Journal of Mathematical Biology最新文献

A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a thorough analysis. We improve and extend the work of Johnston and Hong et al. on network translations to network transformations, where the network is modified while preserving the dynamical system. These transformations can shrink, extend, or retain the stoichiometric subspace. Here, we show that a positive dependent network can be translated to a weakly reversible network. Using the kinetic realizations of (1) calcium signaling in the olfactory system and (2) metabolic insulin signaling, we demonstrate the benefits of transformed systems with positive deficiency for analyzing biochemical systems. Furthermore, we present an algorithm for a network transformation of a weakly reversible non-complex factorizable kinetic (NFK) system to a weakly reversible complex factorizable kinetic (CFK) system, thereby enhancing the Subspace Coincidence Theorem for NFK systems of Nazareno et al. Finally, using the transformed kinetic realization of monolignol biosynthesis in Populus xylem, we study the structural and kinetic properties of transformed systems, including the invariance of concordance and variation of injectivity and mono-/multi-stationarity under network transformation.

Flow of cerebrospinal fluid through perivascular pathways in and around the brain may play a crucial role in brain metabolite clearance. While the driving forces of such flows remain enigmatic, experiments have shown that pulsatility is central. In this work, we present a novel network model for simulating pulsatile fluid flow in perivascular networks, taking the form of a system of Stokes-Brinkman equations posed over a perivascular graph. We apply this model to study physiological questions concerning the mechanisms governing perivascular fluid flow in branching vascular networks. Notably, our findings reveal that even long wavelength arterial pulsations can induce directional flow in asymmetric, branching perivascular networks. In addition, we establish fundamental mathematical and numerical properties of these Stokes-Brinkman network models, with particular attention to increasing graph order and complexity. By introducing weighted norms, we show the well-posedness and stability of primal and dual variational formulations of these equations, and that of mixed finite element discretizations.

Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large interaction matrix with random part. Under some known conditions, a global equilibrium exists and is unique. In this article, we rigorously study its statistical properties in the large dimensional regime. Such an equilibrium vector is known to be the solution of a so-called Linear Complementarity Problem. We describe its statistical properties by designing an Approximate Message Passing (AMP) algorithm, a technique that has recently aroused an intense research effort in the fields of statistical physics, machine learning, or communication theory. Interaction matrices based on the Gaussian Orthogonal Ensemble, or following a Wishart distribution are considered. Beyond these models, the AMP approach developed in this article has the potential to describe the statistical properties of equilibria associated to more involved interaction matrix models.

The purpose of this study is to construct a mortality model that reasonably explains survival curves and mortality rates in terms of the decline in biological function, which is the phenomenon of ageing. In this model, an individual organism is regarded as a collection of subsystems, and for each subsystem, the model defines human mortality by introducing positive self-repair mechanisms and stochastically generated negative external shocks. The probability density function of the time of death is derived explicitly, and the model parameters are estimated using life tables from Japan and the UK, which demonstrate the existence of multiple parameter sets that fit well with the observed data.

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset R^d$ containing a set of small subdomains or interior compartments $U_j$ , $j=1,\dots ,N$ (singularly-perturbed diffusion problems). The domain $\Omega$ could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green's function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary $\partial U_j$ . This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes.

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal foraging principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing producers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent predation behaviors, elucidating biological phenomena such as "compensatory foraging behaviors" and the "stoichiometric extinction effect". The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator-prey dynamics. The environmental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.

Axonal transport, propelled by motor proteins, plays a crucial role in maintaining the homeostasis of functional and structural components over time. To establish a steady-state distribution of moving particles, what conditions are necessary for axonal transport? This question is pertinent, for instance, to both neurofilaments and mitochondria, which are structural and functional cargoes of axonal transport. In this paper we prove four theorems regarding steady state distributions of moving particles in one dimension on a finite domain. Three of the theorems consider cases where particles approach a uniform distribution at large time. Two consider periodic boundary conditions and one considers reflecting boundary conditions. The other theorem considers reflecting boundary conditions where the velocity is space dependent. If the theoretical results hold in the complex setting of the cell, they would imply that the uniform distribution of neurofilaments observed under healthy conditions appears to require a continuous distribution of neurofilament velocities. Similarly, the spatial distribution of axonal mitochondria may be linked to spatially dependent transport velocities that remain invariant over time.

We analyze a stochastic optimal control problem for the PReP vaccine in a model for the spread of HIV. To do so, we use a stochastic model for HIV/AIDS with PReP, where we include jumps in the model. This generalizes previous works in the field. First, we prove that there exists a positive, unique, global solution to the system of stochastic differential equations which makes up the model. Further, we introduce a stochastic control problem for dynamically choosing an optimal percentage of the population to receive PReP. By using the stochastic maximum principle, we derive an explicit expression for the stochastic optimal control. Furthermore, via a generalized Lagrange multiplier method in combination with the stochastic maximum principle, we study two types of budget constraints. We illustrate the results by numerical examples, both in the fixed control case and in the stochastic control case.

This paper is concerned with spatiotemporal dynamics of a fractional diffusive susceptible-infected-susceptible (SIS) epidemic model with mass action infection mechanism. Concretely, we first focus on the existence and stability of the disease-free and endemic equilibria. Then, we give the asymptotic profiles of the endemic equilibrium on small and large diffusion rates, which can reveal the impact of dispersal rates and fractional powers simultaneously. It is worth noting that we have some counter-intuitive findings: controlling the flow of infected individuals will not eradicate the disease, but restricting the movement of susceptible individuals will make the disease disappear.