Mathematical biosciences最新文献

Estuarine ecosystems are among the most dynamic and ecologically significant environments, shaped by intricate interactions among microbial communities, such as proteobacteria and their predator. Proteobacteria, owing to their remarkable tolerance to salinity and unique mixotrophic capabilities, dominate this ecosystem. These traits raise a fundamental ecological question: do proteobacteria act as stabilising agents in estuarine health, and why has evolution favoured their multifunctionality over strict autotrophy or heterotrophy? This study presents a novel theoretical framework, comprising both deterministic and stochastic models, emphasizing key phenomenological traits of mixotrophic proteobacteria in estuarine ecosystems. The autotrophic component is captured using Secchi depth as a proxy for light availability and photosynthetic potential, while heterotrophic behaviour is linked to salinity-driven nutrient uptake. Through analytical exploration and numerical simulations, we find that salinity serves as a crucial control parameter, producing characteristic oscillatory dynamics and a "bubbling effect" that delineates transitions between stability and instability. The photosynthetic capability of mixotrophic proteobacteria emerges as a critical stabilizing mechanism, particularly under fluctuating salinity and turbidity conditions. Our model identifies critical thresholds for Secchi depth, salinity-driven microzooplankton grazing and nutrient inflow-outflow that underpin estuarine stability. The stochastic extension, incorporating Gaussian white noise, demonstrates that under strong environmental noise, microzooplankton are more prone to extinction than proteobacteria. This work lays a theoretical foundation for future ecological modelling and adaptive estuarine management in the context of climate-driven change.

Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both additive and multiplicative, as well as institutional incentives, influence these dynamics. In this paper, we study the replicator-mutator dynamics, with combined additive and multiplicative mutations, for public goods games both in the absence or presence of institutional incentives. For each model, we identify the possible number of (stable) equilibria, demonstrate their attainability, as well as analyse their stability properties. We also characterise the dependence of these equilibria on the model's parameters via bifurcation analysis and asymptotic behaviour. Our results offer rigorous and quantitative insights into the role of institutional incentives and the effect of combined additive and multiplicative mutations on the evolution of cooperation in the context of public goods games.

In the context of global warming, tree populations rely on two primary mechanisms of adaptation: phenotypic plasticity, which enables individuals to adjust their behavior in response to environmental stress, and genetic evolution, driven by natural selection and genetic diversity within the population. Understanding the interplay between these mechanisms is crucial for assessing the impacts of climate change on forest ecosystems and for informing sustainable management strategies. In this manuscript, we focus on a specific phenological adaptation: the ability of trees to enter summer dormancy once a critical temperature threshold is exceeded. Individuals are characterized by this threshold temperature and by their seed production capacity. We first establish a detailed mathematical model describing the population dynamics under these traits, and progressively reduce it to a system of two coupled ordinary differential equations. This simpler macroscopic model is then analyzed numerically, to investigate how the population reacts to a shift in its environment: an temperature increase, a drop in precipitation levels, or a combination of the two. Our results highlight contrasting effects of water stress and temperature stress on population dynamics, as well as the ambivalent effect of the plasticity.

The impacts of fear, refuge-seeking behavior of prey, and modified cooperative hunting among predators are collectively included in a mathematical model to explore predator-prey dynamics. The stability of the system's equilibrium points and the occurrence of different bifurcations are analyzed. The system exhibits bistability, characterized by the presence of two stable equilibrium points. Numerical investigation reveals that elevated fear levels simplify the species' coexistence, even when considering increased refuge and prey birth rate. When hunting cooperation rate is extremely high, prey survival becomes unsustainable, particularly with lower birth rate, unless refuge is sought. Conversely, ample refuge capacity allows prey to persist despite lower birth rates. To create time-series solutions and examine stationary distributions, we run multiple simulations. Notably, species have a tendency to fluctuate around the mean values of the deterministic state when there are minimal external disruptions. Interestingly, an increased noise intensity on predators shifts the system's dynamics to a predator-free equilibrium from coexistence of prey and predators.

Glioblastoma cells form connected cell networks, utilizing tumor microtubes (TMs) to transmit calcium between cells. A new cell type called "periodic cell" is integral in sustaining calcium signalling in a glioblastoma network. Periodic cells are rare, can sustain consistent intracellular calcium transients, are likely to have KCa3.1 pumps, and have on average more TMs than other glioma cells. Here, we adapt an ordinary differential equation model for intracellular as well as intercellular calcium signalling and apply it to a large glioma cell network. Using the model, three main hypotheses were tested for the mechanism behind the sustained calcium oscillations in periodic cells: 1. a fixed and elevated IP₃ concentration, 2. added benefit from influx of calcium due to KCa3.1 pumps, or 3. oscillation in calcium influx into the cell through the plasma membrane. All three hypotheses yield similar calcium oscillation patterns resembling the trends seen in the data of Hausmann et al. 2023. In vivo, glioma networks were shown to have small-world and scale-free network properties. We apply our model to small-world, scale-free and random networks and test how communication is inhibited through removal of cells, removal of tumor microtubes, and inhibition of KCa3.1 pumps. All three network types were more vulnerable to random cell damage than to random TM damage. We find that inhibition of KCa3.1 pumps can have a significant impact on the inhibition of network communication, however, to fully degrade the calcium signalling network, all periodic cells must be eradicated confirming experimental observations.

