UCR

Department of Mathematics



Interdisciplinary Seminar on Mathematical & Computational Modeling


Interdisciplinary Seminar on Mathematical & Computational Modeling

Contact: Dr. Mark Albermalber@ucr.edu 

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Upcoming Talks

October 9, 2018
2:10 - 3:00 Surge 268

Seminar of the Center for Quantitative Modeling in Biology 

Mikahl Banwarth-Kuhn, Department of Mathematics and Center for Quantitative Modeling in Biology, University of California, Riverside, CA

Title: "Novel cell-based model of the generation and maintenance of the shape and structure of the multi-layered shoot apical meristem of Arabidopsis thaliana"

Abstract: One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce the final form, size, structure and function of an organ. To address this problem, a novel, multi-scale, cell-based computational model of the stem cells of the shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test a novel hypothesized mechanism of formation of the shape and structure of the growing, multilayered SAM. It combines contributions of mechanical properties of sub-cellular components of individual cells determining anisotropic cell expansion across three different SAM layers, and varied cell growth rates based on WUS concentrations of individual cells. This suggests a possible novel SAM growth mechanism to be tested in experiments.

A. Nematbakhsh, Department of Mathematics, University of California, Riverside, CA

Title: "MECHANICAL EFFECT ON GROWTH AND MORPHOLOGY OF EPITHELIAL CELLS DURING EARLY DEVELOPMENT"

Abstract: Uncontrolled epithelial growth and dysregulation of epithelial morphology underlie more than ninety percent of tumors. Epithelia serve a critical role as barriers between the environment and internal structures of organs. The growth and morphogenesis of epithelia must be carefully controlled through coordination of cellular properties. Mechanical properties are an important regulator during the development. However, how the mechanical properties in the cell scale contribute to growth and morphogenesis in the tissue scale is still poorly understood. Here, we introduce a subcellular element particle-based model to predict the mechanical properties of epithelial cells to investigate their contribution to the proliferation and morphology in cell and tissue scale. The developed model consists of three sets of nodes: internal nodes represent inner organelles, membrane nodes represent cortex and membrane of cells, and extra cellular nodes represent the extra cellular matrix. These three classes of nodes interact through distinct potential energy functions. Our model incorporates subcellular properties such as cytoplasmic pressure, cortical stiffness, cell adhesion and interactions between the cell membrane and nucleus. We also account for the mechanical interaction between the extracellular matrix and epithelial cells. We found that cytoplasmic pressure is the main driver of cell’s expansion in mitotic phase, while cortical stiffness and cell-cell adhesion are contributors to the roundness of cells before division. Recently, we have extended the model to predict the curvature profile of epithelial cells. Our results show that the level of contraction in the extracellular matrix significantly contributes to the curvature profile of epithelia. To validate this prediction, tissue mechanics were measured experimentally in Drosophila wing imaginal discs, an established biophysical model of epithelial organ development. Furthermore, both computational predictions and experiments establish that the relative cells’ nucleus position contributes to the curvature profile. The right curvature profile of wing disc is essential for wing eversion, the next stage of wing development. Aberrant folding and bending of epithelia can lead to cyst formation, which occurs during early cancer progression.

 

 

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Past Talks

May 8, 2018
2:10 - 3:00 Surge 284

**Colloquium**

Dr. Megan Peters, Department of Bioengineering, UC Riverside

Title: "

An ‘instantaneous’ measure of dynamic functional connectivity"

Abstract: Assessing the function of late-stage cortical processing regions, such as prefrontal cortex, is notoriously challenging. Yet it is these areas that are hypothesized to subserve complex higher-order processes including self-evaluation of decisional uncertainty and even perceptual awareness. How can we measure the degree to which late-stage cortical processing areas have access to the representational content in sensory regions in humans? Assessing time-varying functional connectivity from prefrontal to lower-level sensory areas via fMRI is challenging with conventional approaches, and suffers from poor temporal precision. In this talk I will present a new dynamic functional connectivity metric, based on information theory that we are developing. The metric relies on 40-way multinomial sparse logistic regression decoding, capitalizing on a 38-subject database for which voxel-based representational patterns have been functionally aligned via Procrustean transformations. I will discuss how trial-by-trial functional connectivity between prefrontal and low-level sensory areas may predict prefrontal access, and how this metric could change as a function of training using real-time fMRI and decoded neurofeedback.  These results may shed new light on the critical role played by prefrontal cortex in making a low-level sensory representation available to higher order processing.



