The complexity of the human airway coupled with advances in computational technology have led to the growing interest in the use of computational fluid dynamics (CFD) techniques to simulate airway physiology in order to collect objective data due to inter-individual anatomy and pre- & post-surgical changes. Outcomes from airway surgery are sometimes difficult to predict a priori, and it is not known whether topical medications are reaching target sites within the human air passage. This talk will give an overview of how CFD is used to explore these issues, as well as demonstrate the potential ability of this methodology in pre-surgical planning.

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.

Fluid mechanics plays a crucial role in many cellular processes. One example is the external fluid mechanics of motile cells such as bacteria, spermatozoa, algae, and essentially half of the microorganisms on earth. The most commonly-studied organisms exploit the bending or rotation of a small number of flagella (short whip-like organelles, length scale from a few to tens of microns) to create fluid-based propulsion. Ciliated microorganisms swim by exploiting the coordinated surface beating of many cilia (which are short flagella) distributed along their surface. After a short introduction to the fundamentals of fluid-based locomotion on small scales, we pose separate optimization problems addressing the optimal geometries and locomotion gaits of low-Reynolds-number swimmers. First, we characterize the optimal dynamics of simple flapping swimmers with two degrees of freedom. Second, we derive analytically and computationally the optimal waveform of an elastic flagellum, such as the one employed by eukaryotic cells for propulsion. Third, we investigate the optimal shapes of helical propellers, and use our results to help rationalize the shape selection mechanism in bacterial flagella. Finally, we characterize the optimal locomotion by surface distortions of blunt swimmers, and demonstrate the appearance of waves, reminiscent of the metachronal waves displayed by ciliated organisms.

Inside every eukaryotic cell is the nucleus, organelles, and the surrounding cytoplasm, which typically accounts for 50% of the cell volume. The cytoplasm is a complex mixture of water, protein, and a dynamic polymer network. Cells use cytoplasmic streaming to transmit chemical signals, to distribute nutrients, and to generate forces involved in locomotion. In this talk we present two different models related to cytoplasmic streaming in amoeboid cells. In the first part of the talk, we present a computational model to describe the dynamics of blebbing, which occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. The model is used to explore the relative roles in bleb dynamics of cytoplasmic viscosity, permeability of the cytoskeleton, and elasticity of the membrane and cytoskeleton. In the second part of the talk we examine how flow-induced instabilities of cytoplasm are related to the structural organization of the giant amoeboid cell Physarum polycephalum. We use a multiphase flow model that treats both the cytosol and cytoskeleton as fluids each with its own material properties and internal forces, and we discuss instabilities of the sol/gel mixture that produce flow channels within the gel. We analyze a reduced model and offer a new and general explanation for how fluid flow is involved in cytoskeletal reorganization.

G protein-coupled receptors (GPCRs) are membrane receptors that play a pivotal role in the regulation of reproduction and behavior in humans. Upon binding to specific ligands, they trigger a local cAMP production. Activated receptor are then internalized to different endosomal compartments where they can continue signaling before being recycled or destroyed. Recent studies showed that the different pools of cAMP have different effect on the cell.
In the first part of the talk, I will present a piecewise deterministic Markov process (PDMP) of intracellular signaling. The stochastic part of the model accounts for formation, coagulation, fragmentation and recycling of intracellular vesicles which contain the receptor, whereas the deterministic part of the model represents evolution of chemical reactions due to signaling activity of the receptor. We are interested in the existence of and convergence to a stationary measure. I will present different cases for which we were able to obtain results in this direction.
In the second part of the talk, I will present the numerical workflow (SBML, PEtab and PyPESTO) we use to fit ODEs model of GPCR signaling to longitudinal measure of chemical concentrations (BRET data).

RNA-Seq is a new technology for measuring the content of a transcriptome using high-throughput sequencing technology. I will provide a self-contained introduction to the technology, and proceed to discuss some interesting mathematical questions we have had to address in order to realize the potential of "comparative transcriptomics" for comparing and contrasting transcriptomes. We will start with the "freshman's dream", and proceed to examine issues related to maximum matching, the (phylogenetic) space of trees and Simpson's paradox. This is joint work with my current and former students Natth Bejraburnin, Nicolas Bray, Adam Roberts, Cole Trapnell and Meromit Singer.

A conference in honor of Harold Layton's 60th Birthday (Afternoon Session)

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.

