## Christine Heitsch : The Combinatorics of RNA Branching

- Mathematical Biology ( 304 Views )Understanding the folding of RNA sequences into three-dimensional structures is one of the fundamental challenges in molecular biology. For example, the branching of an RNA secondary structure is an important molecular characteristic yet difficult to predict correctly, especially for sequences on the scale of viral genomes. However, results from enumerative, probabilistic, analytic, and geometric combinatorics yield insights into RNA structure formation, and suggest new directions in viral capsid assembly.

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

- Mathematical Biology ( 259 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.

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

- Mathematical Biology ( 252 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.

## Laura Miller : How jellyfish can inspire mathematics: A case study of the feeding currents generated by upside-down jellyfish

- Mathematical Biology ( 223 Views )The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In this presentation, we develop and test mathematical models describing the pulsing dynamics and the resulting fluid flow generated by the upside down jellyfish, Cassiopea. The kinematics of contraction and distributions of pulse frequencies were obtained from videos and used as inputs into numerical simulations. Particle image velocimetry was used to obtain spatially and temporally resolved flow fields experimentally. The immersed boundary method was then used to solve the fluid-structure interaction problem and explore how changes in morphology and pulsing dynamics alter the resulting fluid flow. Unlike pelagic (swimming) jellyfish, there is no evidence of the formation of a train of vortex rings. Instead, significant mixing occurs around and directly above the oral arms and secondary mouths. We found good agreement between the numerical simulations and experiments, suggesting that the presence of porous oral arms induce net horizontal flow towards the bell and mixing.

## Andrew Brouwer : Harnessing environmental surveillance: mathematical modeling in the fight against polio

- Mathematical Biology ( 213 Views )Israel experienced an outbreak of wild poliovirus type 1 (WPV1) in 2013-14, detected through environmental surveillance of the sewage system. No cases of acute flaccid paralysis were reported, and the epidemic subsided after a bivalent oral polio vaccination (bOPV) campaign. As we approach global eradication, polio will increasingly be detected only through environmental surveillance. However, we have lacked the theory to translate environmental surveillance into public health metrics; it is a priori unclear how much environmental surveillance can even say about population-level disease dynamics. We developed a framework to convert quantitative polymerase chain reaction (qPCR) cycle threshold data into scaled WPV1 and OPV1 concentrations for inference within a deterministic, compartmental infectious disease transmission model. We used differential algebra and profile likelihood techniques to perform identifiability analysis, that is, to assess how much information exists in the data for the model, and to quantify inference uncertainty. From the environmental surveillance data, we estimated the epidemic curve and transmission dynamics, determining that the outbreak likely happened much faster than previously thought. Our mathematical modeling approach brings public health relevance to environmental data that, if systematically collected, can guide eradication efforts.

## Joshua Vogelstein : Consistent Graph Classification applied to Human Brain Connectome Data

- Mathematical Biology ( 193 Views )Graphs are becoming a favorite mathematical object for representation of data. Yet, statistical pattern recognition has focused almost entirely on vector valued data in Euclidean space. Graphs, however, live in graph space, which is non-Euclidean. Thus, most inference techniques are not even defined for graph valued data. Previous work in the classification of graph-valued data typically follows one of two recipes. (1) Vectorize the adjacency matrices of the graphs, and apply standard machine learning techniques. (2) Compute some number of graph invariants (e.g., clustering coefficient, or degree distribution) for each graph, and then apply standard machine learning techniques. We follow a different recipe based in the probabilistic theory of pattern recognition. First, we define a joint graph-class model. Given this model, we derive classifiers which we prove are consistent; that is, they converge to the Bayes optimal classifier. Specifically, we build two consistent classifiers for graph valued data, a parametric and a non-parametric version. In a sense, these classifiers span the spectrum of complexity, the former is consistent for graphs sampled from relatively simple random graph distributions, the latter is consistent for graphs sampled from (nearly) any random graph distribution. Although both classifiers assume that all our graphs have labeled vertices, we generalize these results to also incorporate unlabeled graphs, as well as weighted and multigraphs. We apply these graph classifiers to human brain data. Specifically, using diffusion MRI, we can obtain large brain-graphs (10,000 vertices) for each subject, where vertices correspond to voxels. We then coarsen the graphs spatially to obtain smaller (70 vertex) graphs per subject. Using <50 subjects, we are able to achieve nearly 85% classification accuracy, with results interpretable to neurobiologists with regard to the brain regions of interest.