May 1, 2018
2:10 - 3:00 Chung 205/206

**Colloquium**

Dr. Robert Guy, Department of Mathematics, UC Davis

Title: "Microorganism locomotion in viscoelastic fluids"

Abstract: Low Reynolds number swimming of microorganisms in Newtonian fluids is an extensively studied classical problem. However, many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. Recently, there have been many studies on locomotion in complex fluids, but the effects of fluid elasticity on motility remain poorly understood. We develop computational models that use experimental data from the undulatory motion of C. elegans and the breast stroke motion of C.reinhardtii to explain experimental observations and to explore the effects of fluid elasticity on swimming. Through a combination of computational and asymptotic analysis we show how characteristics of the gait and the body mechanics interact with fluid elasticity to alter swimming speed. This analysis explains seemingly conflicting results from the literature, and it provides mechanistic explanations for previously misunderstood observations.

April 24, 2018
2:10 - 3:00 Genomics Auditorium

**Colloquium**

Dr. John Barton, Department of Physics, UC Riverside

Title: "A Path Integral Method for Analytically Tractable Inference of Evolutionary Dynamics"

Abstract: Understanding the forces that shape genetic evolution is a subject of fundamental importance in biology and one with numerous practical applications. Modern experimental techniques give insight into these questions, but inferring evolutionary parameters from sequence data, such as how an organism's genotype affects its fitness, remains challenging. Here we present a method to infer selection from genetic time-series data using a path integral approach based in statistical physics. This approach allows us to derive an intuitive, closed-form solution for the most likely selection coefficients underlying an observed evolutionary trajectory, while taking into account the influences of mutation and genetic linkage. We illustrate the effectiveness of this approach using several simple examples, such as disentangling the selection coefficients for hitchhiking mutations, as well as tests on real data. Through extensive numerical tests we find that our method meets or exceeds the current state of the art in the successful classification of mutations as beneficial or deleterious in a variety of scenarios, while also yielding substantial improvements in run time compared to Monte Carlo-based methods. Our approach can also be extended to jointly infer other evolutionary parameters such as the effective population size and mutation rates.

April 16, 2018
2:10 - 3:00 Surge 268

**Colloquium**

Dr. Ran Libeskind-Hadas, Department of Computer Science, Harvey Mudd College

Title: "Adventures in Phylogenetic Tree Reconciliation"

Abstract: Phylogenetic tree reconciliation is a widely-used method for studying evolutionary histories of pairs of entities such as species and genes or hosts and parasites. In the Duplication-Transfer-Loss (DTL) model, we seek to reconcile a pair of phylogenetic trees in the presence of duplication, horizontal transfer, and loss events. Since statistical methods are computationally intractable, DTL reconciliation is generally performed using maximum parsimony. In this talk, we describe several tools that we have developed for maximum parsimony DTL reconciliation and the underlying algorithmic methods used in those tools. We also describe a number of open problems that we are currently exploring.

Bio: Ran Libeskind-Hadas received the BA in applied mathematics from Harvard University and the MS and PhD in computer science from the University of Illinois at Urbana-Champaign. He has taught at UIUC, MIT, and Caltech and is the R. Michael Shanahan Professor of Computer Science at Harvey Mudd College. Ran works in the area of algorithmic computational biology and has developed or co-developed several popular reconciliation tools including Jane and Xscape.

April 10, 2018
2:10 - 3:00 Genomics Auditorium

**Colloquium**

Dr. Serj Danielian, Department of Biology, UC Riverside

Title: "Metapopulation Persistence"

 

*March 6, 2018
4:10 - 5:00 Surge 284

**Colloquium**

Dr. William Cannon, Scientist, Team Lead, Biological Systems Science, Pacific Northwest National Laboratory

Title: "Statistical Thermodynamics of Cellular Metabolism and Growth"

Abstract: The modeling and simulation of cell metabolism is challenging because of the lack of rate parameters needed to solve the ordinary differential equations governing the law of mass action. In this talk, I will describe simulations of cell metabolism using a maximum entropy production rate assumption from which rate parameters can be inferred for use in simulating the mass action kinetics of metabolism. Simulation predictions of metabolite levels of central metabolism of Neurospora crassa and Yarrowia lipolytica then allows for inference of enzyme regulation for both fungi. Subsequent simulations with regulation provide predictions of metabolite levels that are comparable to experimental measurements. The simulation results provide a free energy map of metabolic pathways as well as a more complete understanding of biological cells as complex, adaptive dissipative structures. Data analysis using statistical thermodynamics also provides a measurement of the work required to create a bacterial cell (in kJ/gm cells or kJ/mol cells) and the power generated by cells during growth. It is estimated that a bacterial cell produces has approximately the same power/weight ratio as the most efficient fuel cells.

