How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.

The Maximum Entropy Theory of Ecology (METE), is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, “ecological state variables” (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE’s two core functions are derived. These functions, called the “Spatial Structure Function” and the “Ecosystem Structure Function” are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Relationship, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE. We also explore the parameter space defined by the METE’s state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of the basic mathematical structure of METE.

Targeted radionuclide therapy (TRT) has recently seen a surge in popularity with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results, an example being chimeric antigen receptor T cell (CAR-T) therapy in hematologic malignancies. Moreover, TRT and CAR-T therapies possess unique features that require special consideration when determining how to dose as well as the timing and sequence of combination treatments including the distribution of the TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate the additive or synergistic effects of combination therapies and warrant a mathematical treatment that includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here, we combine two previously published mathematical models to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell-based therapies in a multiple myeloma setting. We find that, for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR-T therapies.

Functional trait data enhance climate change research by linking climate change, biodiversity response, and ecosystem functioning, and by enabling comparison between systems sharing few taxa. Across four sites along a 3000–4130 m a.s.l. gradient spanning 5.3 °C in growing season temperature in Mt. Gongga, Sichuan, China, we collected plant functional trait and vegetation data from control plots, open top chambers (OTCs), and reciprocally transplanted vegetation turfs. Over five years, we recorded vascular plant composition in 140 experimental treatment and control plots. We collected trait data associated with plant resource use, growth, and life history strategies (leaf area, leaf thickness, specific leaf area, leaf dry matter content, leaf C, N and P content and C and N isotopes) from local populations and from experimental treatments. The database consists of 6,671 plant records and 36,743 trait measurements (increasing the trait data coverage of the regional flora by 500%) covering 11 traits and 193 plant taxa (ca. 50% of which have no previous published trait data) across 37 families.

Chimeric antigen receptor (CAR) T-cell therapy is potentially an effective targeted immunotherapy for glioblastoma, yet there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid, dexamethasone. Here we present a mathematical model-based analysis of three patient-derived glioblastoma cell lines treated in vitro with CAR T-cells and dexamethasone. Advanced in vitro experimental cell killing assay technologies allow for highly resolved temporal dynamics of tumor cells treated with CAR T-cells and dexamethasone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a nonautonomous, two-species predator-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of dexamethasone. Using time as a bifurcation parameter, we show that (1) dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells in a dose-dependent manner and (2) as dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation. With the model fit to experimental data, we demonstrate that high concentrations of dexamethasone antagonizes CAR T-cell efficacy by exhausting, or reducing the activity of CAR T-cells, and by promoting tumor cell growth. Finally, we identify a critical threshold in the ratio of CAR T-cell death to CAR T-cell proliferation rates that predicts eventual treatment success or failure that may be used to guide the dose and timing of CAR T-cell therapy in the presence of dexamethasone in patients.