Bulletin of Mathematical Biology最新文献

Knowing gene regulatory networks (GRNs) is important for understanding various biological mechanisms. In this paper, we present a method, QWENDY, that uses single-cell gene expression data measured at four time points to infer GRNs. Based on a linear gene expression model, it solves the transformation of the covariance matrices. Unlike its predecessor WENDY, QWENDY avoids solving a non-convex optimization problem and produces a unique solution. We test the performance of QWENDY on three experimental data sets and two synthetic data sets. Compared to previously tested methods on the same data sets, QWENDY ranks the first on experimental data, although it does not perform well on synthetic data.

Virtual population (Vpop) generation is a central component of quantitative systems pharmacology (QSP), involving the sampling of parameter sets that represent physiologically plausible patients (PPs) and capture observed inter-individual variability in clinical outcomes. This approach poses challenges due to the high dimensionality and often non-identifiability nature of many QSP models. In this study, we evaluate the performance of the DREAM(ZS) algorithm, a multi-chain adaptive Markov chain Monte Carlo (MCMC) method for generating Vpop. Using the Van De Pas model of cholesterol metabolism as a case study, we compare DREAM(ZS) to the single-chain Metropolis-Hastings (MH) algorithm adopted by Rieger et al. Our comparison focuses on convergence behavior, parametric diversity, and posterior coverage, in relation to the ability of each method to explore complex parameter distributions and maintain outcomes correlations. DREAM(ZS) demonstrates superior exploration of the parameter space, reducing boundary accumulation effects common in traditional MH sampling, and restoring parameter correlation structures. These advantages are attributed in part to its adaptive proposal mechanism and the use of a bias-corrected likelihood formulation, which together contribute to a better parameters space sampling without compromising model fit. Our findings contribute to the ongoing development of efficient sampling methodologies for high-dimensional biological models, introducing a promising and easy to use alternative for Vpop generation in QSP, expanding the methodological approaches for in silico trial simulation.

The risk and intensity of mosquito-borne disease outbreaks are tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. However, standard models of mosquito-borne disease transmission inherently assume that mosquitoes bite only once per reproductive cycle-an assumption commonly violated in nature. Drivers of multiple biting, such as host defensive behaviors or climate factors, also affect the mosquito gonotrophic cycle duration (GCD), a quantity customarily used to estimate the biting rate. Here, we present a novel framework for incorporating more complex mosquito biting behaviors into transmission models. This framework can account for heterogeneity in and linkages between mosquito biting rates and multiple biting. We provide general formulas for the basic offspring number, $N_0$ , and basic reproduction number, $R_0$ , threshold measures for mosquito population and pathogen transmission persistence, respectively. To exhibit its flexibility, we expand on specific models derived from the framework that arise from empirical, phenomenological, or mechanistic modeling perspectives. Using the gonotrophic cycle duration as a standard quantity to make comparisons among the models, we show that assumptions about the biting process strongly affect the relationship between GCD and $R_0$ . While under the standard assumption of one bite per reproductive cycle, $R_0$ is an increasing linear function of the inverse of the GCD, alternative models of the biting process can exhibit saturating or concave relationships. Critically, from a mechanistic perspective, decreases in the GCD can lead to substantial decreases in $R_0$ . Through sensitivity analysis of the mechanistic model, we determine that parameters related to probing and ingesting success are the most important targets for disease control. This work highlights the importance of incorporating the behavioral dynamics of mosquitoes into transmission models and provides a method for evaluating how individual-level interventions against mosquito biting scale up to determine population-level mosquito-borne disease risk.

We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian principles and consists of specialized Markov chain Monte Carlo computational schemes that rely on modified Hamiltonian Monte Carlo to align with constraints induced by summary statistics and a novel elliptical slice sampler adapted to the parameters of biological models. We benchmark our methods with synthetic data on microbial growth in batch culture and test them with real growth curve data from laboratory replication experiments on Prochlorococcus microbes. The results indicate that our learning framework can utilize experimental or historical data and lead to robust parameter estimation and data assimilation in ODE models that outperform least-squares fitting.

