the most probable results of a group of experiments or the probability of a specific result for each experiment. This method is also generalized to other situations. Besides, we solve a problem: how to design experiments so that such a method can be applied most efficiently.

We study the dynamics of epidemics in a networked metapopulation model. In each subpopulation, representing a locality, the disease propagates according to a modified susceptible-exposed-infected-recovered (SEIR) dynamics. In the modified SEIR dynamics, individuals reduce their number of contacts as a function of the weighted sum of cumulative number of cases within the locality and in neighboring localities. We consider a scenario with two localities where disease originates in one locality and is exported to the neighboring locality via travel of exposed (latently infected) individuals. We establish a lower bound on the outbreak size at the origin as a function of the speed of spread. Using the lower bound on the outbreak size at the origin, we establish an upper bound on the outbreak size at the importing locality as a function of the speed of spread and the level of preparedness for the low mobility regime. We evaluate the critical levels of preparedness that stop the disease from spreading at the importing locality. Finally, we show how the benefit of preparedness diminishes under high mobility rates. Our results highlight the importance of preparedness at localities where cases are beginning to rise such that localities can help stop local outbreaks when they respond to the severity of outbreaks in neighboring localities.

Recent experimental and mathematical work has shown the interdependence of the rod and cone photoreceptors with the retinal pigment epithelium in maintaining sight. Accelerated intake of glucose into the cones via the theoredoxin-like rod-derived cone viability factor (RdCVF) is needed as aerobic glycolysis is the primary source of energy production. Reactive oxidative species (ROS) result from the rod and cone metabolism and recent experimental work has shown that the long form of RdCVF (RdCVFL) helps mitigate the negative effects of ROS. In this work we investigate the role of RdCVFL in maintaining the health of the photoreceptors. The results of our mathematical model show the necessity of RdCVFL and also demonstrate additional stable modes that are present in this system. The sensitivity analysis shows the importance of glucose uptake, nutrient levels, and ROS mitigation in maintaining rod and cone health in light-damaged mouse models. Together, these suggests areas on which to focus treatment in order to prolong the photoreceptors, especially in situations where ROS is a contributing factor to their death such as retinitis pigmentosa.

A series of prior publications has reported unusual properties of the set of genetically encoded amino acids shared by all known life. This work uses quantitative measures (descriptors) of size, charge and hydrophobicity to compare the distribution of the genetically encoded amino acids with random samples of plausible alternatives. Results show that the standard "alphabet" of amino acids established by the time of LUCA is distributed with unusual evenness over a broad range for the three, key physicochemical properties. However, different publications have used slightly different assumptions, including variations in the precise descriptors used, the set of plausible alternative molecules considered, and the format in which results have been presented. Here we consolidate these findings into a unified framework in order to clarify unusual features. We find that in general, the remarkable features of the full set of 20 genetically encoded amino acids are robust when compared with random samples drawn from a densely populated picture of plausible, alternative L-α-amino acids. In particular, the genetically encoded set is distributed across an exceptionally broad range of volumes, and distributed exceptionally evenly within a modest range of hydrophobicities. Surprisingly, range and evenness of charge (pKa) is exceptional only for the full amino acid structures, not for their sidechains - a result inconsistent with prior interpretations involving the role that amino acid sidechains play within protein sequences. In stark contrast, these remarkable features are far less clear when the prebiotically plausible subset of genetically encoded amino acids is compared with a much smaller pool of prebiotically plausible alternatives. By considering the nature of the "optimality theory" approach taken to derive these and prior insights, we suggest productive avenues for further research.

Tissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue's moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and to simulate root hair growth. We also provide user-friendly MATLAB code to implement the algorithms.

