Mathematical Biosciences最新文献

The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.

In the wake of epidemics, quarantine measures are typically recommended by health authorities or governments to help control the spread of the disease. Compared with mandatory quarantine, voluntary quarantine offers individuals the liberty to decide whether to isolate themselves in case of infection exposure, driven by their personal assessment of the trade-off between economic loss and health risks as well as their own sense of social responsibility and concern for public health. To better understand self-motivated health behavior choices under these factors, here we incorporate voluntary quarantine into an endemic disease model – the susceptible–infected–susceptible (SIS) model – and perform comprehensive agent-based simulations to characterize the resulting behavior-disease interactions in structured populations. We quantify the conditions under which voluntary quarantine will be an effective intervention measure to mitigate disease burden. Furthermore, we demonstrate how individual decision-making factors, including the level of temptation to refrain from quarantine and the degree of social compassion, impact compliance levels of voluntary quarantines and the consequent collective disease mitigation efforts. We find that successful disease control requires either a sufficiently low level of temptation or a sufficiently high degree of social compassion, such that even complete containment of the epidemic is attainable. In addition to well-mixed populations, we have also analyzed other more realistic social networks of contacts, including spatial lattices, small-world networks, and real social networks. Our work offers new insights into the fundamental social dilemma aspect of disease control through non-pharmaceutical interventions, such as voluntary quarantine and isolation, where the collective outcome of individual decision-making is crucial.

Background:

The increased application of immune checkpoint inhibitors (ICIs) targeting PD-1/PD-L1 in lung cancer treatment generates clinical need to reliably predict individual patients’ treatment outcomes.

Methods:

To bridge the prediction gap, we examine four different mathematical models in the form of ordinary differential equations, including a novel delayed response model. We rigorously evaluate their individual and combined predictive capabilities with regard to the patients’ progressive disease (PD) status through equal weighting of model-derived outcome probabilities.

Results:

Fitting the complete treatment course, the novel delayed response model ($R^2=0.938$) outperformed the simplest model ($R^2=0.865$). The model combination was able to reliably predict patient PD outcome with an overall accuracy of 77% (sensitivity = 70%, specificity = 81%), solely through calibration with primary tumor longest diameter measurements. It autonomously identified a subset of 51% of patients where predictions with an overall accuracy of 81% (sensitivity = 81%, specificity = 81%) can be achieved. All models significantly outperformed a fully data-driven machine learning-based approach.

Implications

: These modeling approaches provide a dynamic baseline framework to support clinicians in treatment decisions by identifying different treatment outcome trajectories with already clinically available measurement data.

Limitations and future directions:

Conjoint application of the presented approach with other predictive tools and biomarkers, as well as further disease information (e.g. metastatic stage), could further enhance treatment outcome prediction. We believe the simple model formulations allow widespread adoption of the developed models to other cancer types. Similar models can easily be formulated for other treatment modalities.

Vaccination against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in transient antibody response against the spike protein. The individual immune status at the time of vaccination influences the response. Using mathematical models of antibody decay, we determined the dynamics of serum immunoglobulin G (IgG) and serum immunoglobulin A (IgA) over time. Data fitting to longitudinal IgG and IgA titers was used to quantify differences in antibody magnitude and antibody duration among infection-naïve and infection-positive vaccinees. We found that prior infections result in more durable serum IgG and serum IgA responses, with prior symptomatic infections resulting in the most durable serum IgG response and prior asymptomatic infections resulting in the most durable serum IgA response. These findings can guide vaccine boosting schedules.

The paper studies multi-competitive continuous-time epidemic processes. We consider the setting where two viruses are simultaneously prevalent, and the spread occurs due to individual-to-individual interaction. In such a setting, an individual is either not affected by any of the viruses, or infected by one and exactly one of the two viruses. One of the equilibrium points is the coexistence equilibrium, i.e., multiple viruses simultaneously infect separate fractions of the population. We provide a sufficient condition for the existence of a coexistence equilibrium. We identify a condition such that for certain pairs of spread matrices either every coexistence equilibrium lies on a line that is locally exponentially attractive, or there is no coexistence equilibrium. We then provide a condition that, for certain pairs of spread matrices, rules out the possibility of the existence of a coexistence equilibrium, and, as a consequence, establishes global asymptotic convergence to the endemic equilibrium of the dominant virus. Finally, we provide a mitigation strategy that employs one virus to ensure that the other virus is eradicated. The theoretical results are illustrated using simulations.

Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test.

Global climate change projections indicate that the atmospheric concentration of carbon dioxide will increase twofold by the end of this century. However, how the elevated carbon dioxide affects aquatic carbon sequestration and species composition within aquatic microbial communities remains inconclusive. To address this knowledge gap, we formulate a bacteria-algae interaction model to characterize the effects of elevated carbon dioxide on aquatic ecosystems and rigorously derive the thresholds determining the persistence and extinction of algae or bacteria. We explore the impacts of abiotic factors, such as light intensity, nutrient concentration, inorganic carbon concentration and water depth, on algae and bacteria dynamics. The main findings indicate that the elevated atmospheric carbon dioxide will increase algae biomass and thus facilitate carbon sequestration. On the other hand, the elevated atmospheric carbon dioxide will reduce bacterial biomass, and excessive carbon dioxide concentrations can even destroy bacterial communities. Numerical simulations indicate that eutrophication and intensified light intensity can reduce aquatic carbon sequestration, while elevated atmospheric carbon dioxide levels can mitigate eutrophication. Furthermore, higher algae respiration and death rates are detrimental to carbon sequestration, whereas the increased bacterial respiration rates promote carbon sequestration.