Bulletin of Mathematical Biology最新文献

A variety of biomedical systems are modeled by networks of deterministic differential equations with stochastic inputs. In some cases, the network output is remarkably constant despite a randomly fluctuating input. In the context of biochemistry and cell biology, chemical reaction networks and multistage processes with this property are called robust. Similarly, the notion of a forgiving drug in pharmacology is a medication that maintains therapeutic effect despite lapses in patient adherence to the prescribed regimen. What makes a network robust to stochastic noise? This question is challenging due to the many network parameters (size, topology, rate constants) and many types of noisy inputs. In this paper, we propose a summary statistic to describe the robustness of a network of linear differential equations (i.e. a first-order mass-action system). This statistic is the variance of a certain random walk passage time on the network. This statistic can be quickly computed on a modern computer, even for complex networks with thousands of nodes. Furthermore, we use this statistic to prove theorems about how certain network motifs increase robustness. Importantly, our analysis provides intuition for why a network is or is not robust to noise. We illustrate our results on thousands of randomly generated networks with a variety of stochastic inputs.

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid (tau )-leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

This paper offers advice to early-mid career researchers in Mathematical Biology from ten past and current Presidents of the Society for Mathematical Biology. The topics covered include deciding if a career in academia is right for you; finding and working with a mentor; building collaborations and working with those from other disciplines; formulating a research question; writing a paper; reviewing papers; networking; writing fellowship or grant proposals; applying for faculty positions; and preparing and giving lectures. While written with mathematical biologists in mind, it is hoped that this paper will be of use to early and mid career researchers across the mathematical, physical and life sciences, as they embark on careers in these disciplines.

Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease progression and control. Here we developed mathematical models of HBV infection which either lack terms for adaptive immune responses, or assume adaptive immune responses in the form of cytolytic immune killing, non-cytolytic immune cure, or non-cytolytic-mediated block of viral production. We validated the model that does not include immune responses against temporal serum hepatitis B DNA (sHBV) and temporal serum hepatitis B surface-antigen (HBsAg) experimental data from mice engrafted with human hepatocytes (HEP). Moreover, we validated the immune models against sHBV and HBsAg experimental data from mice engrafted with HEP and human immune system (HEP/HIS). As expected, the model that does not include adaptive immune responses matches the observed high sHBV and HBsAg concentrations in all HEP mice. By contrast, while all immune response models predict reduction in sHBV and HBsAg concentrations in HEP/HIS mice, the Akaike Information Criterion cannot discriminate between non-cytolytic cure (resulting in a class of cells refractory to reinfection) and antiviral block functions (of up to (99%) viral production 1–3 weeks following peak viral load). We can, however, reject cytolytic killing, as it can only match the sHBV and HBsAg data when we predict unrealistic levels of hepatocyte loss.

Abstract

Models of social interaction dynamics have been powerful tools for understanding the efficiency of information spread and the robustness of task allocation in social insect colonies. How workers spatially distribute within the colony, or spatial heterogeneity degree (SHD), plays a vital role in contact dynamics, influencing information spread and task allocation. We used agent-based models to explore factors affecting spatial heterogeneity and information flow, including the number of task groups, variation in spatial arrangements, and levels of task switching, to study: (1) the impact of multiple task groups on SHD, contact dynamics, and information spread, and (2) the impact of task switching on SHD and contact dynamics. Both models show a strong linear relationship between the dynamics of SHD and contact dynamics, which exists for different initial conditions. The multiple-task-group model without task switching reveals the impacts of the number and spatial arrangements of task locations on information transmission. The task-switching model allows task-switching with a probability through contact between individuals. The model indicates that the task-switching mechanism enables a dynamical state of task-related spatial fidelity at the individual level. This spatial fidelity can assist the colony in redistributing their workforce, with consequent effects on the dynamics of spatial heterogeneity degree. The spatial fidelity of a task group is the proportion of workers who perform that task and have preferential walking styles toward their task location. Our analysis shows that the task switching rate between two tasks is an exponentially decreasing function of the spatial fidelity and contact rate. Higher spatial fidelity leads to more agents aggregating to task location, reducing contact between groups, thus making task switching more difficult. Our results provide important insights into the mechanisms that generate spatial heterogeneity and deepen our understanding of how spatial heterogeneity impacts task allocation, social interaction, and information spread.