In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state space), then constructing two one-dimensional birth and death processes that lower and upper bound the initial process under simple assumptions on the infinitesimal generators of the processes. The construction of these bounding processes is based on coupling arguments and transport theory. The bounding processes are easy to analyse analytically and numerically and allow us to derive properties on the initial continuous-time Markov chain. We focus on two important properties: the behavior of the process at infinity through the existence of a stationary distribution and the error in truncating the state space to numerically solve the master equation describing the time evolution of the probability distribution of the process. We derive explicit formulas for constructing the optimal bounding processes for a given partition, making the method easy to use in practice. We finally discuss the importance of the choice of the partition to obtain relevant results and illustrate the method on two examples of chemical reaction network.

Mechanistic models in systems biology enable biophysically-backed testing of hypothesised mechanisms. However, determination of their parameter values is highly challenging, and the data available for calibration is frequently qualitative in nature. Acknowledging this, many approaches abandon mechanistic description, avoiding parameterisation and simulating biological network behaviours in a qualitative fashion. Appealing are the methods that capture some of the best of both types of approach, maintaining a qualitative perspective while using mechanistic models that naturally generalise to quantitative data and carry biochemical implications. Here, using a pea branching network model as an exemplar, we demonstrate the conversion of biological hypotheses into simplified, parameter-free mathematical models, elucidating the biophysical assumptions implicitly made by this approach and analysing the exemplar model's behaviour. Using likelihood-free Bayesian calibration, we compare the parameter-free model to the set of plausible calibrations of its parameterised analog, hence demonstrating that almost all of the qualitative conclusions given data - including both suitability of a hypothesised network structure, and sensitivity analysis - are obtained by the parameter-free paradigm. Altogether, our findings highlight the usefulness of parameter-free treatments of quantitative models, and also deepen understanding of branching network function across mutant and grafted plants.

The tumor-immune system plays a critical role in colorectal cancer progression. Recent preclinical and clinical studies showed that combination therapy with anti-PD-L1 and cancer vaccines improved treatment response. In this study, we developed a multiscale mathematical model of interactions among tumors, immune cells, and cytokines to investigate tumor evolutionary dynamics under different therapeutic strategies. Additionally, we established a computational framework based on approximate Bayesian computation to generate virtual tumor samples and capture inter-individual heterogeneity in treatment response. The results demonstrated that a multiple low-dose regimen significantly reduced advanced tumor burden compared to baseline treatment in anti-PD-L1 therapy. In contrast, the maximum dose therapy yielded superior tumor growth control in cancer vaccine therapy. Furthermore, cytotoxic T cells were identified as a consistent predictive biomarker both before and after treatment initiation. Notably, the cytotoxic T cells-to-regulatory T cells ratio specifically served as a robust pre-treatment predictive biomarker, offering potential clinical utility for patient stratification and therapy personalization.

Clonorchiasis is a zoonotic disease mainly caused by eating raw fish and shrimp, and there is no vaccine to prevent it. More than 30 million people are infected worldwide, of which China alone accounts for about half, and is one of the countries most seriously affected by Clonorchiasis. In this work, we formulate a novel Ordinary Differential Equation (ODE) model to discuss the biological attributes of fish within authentic ecosystems and the complex lifecycle of Clonorchis sinensis. This model includes larval fish, adult fish, infected fish, humans, and cercariae. We derive the basic reproduction number and perform a rigorous stability analysis of the proposed model. Numerically, we use data from 2016 to 2021 in Guangxi, China, to discuss outbreaks of Clonorchiasis and obtain the basic reproduction number R₀=1.4764. The fitted curve appropriately reflects the overall trend and replicates a low peak in the case number of Clonorchiasis. By reducing the release rate of cercariae in 2018, the fitted values of Clonorchiasis cases dropped rapidly and almost disappeared. If we decrease the transmission rate from infected fish to humans, Clonorchiasis can be controlled. Our studies also suggest that strengthening publicity education and cleaning water quality can effectively control the transmission of Clonorchiasis in Guangxi, China.