Carcinogenesis is the transformation of normal cells into cancer cells. This process has been shown to be of a multistage nature, with stem cells that go through a series of (stochastic) genetic and epigenetic changes that eventually lead to a malignancy. Since the origins of the multistage theory in the 1950s, mathematical modeling has played a prominent role in the investigation of the mechanisms of carcinogenesis. In particular, two stochastic (mechanistic) models, the Armitage-Doll and the two-stage clonal expansion (TSCE) model, have been widely used in the past for cancer risk assessment and for the analysis of cancer population and experimental data. In this talk, I will introduce some of the biological and mathematical concepts behind the theory of multistage carcinogenesis, and discuss in detail the use of these models in cancer epidemiology and cancer prevention and control. Recent applications of multistage and state-transition Markov models to assess the potential impact of lung cancer screening in the US will be reviewed.

This talk provides some fundamentals of statistical techniques for data on non-Euclidean spaces. Such data occur in the analysis of shape of geometrical objects, e.g. in applications studying biological growth. Naturally, shape is modeled on a manifold quotient (e.g. unit size objects) under a Lie group action (e.g. translations and rotations) which can be given a manifold structure, possibly with singularities. We show how this scenario allows for one and two sample tests as well as principal component analysis.

Cartilage physiology is regulated by a single population of specialized cells called chondrocytes. The chondroyctes are sparsely distributed within the extracellular matrix (ECM) and maintain a state of homeostasis in healthy tissue. ECM degeneration due to osteoarthritis can lead to compete degradation of cartilage surfaces, necessitating total joint replacement. Chondrocytes can be utilized to regenerate cartilage via tissue engineering approaches in which these cells are seeded in biocompatible and degradable biopolymer or hydrogel scaffolds. In such systems, biosynthetic activity of the cells in response to their non-native environment results in regeneration and accumulation of ECM constituents concurrent with degradation of the surrounding scaffold material. In this talk, mixture models are presented for interactions between biosynthesis of ECM constituents and ECM linking in cell-seeded scaffolds. Both ODE-based (temporal) models for evolution of average apparent densities and PDE-based (spatio-temporal) models will be presented for variables including unlinked ECM, linked ECM and scaffold. Model extensions accounting for cell proliferation will also be discussed. Of particular interest are model predictions for the evolution of solid phase apparent density, which is correlated with the compressive elastic modulus of the tissue construct. These models provide a quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.

Mathematical modeling has become a widely-used tool for integrating
biological data, designing experiments, and ultimately understanding
biological systems. In recent years two important challenges for the
successful use of mathematical models have become apparent. One is that
models contain parameters that determine the behavior of the model, and
the values of these parameters are often hard to determine from the
available biological data. The other challenge is that many biological
systems exhibit a great deal of heterogeneity in behavior, so even if the
model parameters could be perfectly calibrated by pooling cell behaviors
to produce an “average cell model”, this model may not provide a good
description of any single cell in the population. In this seminar I will
describe a technique that we are using to integrate mathematical modeling
into experimental studies in a way that addresses both of these challenges.
We study endocrine pituitary cells that release a variety of hormones into
the blood, and our aim is to develop an approach for modeling the
behaviors of these cells with enough accuracy so that we can use the
models to make and test predictions in real time.

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.

I consider two kinds of biological novelty using shape of the Drosophila wing as a focal phenotype. Quantitative novelty is the evolution of more or less of the same elements already present in the ancestor, or evolution within one topological space. Qualitative novelty is gain of elements not present in the ancestor, or perhaps the loss of such elements, making a transition from one topological space to another. A quantitative genetic approach allows us to studying the major determinants of quantitative novelty, standing genetic variation and mutational variation. I will present measurements of both mutation and standing variation for a multivariate phenotype, the fly wing. Mathematical and statistical challenges in quantitative novelty involve the identification of subspaces within a topological space with genetic variation, and their relationship to the subspaces found in other samples. Qualitative novelty is easy to identify among species, but its evolution is difficult to study, as by definition it is absent in the ancestor. The process of development, where qualitatively different structures are progressively introduced during most life cycles, provides a framework to understand the evolution of novelty. Developmental studies show that continuous changes in gene expression precede transitions to a new shape topology. Gene expression state within a shape is more complex object that shape itself, adding dimensions that may allow us to identify regions of one shape topology that are neighbors to other topologies.