ABSTRACT: The past decade has seen a number of engineering innovations that make construction of devices of micro- and even nanometric dimensions feasible. Hence, there is a growing interest in exploring new and efficient ways to generate propulsion at these small scales. Here we explore optimization of one particular type of low Reynolds number propulsion mechanism – flagella. Beyond the general challenges associated with optimization, there are a number of issues that are unique to swimming at low Reynolds numbers. At small scales, the fluid equations of motion are linear and time-reversible, hence reciprocal motion – i.e., strokes that are symmetric with respect to time reversal – cannot generate any net translation (a limitation commonly referred to as the Scallop Theorem). One possible way to break this symmetry is through carefully chosen morphologies and kinematics. One symmetry-breaking solution commonly employed by eukaryotic microorganisms is to select nonreciprocal stroke patterns by actively generating torques at fixed intervals along the organism. Hence, we will address the question: For a given morphology, what are the optimal kinematics? In this talk we present optimal stroke patterns using biologically inspired geometries such as single-tailed spermatozoa and the double-tail morphology of Chlamydomonas, a genus of green alga widely considered to be a model system in molecular biology.

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.

A major feature of biological sciences in the 21st Century is their transition from phenomenological and descriptive disciplines to quantitative and predictive ones. However, the emergence of complexity in self-organizing biological systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in complex biological systems. We discuss a multiscale multiphysics and multidomain paradigm for biomolecular systems. We describe macromolecular system, such as protein, DNA, ion channel, membrane, molecular motors etc., by a number of approaches, including macroscopic electrostatics and elasticity and/or microscopic molecular mechanics and quantum mechanics; while treating the aqueous environment as a dielectric continuum or electrolytic fluids. We use differential geometry theory of surfaces to couple various microscopic and macroscopic domains on an equal footing. Based on the variational principle, we derive the coupled Poisson-Boltzmann, Nernst-Planck, Kohn-Sham, Laplace-Beltrami, Newton, elasticity and/or Navier-Stokes equations for the structure, function, dynamics and transport of protein, protein-ligand binding and ion-channel systems.

Fluid-structure interaction problems with composite structures arise in many applications. One example is the interaction between blood flow and arterial walls. Arterial walls are composed of several layers, each with different mechanical characteristics and thickness. No mathematical results exist so far that analyze existence of solutions to nonlinear, fluid-structure interaction problems in which the structure is composed of several layers. In this talk we will summarize the main difficulties in studying this class of problems, and present a computational scheme based on which a proof of the existence of a weak solution was obtained. Our results reveal a new physical regularizing mechanism in FSI problems: inertia of the thin fluid-structure interface with mass regularizes evolution of FSI solutions. Implications of our theoretical results on modeling the human cardiovascular system will be discussed. This is a joint work with Boris Muha (University of Zagreb, Croatia), Martina Bukac (U of Notre Dame, US) and Roland Glowinski (UH). Numerical results with vascular stents were obtained with S. Deparis and D. Forti (EPFL, Switzerland), and with A. Quaini (UH). Collaboration with medical doctors Dr. S. Little (Methodist Hospital Houston) and Dr. Z. Krajcer (Texas Heart Institute) is also acknowledged.

Complex interactions occur between tumor and host immune system during cancer development and treatment, and a weak systemic immune response can be prognostic of poor patient outcomes. We strive to not only better understand the dynamic behavior of circulating immune cell populations before and during cancer therapy, but also to monitor these dynamic changes to facilitate real-time prediction of patient outcomes and potentially therapy adaptation. I will provide examples of both theoretical (mathematical) and data-driven (epidemiological) approaches to incorporating established systemic immune markers into clinical decision-making. First, coupling models of local tumor-immune dynamics and systemic T cell trafficking allows us to simulate the evolution of tumor and immune cell populations in anatomically distant sites following local therapy, in turn identifying the optimal treatment target for maximum reduction of global tumor burden. Second, improved understanding of how circulating immune markers vary both within and between individual patients can allow more accurate risk stratification at diagnosis, and personalized prediction of patient response to therapy. The importance of multi-disciplinary collaborations in making predictive and prognostic models clinically relevant will be discussed.

Genetic intratumoral heterogeneity is a natural consequence of imperfect DNA replication. Any two randomly selected cells, whether normal or cancerous, are therefore genetically different. I will discuss the extent of genetic heterogeneity within untreated cancers with particular regard to its clinical relevance. While genomic heterogeneity within primary tumors is associated with relapse, heterogeneity among treatment‑naïve metastases has not been comprehensively assessed. We analyzed sequencing data for 76 untreated metastases from 20 patients and inferred cancer phylogenies for breast, colorectal, endometrial, gastric, lung, melanoma, pancreatic, and prostate cancers. We found that within individual patients a large majority of driver gene mutations are common to all metastases. Further analysis revealed that the driver gene mutations that were not shared by all metastases are unlikely to have functional consequences. A mathematical model of tumor evolution and metastasis formation provides an explanation for the observed driver gene homogeneity. Last, we found that individual metastatic lesions responded concordantly to targeted therapies in 91% of 44 patients. These data indicate that the cells within the primary tumors that gave rise to metastases are genetically homogeneous with respect to functional driver gene mutations and suggest that future efforts to develop combination therapies have the capacity to be curative.

