Bulletin of Mathematical Biology最新文献

Density-dependent population dynamic models strongly influence many of the world’s most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40–50 percent of carrying capacity to maximize sustainable harvest, no matter the species’ population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69–81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.

During embryonic development of the retina of the eye, astrocytes, a type of glial cell, migrate over the retinal surface and form a dynamic mesh. This mesh then serves as scaffolding for blood vessels to form the retinal vasculature network that supplies oxygen and nutrients to the inner portion of the retina. Astrocyte spreading proceeds in a radially symmetric manner over the retinal surface. Additionally, astrocytes mature from astrocyte precursor cells (APCs) to immature perinatal astrocytes (IPAs) during this embryonic stage. We extend a previously-developed continuum model that describes tension-driven migration and oxygen and growth factor influenced proliferation and differentiation. Comparing numerical simulations to experimental data, we identify model equation components that can be removed via model reduction using approximate Bayesian computation (ABC). Our results verify experimental studies indicating that the choroid oxygen supply plays a negligible role in promoting differentiation of APCs into IPAs and in promoting IPA proliferation, and the hyaloid artery oxygen supply and APC apoptosis play negligible roles in astrocyte spreading and differentiation.

We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cell-scale dynamics to colony-scale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycle-averaged flagellar force dynamics and statistical models for demographic cell-to-cell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including cell-to-cell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chain-like configurations.

Cancer cells exhibit significant alterations in their metabolism, characterised by a reduction in oxidative phosphorylation (OXPHOS) and an increased reliance on glycolysis, even in the presence of oxygen. This metabolic shift, known as the Warburg effect, is pivotal in fuelling cancer's uncontrolled growth, invasion, and therapeutic resistance. While dysregulation of many genes contributes to this metabolic shift, the tumour suppressor gene p53 emerges as a master player. Yet, the molecular mechanisms remain elusive. This study introduces a comprehensive mathematical model, integrating essential p53 targets, offering insights into how p53 orchestrates its targets to redirect cancer metabolism towards an OXPHOS-dominant state. Simulation outcomes align closely with experimental data comparing glucose metabolism in colon cancer cells with wild-type and mutated p53. Additionally, our findings reveal the dynamic capability of elevated p53 activation to fully reverse the Warburg effect, highlighting the significance of its activity levels not just in triggering apoptosis (programmed cell death) post-chemotherapy but also in modifying the metabolic pathways implicated in treatment resistance. In scenarios of p53 mutations, our analysis suggests targeting glycolysis-instigating signalling pathways as an alternative strategy, whereas targeting solely synthesis of cytochrome c oxidase 2 (SCO2) does support mitochondrial respiration but may not effectively suppress the glycolysis pathway, potentially boosting the energy production and cancer cell viability.

Subaerial biofilms (SAB) are intricate microbial communities living on terrestrial surfaces, of interest in a variety of contexts including cultural heritage preservation, microbial ecology, biogeochemical cycling, and biotechnology. Here we propose a mathematical model aimed at better understanding the interplay between cyanobacteria and heterotrophic bacteria, common microbial SAB constituents, and their mutual dependence on local environmental conditions. SABs are modeled as thin mixed biofilm-liquid water layers sitting on stone. A system of ordinary differential equations regulates the dynamics of key SAB components: cyanobacteria, heterotrophs, polysaccharides and decayed biomass, as well as cellular levels of organic carbon, nitrogen and energy. These components are interconnected through a network of energetically dominant metabolic pathways, modeled with limitation terms reflecting the impact of biotic and abiotic factors. Daily cylces of temperature, humidity, and light intensity are considered as input model variables that regulate microbial activity by influencing water availability and metabolic kinetics. Relevant physico-chemical processes, including pH regulation, further contribute to a description of the SAB ecology. Numerical simulations explore the dynamics of SABs in a real-world context, revealing distinct daily activity periods shaped by water activity and light availability, as well as longer time scale survivability conditions. Results also suggest that heterotrophs could play a substantial role in decomposing non-volatile carbon compounds and regulating pH, thus influencing the overall composition and stability of the biofilm.