Many pulse-coupled dynamical systems possess synchronous attracting states. Even stochastically driven model networks of Integrate and Fire neurons demonstrate synchrony over a large range of parameters. We study the interplay between fluctuations which de-synchronize and synaptic coupling along the network connections that synchronize the network by calculating the probability to see repeated cascading total firing events, during which all the neurons in the network fire at once. Using this characterization of synchrony we investigate the significance of the local network topology and of more physiological additions to the model on the model neuronal networks ability to synchronize. The mean time between total firing events characterizes the perfectly synchronous state, and we compute this from a first-passage time problem in terms of a Fokker-Planck equation for a single neuron.

A major focus of synthetic biology is to engineer gene circuits to perform user-defined functions. These gene circuits can serve as well-defined models to probe basic biological questions of broad significance. In this talk, I will discuss our efforts along this line of research, whereby we have engineered gene circuits to program bacterial dynamics in time and space, guided by quantitative modeling and experiments. Insights learnt from these circuits have implications for developing new strategies to combat bacterial pathogens or to fabricate new materials.

Tissues grow, change shape, and differentiate, function normally or abnormally, get diseased or injured, repair themselves, and sometimes atrophy. This complex suite of behaviors is governed by a complex suite of controls. Nonetheless, we can identify some general principles at work in the dynamics of tissues. Our goal is to understand how a tissue’s mechanics and biology regulate each other. Our models use a biologically-based framework to track the mechanics, biology, and mechanobiology of the component cells, fluids, signaling molecules, and extracellular matrix materials. The presentation will describe our modeling approach, reveal some of the general principles we have identified, and discuss some of the questions our findings have raised about specific morphogenetic systems such as the lung.

Insulin resistance, a major factor in type 2 diabetes development, is a systemic defect characterized by reduced intracellular insulin signaling. Although there are many proposed causes of insulin resistance, the precise mechanisms that influence its long-term progression remain unclear. In this talk, we develop mathematical models to study the hypothesized role of oxidative stress and mitochondrial dysfunction in skeletal muscle insulin resistance. Simulation results suggest that a perfect storm of environmental and genetic factors leading to oxidative stress can confer protection on the individual cell via insulin resistance.

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.

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.

I will briefly describe mathematical models of networks of neurons and chemical reactions within neurons that generate daily (circadian) timekeeping. The numerical and analytical challenges of these models as well as the benefits in terms of biological predications will be highlighted. I will then explain how models can be used to find schedules that decrease the time needed to adjust to a new timezone by a factor of 2 or more. These optimal schedules have been implemented into a smartphone app, ENTRAIN, which collects data from users and in return helps them avoid jet-lag. We will use the data from this app to determine how the world sleeps. This presents a new paradigm in mathematical biology research where large-scale computing bridges the gap between basic mechanisms and human behavior and yields hypotheses that can be rapidly tested using mobile technology.

This talk will trace many years of work mathematical modeling hematological diseases. The ‘understand’ part talks about the use of mathematical to figure out what causes cyclical neutropenia, and the ‘treat’ part refers to work on treating cyclical neutropenia using recombinant cytokines. The ‘avoid’ part deals with current ongoing work trying to obviate the deleterious effects of chemotherapy on blood cell production—one of the major negative side effects of chemotherapy.

Elevations in systolic blood pressure are believed to be closely linked to the pathogenesis and progression of renal diseases. It has been hypothesized that the afferent arteriole (AA) protects the glomerulus from the damaging effects of hypertension by sensing increases in systolic blood pressure and responding with a compensatory vasoconstriction. To investigate this hypothesis, we developed a mathematical model of the myogenic response of an AA smooth muscle cell, based on an arteriole model by Gonzalez-Fernandez and Ermentrout (Math Biosci 1994). renal hemodynamic regulation. The model incorporates ionic transport, cell membrane potential, contraction of the AA smooth muscle cell, and the mechanics of a thick-walled cylinder. The model represents a myogenic response based on a pressure-induced shift in the voltage dependence of calcium channel openings: with increasing transmural pressure, model vessel diameter decreases; and with decreasing pressure, vessel diameter increases. Further, the model myogenic mechanism includes a rate-sensitive component that yields constriction and dilation kinetics similar to behaviors observed in vitro. A parameter set is identified based on physical dimensions of an AA in a rat kidney. Model results suggest that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, gives rise to periodicity in the transport of the two ions. This results in a time-periodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridges formation with the attending muscle stress. Further, the model predicts myogenic responses that agree with experimental observations, most notably those which demonstrate that the renal AA constricts in response to increases in both steady and systolic blood pressures. The myogenic model captures these essential functions of the renal AA, and it may prove useful as a fundamental component in a multi-scale model of the renal microvasculature suitable for investigations of the pathogenesis of hypertensive renal diseases.

