Bulletin of Mathematical Biology最新文献

In vivo observations show that oxygen levels in tumours can fluctuate on fast and slow timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Yet, little is known about the response and adaptation of cancer cells to cyclic, rather than, constant hypoxia. Further, existing in vitro models of cyclic hypoxia fail to capture the complex and heterogeneous oxygen dynamics of tumours growing in vivo. Mathematical models can help to overcome current experimental limitations and, in so doing, offer new insights into the biology of tumour cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. We develop an individual-based model to investigate how cell cycle progression and cell fate determination of cancer cells are altered following exposure to cyclic hypoxia. Our model can simulate standard in vitro experiments, such as clonogenic assays and cell cycle experiments, allowing for efficient screening of cell responses under a wide range of cyclic hypoxia conditions. Simulation results show that the same cell line can exhibit markedly different responses to cyclic hypoxia depending on the dynamics of the oxygen fluctuations. We also use our model to investigate the impact of changes to cell cycle checkpoint activation and damage repair on cell responses to cyclic hypoxia. Our simulations suggest that cyclic hypoxia can promote heterogeneity in cellular damage repair activity within vascular tumours.

The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of research. In this paper, we concentrate on two biologically relevant families of reaction networks that model multisite phosphorylation and dephosphorylation of a substrate at n sites. For small values of n, it had previously been shown that the parameter region of multistationarity is connected. Here, we extend these results and provide a proof that applies to all values of n. Our techniques are based on the study of the critical polynomial associated with these reaction networks together with polyhedral geometric conditions of the signed support of this polynomial.

Drugs exhibiting nonlinear pharmacokinetics hold significant importance in drug research and development. However, evaluating drug exposure accurately is challenging with the current formulae established for linear pharmacokinetics. This article aims to investigate the steady-state drug exposure for a one-compartment pharmacokinetic (PK) model with sigmoidal Hill elimination, focusing on three key topics: the comparison between steady-state drug exposure of repeated intravenous (IV) bolus ( ${\text{AUC}}_{\mathrm{ss}}$ ) and total drug exposure after a single IV bolus ( ${\text{AUC}}_{0-\infty }$ ); the evolution of steady-state drug concentration with varying dosing frequencies; and the control of drug pharmacokinetics in multiple-dose therapeutic scenarios. For the first topic, we established conditions for the existence of ${\text{AUC}}_{\mathrm{ss}}$ , derived an explicit formula for its calculation, and compared it with ${\text{AUC}}_{0-\infty }$ . For the second, we identified the trending properties of steady-state average and trough concentrations concerning dosing frequency. For the third, we developed formulae to compute dose and dosing time for both regular and irregular dosing scenarios. As an example, our findings were applied to a real drug model of progesterone used in lactating dairy cows. In conclusion, these results provide a theoretical foundation for designing rational dosage regimens and conducting therapeutic trials.

Cancers are typically fueled by sequential accumulation of driver mutations in a previously healthy cell. Some of these mutations, such as inactivation of the first copy of a tumor suppressor gene, can be neutral, and some, like those resulting in activation of oncogenes, may provide cells with a selective growth advantage. We study a multi-type branching process that starts with healthy tissue in homeostasis and models accumulation of neutral and advantageous mutations on the way to cancer. We provide results regarding the sizes of premalignant populations and the waiting times to the first cell with a particular combination of mutations, including the waiting time to malignancy. Finally, we apply our results to two specific biological settings: initiation of colorectal cancer and age incidence of chronic myeloid leukemia. Our model allows for any order of neutral and advantageous mutations and can be applied to other evolutionary settings.