January 30, 2018
10:00 - 10:50 Genomics Auditorium

Dr. Oleg Kim, Department of Mathematics, UCR

Title: "Quantitative Study of Blood Clot Contraction"

Abstract: Blood clot contraction plays an important role because of its impact on prevention of bleeding (hemostasis) and thrombotic disorders. Here we unveil and quantify the structural mechanisms of clot contraction at the level of single platelets interacting with fibrin fibers. A key elementary step of contraction is sequential extension-retraction of platelet filopodia causing bending and shortening of platelet-attached fibrin fibers. When attached to multiple fibers, platelets cause densification of filamentous fibrin network by pulling on fibers in the direction of tension imposed by the contracting cells. As a result of this pulling and fiber compaction, platelets and platelet aggregates approach each other, cluster and fuse into larger platelet-fibrin associates. Kinetic analysis of clot contraction based on the time course of the contractile stress and the overall structural changes revealed distinct phases in clot contraction including the “pre-contraction” phase followed by active contraction and the contraction termination phase. The nonlinear kinetics of clot contraction is determined by the interplay of the platelet contractile machinery and αIIbβ3-mediated platelet-fibrin interactions at the level of individual cells and fibers. To model contraction of blood clots, we extend our discrete worm-like chain-based model of the fibrin network by adding active contracting platelets inside the network using platelet-fibrin interaction data. Model calibration is achieved by implementing structural properties of the network and platelet spatial distributions inside the clot obtained using confocal microcopy of contracting clots. We apply the known contractile force generated by individual platelets in the network to track both mechanical and structural dynamics of the clot to compare with rheological tests of contracting clots of known structures and distributions of platelets. The model permits examination of how the contractile function of platelets, their distribution within the fibrin network and fibrin properties affect the mechanical response of the clot to applied stresses in blood flow and clot stability. The revealed platelet-driven mechanisms of blood clot contraction demonstrate an important new biological application of cell motility principles. 

Oleg V. KimRustem I. LitvinovMark S. Alber  and John W. Weisel

Quantitative structural mechanobiology of platelet-driven blood clot contraction, 

Nature Communications 8: 1274 (2017).

January 25, 2018
10:00 - 10:50 Genomics Auditorium

Mikahl Banwarth-Kuhn1, Ali Nematbakhsh1, Weitao Chen1, Stephen Snipes2, Andrew Whitaker2, Venugopala Gonehal2, Mark Alber1

1Department of Mathematics, UC Riverside

2Department of Botany and Plant Sciences, UC Riverside

Title: "Coupled experimental and computational study of interplay of mechanical properties and chemical signaling in patterns of stem cell division and differentiation in plants"

Abstract: One of the central problems in developmental biology is determination of how chemical and mechanical signals interact within a tissue to produce the final form, size and function of an organ.  Cell wall extensibility and distribution of stress on the wall contribute to determining rates of cell expansion and orientation of cell division.  How cell wall mechanical properties influence cell behavior and how the chemical gradient regulating cell mechanical properties is maintained are still largely unknown. First, the biological background of development in the shoot apical meristem (SAM) of Arabidopsis will be presented.  Second, a novel, multi-scale, computational model that captures the mechanical properties of the system will be described along with model calibration using experimental data.  Third, a novel signaling model will be presented and demonstrated.  Model predictive simulations reveal relative impacts of cell wall extensibility, distribution of stress, and chemical signals on growth rate and division plane orientation in the SAMs resulting in better understanding of the relationship between local morphogenetic processes and global tissue patterns in stem cell maintenance and differentiation.

*November 20, 2017
12:10 - 1:10 *Surge 268

Dr. Leonid Berlyand, University of Pennsylvania, Department of Mathematics

Title: "Phase Field and Free Boundary Models of Cell Motility"

Abstract: We study two types of models describing the motility of  eukaryotic cells on substrates. The first, a phase-field model, consists of  the Allen-Cahn equation for the scalar phase field function coupled  with a vectorial parabolic equation for the orientation of the actin filament network. The  key properties of this system are (i) presence of gradients in the coupling termsand (ii) mass (volume) preservation constraints. We pass to the sharp interface limit to derive the equation of the motion of the cell boundary, which is mean curvature motion modified by a novel nonlinear term. We establish the existence of two distinct regimes of the physical parameters and prove existence of traveling waves in the supercritical regime. The traveling waves describe persistent motion of the cell without external cues or stimuli which is a signature of cell motility.

