Bulletin of Mathematical Biology最新文献

In mammals, the immune system recognizes and combats pathogens while retaining a memory of prior encounters. In the thymus, naïve T cells capable of recognizing specific antigens are generated through random gene rearrangement, ensuring a diverse immune repertoire. However, the production rate of naïve T cells declines with age, typically following an exponential or power-law function-a phenomenon known as thymic involution, which is often regarded as a deterioration of biological function (immunosenescence). In this paper, we propose a novel theory suggesting that thymic involution may represent an adaptive strategy. As individuals age, repeated exposure to diverse pathogens leads to the accumulation of memory T cells, thereby reducing the need for newly generated naïve T cells to combat infections. Moreover, naïve T cells can persist in the periphery and retain the capacity to initiate immune responses against novel antigens. Using Pontryagin's Maximum Principle, we calculate the optimal schedule of naïve T cell production. The results show that the production rate peaks during a brief period shortly after birth, followed by an exponential decline throughout life, eventually reaching a phase in which naïve T cell production ceases. If peripheral naïve T cells decay very slowly, the optimal strategy may consist of producing all cohorts at birth, with no subsequent production.

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread adoption of this individual-based fitting, it is becoming increasingly common to take a hierarchical approach to parameter estimation, where modellers characterize the population parameter distributions, rather than considering each individual independently. This hierarchical parameter estimation is standard in pharmacometric modelling. However, many of the existing techniques for parameter identifiability do not immediately translate from the individual-based fitting to the hierarchical setting. In this work, we propose a nonparametric approach to study practical identifiability within a hierarchical parameter estimation framework. We focus on the commonly used nonlinear mixed effects framework and investigate two well-studied examples from the pharmacometrics and viral dynamics literature to illustrate the potential utility of our approach.

Synonymous codon usage can influence protein expression, since codons with high numbers of corresponding tRNAs are naturally translated more rapidly than codons with fewer corresponding tRNAs. Although translation efficiency ultimately depends on the concentration of aminoacylated (charged) tRNAs, many theoretical models of translation have ignored tRNA dynamics and treated charged tRNAs as fixed resources. This simplification potentially limits these models from making accurate predictions in situations where charged tRNAs become limiting. Here, we derive a mathematical model of translation with explicit tRNA dynamics and tRNA re-charging, based on a stochastic simulation of this system that was previously applied to investigate codon usage in the context of gene overexpression. We use the mathematical model to systematically explore the relationship between codon usage and the protein expression rate, and find that in the regime where tRNA charging is a limiting reaction, it is always optimal to match codon frequencies to the tRNA pool. Conversely, when tRNA charging is not limiting, using 100% of the preferred codon is optimal for protein production. We also use the tRNA dynamics model to augment a whole-cell simulation of bacteriophage T7. Using this model, we demonstrate that the high expression rate of the T7 major capsid gene causes rare charged tRNAs to become entirely depleted, which explains the sensitivity of the major capsid gene to codon deoptimization.

In both human and wildlife disease systems, temporal shifts in host immunity may shape the timing and severity of epidemics. Yet, immune responses, as well as seasonal patterns in their expression, are difficult to measure. Rather, field studies collect phenomenological data on infection outcomes. Pairing epidemic data of multiple outbreaks with models that directly parameterize immune metrics can be a powerful approach for exploring the role of time-varying immunity on disease. Field data can be used to determine how well a parameterized model can reproduce trends and differences observed among outbreaks.Previous work in the Daphnia dentifera-Metschnikowia bicuspidata focal host-fungal pathogen disease system has not taken full advantage of coupling patterns in nature with mechanisms predicted by theory. Here, we study a mathematical model accounting for host immunity in the form of resistance to and recovery from M. bicuspidata infections and temporal variation in key aspects of the system's epidemiology and ecology. Specifically, host population birth, predation and transmission rates, the fraction of recovering hosts, as well as the fungal spore yield were allowed to vary within the epidemic season. Modifying the system's carrying capacity produces good correspondence between observed and model-estimated densities. Adjusting the transmission rate, spore yield, and the fraction of recovering hosts, captures the timing of disease outbreaks, as well as other qualitative features of outbreaks, such as the disparity between the prevalence of early- and late-stage infections. Our findings suggest that host immunological parameters are an important within-host constraint on disease dynamics.