Spontaneous filling and voiding cycles represent a key dynamical feature of the healthy lower urinary tract. Some urinary tract dysfunctions, such as over-flow incontinence, may alter the natural occurrence of these cycles. As the function of the lower urinary tract arises from the interplay of a multitude of factors, it is difficult to determine which of them can be modulated to regain spontaneous cycles. In this study, we develop a mathematical model of the lower urinary tract that can capture filling and voiding cycles in the form of periodic solutions of a system of ordinary differential equations. After experimental validation, we utilize this model to study the effect that several physiological quantities have on the onset of cycles. We find that some parameters have an associated numerical threshold that determines whether the system exhibits healthy cycles or settles in a state of constant overflow.

In comparison to phylogenetic trees, phylogenetic networks are more suitable to represent complex evolutionary histories of species whose past includes reticulation such as hybridisation or lateral gene transfer. However, the reconstruction of phylogenetic networks remains challenging and computationally expensive due to their intricate structural properties. For example, the small parsimony problem that is solvable in polynomial time for phylogenetic trees, becomes NP-hard on phylogenetic networks under softwired and parental parsimony, even for a single binary character and structurally constrained networks. To calculate the parsimony score of a phylogenetic network N, these two parsimony notions consider different exponential-size sets of phylogenetic trees that can be extracted from N and infer the minimum parsimony score over all trees in the set. In this paper, we ask: What is the maximum difference between the parsimony score of any phylogenetic tree that is contained in the set of considered trees and a phylogenetic tree whose parsimony score equates to the parsimony score of N? Given a gap-free sequence alignment of multi-state characters and a rooted binary level-k phylogenetic network, we use the novel concept of an informative blob to show that this difference is bounded by $k+1$ times the softwired parsimony score of N. In particular, the difference is independent of the alignment length and the number of character states. We show that an analogous bound can be obtained for the softwired parsimony score of semi-directed networks, while under parental parsimony on the other hand, such a bound does not hold.

Virtual clinical trials (VCTs) are growing in popularity as a tool for quantitatively predicting heterogeneous treatment responses across a population. In the context of a VCT, a plausible patient is an instance of a mathematical model with parameter (or attribute) values chosen to reflect features of the disease and response to treatment for that particular patient. A number of techniques have been introduced to determine the set of model parametrizations to include in a virtual patient cohort. These methodologies generally start with a prior distribution for each model parameter and utilize some criteria to determine whether a parameter set sampled from the priors should be included or excluded from the plausible population. No standard technique exists, however, for generating these prior distributions and choosing the inclusion/exclusion criteria. In this work, we rigorously quantify the impact that VCT design choices have on VCT predictions. Rather than use real data and a complex mathematical model, a spatial model of radiotherapy is used to generate simulated patient data and the mathematical model used to describe the patient data is a two-parameter ordinary differential equations model. This controlled setup allows us to isolate the impact of both the prior distribution and the inclusion/exclusion criteria on both the heterogeneity of plausible populations and on predicted treatment response. We find that the prior distribution, rather than the inclusion/exclusion criteria, has a larger impact on the heterogeneity of the plausible population. Yet, the percent of treatment responders in the plausible population was more sensitive to the inclusion/exclusion criteria utilized. This foundational understanding of the role of virtual clinical trial design should help inform the development of future VCTs that use more complex models and real data.

Mobility is a crucial element in comprehending the possible expansion of the transmission chain in an epidemic. In the initial phases, strategies for containing cases can be directly linked to population mobility restrictions, especially when only non-pharmaceutical measures are available. During the pandemic of COVID-19 in Brazil, mobility limitation measures were strongly opposed by a large portion of the population. Hypothetically, if the population had supported such measures, the sharp rise in the number of cases could have been suppressed. In this context, computational modeling offers systematic methods for analyzing scenarios about the development of the epidemiological situation taking into account specific conditions. In this study, we examine the impacts of interstate mobility in Brazil. To do so, we develop a metapopulational model that considers both intra and intercompartmental dynamics, utilizing graph theory. We use a parameter estimation technique that allows us to infer the effective reproduction number in each state and estimate the time-varying transmission rate. This makes it possible to investigate scenarios related to mobility and quantify the effect of people moving between states and how certain measures to limit movement might reduce the impact of the pandemic. Our results demonstrate a clear association between the number of cases and mobility, which is heightened when states are closer to each other. This serves as a proof of concept and shows how reducing mobility in more heavily trafficked areas can be more effective.