The second model  is a non-linear free boundary problem. It consists of an elliptic equation describing the flow of cytoskeleton gel coupled with  a convection-diffusion  PDE  for the  density of myosin motors. The  key properties of this problem are (i) presence of the cross diffusion as in the classical  Keller-Segel  problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from  a family of  radially symmetric steady states. We also study breaking of symmetry by proving existence of non-radial steady states. Existence of both traveling waves and non-radial steady states is established via Leray-Schauder degree theory applied to a Liouville-type equation (which is obtained via a reduction of the original system) in a free boundary setting. 

These results were obtained in collaboration  with J. Fuhrmann, M. Potomkin, and V. Rybalko

November 14, 2017
2:10 - 3:10 Surge 284

Rustem I. Litvinov, PhD Department of Cell and Developmental Biology,
University of Pennsylvania School of Medicine, Philadelphia, PA

Title: "Interactions of the platelet integrin alphaIIbbeta3 with fibrin"

Abstract: Although the integrin aIIbb3 mediates platelet spreading on surfaces artificially-coated with fibrinogen, the physiologic relevance of this phenomenon is not clear.  By contrast, the interaction of aIIbb3 with fibrin is responsible for clot retraction, an event important for efficient hemostasis in the hemodynamic environment of flowing blood. Moreover, whereas resting aIIbb3 can interact with immobilized fibrinogen, platelet-fibrin interactions are mediated by activated aIIbb3. Lastly, the efficacy of aIIbb3 antagonists with regard to clot contraction versus platelet aggregation mediated by aIIbb3 binding to fibrinogen interactions is different, perhaps because additional aIIbb3 binding sites are exposed when fibrinogen is converted to fibrin. Here, we have compared nanomechanical measurements of the direct interaction of aIIbb3 with fibrin and fibrinogen in order to explain these differential effects. We used optical laser tweezers-based force spectroscopy for these measurements.  Briefly, a bead covalently coated with purified aIIbb3 was captured by a focused laser beamand repeatedly brought into contact with surface-attached fibrinogen, monomeric fibrin, or a naturally-formed hydrated fibrin fiber at the edge of a plasma clot. When an aIIbb3-ligand complex was detected, the nanomechanical force required to dissociate the complex was measured at piconewton resolution. By analyzing distributions of these rupture forces, we were able to determine the overall reactivity and the strength of the interactions between the interacting protein pairs. Beside native fibrinogen, experiments were performed with recombinant fibrinogen variants as well. Monomeric fibrin displayed higher cumulative probability of interacting with aIIbb3 (a greater force-free on-rate) and binding strength (a smaller forced off-rate). aIIbb3-fibrin interactions were less sensitive to the effects of abciximab and eptifibatide compared to fibrinogen, suggesting that they had different binding specificity. Both fibrinogen- and fibrin-integrin interactions were partially blocked by the RGD-containing peptides, suggesting the existence of common RGD integrin-binding sites. This assumption was supported using fibrin variants αD97E or αD574E with impaired RGD motifs, which were less reactive with aIIbb3 than the wild type fibrin. Monomeric fibrin made from a homodimeric fibrinogen splice variant of the g chain (g´) that lacks the γC aIIbb3 site was more reactive with aIIbb3 than the parent fibrinogen, suggesting that this binding site is less important in fibrin. Polymeric fibrin displayed a rupture force profile similar to fibrinogen and monomeric fibrin with moderate (20-60 pN) and strong (>60 pN) forces that peaked at 70-80 pN. Interactions forces >60 pN were more effectively reduced by EDTA than by any of the inhibitory peptides, indicating their dependence on the structural integrity and functionality of aIIbb3. The free γC dodecapeptide was less efficient than the cRGD peptides or integrilin in preventing the stronger interactions. Taken together, these data demonstrate that surface-bound fibrinogen and monomeric as well as polymeric fibrin are highly reactive with the aIIbb3. Fibrin is more reactive than fibrinogen in terms of binding probability and has higher binding strength. Fibrin-aIIbb3 binding is less sensitive to specific b3 integrin inhibitors, suggesting that fibrin and fibrinogen have distinct specificities towards aIIbb3. 

