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While a standard calculus course may include some neatly-packaged applications of rate of change or Riemann sums to problems of kinematics, majors from biology and medicine are in urgent need of mathematics taught from a modeling perspective. Yet, the art of modeling is scarce in tertiary mathematics classrooms in part because, much like in schools, many mathematicians may lack (a) the relevant real-world concepts (beyond simple physics and engineering) (b) knowledge of the mathematics from a modeling perspective or (c) confidence to change their classroom practices. To remedy this, we trialed a professional development workshop for faculty to learn to mathematically model biological contexts with dynamical systems. The workshop enacted the field’s recommendations for professional development with teachers. We observed gains in faculty’s self-reported comfort with mathematics and biology concepts and teaching mathematics with a modeling perspective. 

Abstract The recurrence of cancer following chemotherapy treatment is a major cause of death across solid and hematologic cancers. In B-cell acute lymphoblastic leukemia (B-ALL), relapse after initial chemotherapy treatment leads to poor patient outcomes. Here we test the hypothesis that chemotherapy-treated versus control B-ALL cells can be characterized based on cellular physical phenotypes. To quantify physical phenotypes of chemotherapy-treated leukemia cells, we use cells derived from B-ALL patients that are treated for 7 days with a standard multidrug chemotherapy regimen of vincristine, dexamethasone, and L-asparaginase (VDL). We conduct physical phenotyping of VDL-treated versus control cells by tracking the sequential deformations of single cells as they flow through a series of micron-scale constrictions in a microfluidic device; we call this method Quantitative Cyclical Deformability Cytometry. Using automated image analysis, we extract time-dependent features of deforming cells including cell size and transit time (TT) with single-cell resolution. Our findings show that VDL-treated B-ALL cells have faster TTs and transit velocity than control cells, indicating that VDL-treated cells are more deformable. We then test how effectively physical phenotypes can predict the presence of VDL-treated cells in mixed populations of VDL-treated and control cells using machine learning approaches. We find that TT measurements across a series of sequential constrictions can enhance the classification accuracy of VDL-treated cells in mixed populations using a variety of classifiers. Our findings suggest the predictive power of cell physical phenotyping as a complementary prognostic tool to detect the presence of cells that survive chemotherapy treatment. Ultimately such complementary physical phenotyping approaches could guide treatment strategies and therapeutic interventions. Insight box Cancer cells that survive chemotherapy treatment are major contributors to patient relapse, but the ability to predict recurrence remains a challenge. Here we investigate the physical properties of leukemia cells that survive treatment with chemotherapy drugs by deforming individual cells through a series of micron-scale constrictions in a microfluidic channel. Our findings reveal that leukemia cells that survive chemotherapy treatment are more deformable than control cells. We further show that machine learning algorithms applied to physical phenotyping data can predict the presence of cells that survive chemotherapy treatment in a mixed population. Such an integrated approach using physical phenotyping and machine learning could be valuable to guide patient treatments. 

Computational methodologies are increasingly addressing modeling of the whole cell at the molecular level. Proteins and their interactions are the key component of cellular processes. Techniques for modeling protein interactions, thus far, have included protein docking and molecular simulation. The latter approaches account for the dynamics of the interactions but are relatively slow, if carried out at all-atom resolution, or are significantly coarse grained. Protein docking algorithms are far more efficient in sampling spatial coordinates. However, they do not account for the kinetics of the association (i.e., they do not involve the time coordinate). Our proof-of-concept study bridges the two modeling approaches, developing an approach that can reach unprecedented simulation timescales at all-atom resolution. The global intermolecular energy landscape of a large system of proteins was mapped by the pairwise fast Fourier transform docking and sampled in space and time by Monte Carlo simulations. The simulation protocol was parametrized on existing data and validated on a number of observations from experiments and molecular dynamics simulations. The simulation protocol performed consistently across very different systems of proteins at different protein concentrations. It recapitulated data on the previously observed protein diffusion rates and aggregation. The speed of calculation allows reaching second-long trajectories of protein systems that approach the size of the cells, at atomic resolution. 

With the recent explosion in the size of libraries available for screening, virtual screening is positioned to assume a more prominent role in early drug discovery’s search for active chemical matter. In typical virtual screens, however, only about 12% of the top-scoring compounds actually show activity when tested in biochemical assays. We argue that most scoring functions used for this task have been developed with insufficient thoughtfulness into the datasets on which they are trained and tested, leading to overly simplistic models and/or overtraining. These problems are compounded in the literature because studies reporting new scoring methods have not validated their models prospectively within the same study. Here, we report a strategy for building a training dataset (D-COID) that aims to generate highly compelling decoy complexes that are individually matched to available active complexes. Using this dataset, we train a general-purpose classifier for virtual screening (vScreenML) that is built on the XGBoost framework. In retrospective benchmarks, our classifier shows outstanding performance relative to other scoring functions. In a prospective context, nearly all candidate inhibitors from a screen against acetylcholinesterase show detectable activity; beyond this, 10 of 23 compounds have IC 50 better than 50 μM. Without any medicinal chemistry optimization, the most potent hit has IC 50 280 nM, corresponding to K i of 173 nM. These results support using the D-COID strategy for training classifiers in other computational biology tasks, and for vScreenML in virtual screening campaigns against other protein targets. Both D-COID and vScreenML are freely distributed to facilitate such efforts.