## Dean Bottino : Evaluating Strategies for Overcoming Rituximab (R) Resistance Using a Quantitative Systems Pharmacology (QSP) model of Antibody-Dependent Cell-mediated Cytotoxicity & Phagocytosis (ADCC & ADCP): An Academic/Industrial Collaboration

- Mathematical Biology ( 35 Views )Despite the impressive performance of rituximab (R) containing regimens like R-CHOP in CD20+ Non-Hodgkin’s Lymphoma (NHL), 30-60% of R-naïve NHL patients are estimated to be resistant, and approximately 60% of those patients will not respond to subsequent single agent R treatment. Given that antibody dependent cell mediated cytotoxicity (ADCC) and phagocytosis (ADCP) are thought to be the major mechanisms of action of Rituximab, increasing the activation levels of natural killer (NK) and macrophage (MP) cells may be one strategy for overcoming R resistance.

During (and after) the Fields Institute Industrial Problem Solving Workshop in August 2019, academic participants and industry mentors developed and calibrated to literature data a quantitative systems pharmacology (QSP) model of ADCC/ADCP to interrogate which mechanisms of R resistance could be overcome by increased NK or MP activation, and how much effector cell activation would be required to overcome a given degree and mechanism of R resistance.

This work was motivated by a real-world pharmaceutical drug development question, and the academic-industry interactions during and after the workshop resulted in sharknado plots as well as a published QSP model (presented at American Association of Cancer Research Annual Meeting, 2021) that was able to address some of the key questions around overcoming R resistance. The published model was then incorporated into an in-house QSP model supporting the development of a Takeda investigational drug which is being developed to restore R sensitivity in an R-resistant patient population.

## Chun-Hung Liu : Assouad-Nagata dimension of minor-closed metrics

- Mathematical Biology ( 61 Views )Assouad-Nagata dimension addresses both large-scale and small-scale behaviors of metric spaces and is a refinement of Gromov’s asymptotic dimension. A metric space is a minor-closed metric if it is defined by the distance function on the vertices of an edge-weighted graph that satisfies a fixed graph property preserved under vertex-deletion, edge-deletion, and edge-contraction. In this talk, we determine the Assouad-Nagata dimension of every minor-closed metric. It is a common generalization of known results about the asymptotic dimension of H-minor free unweighted graphs, about the Assouad-Nagata dimension of complete Riemannian surfaces with finite Euler genus, and about their corollaries on weak diameter coloring of minor-closed families of graphs and asymptotic dimension of minor-excluded groups.

## Jesse Zhang : Geodesic complexity of convex polyhedra

- Mathematical Biology ( 84 Views )Geodesic complexity of the d-dimensional boundary S of a convex polytope of dimension d+1 is intimately related to the combinatorics of nonoverlapping unfolding of S into a Euclidean space R^d following Miller and Pak (2008). This combinatorics is based on facet sequences, which are lists of adjacent facets traversed by geodesics in S. Our main result bounds the geodesic complexity of S from above by the number of distinct maximal facet sequences traversed by shortest paths in S. For d=2, results from the literature on nonoverlapping unfolding imply that this bound is polynomial in the number of facets. In arbitrary dimension d, a reinterpretation of conjectures by Miller and Pak (2008) leads to the conjecture that the geodesic complexity of S is polynomial in the number of facets. The theory and results developed here hold more generally for convex polyhedral complexes. This is joint work with Ezra Miller.

## Stephan Huckemann : Statistical challenges in shape prediction of biomolecules

- Mathematical Biology ( 150 Views )The three-dimensional higher-order structure of biomolecules
determines their functionality. While assessing primary structure is
fairly easily accessible, reconstruction of higher order structure is
costly. It often requires elaborate correction of atomic clashes,
frequently not fully successful. Using RNA data, we describe a purely
statistical method, learning error correction, drawing power from a
two-scale approach. Our microscopic scale describes single suites by
dihedral angles of individual atom bonds; here, addressing the
challenge of torus principal component analysis (PCA) leads to a
fundamentally new approach to PCA building on principal nested spheres
by Jung et al. (2012). Based on an observed relationship with a
mesoscopic scale, landmarks describing several suites, we use Fréchet
means for angular shape and size-and-shape, correcting
within-suite-backbone-to-backbone clashes. We validate this method by
comparison to reconstructions obtained from simulations approximating
biophysical chemistry and illustrate its power by the RNA example of
SARS-CoV-2.