Mechanistic mathematical models are important tools for understanding the processes that shape ecological systems. Models have been used to describe life cycles of individuals, population dynamics, behavior, and more. However, in order for these models to reach their full potential as both tools for understanding and for prediction we must be able to link modeled quantities to data and infer model parameters. However, general methods of parameter inference for many of these models, including Individual Based Models (IBMs) or their component models, are not available. In addition, some models include components that are unmeasurable or poorly known, which can impact parameter inference and thus prediction. Here I discuss two examples of ecological models of these types. First is a bioenergetic model of individual growth and reproduction in a dynamic environment. This example highlights how input mis-specification can affect inference, and the consequences for prediction for both individuals and populations. The second example uses an example of an IBM developed to describe the spread of Chytridiomycosis in a population of frogs. This case study shows how one can perform inference for IBMs that exhibit certain characteristics with a traditional likelihood-based approach.

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.

A ureteric stent is a slender polymer tube that can be placed within the ureter (the muscular tube that conveys urine from the kidney to the bladder) to relieve a blockage due, for example, to a kidney stone in transit, or to external pressure from a tumor. A urinary catheter can be placed similarly within the urethra (the muscular tube conveying urine from the bladder out of the body), either again to relieve a blockage, or to allow control of urination in incontinent patients or those recovering from surgery. Several clinical complications are associated with each of these biomedical devices. Both become encrusted, over time, with salts that precipitate out from the urine. Such encrustation is often associated with infection and the presence of bacterial biofilm on the device and, if severe, can make removal of the device difficult and painful. Ureteric stents are also associated with urinary reflux: retrograde flow of urine back towards the kidney. This arises because the stent prevents proper function of the sphincter between ureter and bladder that normally closes off when bladder pressure rises. Such reflux can expose the kidney to dangerously high pressures, and increase the risk of renal infection, both of which can lead to long-term damage. This talk will highlight aspects of our interdisciplinary work on such problems. We present mathematical models of the reflux and encrustation processes and consider the implications for device design and clinical practice.

Glutathione (GSH), a tripeptide formed from glutamate, cysteine, and
glycine, is arguably the most important antioxidant in the body. NAPQI, a
byproduct of acetaminophen (APAP) metabolism which is toxic to liver
cells, is neutralized by GSH. Although produced in great quantity by the
liver, in cases of APAP overdose demand for GSH can outstrip supply,
causing liver failure. Currently, patients presenting to the ER with APAP
overdose are given an infusion of cysteine since it is believed to be the
rate-limiting amino acid in GSH synthesis, however, there is evidence that
under some circumstances glutamate can become rate-limiting. Complicating
the issue is that in most hepatocytes, glutamate is not absorbable from
blood plasma but is formed from glutamine, which is produced in large
amounts by the skeletal muscle. In order to develop better rescue
protocols for APAP overdose, we have developed a mathematical model of
glutamate and glutamine metabolism in the rat. We have also investigated
how model parameters should change in the case of increased cortisol
production, such as occurs during sepsis, trauma, burns, and other
pathological states; the cortisol-stressed state has been studied in rats
by giving them dexamethasone. We compare model predictions with
experimental data for the normal, healthy rat and dexamethasone-stressed
rat. Biological parameters are taken from the literature wherever possible.

I present an overview of models of the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Starting from a stochastic birth and death process, several types of deterministic or probabilistic models can be derived. When advantageous mutations are rare and small, a time scale separation takes place in the models leading to the concentration of the population along a few selected traits. Those then evolve according to a PDE of Hamilton-Jacobi type or to the canonical equation of adaptive dynamics.