Periodic travelling waves (PTWs) are a common solution type of models describing spatio-temporal patterns in biology and ecology. Particularly in ecology, pattern formation is regarded as a resilience mechanism and an ecosystem's ability to change its pattern wavelength is seen as a tool to adapt to environmental change. PTW solutions of corresponding mathematical models also possess this ability and typically undergo a cascade of wavelength changes in response to a gradual change in a bifurcation parameter. Extensive analysis has been conducted to develop a predictive understanding of parameter thresholds leading to wavelength changes. By contrast, theory on what determines PTW wavelength selection during a wavelength change is currently lacking and most conjectures stem from limited observations of specific simulations, or apply to special cases only. In this unsolved problems article, we first provide a review of how linear stability analysis and Busse balloon theory are used to predict parameter values at which PTW wavelength changes occur. On the topic of wavelength selection, we review the special case of PTWs in $\lambda$ - $\omega$ systems, often used to predict wavelengths of predator-prey dynamics in the wake of an invasion front. For more general systems, we highlight that the Busse balloon theory that is so successful in determining parameter values of wavelength changes is unlikely able to provide information on PTW wavelength selection. Finally, we present new numerical trends of PTW wavelength selection during PTW-to-PTW transitions that highlight that some stable wavelengths are more frequently selected than others, and that cascades of wavelength changes can also result in extinction events despite bistability of the extinction state with PTWs. We conclude with a tentative list of potential approaches to unravel a deeper understanding of this topic. Combined, we aim to stimulate new approaches to gain more insights into the unsolved problem of PTW wavelength selection during PTW-to-PTW transitions.

Tumor growth and angiogenesis drive complex spatiotemporal variation in micro-environmental oxygen levels. Previous experimental studies have observed that cancer cells exposed to chronic hypoxia retained a phenotype characterized by enhanced migration and reduced proliferation, even after being shifted to normoxic conditions, a phenomenon which we refer to as hypoxic memory. However, because dynamic hypoxia and related hypoxic memory effects are challenging to measure experimentally, our understanding of their implications in tumor invasion is quite limited. Here, we propose a novel phenotype-structured partial differential equation modeling framework to elucidate the effects of hypoxic memory on tumor invasion along one spatial dimension in a cyclically varying hypoxic environment. We incorporated hypoxic memory by including time-dependent changes in hypoxic-to-normoxic phenotype transition rate upon continued exposure to hypoxic conditions. Our model simulations demonstrate that hypoxic memory significantly enhances tumor invasion without necessarily reducing tumor volume. This enhanced invasion was sensitive to the induction rate of hypoxic memory, but not the dilution rate. Further, shorter periods of cyclic hypoxia contributed to a more heterogeneous profile of hypoxic memory in the population, with the tumor front dominated by hypoxic cells that exhibited stronger memory. Overall, our model highlighted the complex interplay between hypoxic memory and cyclic hypoxia in shaping heterogeneous tumor invasion patterns.

This article introduces a computational method, called Recapture of Diffusive Agents & Particle Swarm Optimization (RDA-PSO), designed to estimate the dispersal parameter of diffusive insects in mark-release-recapture (MRR) field experiments. In addition to describing the method, its properties are discussed, with particular focus on robustness in estimating the observed diffusion coefficient in the presence of uncertainty. It is shown that RDA-PSO provides a simple and reliable approach to quantify insect dispersal that can handle low recapture rates and uneven capture site distributions without the need for area corrections. Tests on synthetic data, for which the actual diffusion coefficient is known, show the method outperforms three techniques based on the solution of the diffusion equation, which are also introduced in this work. Examples of application to real field data for the yellow fever mosquito are provided.

Evolvability is defined as the ability of a population to generate heritable variation to facilitate its adaptation to new environments or selection pressures. In this article, we consider evolvability as a phenotypic trait subject to evolution and discuss its implications in the adaptation of populations of asexual individuals. We explore the evolutionary dynamics of an actively proliferating population of individuals, subject to changes in their proliferative potential and their evolvability, through mathematical simulations of a stochastic individual-based model and its deterministic continuum counterpart. We find robust adaptive trajectories that rely on individuals with high evolvability rapidly exploring the phenotypic landscape and reaching the proliferative potential with the highest fitness. The strength of selection on the proliferative potential, and the cost associated with evolvability, can alter these trajectories such that, if both are sufficiently constraining, highly evolvable populations can become extinct in our individual-based model simulations. We explore the impact of this interaction at various scales, discussing its effects in undisturbed environments and also in disrupted contexts, such as cancer.

Visual stimuli with constant temporal frequency input are known to induce peaks in the driving frequency of the power spectrum of the electroencephalogram (EEG) over the visual cortex. While EEG responses with random temporal frequencies (m-sequences) of scenes alternating between two images have been studied, the underlying mechanisms that shape these responses are not fully understood. We analyze our new EEG data from a controlled experiment with m-sequence inputs and model the EEG using statistical time series models: an autoregressive (AR) model, adding exogenous input to AR (ARX), adding moving average terms (ARMAX), and finally adding a seasonality term (SARMAX). We implement computational methods to robustly handle model instabilities induced by this data, fitting these models with the Box-Jenkins methodology and assessing prediction accuracy of some statistical aspects of the EEG for long periods of several seconds out-of-sample. We find in-sample fits are good in all models despite the complexities of the visual pathway, and that all models can predict aspects of EEG: including the distribution of point-wise values in time, the point-wise Pearson's correlation of EEG and model, and the frequency content. Surprisingly, we find little variation in the performance among these models, with the most sophisticated model (SARMAX) performing comparatively poorly in some instances. Our results suggest the simplest AR model is viable and can outperform more complicated models. Since these models are relatively simple and more transparent than contemporary models with numerous parameters, our study could inform future mechanistic studies of the temporal dynamics of human EEG responses to visual stimuli.