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October 18, 2017
1:10 - 2:00 p.m. Surge 268

Junping Shi, Margaret Hamilton Professor of Mathematics, College of William and Mary

Title: "Modeling Chesapeake Bay oyster population"

Abstract: Native oyster populations in Chesapeake Bay have been the focus of three decades of restoration attempts, which have generally failed to rebuild the populations and oyster reef structure. Recent restoration successes and field experiments indicate that the vertical relief of reefs is critical to reef persistence. I will describe an interdisciplinary research effort on oyster population and related problems. More specifically, I will talk about (i) ordinary differential equation models of live oysters, dead oyster shells, and sediment, (ii) ordinary differential equation model of multiple reefs displaying bistability, and (iii) partial differential equation models of oyster or mussel shoreline pattern formation.


Bio: Junping Shi is the Margaret Hamilton Professor of Mathematics in College of William and Mary. He studied mathematics in Nankai University of China, and he obtained PhD in mathematics from Brigham Young University in 1998. His research areas include nonlinear elliptic and parabolic equations, bifurcation theory and mathematical biology, and his research is supported by the mathematical biology program in National Science Foundation. He is an associate editor of  4 journals in analysis and differential equations. He has received Plumeri Awards for Faculty Excellence (2013), Arts and Sciences Distinguished Associate Professor (2010), and Phi Beta Kappa Faculty Award for the Advancement of Scholarship (2008) in College of William and Mary. He is the director of William and Mary NSF EXTREEMS-QED program.

June 5, 2017
12:10 - 1:10 p.m. Surge 268

Sakhrat Khizroev, Florida International University

Title: "Applications of Magnetoelectric Nanoparticles in Cancer Research"

Abstract: In regard to cancer therapy, magnetoelectric nanoparticles (MENs) have proven to be in a class of its own when compared to any other nanoparticle type. Like conventional magnetic nanoparticles, they can be used for externally controlled drug delivery via application of a magnetic field gradient and image-guided delivery. However unlike conventional nanoparticles, due to the presence of a non-zero magnetoelectric effect, MENs provide a unique mix of important properties to address key challenges in modern cancer therapy: (i) a targeting mechanism driven by a physical force rather than antibody matching, (ii) a high-specificity delivery to enhance the cellular uptake of therapeutic drugs across the cancer cell membranes only, while sparing normal cells, (iii) an externally controlled mechanism to release drugs on demand, and (iv) a capability for image guided precision medicine. These properties separate MENs-based targeted delivery from traditional biotechnology approaches and lay a foundation for the complementary approach of technobiology. The biotechnology approach stems from the underlying biology and exploits bioinformatics to find the right therapy. In contrast, the technobiology approach is geared towards using the physics of molecular-level interactions between cells and nanoparticles to treat cancer at the most fundamental level and thus can be extended to all the cancers. This presentation gives an overview of the MENs-based underlying physics of potential cancer therapy.

Bio: Professor Sakhrat Khizroev holds a joint appointment at the College of Engineering and the College of Medicine of Florida International University. His research focus is at the intersection of nanotechnology and medicine. Prior to returning to FIU in 2011 to lead the university-wide nanomedicine research, Khizroev was a tenured Professor of Electrical Engineering at the University of California, Riverside. Prior to joining academia, he spent four years with Seagate Research and one year with IBM Almaden Research Center. In the past, as an electrical engineer, he is most known for leading groundbreaking experiments which resulted in the multi-billion-dollar data storage industry’s shift towards perpendicular magnetic recording – the core modern technology. Fellow of National Academy of Inventors, he holds over 32 issued US patents in the field of nanomagnetic and spintronic devices. He received B.S./M.S. degrees in Physics from Moscow Institute of Physics and Technology in 1992/1994 and a PhD degree in Electrical and Computer Engineering from Carnegie Mellon University in 1999.

May 22, 2017
12:10 - 1:10 p.m. Surge 268

Dr. Roya Zandi, Department of Physics, UC Riverside

Title: "The self-assembly of virus-like particles: From small symmetric nanoshells to conical HIV structures"

Abstract: Viruses infect all kinds of hosts (bacteria, plants, and animals) of these viruses involve a spherical shell (capsid), that protects their genome. Amazingly enough, despite the tremendous diversity in the protein building blocks of these capsids, the structures they adopt almost always have icosahedral symmetry. Many studies have shown that symmetric shells appear in nature as a result of the free energy minimization of a generic interaction between their constituent subunits. Here, we study the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits.

I will also discuss the structure of conical viruses. I will show that the continuum theory of elastic shells combined with the nonequilibrium assembly process is able to predict the formation of structures pertinent to retroviruses (such as HIV). Our minimal model of assembly yields a unified one-­dimensional phase diagram in which the appearance of spherical, irregular, conical and cylindrical structures of retroviruses are seen to be governed by the spontaneous curvature of protein subunits.