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.

In recent years it has become increasingly clear that stochasticity plays
an important role in many biological processes. Examples include bistable
genetic switches, noise enhanced robustness of oscillations, and fluctuation
enhanced sensitivity or "stochastic focusing." Numerous cellular systems
rely on spatial stochastic noise for robust performance. We examine the
need for stochastic models, report on the state of the art of algorithms and
software for modeling and simulation of stochastic biochemical systems, and
identify some computational challenges.

Recent studies of cholesterol-rich membrane microdomains, called caveolae, reveal that caveolae are reservoirs of recruitable sodium ion channels. Caveolar channels constitute a substantial and previously unrecognized source of sodium current in cardiac cells. In this talk, I will present a family of DE and PDE models to investigate caveolar sodium currents and their contributions to cardiac action potential morphology. We show that the b-agonist-induced opening of caveolae may have substantial impacts on peak overshoot, maximum upstroke velocity, and conduction velocity. Additionally, we show that prolonged action potentials and the formation of potentially arrhythmogenic afterdepolarizations, can arise if caveolae open intermittently throughout the action potential.

Certain neurons can, in isolation, generate a bursting rhythm, in which phases of active spiking alternative repetitively with phases of quiescence. This behavior is itself mathematically interesting, and neurons with this capability have been found in the mammalian respiratory brain stem, suggesting that they might drive the respiratory rhythm. In this talk, I will survey some mathematical and computational work that runs counter to this suggestion. The methods involved include slow-fast decomposition and associated bifurcation analysis in single-neuron and few-neuron ODE models as well as a genetic algorithm applied to larger network models. The larger network results may have general implications for networks of nodes with heterogeneous dynamics, coupled in small-world, scale-free, and other architectures

In butterflies and moths, wing scales provide the cellular basis for coloration. Many times these scales are filled with pigments providing colors such as black, brown, red, and yellow. In some cases, however, color is generated structurally, which is often the case for green and blue coloration. Optical physicists have done a remarkable job defining how wing nanostructures create structural color, but we know little about the developmental basis for creating the patterned nanostructures. I will describe our work to understand the developmental and cellular basis for scale formation and the generation of structural color, focusing on a group of butterflies known as the Achillides swallowtails. The scales of these butterflies use a combination of multilayer reflection and scale geometry to create a range of colors. Developmentally, the scale geometry appears to be controlled by cytoskeletal reorganization, and evolutionary changes in geometry appear to contribute to variation between species, between populations, and between seasonal variants.

One of the first immunologic responses against HIV infection is the presence of neutralizing antibodies that seem able to inactivate several HIV strains. Moreover, in vitro studies have shown the existence of monoclonal antibodies that exhibit broad crossclade neutralizing potential. Yet their number is low and slow to develop in vivo. In this paper, we investigate the potential benefits of inducing poly-specific neutralizing antibodies in vivo throughout immunization. We develop a mathematical model that considers the activation of families of B lymphocytes producing poly-specific and strain-specific antibodies and use it to demonstrate that, even if such families are successful in producing neutralizing antibodies, competition between them may limit the poly-specific response allowing the virus to escape. We modify this model to account for viral evolution under the pressure of antibody responses in natural HIV infection as well as the need to neutralize more than one viral spike. The model can reproduce viral escape under certain conditions of B lymphocyte competition. Using these models we provide explanations for the observed antibody failure in controlling natural infection and predict quantitative measures that need to be satisfied for long-term control of HIV infection.

Certain strains of the influenza virus form coherent single, globally circulating viral populations. Multiple models of viral evolution have considered the virus on this level, identifying immune and structural factors underlying the observed changes in viral genotype. In this talk, I outline an alternative approach for studying viral evolution, considering events at the level of within-host viral growth and transmission. In particular, I describe statistical approaches to infer the extent to which natural selection acts upon the viral population within the course of a single infection, on the basis of genome sequencing data from Sanger sequencing, and next-generation technologies. Examining data from evolutionary experiments conducted with a reassortant H5N1 influenza virus, I discuss the potential for using data from evolutionary experiments to predict the potential evolution of this virus in a human population.