## David Basanta : The ecology of cancer: mathematical modelling and clinical implications

- Mathematical Biology ( 179 Views )Decades of research in cancer have yielded scant results other than highlighting the need for new approaches that could go beyond the tried and tested molecular-based ones. Recent clinical studies show that tumour heterogeneity and selection, the ingredients of Darwinian evolution, can explain cancer progression towards malignancy as well as recurrence after treatment. In this talk I will describe mathematical and computational models that explore cancer evolutionary dynamics and that can explain how the interactions between the tumour with its environment (the tumour ecosystem) can yield a better understanding of cancer biology and lead to better and more efficacious treatments for cancer patients.

## Seth Sullivant : Statistically-Consistent k-mer Methods for Phylogenetic Tree Reconstruction

- Mathematical Biology ( 166 Views )Frequencies of k-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between k-mer vectors to approximate a tree metric can be statistically inconsistent. To remedy this, we derive model-based distance corrections for orthologous sequences without gaps, which lead to consistent tree inference. The identifiability of model parameters from k-mer frequencies is also studied. Finally, we report simulations showing the corrected distance out-performs many other k-mer methods, even when sequences are generated with an insertion and deletion process. These results have implications for multiple sequence alignment as well, since k-mer methods are usually the first step in constructing a guide tree for such algorithms. This is joint work with Elizabeth Allman and John Rhodes.

## Darryl Shibata : Reconstructing Human Tumor Ancestries from their Genomes: Making Human Tissues Talk

- Mathematical Biology ( 163 Views )It is well-known that genomes encode ancestry through replication errors - on average the greater the numbers of differences between two genomes, the greater the time since they shared a common ancestor ("molecular clock hypothesis"). This approach is commonly used to infer ancestries of species and populations, and these same tools can be applied to somatic cell evolution, in particular to better infer ancestries of normal and neoplastic tissues. For example, by sampling from opposite sides of the same human colorectal tumor, one can coalesce back to the earliest tumor cells. Such studies reveal that many human colorectal tumors are simple single "Big Bang" expansions, with evidence of neutral evolution during growth. It may be possible to understand in detail what is impossible to directly observe - the first few divisions of human tumors.

## Aziz Yakubu : Mathematical Models of Malaria with Applications to Mali and USA

- Mathematical Biology ( 148 Views )In this talk, we will introduce a deterministic malaria model for determining the drug administration protocol that leads to the smallest first malaria episodes during the wet season. To explore the effects of administering the malaria drug on different days during wet season while minimizing the potential harmful effects of drug overdose, we will define 40 drug administration protocols. Our results fit well with the clinical studies of Coulibaly et al. at a site in Mali. In addition, we will provide protocols that lead to small number of first malaria episodes during the wet season than the protocol of Coulibaly et al. In the second part of the talk, we will use our malaria model to "capture" the 2013 Centers of Disease Control and Prevention (CDC) reported data on the 2011 number of imported malaria cases in the US. Furthermore; we will use our "fitted" malaria models for the top 20 countries of malaria acquisition by US residents to study the impact of protecting US residents from malaria infection when they travel to malaria endemic areas, the impact of protecting residents of malaria endemic regions from mosquito bites and the impact of killing mosquitoes in those endemic areas on the 2013 CDC malaria surveillance data.

## Rick Durrett : Branching Process Models of Cancer

- Mathematical Biology ( 145 Views )It is common to use a multitype branching process to model the accumulation of mutations that leads to cancer progression, metastasis, and resistance to treatment. In this talk I will describe results about the time until the first type k (cell with k mutations) and the growth of the type k population obtained in joint work with Stephen Moseley, and their use in evaluating possible screening strategies for ovarian cancer, work in progress with Duke undergraduate Kaveh Danesh. The point process representation of the limit, which is a one-sided stable law, together with results from 10-60 years ago leads to remarkable explicit formulas for Simpson's index and the size of the largest clone. These results are important in understanding tumor diversity which can present serious obstacles to treatment. The last topic is joint work with Jasmine Foo, Kevin Leder, John Mayberry, and Franziska Michor

## Joshua Vogelstein : Two-Sample Testing of Non-Euclidean (eg, Graph-Valued) Data via Manifold Learning

- Mathematical Biology ( 140 Views )Two-sample tests are an important class of problems in statistics, with abundant applications ranging from astrophysics to zoology. However, much of the previous art assumes the data samples live in finite dimensional Euclidean space. Here, we consider a foray into two-sample testing when the objects live in a non-Euclidean space, with special emphasis on graph valued observations. Via embedding each graph into Euclidean space, and then learning a manifold along which the reside, we demonstrate the existence of a test such that for a given confidence level alpha, we obtain power > alpha. Simulations and real data applications demonstrate the pragmatic utility of our approach even for very large graphs.