This is joint work with Benjamin Eltzner, Kanti V. Mardia and Henrik
Wiechers.

Literature:

Eltzner, B., Huckemann, S. F., Mardia, K. V. (2018):
Torus principal component analysis with applications to RNA
structure. Ann. Appl. Statist. 12(2), 1332?1359.

Jung, S., Dryden, I. L., Marron, J. S. (2012):
Analysis of principal nested spheres. Biometrika, 99 (3), 551-568

Mardia, K. V., Wiechers, H., Eltzner, B., Huckemann, S. F. (2022).
Principal component analysis and clustering on manifolds. Journal of
Multivariate Analysis, 188, 104862,
https://www.sciencedirect.com/science/article/pii/S0047259X21001408

Wiechers, H., Eltzner, B., Mardia, K. V., Huckemann, S. F. (2021).
Learning torus PCA based classification for multiscale RNA backbone
structure correction with application to SARS-CoV-2. To appear in the
Journal of the Royal Statistical Society, Series C,
bioRxiv https://doi.org/10.1101/2021.08.06.455406

## Casey Diekman : Data Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment

- Mathematical Biology ( 101 Views )Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earth’s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.

## Elliot Cartee : Control-Theoretic Models of Environmental Crime

- Mathematical Biology ( 162 Views )We present two models of perpetrators' decision-making in extracting resources from a protected area. It is assumed that the authorities conduct surveillance to counter the extraction activities, and that perpetrators choose their post-extraction paths to balance the time/hardship of travel against the expected losses from a possible detection. In our first model, the authorities are assumed to use ground patrols and the protected resources are confiscated as soon as the extractor is observed with them. The perpetrators' path-planning is modeled using the optimal control of randomly-terminated process. In our second model, the authorities use aerial patrols, with the apprehension of perpetrators and confiscation of resources delayed until their exit from the protected area. In this case the path-planning is based on multi-objective dynamic programming. Our efficient numerical methods are illustrated on several examples with complicated geometry and terrain of protected areas, non-uniform distribution of protected resources, and spatially non-uniform detection rates due to aerial or ground patrols.

## Sharon Lubkin : Notochord eccentricity and its relation to cell packing

- Mathematical Biology ( 219 Views )The notochord, the defining feature of chordates, is a pressurized tube which actuates elongation of the chordate embryo. The zebrafish notochord consists of large vacuolated cells surrounded by a thin sheath. We characterized the patterns of the cells’ packing, and their relationship to the known regular patterns from the study of foams, and irregular patterns in a gel bead system. Disruption of the wild type packing pattern leads to developmental defects. We characterize the bifurcations between the relevant regular patterns in terms of nondimensional geometrical and mechanical ratios, and suggest an important developmental role for the eccentric "staircase" pattern.

## John Gemmer : Nature’s Forms are Frilly, Flexible and Functional

- Mathematical Biology ( 238 Views )Many patterns in Nature and industry arise from the system minimizing an appropriate energy. Torn plastic sheets and growing leaves provide striking examples of pattern forming systems which can transition from single wavelength geometries (leaves) to complex fractal-like shapes (lettuce). These fractal-like patterns seem to have many length scales, i.e. the same amount of extra detail can be seen when looking closer (“statistical self-similarity”). It is a mystery how such complex patterns could arise from energy minimization alone. In this talk I will address this puzzle by showing that such patterns naturally arise from the sheet adopting a hyperbolic non-Euclidean geometry. However, there are many different hyperbolic geometries that the growing leaf could select. I will show using techniques from analysis, differential geometry and numerical optimization that the fractal like patterns are indeed the natural minimizers for the system. I will also discuss the implications of our work to developing shape changing soft matter which can be implemented in soft machines.