The chemotaxis network of bacteria such as E. coli is remarkable for its sensitivity to minute relative changes in chemical concentrations in the environment. Indeed, E. coli cells can detect concentration changes corresponding to only ~3 molecules in the volume of a cell. Much of this acute sensitivity can be traced to the collective behavior of teams of chemoreceptors on the cell surface. Instead of receptors switching individually between active and inactive configurations, teams of 6-20 receptors switch on and off, and bind or unbind ligand, collectively. Similar to the binding and unbinding of oxygen molecules by tetramers of hemoglobin, the result is a sigmoidal binding curve. Coupled with a system for adaptation that tunes the operating point to the steep region of this sigmoidal curve, the advantage for chemotaxis is gain – i.e., small relative changes in chemical concentrations are transduced into large relative changes in signaling activity (specifically, the rate of phosphorylation of the response regulator CheY).  However, something is troubling about this simple explanation: in addition to providing gain, the coupling of receptors into teams also increases noise, and the net result is a decrease in the signal-to-noise ratio of the network. Why then are chemoreceptors observed to form cooperative teams? We present a novel hypothesis that the run-and-tumble chemotactic strategy of bacteria leads to a “noise threshold”, below which noise does not significantly decrease chemotactic velocity, but above which noise dramatically decreases this velocity.

This talk presents a work in progress with Sylvain Billard, Regis Ferriere and Chi Viet Tran. How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. The dynamics is ruled by births and deaths, mutations at birth and competition between individuals. The ecological phenomena depend only on the trait values but we expect that these effects influence the generation and maintenance of neutral variation. Considering a large population limit with rare mutations, but where the marker mutates faster than the trait, we prove the convergence of our stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process. This process restricted to the trait space is the Trait Substitution Sequence introduced by Metz et al. (1996). During the invasion of a favorable mutation, the marker associated with this favorable mutant is hitchhiked, creating a genetical bottleneck. The hitchhiking effect and how the neutral diversity is restored afterwards are studied. We show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions and that time-scale separation phenomena occur. The SFVP has important and relevant implications that are discussed and illustrated by simulations. We especially show that after a selective sweep, the neutral diversity restoration depend on mutations, ecological parameters and trait values.

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.

Heterogeneity in cancer is an observed fact, both genotypically and phenotypically. Cell-cell variation is seen in almost all aspects of cancer from early development all the way through to invasion and subsequent metastasis. Our current understanding of this heterogeneity has mainly focused at the genetic scale with little information on how this variation translates to actual changes in cell phenotypic behavior. Given that many genotypes can lead to the same cellular phenotype, it is important that we quantify the range and scope of this heterogeneity at the phenotypic scale as ultimately this variability will dictate the aggressiveness of the tumor and its treatability. Central to our understanding of this heterogeneity is how the tumor cells interact with each other and with their microenvironment. Since it is these very interactions that drive selection and that ultimately define the ecology of the tissue in which the tumor is developing. Considering an organ as an ecological system, means that we should view normal tissue homeostasis as an equilibrium that cancer cells must disrupt if they are to be successful. Disruption of this equilibrium is often one of the first events in cancer development, as the normal control mechanisms of the tissue are damaged or ignored. We will discuss the interplay between homeostasis, heterogeneity, evolution and ecology in cancer progression and treatment failure with an emphasis on the metabolism of breast cancer.

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.

The locust olfactory system interfaces with the external world through antennal receptor neurons (ORNs), which represent odors in a distributed, combinatorial manner. ORN axons bundle together to form the antennal nerve, which relays sensory information centrally to the antennal lobe (AL). Within the AL, an odor produces a stimulus-specific temporal progression of neuronal spiking, inspiring the hypothesis that the AL encodes odors through dynamically evolving ensembles of active cells. Such a coding strategy, however, requires higher olfactory centers to integrate a prolonged dynamic profile of AL signals prior to stimulus assessment, a process that is likely to be slow and inconsistent with the generation of quick behavioral responses. Our modeling work has led us to propose an alternate hypothesis: the dynamical interplay of fast and slow inhibition within the locust AL induces transient correlations in the spiking activity of an odor-dependent neural subset, giving rise to a temporal binding code and allowing rapid stimulus detection by downstream elements.