## Jean Clairambault : Drug resistance in cancer: biological and medical issues, and continuous models of structured population dynamics

- Mathematical Biology ( 134 Views )Considering cancer as an evolutionary disease, we aim at understanding the means by which cancer cell populations develop resistance mechanisms to drug therapies, in order to circumvent them by using optimised therapeutic combinations. Rather than focusing on molecular mechanisms such as overexpression of intracellular drug processing enzymes or ABC transporters that are responsible for resistance at the individual cell level, we propose to introduce abstract phenotypes of resistance structuring cancer cell populations. The models we propose rely on continuous adaptive dynamics of cell populations, and are amenable to predict asymptotic evolution of these populations with respect to the phenotypic traits of interest. Drug-induced drug resistance, the question we are tackling from a theoretical and experimental point of view, may be due to biological mechanisms of different natures, mere local regulation, epigenetic modifications (reversible, nevertheless inheritable) or genetic mutations (irreversible), according to the extent to which the genome of the cells in the population is affected. In this respect, the models we develop are more likely to be biologically corresponding to epigenetic modifications, although eventual induction of emergent resistant cell clones due to mutations under drug pressure is not to be completely excluded. From the biologist's point of view, we study phenotypically heterogeneous, but genetically homogeneous, cancer cell populations under stress by drugs. According to the cell populations at stake and to the exerted drug pressure, is drug resistance in cancer a permanently acquired phenotypic trait or is it reversible? Can it be avoided or overcome by rationally (model-guided) designed combinations of drugs? These are some of the questions we will try to answer in a collaboration between a team of mathematicians and another one of biologists, both dealing with cancer and Darwinian - possibly also Lamarckian - evolution of cell populations.

## Guillaume Lajoie : Artificially-induced synaptic plasticity in motor cortex: a theoretical model of a bidirectional brain-computer interface

- Mathematical Biology ( 132 Views )Experiments on macaque monkeys show that spike-triggered stimulation performed by a Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen synaptic connections between distant neural sites in Motor Cortex (MC) and even between MC and spinal cord, with changes that last several days. Here, a neural implant records from some neurons in MC and electrically stimulates others after set delays. The working hypothesis is that this stimulation procedure, which interacts with the very fast spiking activity of cortical circuits (on the order of milliseconds), induces changes mediated by synaptic plasticity mechanisms on much longer timescales (hours and days). The field of online, closed-loop BBCI's is rapidly evolving, with applications ranging from a science-oriented tool to clinical treatments of motor injuries. However, with the enhanced capability of novel devices that can record and stimulate an ever-growing number of neural sites comes growing complexity. It is therefore crucial to develop a theoretical understanding of the effects of closed-loop artificial stimulation in the highly recurrent neural circuits found in cortex, and how such protocols affect functional cotex-to-muscle mappings across a range of timescales. In parallel with ongoing experiments, we are developing a mathematical model of recurrent MC networks with probabilistic spiking mechanisms and spike-time-dependent plastic synapses (STDP) capable of capturing both neural and synaptic activity statistics relevant to BBCI protocols. This model successfully reproduces key experimental results and we use analytical derivations to predict optimal operational regimes for BBCIs. We make experimental predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity such as awake behaving states or sleep. Importantly, this work provides a first step toward a theoretical framework aimed at the design and development of next-generations applications of BBCI's.

## Doron Levy : Modeling the role of the immune response in chronic myelogenous leukemia

- Mathematical Biology ( 130 Views )Tyrosine kinase inhibitors (TKIs), such as imatinib (IM), have significantly improved treatment of chronic myelogenous leukemia (CML). However, the majority of patients are not cured for undetermined reasons. It turns out that many patients who otherwise responded well to IM therapy still show variations in their BCR-ABL transcripts. In this talk we will overview mathematical models for leukemia, drug resistance, and stem cells. Our main focus will be on our recent results concerning mathematical models that integrate CML and an autologous immune response. This is a joint work with G. Clapp, T. Lepoutre, and F. Nicolini.