Gastric cancer is regarded as a major health issue for human being nowadays. The Helicobacter pylori (H. pylori) infection has been found to accelerate the development of gastritis and gastric cancer. Significant efforts have been made towards the understanding of the biology of gastric cancer on both genetic and epigenetic levels. However the physical mechanism behind the gastric cancer formation is still elusive. In this study, we constructed a model for investigating gastric cancer formation by explored the gastric cancer landscape and the flow flux. We uncovered three stable state attractors on the landscape: normal, gastritis and gastric cancer. The definition of each attractor is based on the biological function and gene expression levels. The global stabilities and the switching processes were quantified through the barrier heights and dominant kinetic paths. To investigate the underlying mechanism of the process from normal through the gastritis to the gastric cancer caused by genetic or epigenetic factors, we simulate the oncogenesis of gastric cancer through changes of several gene regulation strengths and H. pylori infection. The simulated results can illustrate the developmental and metastasis process of gastric cancer. Different H. pylori infection degrees accelerating the process from gastritis to gastric cancer can be quantified. Then we applied global sensitivity analysis, one key gene and four key regulations were found. These results are consist with the experimental results and can be used to design the polygenic anti-cancer agents through multiple key genes or regulations. The landscape approach provides a physical and simple strategy for analyzing gastric cancer in a systematic and quantitative way. It also offers new insight into treatment strategy for gastric cancer by adjusting relevant polygenic genes and regulations.

A predator that preys on randomly-distributed stationary energetically-equivalent small prey will probably choose its next prey to be the nearest one. But what if no prey is found within the detection range of the predator? It is hypothesized that in this case the predator will move along an arbitrary chosen direction until a prey is detected, and turn towards it. In a stochastic environment this strategy leads to a certain distribution function of distances that the predator moves between consequent prey catches. It is shown that when the detection range of the predator exceeds the average distance between prey, this distribution function becomes the nearest neighbor distribution function, whereas; wherew when the detection range is small as compared with the average distance between prey, it becomes the exponential distribution, as the distribution of distances between neighbors on a line. In the first case, the average distance between catches becomes roughly half the average distance between prey; in the second case, it becomes inversely proportional to the square of the detection range. Ocean sunfish preys on practically stationary jellyfish at depth of more than a hundred meters, in dim light. Plausibly, it can detect jellyfish only at close quarters, and hence its detection range is probably small as compared with the average distance between prey. Analysis of the tracking data from seven animals over a few days yielded many thousands of swimming segments separating consequent prey catches. Indeed, lengths of these segments were shown to have the exponential distribution. This finding not only supports the initial hypothesis of this study, but also reveals the fragility of the energetic balance of this animal. A two-fold decrease in the detection range (e.g. due to a decreased visibility) is expected to increase the average distance it moves between catches four-fold, and hence decrease its specific energy intake (the number of jellyfishes per distance moved) by the same rate.

With the aid of the evolutionary vaccination game on a scale-free network, we design a new subsidy policy, named degree dependent subsidy, where cooperative agents get incentives according to their connectivity or degree. That is, agents, having a greater degree, receive a higher incentive, and vice versa. Here we presume that vaccinators are cooperative agents. The new scheme can be said to an intermediate policy between two previously studies policies, namely free ticket and flat discount policies. The former policy distributes free tickets to cooperative hub agents as a priority, whereas the latter dispenses a fixed discount to every cooperator. We compare the efficiency of each policy in terms of having a less infectious state with a minimum social cost. While investigating the performance of the three policies in terms of average social payoff-which takes into account the cost of vaccination as well as infection-the free ticket scheme is found to be the most appealing policies among the three when the budget for subsidy is quite low. The degree dependent subsidy policy outperforms others for a moderate budget size, while the flat discount policy requires a higher budget to effectively suppress the disease. We further estimate threshold levels of the subsidy budget for each policy beyond which subsidizing results in excessive use of vaccination. As a whole, concerning vaccination coverage and final epidemic size, the degree-dependent subsidy scheme outperforms the flat discount scheme, but is dominated by the free ticket policy.

The majority of biologically inspired dynamic problems are essentially defined by the complexity of the contact surface where such motion takes place. From a statistical point of view, such a surface in many biological problems is typically a combination of a universal scale invariant (fractal) component and a well-defined component having a characteristic scale. If the biological object, here a dung ball, or its parts have a size comparable to the dimensions of the surface peculiarities, one can expect a strong influence on the motion. To avoid competition for the same food resource, some dung-feeding insect species form a dung ball and roll it away from the dung pile. In order to quickly escape competition, dung beetles seem to strictly follow an initial bearing. On flat terrain, they manage to roll a dung ball along a nearly perfect straight path. However, on a more realistic terrain, which normally includes both components mentioned above, the motion is more complex. In this study, we numerically model the ball transportation on terrain with different scales of surface profile. A strong correlation is observed between effective ball transportation (time, distance, work) and the ratio of the size of the ball relative to the size of the terrain roughness. Surface irregularities, with a characteristic size comparable to the ball diameter, are negatively correlated to the efficiency of ball transportation. In addition a strong correlation is found between the quasi random noise, numerically simulating the activity of a dung beetle trying to escape from a valley in which it is trapped, and the success in ball transportation.