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the reactivity of the non-spatial and spatial dynamics, stability analyses, and numerical continuation to uncover detailed aspects of this system's pattern-forming potential. In addition to patterning in Turing unstable parameter regimes, reactivity of the spatial system can itself lead to a range of parameters where a spatially uniform state is asymptotically stable, but exhibits transient growth that can induce pattern formation. We show that this occurs in the bistable region of a subcritical Turing bifurcation. Intriguingly, such bistable regions appear in two spatial dimensions, but not in a one-dimensional domain, suggesting important interplays between geometry, transient growth, and the emergence of multistable patterns. We discuss the implications of our analysis for the bacterial soil organic carbon system, as well as for reaction-transport modeling more generally.

Cell heterogeneity plays an important role in patient responses to drug treatments. In many cancers, it is associated with poor treatment outcomes. Many modern drug combination therapies aim to exploit cell heterogeneity, but determining how to optimise responses from heterogeneous cell populations while accounting for multi-drug synergies remains a challenge. In this work, we introduce and analyse a general optimal control framework that can be used to model the treatment response of multiple cell populations that are treated with multiple drugs that mutually interact. In this framework, we model the effect of multiple drugs on the cell populations using a system of coupled semi-linear ordinary differential equations and derive general results for the optimal solutions. We then apply this framework to three canonical examples and discuss the wider question of how to relate mathematical optimality to clinically observable outcomes, introducing a systematic approach to propose qualitatively different classes of drug dosing inspired by optimal control.

The linear framework is an approach to analysing biochemical systems based on directed graphs with labelled edges. When applied to individual molecular systems, graph vertices correspond to system states, directed edges to transitions, and edge labels to transition rates. Such a graph specifies the infinitesimal generator of a continuous-time Markov process. The master equation of this Markov process, which describes the forward evolution of vertex probabilities, is a linear differential equation, after which the framework is named, whose operator is the Laplacian matrix of the graph. The Matrix-Tree theorem, when applied to this Laplacian matrix, allows the steady-state probabilities of the Markov process to be expressed as rational algebraic functions of the transition rates. This capability gives algebraic access to problems that have otherwise been treated by approximations or numerical simulations, and enables theorems to be proved about biochemical systems that rise above their underlying molecular complexity. Here, we extend this capability from the steady state to the transient regime. We use the All-Minors Matrix-Tree theorem to express the moments of the conditional first-passage time distribution, and the corresponding splitting probabilities, as rational algebraic functions of the transition rates. This extended capability brings many new biological problems within the scope of the linear framework.

Chase-and-run dynamics, in which one population pursues another that flees from it, are found throughout nature, from predator-prey interactions in ecosystems to the collective motion of cells during development. Intriguingly, in many of these systems, the movement is not straight; instead, 'runners' veer off at an angle from their pursuers. This angled movement often exhibits a consistent left-right asymmetry, known as lateralisation or chirality. Inspired by such phenomena in zebrafish skin patterns and evasive animal motion, we explore how chirality shapes the emergence of patterns in nonlocal (integro-differential) advection-diffusion models. We extend such models to allow movement at arbitrary angles, uncovering a rich landscape of behaviours. We find that chirality can enhance pattern formation, suppress oscillations, and give rise to entirely new dynamical structures, such as rotating pulses of chasers and runners. We also uncover how chase-and-run dynamics can cause populations to mix or separate. Through linear stability analysis, we identify physical mechanisms that drive some of these effects, whilst also exposing striking limitations of this theory in capturing more complex dynamics. Our findings suggest that chirality could have roles in ecological and cellular patterning beyond simply breaking left-right symmetry.

The coexistence of species in predator-prey systems is a critical ecological issue due to the intricate interactions among multiple influencing factors. In this study, we develop a predator-prey model that incorporates prey herd behavior, cooperative hunting strategies among predators, and the establishment of a reserved area for prey protection. We establish conditions for the positivity and boundedness of the system to ensure long-term biological feasibility. The existence and stability of equilibrium points, along with the conditions for Hopf and saddle-node bifurcations, are rigorously analyzed. Numerical simulations are performed to validate the analytical findings. Global sensitivity analysis reveals that key parameters, including the size of the reserved area, predator cooperation, and migration rates, significantly affect system dynamics and species coexistence. Our numerical results suggest that expanding the reserved area promotes prey recovery, with predator populations initially growing but eventually declining towards extinction. Increased hunting cooperation among predators initially boosts predator populations but ultimately accelerates prey depletion, leading to predator collapse due to overhunting.