## Marisa Eisenberg : Forecasting and uncertainty in modeling disease dynamics

- Mathematical Biology ( 129 Views )Connecting dynamic models with data to yield predictive results often requires a variety of parameter estimation, identifiability, and uncertainty quantification techniques. These approaches can help to determine what is possible to estimate from a given model and data set, and help guide new data collection. Here, we examine how parameter estimation and disease forecasting are affected when examining disease transmission via multiple types or pathways of transmission. Using examples taken from the West Africa Ebola epidemic, HPV, and cholera, we illustrate some of the potential difficulties in estimating the relative contributions of different transmission pathways, and show how alternative data collection may help resolve this unidentifiability. We also illustrate how even in the presence of large uncertainties in the data and model parameters, it may still be possible to successfully forecast disease dynamics.

## Carina Curto : Convex neural codes

- Mathematical Biology ( 125 Views )Cracking the neural code is one of the central challenges of neuroscience. Typically, this has been understood as finding the relationship between single neurons and the stimuli they represent. More generally, neural activity must also reflect relationships between stimuli, such as proximity between locations in an environment. Convex codes, comprised of activity patterns for neurons with classical receptive fields, may be the brain's solution to this problem. These codes have been observed in many areas, including sensory cortices and the hippocampus. What makes a code convex? Using algebra, we can uncover intrinsic signatures of convexity and dimension in neural codes. I will report on some recent results by multiple authors, including participants in my 2014 AMS Math Research Community.

## Ezra Miller : Applying persistent homology to brain artery and vein imaging

- Mathematical Biology ( 125 Views )Persistent homology measures geometric structures using topological invariants. When the structures are magnetic resonance images of branching arteries, for example, persistent homology records the connectedness of an increasing subset of the vessels. Although the theory of persistent homology is relatively well developed, and many aspects of its behavior are understood in synthetic examples, only recently have applications to genuine experimental data begun. This talk explains what we have learned about the geometry of blood vessels in aging human brains, as well as lessons this exploration has taught us about applications of persistent homology in general. These lessons inform further potential applications of persistent homology in statistical problems from biological and medical imaging. The main results are joint with Paul Bendich, Steve Marron, Aaron Pieloch, and Sean Skwerer (Math junior faculty, Stat faculty, Math undergrad, and Operations Research grad student). The talk will be accessible to advanced mathematics and statistics undergraduates, medical and biological researchers, statistics and mathematics faculty, and everybody in between.

## Jim Keener : Mechanisms of length regulation of flagella in Salmonella

- Mathematical Biology ( 120 Views )Abstract: The construction of flagellar motors in motile bacteria such as Salmonella is a carefully regulated genetic process. Among the structures that are built are the hook and the filament. The length of the hook is tightly controlled while the length of filaments is less so. However, if a filament is broken off it will regrow, while a broken hook will not regrow. The question that will be addressed in this talk is how Salmonella detects and regulates the length of these structures. This is related to the more general question of how physical properties (such as size or length) can be detected by chemical signals and what those mechanisms are. In this talk, I will present mathematical models for the regulation of hook and filament length. The model for hook length regulation is based on the hypothesis that the hook length is determined by the rate of secretion of the length regulatory molecule FliK and a cleavage reaction with the gatekeeper molecule FlhB. A stochastic model for this interaction is built and analyzed, showing excellent agreement with hook length data. The model for filament length regulation is based on the hypothesis that the growth of filaments is diffusion limited and is measured by negative feedback involving the regulatory protein FlgM. Thus, the model includes diffusion on a one-dimensional domain with a moving boundary, coupled with a negative feedback chemical network. The model shows excellent qualitative agreement with data, although there are some interesting unresolved issues related to the quantitative results.

## Helen Moore : Optimal Control Applied to Drug Development.

- Mathematical Biology ( 119 Views )In the biopharma industry of drug development, figuring out the best doses to use is considered a high priority. It can mean the difference between having an effective drug and having one that gives no benefit. It can reduce toxicities that otherwise could prevent the drug from being used. And proposing a dose that later turns out to be excessive not only looks bad, it can also mean substantial revenue loss.

The type of control theory used in academia for many decades is now being looked at by industry as a potential way to address the problem of dose selection. The problem becomes even harder when a drug will be used in combination with one or more other drugs. I will explain some of the mathematics and show examples of how control theory can be used to optimize dose regimens.

## John Tyson : Irreversible Transitions, Bistability and Checkpoints in the Eukaryotic Cell Cycle

- Mathematical Biology ( 113 Views )

"Perhaps a proper understanding of the complex

regulatory networks making up cellular systems

like the cell cycle will require a shift from common

sense thinking...to a more abstract world, more

readily analyzable in terms of mathematics."