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via "mean-field coupling," whereby the likelihood that a gamete survives is an increasing function of its size relative to the population's mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Although the evolutionary response to random genetic drift is classically modelled as a sampling process for populations with fixed abundance, the abundances of populations in the wild fluctuate over time. Furthermore, since wild populations exhibit demographic stochasticity and since random genetic drift is in part due to demographic stochasticity, theoretical approaches are needed to understand the role of demographic stochasticity in eco-evolutionary dynamics. Here we close this gap for quantitative characters evolving in continuously reproducing populations by providing a framework to track the stochastic dynamics of abundance density across phenotypic space using stochastic partial differential equations. In the process we develop a set of heuristics to operationalize the powerful, but abstract theory of white noise and diffusion-limits of individual-based models. Applying these heuristics, we obtain stochastic ordinary differential equations that generalize classical expressions of ecological quantitative genetics. In particular, by supplying growth rate and reproductive variance as functions of abundance densities and trait values, these equations track population size, mean trait and additive genetic variance responding to mutation, demographic stochasticity, random genetic drift, deterministic selection and noise-induced selection. We demonstrate the utility of our approach by formulating a model of diffuse coevolution mediated by exploitative competition for a continuum of resources. In addition to trait and abundance distributions, this model predicts interaction networks defined by niche-overlap, competition coefficients, or selection gradients. Using a high-richness approximation, we find linear selection gradients and competition coefficients are uncorrelated, but magnitudes of linear selection gradients and quadratic selection gradients are both positively correlated with competition coefficients. Hence, competing species that strongly affect each other's abundance tend to also impose selection on one another, but the directionality is not predicted. This approach contributes to the development of a synthetic theory of evolutionary ecology by formalizing first principle derivations of stochastic models tracking feedbacks of biological processes and the patterns of diversity they produce.

The evolution of cooperation has been one of the main topics in evolutionary biology. If cooperators maintain interaction with cooperators and halt interaction with defectors, then cooperation can pay and can be favored by natural selection. This is called an exit option. Here, not only cooperation in dyadic interactions but also cooperation in sizable groups can be observed. Rivalry is about whether usage of the benefit by one individual reduces its availability to others or not. A common good is a rivalrous good, whereas a public good is a non-rivalrous good. In this paper, by analyzing n-player prisoner's dilemma games, we examine whether the effect of the group size on cooperation is positive or negative in the context of exit option. When goods are common goods, defectors always dominate cooperators when the group size is infinitely large. Thus, the group size has only negative effects on the evolution of cooperation when goods are common goods. In contrast, when goods are public goods, an increase in group size has positive effects as well as negative effects on the evolution of cooperation. In addition, we reveal that it has both positive and negative effects on the evolution of cooperation for cooperators to tolerate some defection and hope to keep the interaction.

While most of the countries around the globe are combating the pandemic of COVID-19, the level of its impact is quite variable among different countries. In particular, the data from Nepal, a developing country having an open border provision with highly COVID-19 affected country India, has shown a biphasic pattern of epidemic, a controlled phase (until July 21, 2020) followed by an outgrown phase (after July 21, 2020). To uncover the effective strategies implemented during the controlled phase, we develop a mathematical model that is able to describe the data from both phases of COVID-19 dynamics in Nepal. Using our best parameter estimates with 95% confidence interval, we found that during the controlled phase most of the recorded cases were imported from outside the country with a small number generated from the local transmission, consistent with the data. Our model predicts that these successful strategies were able to maintain the reproduction number at around 0.21 during the controlled phase, preventing 442,640 cases of COVID-19 and saving more than 1,200 lives in Nepal. However, during the outgrown phase, when the strategies such as border screening and quarantine, lockdown, and detection and isolation, were altered, the reproduction number raised to 1.8, resulting in exponentially growing cases of COVID-19. We further used our model to predict the long-term dynamics of COVID-19 in Nepal and found that without any interventions the current trend may result in about 18.76 million cases (10.70 million detected and 8.06 million undetected) and 89 thousand deaths in Nepal by the end of 2021. Finally, using our predictive model, we evaluated the effects of various control strategies on the long-term outcome of this epidemics and identified ideal strategies to curb the epidemic in Nepal.

