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Abstract In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model in the form of a system of two partial differential equations (PDEs) incorporating both migration and growth terms, and show that it more accurately fits our data compared to simpler PDE models. We show that traveling-wave speeds are strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a “Go-or-Grow”-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age and survival. 

Abstract Tomopterids are mesmerizing holopelagic swimmers. They use two modes of locomotion simultaneously: drag-based metachronal paddling and bodily undulation.Tomopterishas two rows of flexible, leg-like parapodia positioned on opposite sides of its body. Each row metachronally paddles out of phase to the other. Both paddling behaviors occur in concert with a lateral bodily undulation. However, when looked at independently, each mode appears in tension with the other. The direction of the undulatory wave is opposite of what one may expect for forward (FWD) swimming and appears to actively work act against the direction of swimming initiated by metachronal paddling. To investigate how these two modes of locomotion synergize to generate effective swimming, we created a self-propelled, fluid-structure interaction model of an idealizedTomopteris. We holistically explored swimming performance over a 3D mechanospace comprising parapodia length, paddling amplitude, and undulatory amplitude using a machine learning framework based on polynomial chaos expansions. Although undulatory amplitude minimally affected FWD swimming speeds, it helped mitigate the larger costs of transport that arise from either using more mechanically expensive (larger) paddling amplitudes and/or having longer parapodia. 

Abstract The electron-induced secondary electron emission (SEE) yields of imidazolium-based ionic liquids are presented for primary electron beam energies between 30 and 1000 eV. These results are important for understanding plasma synthesis of nanoparticles in plasma discharges with an ionic liquid electrode. Due to their low vapor pressure and high conductivity, ionic liquids can produce metal nanoparticles in low-pressure plasmas through reduction of dissolved metal salts. In this work, the low vapor pressure of ionic liquids is exploited to directly measure SEE yields by bombarding the liquid with electrons and measuring the resulting currents. The ionic liquids studied are [BMIM][Ac], [EMIM][Ac], and [BMIM][BF₄]. The SEE yields vary significantly over the energy range, with maximum yields of around 2 at 200 eV for [BMIM][Ac] and [EMIM][Ac], and 1.8 at 250 eV for [BMIM][BF₄]. Molecular orbital calculations indicate that the acetate anion is the likely electron donor for [BMIM][Ac] and [EMIM][Ac], while in [BMIM][BF₄], the electrons likely originate from the [BMIM]⁺cation. The differences in SEE yields are attributed to varying ionization potentials and molecular structures of the ionic liquids. These findings are essential for accurate modeling of plasma discharges and understanding SEE mechanisms in ionic liquids. 

Abstract Despite the revolutionary impact of immune checkpoint inhibition on cancer therapy, the lack of response in a subset of patients, as well as the emergence of resistance, remain significant challenges. Here we explore the theoretical consequences of the existence of multiple states of immune cell exhaustion on response to checkpoint inhibition therapy. In particular, we consider the emerging understanding that T cells can exist in various states: fully functioning cytotoxic cells, reversibly exhausted cells with minimal cytotoxicity, and terminally exhausted cells. We hypothesize that inflammation augmented by drug activity triggers transitions between these phenotypes, which can lead to non-genetic resistance to checkpoint inhibitors. We introduce a conceptual mathematical model, coupled with a standard 2-compartment pharmacometric (PK) model, that incorporates these mechanisms. Simulations of the model reveal that, within this framework, the emergence of resistance to checkpoint inhibitors can be mitigated through altering the dose and the frequency of administration. Our analysis also reveals that standard PK metrics do not correlate with treatment outcome. However, we do find that levels of inflammation that we assume trigger the transition from the reversibly to terminally exhausted states play a critical role in therapeutic outcome. A simulation of a population that has different values of this transition threshold reveals that while the standard high-dose, low-frequency dosing strategy can be an effective therapeutic design for some, it is likely to fail a significant fraction of the population. Conversely, a metronomic-like strategy that distributes a fixed amount of drug over many doses given close together is predicted to be effective across the entire simulated population, even at a relatively low cumulative drug dose. We also demonstrate that these predictions hold if the transitions between different states of immune cell exhaustion are triggered by prolonged antigen exposure, an alternative mechanism that has been implicated in this process. Our theoretical analyses demonstrate the potential of mitigating resistance to checkpoint inhibitors via dose modulation. 

Abstract Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data. 

Math anxiety is negatively correlated with student performance and can result in avoidance of further math/STEM (science, technology, engineering, and mathematics) classes and careers. Cooperative learning (i.e., group work) is a proven strategy that can reduce math anxiety and has additional social and pedagogical benefits. However, depending on the group individuals, some peer interactions can mitigate anxiety, while others exacerbate it. We propose a mathematical modeling approach to help untangle and explore this complex dynamic. We introduce a modification of the Hegselmann–Krause bounded confidence model, including both attractive and repulsive interactions to simulate how math anxiety levels are affected by pairwise student interactions. The model is simple but provides interesting qualitative predictions. In particular, Monte Carlo simulations show that there is an optimal group size to minimize average math anxiety, and that switching group members randomly at certain frequencies can dramatically reduce math anxiety levels. The model is easily adaptable to incorporate additional personal and societal factors, making it ripe for future research. 

A large diversity of fluid pumps is found throughout nature. The study of these pumps has provided insights into fundamental fluid dynamic processes and inspiration for the development of micro-fluid devices. Recent work by Thiria and Zhang [Appl. Phys. Lett. 106, 054106 (2015)] demonstrated how a reciprocal, valveless pump with a geometric asymmetry could drive net fluid flow due to an impedance mismatch when the fluid moves in different directions. Their pump's geometry is reminiscent of the asymmetries seen in the chains of contractile chambers that form the insect heart and mammalian lymphangions. Inspired by these similarities, we further explored the role of such geometric asymmetry in driving bulk flow in a preferred direction. We used an open-source implementation of the immersed boundary method to solve the fluid-structure interaction problem of a viscous fluid moving through a sawtooth channel whose walls move up and down with a reciprocal motion. Using a machine learning approach based on generalized polynomial chaos expansions, we fully described the model's behavior over the target 3-dimensional design space, composed of input Reynolds numbers (Rein), pumping frequencies, and duty cycles. Scaling studies showed that the pump is more effective at higher intermediate Rein. Moreover, greater volumetric flow rates were observed for near extremal duty cycles, with higher duty cycles (longer contraction and shorter expansion phases) resulting in the highest bulk flow rates.