May 15, 2017
12:10 - 1:10 p.m. Surge 268

Juan Carlos del Alamo, Department of Mechanical and Aerospace Engineering University of California San Diego

Title: "Quantifying Intracardiac Flow in the Clinical Setting"

Abstract: Recent advances in imaging techniques now allow physicians to obtain robust measurements of intracardiac flows in the clinical setting. Flow patterns inside the normal left ventricle (LV) are characterized by the formation of diastolic vortices, generated during filling that eventually last until the aortic valve is opened. In the failing LV, progressive adverse remodeling leads to abnormal vortex patterns that may vary the pumping efficiency. This talk will summarize recent clinical research about the contribution of intraventricular flow to LV function via three mechanisms 1) In diastole: by facilitating fluid transport and constraining the inflow to minimize pressure loss. 2) In systole: although currently being debated, by efficiently transferring kinetic energy from diastole to ejection. 3) In transport and mixing: by minimizing the number of cardiac cycles that blood stays in ventricular transit. We will illustrate how intraventricular flow quantification can be used to characterize and optimize the impact of clinical interventions and device implantation on intraventricular flow. Finally, we will provide an example of a prospective clinical study in which clinical analysis of intraventricular flow has been used predict intracardiac thrombus formation with the aim of guiding the prescription of anticoagulant therapy.

Bio: Prof. del Alamo received a B.S., M.S. and Ph. D. in Aerospace Engineering at the Polytechnic University in Madrid. He was a Fulbright postdoctoral fellow at Harvard University and UC Sand Diego, where he received training in experimental cell mechanics and cardiovascular flows. Prof. del Alamo’s lab at UCSD focuses on biological fluid mechanics, cellular locomotion and non-invasive characterization of cardiac flows. This research has been recognized with a US Geological Survey Director’s Award (2010), the NSF CAREER Award (2011), the Hellman Family Fellowship (2012), and the William Parmley Award from American College of Cardiology (2015).

April 24, 2017
12:10 - 1:10 p.m. Surge 268

Oleg Kim, UC Riverside Department of Mathematics

Title: "Combined modeling and experimental study of fibrin networks"

Abstract: Fibrin network is a major structural component of protective hemostatic clots and pathological obstructive thrombi that largely determines their mechanical stability in response to external loads including shear and compressive forces. In particular, fibrin networks reveal a unique nonlinear mechanical behavior characterized by a dual softening-stiffening transition as the networks are exposed to compressive loads, with softening occurring at small and intermediate compressive strains, while hardening developing at larger degrees of compression. Using a combination of confocal microscopy and rheological measurements, we demonstrate that these non-linear mechanical properties originated from structural rearrangements of the entire fibrin network, as well as alterations of individual fibers including fiber buckling, bending and reorientation. The network hardening strongly correlates with an increase in the number of intersecting fibers, resulting from densification of the compressed network and reorientation of the whole fibrillar network toward a planar structural architecture perpendicular to the direction of negative strain.We model this nonlinear behavior using a continuum theory of phase transitions and analytically predicted the storage and loss moduli which were in good agreement with the experimental data. We also demonstrate that permeability of the fibrin network and protein diffusivity are important factors determining the transport of blood proteins inside the thrombus.

April 17, 2017
12:10 - 1:10 p.m. Surge 268

Dr. Russell Rockne Director, Division of Mathematical Oncology, Department of Information Sciences, City of Hope

Title: "Using Mathematical Models to Define Cancer Phenotypes"

Abstract: In this talk, I will show how mathematical models have been used to predict tumor growth and response to therapy. In particular, I will focus on partial differential equation models for brain tumors that are parameterized from MRI data. I will show how the clinical motivations for these models, and how the use of mathematical models is starting to impact cancer research and treatment at City of Hope.