(Paul Nurse, Cell, 7 January 2000)

The cell cycle is a striking example of the necessity of systems-level

thinking in 21st century molecular cell biology. The resolute reductionism

of the last century, albeit necessary for identifying the molecular

components of cellular control systems and their interactions, has failed

to provide a comprehensive, integrative understanding of the molecular

basis of cell physiology. Putting the pieces back together requires new

ways of thinking about and doing molecular biology--an approach now

known as molecular systems biology. In this lecture I will show how

systems-level thinking reveals deep and unexpected principles of cell

cycle regulation.

## Niall Mangan : Identifying models from data

- Mathematical Biology ( 112 Views )Building models for biological, chemical, and physical systems has traditionally relied on domain specific intuition about which interaction and features most strongly influence a system. Statistical methods based in information criteria provide a framework to balance likelihood and model complexity. Recently developed for and applied to dynamical systems, sparse optimization strategies can select a subset of terms from a library that best describe data, automatically interfering model structure. I will discuss my group's application and development of data driven methods for model selection to 1) find simple statistical models to use wastewater surveillance to track the COVID pandemic and 2) recover chaotic systems models from data with hidden variables. I'll briefly discuss current preliminary work and roadblocks in developing new methods for model selection of biological metabolic and regulatory networks.

## Samuel Friedman : Using MultiCellDS and digital cell lines to initialize large-scale 3-D agent-based cancer simulations (up to 0.5M cells)

- Mathematical Biology ( 110 Views )Understanding and predicting cancer progression requires detailed interacting models of tumor and stromal cells, all calibrated to experimental data. Work to date has been limited by a lack of standardization of data representations of multicellular systems, though this is now being addressed through MultiCellDS (MultiCellular Data Standard) and digital cell lines, which are standardized representations of microenvironment-dependent cell phenotypes. Computational cancer modelers require biologically and mathematically consistent initialization routines to seed simulations with cells defined in digital cell lines. In this talk, we will briefly introduce a 3-D agent-based model designed for use in integrative computational biology. We introduce a ?snapshot generator? that can take a digital cancer cell line and produce for the agent-based model an initial cell arrangement and a phenotypic state based upon analyses of the digital cell line data elements. We demonstrate 2-D monolayer and 3-D hanging drop simulations up to 500k MCF7 cells, a common breast cancer cell line. We additionally demonstrate the production of digital snapshots, standardized simulation output that will facilitate computational model comparison with a common core of analytical tools. With an early version of these tools, we assess the match between simulations and in vitro experiments. In the future, this work will be used to create and simulate combinations of tumor and stromal cells from appropriate digital cell lines in realistic tissue environments in order to understand, predict, and eventually control cancer progression in individual patients.

## Scott Schmidler : Stochastic Models of Protein Evolution

- Mathematical Biology ( 109 Views )Stochastic evolutionary models of biological sequences are widely used for phylogenetic inference and ancestral reconstruction. However, at long divergence times sequences enter the "twilight zone" of homology detection and reconstruction becomes very difficult. We describe a stochastic evolutionary model for protein 3D structure using elements of shape theory. This model significantly resolves this uncertainty and stabilizes evolutionary inferences. We also provide theoretical bounds on inferring evolutionary divergence times via connections to the probabilistic "cutoff phenomenon", in which a Markov chain remains far equilibrium for an extended period followed by a rapid transition into equilibrium. We show that this cutoff explains several previously reported problems with common default priors for Bayesian phylogenetic analysis, and suggest a new class of priors to address these problems.

## Sayan Mukherjee : Modeling a Male-Male Sex Network in South India for Spread of Disease and Behavior

- Mathematical Biology ( 109 Views )A preliminary examination of a very rich data set consisting of a detailed survey of individuals in male-male sex networks in South India. The motivation for the study is to understand the spread of HIV in male-male sex networks in South India. The data contains survey information from participants, as well as their cell phone contacts and incomplete information on the contacts by participants. We provide predictive models of attributes of contacts given participant attributes, as well as predictive models of the attributes, such as sexual position. We study how model parameters vary as a function of connectedness of individuals and how modeling network interactions has an effect on the model.

## Paul Magwene : Taking a dip in the gene pool: Insights from pooled population sequencing

- Mathematical Biology ( 109 Views )Advances in high-throughput genomics have facilitated the development of pooled population sequencing techniques which involve the en masse sequencing of tens to hundreds of individual genomes in a single sequencing reaction. Pooled population sequencing methods have numerous applications in quantitative, population and evolutionary genetics. I will discuss some of the statistical and computational challenges associated with the analysis of pooled sequence data in the context of quantitative trait locus (QTL) mapping and detecting selection during experimental evolution.