Guinea-worm disease (GWD) was thought to be almost eliminated in Chad when it reemerged in 2010. The disease now shows a peculiar pattern of spreading along Chari River and its tributaries, rather than clustering around a particular drinking water source. We create a mathematical model of GWD that includes the population dynamics of the parasite as well as the dynamics of its hosts (copepods, fish, humans, and domestic dogs). We calibrate our model based on data from the literature and validate it on the recent GWD annual incidence data from Chad. The effective reproduction number predicted by our model agrees well with the empirical value of roughly 1.25 derived directly from the data. Our model thus supports the hypothesis that the parasite now uses fish as intermediate transport hosts. We predict that GWD transmission can be most easily interrupted by avoiding eating uncooked fish and by burying the fish entrails to prevent transmission through dogs. Increasing the mortality of copepods and even partially containing infected dogs to limit their access to water sources is another important factor for GWD eradication.

Non-pharmaceutical interventions (NPIs) involving social-isolation strategies such as self-quarantine (SQ) and social-distancing (SD) are useful in controlling the spread of infections that are transmitted through human-to-human contacts, e.g., respiratory diseases such as COVID-19. In the absence of a safe and effective cure or vaccine during the first ten months of the COVID-19 pandemic, countries around the world implemented these social-isolation strategies and other NPIs to reduce COVID-19 transmission. But, individual and public perception play a crucial role in the success of any social-isolation measure. Thus, in spite of governments' initiatives to use NPIs to combat COVID-19 in many countries around the world, individual choices rendered social-isolation unsuccessful in some of these countries. This resulted in huge outbreaks that imposed a substantial morbidity, mortality, hospitalization, economic, etc., toll on human lives. In particular, human choices pose serious challenges to public health strategic decision-making in controlling the COVID-19 pandemic. To unravel the impact of this behavioral response to social-isolation on the burden of the COVID-19 pandemic, we develop a model framework that integrates COVID-19 transmission dynamics with a multi-strategy evolutionary game approach of individual decision-making. We use this integrated framework to characterize the evolution of human choices in social-isolation as the disease progresses and public health control measures such as mandatory lockdowns are implemented. Analysis of the model illustrates that SD plays a major role in reducing the burden of the disease compared to SQ. Parameter estimation using COVID-19 incidence data, as well as different lockdown data sets from India, and scenario analysis involving a combination of Voluntary-Mandatory implementation of SQ and SD shows that the effectiveness of this approach depends on the type of isolation, and the time and period of implementation of the selected isolation measure during the outbreak.

Glioblastoma originates in the brain and is one of the most aggressive cancer types. Glioblastoma represents 15% of all brain tumours, with a median survival of 15 months. Although the current standard of care for such a tumour (the Stupp protocol) has shown positive results for the prognosis of patients, O-6-methylguanine-DNA methyltransferase (MGMT) driven drug resistance has been an issue of increasing concern and hence requires innovative approaches. In addition to the well established drug resistance factors such as tumour location and blood brain barriers, it is also important to understand how the genetic and epigenetic dynamics of the glioblastoma cells can play a role. One important aspect of this is the study of methylation status of MGMT following administration of temozolomide. In this paper, we extend our previously published model that simulated MGMT expression in glioblastoma cells to incorporate the promoter methylation status of MGMT. This methylation status has clinical significance and is used as a marker for patient outcomes. Using this model, we investigate the causative relationship between temozolomide treatment and the methylation status of the MGMT promoter in a population of cells. In addition by constraining the model to relevant biological data using Approximate Bayesian Computation, we were able to identify parameter regimes that yield different possible modes of resistances, namely, phenotypic selection of MGMT, a downshift in the methylation status of the MGMT promoter or both simultaneously. We analysed each of the parameter sets associated with the different modes of resistance, presenting representative solutions as well as discovering some similarities between them as well as unique requirements for each of them. Finally, we used them to devise optimal strategies for inhibiting MGMT expression with the aim of minimising live glioblastoma cell numbers.