April 3, 2017
12:10 - 1:10 p.m. Surge 268

Ali Nematbakhsh, Department of Bioengineering, UC Riverside

Title: "Multi-scale computational model for studying mechanics of epithelial cells"

Abstract: Multicellular development depends in large part on the growth, patterning and morphogenesis of epithelial sheets. How individual epithelial cells coordinate tissue-scale processes is still poorly understood due to the inherent complexity of emergent systems-level behavior. Testing hypothetical novel biophysical mechanisms across spatial scales requires computational models that can span subcellular to tissue levels. We will describe in this talk novel multi-scale modeling environment called Epi-Scale for simulating epithelial tissue mechanics based on the Subcellular Element (SCE) modeling approach. Epi-Scale explicitly simulates the separate mechanical contributions of multiple cellular components. Computational implementation of the model is based on an efficient parallelization algorithm that utilizes clusters of Graphical Processing Units (GPUs) for simulating large numbers of cells within a reasonable computational time. As an example of predictive power of the model we have studied mitotic rounding (MR) before cell division which ss critical for the robust segregation of chromosomes into daughter cells, and is frequently perturbed in cancerous cells. Regression analysis of parameters involved in mitotic rounding reveals relative contributions of osmotic pressure, cell-cell adhesion and cortical stiffness to the roundness and expansion of cells before division.

*March 20, 2017
12:10 - 1:10 p.m. Surge 268

Dimitrios Morikis, Department of Bioengineering, UC Riverside

Title: "Computational Modeling of Protein Dynamics and Interactions"

Abstract: We will present our recent work on the dynamics of protein-protein interactions at different scales. The common theme in our presentation is modeling of components of the immune system. First, we will discuss our ODE system that describes biochemical reactions of the activation pathways of the complement system, a component of the innate immune system and a link between innate and adaptive immunity. Second, we will discuss our computational framework AESOP for the analysis of Poisson-Boltzmann electrostatic potentials to determine the role of electrostatics in protein-protein recognition and binding for families of related proteins. Third, we will discuss the analysis of microsecond molecular dynamics simulations of a chemokine receptor in its free and ligand-bound states to delineate functional local and global conformational transitions in response to biased ligand binding. We will discuss applications in modeling disease states and personalized medicine, and in protein design and drug discovery.

March 13, 2017
12:10 - 1:10 p.m. Surge 268

Steve Cook, Computer Science & Engineering, UC Riverside

Title: "A Micro-Macro Framework for Analyzing Steric and Hydrodynamic Interactions in Gliding Assays"

Abstract: Macroscopic flows of filament-motor mixtures, driven by the hydrolysis of ATP, are important to many cellular processes such as cytoplasmic streaming in Drosophila oocytes and cortical flow in the first cell division of C.~elegans. Gliding assays, reduced in vitro model systems where motor proteins adsorbed onto a planar substrate bind to and move filaments, recreate large-scale dynamic patterns like coherent swarming motion and density waves. These systems are sensitive to the microscopic behavior such as the motor protein binding and unbinding dynamics, which take place on a faster timescale than the direct and fluid-mediated filament interactions. In this work, we present a multiscale modeling and simulation framework for gliding assays that allows detailed microscopic motor modeling as well as both steric and hydrodynamic interactions between filaments. Our model is based on continuum kinetic theory, and our implementation utilizes CPU and GPU parallelism to track the sparse but high-dimensional state space arising from the microscopic motor protein configurations. We find that steric interactions play a role in the formation of spatiotemporally coherent flow structures, and qualitatively reproduce experimentally observed behaviors including filament crossover and alignment, and clump formation, merging, and splitting.

February 27, 2017
12:10 - 1:10 p.m. Surge 268

Juan Carlos del Alamo, Department of Mechanical and Aerospace Engineering, UCSD

Title: "Quantifying Intracardiac Flow in the Clinical Setting"

Abstract: 

Recent advances in imaging techniques now allow physicians to obtain robust measurements of intracardiac flows in the clinical setting.  Flow patterns inside the normal left ventricle (LV) are characterized by the formation of diastolic vortices, generated during filling that eventually last until the aortic valve is opened. In the failing LV, progressive adverse remodeling leads to abnormal vortex patterns that may vary the pumping efficiency. This talk will summarize recent clinical research about the contribution of intraventricular flow to LV function via three mechanisms 1) In diastole: by facilitating fluid transport and constraining the inflow to minimize pressure loss. 2) In systole: although currently being debated, by efficiently transferring kinetic energy from diastole to ejection. 3) In transport and mixing: by minimizing the number of cardiac cycles that blood stays in ventricular transit. We will illustrate how intraventricular flow quantification can be used to characterize and optimize the impact of clinical interventions and device implantation on intraventricular flow. Finally, we will provide an example of a prospective clinical study in which clinical analysis of intraventricular flow has been used predict intracardiac thrombus formation with the aim of guiding the prescription of anticoagulant therapy.