Abstract

Forest plantations are economically and environmentally relevant, as they play a key role in timber production and carbon capture. It is expected that the future climate change scenario affects forest growth and modify the rotation age for timber production. However, mathematical models on the effect of climate change on the rotation age for timber production remain still limited. We aim to determine the optimal rotation age that maximizes the net economic benefit of timber volume in a negative scenario from the climatic point of view. For this purpose, a bioeconomic optimal control problem was formulated from a system of Ordinary Differential Equations (ODEs) governed by the state variables live biomass volume, intrinsic growth rate, and area affected by fire. Then, four control variables were associated to the system, representing forest management activities, which are felling, thinning, reforestation, and fire prevention. The existence of optimal control solutions was demonstrated, and the solutions of the optimal control problem were also characterized using Pontryagin’s Maximum Principle. The solutions of the model were approximated numerically by the Forward–Backward Sweep method. To validate the model, two scenarios were considered: a realistic scenario that represents current forestry activities for the exotic species Pinus radiata D. Don, and a pessimistic scenario, which considers environmental conditions conducive to a higher occurrence of forest fires. The optimal solution that maximizes the net benefit of timber volume consists of a strategy that considers all four control variables simultaneously. For felling and thinning, regardless of the scenario considered, the optimal strategy is to spend on both activities depending on the amount of biomass in the field. Similarly, for reforestation, the optimal strategy is to spend as the forest is harvested. In the case of fire prevention, in the realistic scenario, the optimal strategy consists of reducing the expenses in fire prevention because the incidence of fires is lower, whereas in the pessimistic scenario, the opposite is true. It is concluded that the optimal rotation age that maximizes the net economic benefit of timber volume in P. radiata plantations is 24 and 19 years for the realistic and pessimistic scenarios, respectively. This corroborates that the presence of fires influences the determination of the optimal rotation age, and as a consequence, the net economic benefit.

This study addresses COVID-19 testing as a nonlinear sampling problem, aiming to uncover the dependence of the true infection count in the population on COVID-19 testing metrics such as testing volume and positivity rates. Employing an artificial neural network, we explore the relationship among daily confirmed case counts, testing data, population statistics, and the actual daily case count. The trained artificial neural network undergoes testing in in-sample, out-of-sample, and several hypothetical scenarios. A substantial focus of this paper lies in the estimation of the daily true case count, which serves as the output set of our training process. To achieve this, we implement a regularized backcasting technique that utilize death counts and the infection fatality ratio (IFR), as the death statistics and serological surveys (providing the IFR) as more reliable COVID-19 data sources. Addressing the impact of factors such as age distribution, vaccination, and emerging variants on the IFR time series is a pivotal aspect of our analysis. We expect our study to enhance our understanding of the genuine implications of the COVID-19 pandemic, subsequently benefiting mitigation strategies.

Carcinomas often utilize epithelial-mesenchymal transition (EMT) programs for cancer progression and metastasis. Numerous studies report SNAIL-induced miR200/Zeb feedback circuit as crucial in regulating EMT by placing cancer cells in at least three phenotypic states, viz. epithelial (E), hybrid (h-E/M), mesenchymal (M), along the E-M phenotypic spectrum. However, a coherent molecular-level understanding of how such a tiny circuit controls carcinoma cell entrance into and residence in various states is lacking. Here, we use molecular binding data and mathematical modeling to report that the miR200/Zeb circuit can essentially utilize combinatorial cooperativity to control E-M phenotypic plasticity. We identify minimal combinatorial cooperativities that give rise to E, h-E/M, and M phenotypes. We show that disrupting a specific number of miR200 binding sites on Zeb as well as Zeb binding sites on miR200 can have phenotypic consequences-the circuit can dynamically switch between two (E, M) and three (E, h-E/M, M) phenotypes. Further, we report that in both SNAIL-induced and SNAIL knock-out miR200/Zeb circuits, cooperative transcriptional feedback on Zeb as well as Zeb translation inhibition due to miR200 are essential for the occurrence of intermediate h-E/M phenotype. Finally, we demonstrate that SNAIL can be dispensable for EMT, and in the absence of SNAIL, the transcriptional feedback can control cell state transition from E to h-E/M, to M state. Our results thus highlight molecular-level regulation of EMT in miR200/Zeb circuit and we expect these findings to be crucial to future efforts aiming to prevent EMT-facilitated dissemination of carcinomas.

Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values. Next, using a mouse-parameterized two-compartment model of 5-fluorouracil, we show that schedule viability depends on initial tumor volume. Finally, we illustrate the trade-off between tumor response and lean mass preservation. Mathematical modeling indicates that high variance dose schedules provide a potential path forward in mitigating the risk of chemotherapy-associated cachexia by preserving lean mass without sacrificing tumor response.

Alzheimer's disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer's mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.