Dispersal of propagules (seeds, spores) from a geographically isolated habitat into an uninhabitable matrix can play a decisive role in driving population dynamics. ODE and integrodifference models of these dynamics commonly feature a "dispersal success" parameter representing the average proportion of dispersing propagules that remain in viable habitat. While dispersal success can be estimated by empirical measurements or by integration of dispersal kernels, one may lack resources for fieldwork or details on dispersal kernels for numerical computation. Here we derive simple upper bounds on the proportion of propagule loss-the complement of dispersal success-that require only habitat area, habitat perimeter, and the mean dispersal distance of a propagule. Using vector calculus in a probabilistic framework, we rigorously prove bounds for the cases of both symmetric and asymmetric dispersal. We compare the bounds to simulations of integral models for the population of Asclepias syriaca (common milkweed) at McKnight Prairie-a 14 hectare reserve surrounded by agricultural fields in Goodhue County, Minnesota-and identify conditions under which the bounds closely estimate propagule loss.

Evolution of dispersal is a fascinating topic at the intersection of ecology and evolutionary dynamics that has generated many challenging problems in the analysis of reaction-diffusion equations. Early results indicated that lower random diffusion rates are generally beneficial. However, in riverine environments with downstream drift, high diffusion may be optimal, depending on downstream boundary conditions. Most of these results were obtained from modeling a single river reach, yet many rivers form intricate tree-shaped networks. We study the evolution of dispersal on a metric graph representing the simplest such possible network: two upstream segments joining to form one downstream segment. We first show that the shape of the positive steady state of a single population depends crucially on the geometry of the network, here considered as the relative length of the three segments. We then study the evolution of dispersal by considering the possibility of "invasion" of a second type (invader) at the steady state of the first type (resident). We show that the geometry of the network determines whether higher or intermediate dispersal is favored.

Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.

Continuous-time predator-prey models admit limit cycle solutions that are vulnerable to the phenomenon of phase-sensitive tipping (P-tipping): The predator-prey system can tip to extinction following a rapid change in a key model parameter, even if the limit cycle remains a stable attractor. In this paper, we investigate the existence of P-tipping in an analogous discrete-time system: a host-parasitoid system, using the economically damaging forest tent caterpillar as our motivating example. We take the intrinsic growth rate of the consumer as our key parameter, allowing it to vary with environmental conditions in ways consistent with the predictions of global warming. We find that the discrete-time system does admit P-tipping, and that the discrete-time P-tipping phenomenon shares characteristics with the continuous-time one: Both require an Allee effect on the resource population, occur in small subsets of the phase plane, and exhibit stochastic resonance as a function of the autocorrelation in the environmental variability. In contrast, the discrete-time P-tipping phenomenon occurs when the environmental conditions switch from low to high productivity, can occur even if the magnitude of the switch is relatively small, and can occur from multiple disjoint regions in the phase plane.

The mechanism of cytoplasmic incompatibility (CI) is important in the study of Wolbachia invasion in wild mosquitoes. Su et al. (Bull Math Biol 84(9):95, 2022) proposed a delay differential equation model by relating the CI effect to maturation delay. In this paper, we investigate the dynamics of this model by allowing the same density-dependent death rate and distinct density-independent death rates. Through analyzing the existence and stability of equilibria, we obtain the parameter conditions for Wolbachia successful invasion if the maternal transmission is perfect. While if the maternal transmission is imperfect, we give the ranges of parameters to ensure failure invasion, successful invasion and partially suppressing, respectively. Meanwhile, numerical simulations indicate that the system may exhibit monostable and bistable dynamics when parameters vary. Particularly, in the bistable situation an unstable separatrix, like a line, exists when choosing constant functions as initial values; and the maturation delay affects this separatrix in an interesting way.

The two main components of the planktonic ecosystem are phytoplankton and zooplankton. Fungal parasites can infect zooplankton and spread between them. In this paper, we construct a dynamic model to describe the spread of fungal parasites among zooplankton. Basic reproduction number for fungal parasite transmission among zooplankton are rigorously derived. The dynamics of this system are analyzed including dissipativity and equilibria. We further explore the effects of ecological factors on population dynamics and the relationship between fungal parasite transmission and phytoplankton blooms. Interestingly, our theoretical and numerical results indicate that a low-light or oligotrophic aquatic environment is helpful in mitigating the transmission of fungal parasites. We also show that fungal parasites on zooplankton can increase phytoplankton biomass and induce blooms.