February 13, 2017
12:10 - 1:10 p.m. Surge 268

Presentations by Graduate Students

Titles/Abstracts: TBA

 

February 6, 2017
12:10 - 1:10 p.m. Surge 268

Amir Moradifam, Department of Mathematics, UC Riverside

Title: "Imaging electrical conductivities from their induced current and network tomography for random walks on graphs" 

Abstract

January 30, 2017
12:10 - 1:10 p.m. Surge 268

Wenlong Jin, Department of Civil and Environmental Engineering, Calit2

Title: "Nonstandard second-order formulation of the LWR model" 

Abstract:

The seminal LWR model (Lighthill and Whitham, 1955; Richards, 1956) has many equivalent first-order formulations in both Eulerian and Lagrangian coordinates. In this study, we present a second-order formulation of the LWR model based on Phillips’ model (Phillips, 1979); but the model is nonstandard with a hyperreal infinitesimal relaxation time. Since the original Phillips model is unstable with three different definitions of stability in both Eulerian and Lagrangian coordinates, we cannot use traditional methods to prove the equivalence between the second-order model, which can be considered the zero-relaxation limit of Phillips’ model, and the LWR model, which is the equilibrium counterpart of Phillips’ model. Instead, we resort to a nonstandard method based on the equivalence relationship between second-order continuum and car-following models established in (Jin, 2016) and prove that the nonstandard model and the LWR model are equivalent, since they have the same anisotropic car-following model and stability property. We further derive conditions for the nonstandard model to be forward-traveling and collision-free, prove that the collision-free condition is consistent with but more general than the CFL condition (Courant et al., 1928), and demonstrate that only anisotropic and symplectic Euler discretization methods lead to physically meaningful solutions. We numerically solve the lead-vehicle problem and show that the nonstandard second-order model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a non-concave fundamental diagram we show that the collision-free condition, but not the CFL condition, yields physically meaningful results. Finally we present a correction method to eliminate negative speeds and collisions in general second-order models, and verify the method with a numerical example. Together with (Jin, 2016), this study presents a new approach to address the two critiques on second-order continuum models in (Daganzo, 1995a) and can help to guide the development and discretization of more physically meaningful second-order continuum and car-following models.
December 5, 2016
12:10 - 1:10 p.m. Surge 268

Jianzhong Wu, Department of Chemical Engineering, UC Riverside

Title: "Bayesian Statistics for Many-Body Systems" 

Abstract:

Both classical and quantum mechanics have been well established in terms of the temporal evolutions of the dynamic variables of individual particles. Whereas the equations of motion are equally applicable to one-body as well as many-body systems, the numerical complexity rises rapidly as the number of particles increases yet dynamic uncertainty makes it imperative to describe the properties of many-body systems from a statistical perspective. In this lecture, I outline a generic and computationally efficient procedure to predict the properties of many-body systems based on Bayesian statistics in conjunction with the Hohenberg-Kohn-Mermin theorem.  Illustrative examples will be discussed for many-body systems consisting of the Langevin particles, hard spheres, fermions, and hybrid mixtures with both quantum and classical components.  
November 28, 2016
12:10 - 1:10 p.m. Surge 268

Jim Kelliher, Department of Mathematics, UC Riverside

Title: "High-Reynolds number fluid flow and the accumulation of vorticity on the boundary: Prandtl, Chorin, and Kato" 

Abstract:

Though the equations describing the motion of a viscous classical incompressible fluid have been studied for almost 200 years, the behavior of such a fluid as it interacts with a solid boundary is still poorly understood, in particular at low viscosity. Three theories of this behavior are those initiated by Ludwig Prandtl in 1904, Alexander Chorin in 1973, and Tosio Kato in 1983. Prandtl's and Chorin's theories are heuristic, making appealing and reasonable-seeming assumptions about the behavior of the fluid near the boundary. In their simplest form, they are expected to apply only to laminar flows, but even for such flows they have never been proved to hold (or to fail to hold). Kato's theory is mathematically precise, but conditional by nature; nonetheless, it can be used as a "probe" into the validity of the other two theories. I will give a brief overview of the three theories and describe the beginning of a synthesis of them, in particular the three different, though potentially complementary, ways in which they depict the accumulation of vorticity on the boundary in the limit as the viscosity is taken to zero.
November 21, 2016
12:10 - 1:10 p.m. Surge 268

Craig Schroeder, Department of Computer Sciences & Engineering, UC Riverside

Title: "Hybrid Simulation Methods: Simulating the World Around You" 

Abstract:

Hybrid particle/grid numerical methods have been around for a long time, and their usage is common in some fields, from plasma physics to artist-directed fluids. I will explore the use of hybrid methods to simulate many different complex phenomena occurring all around you, from wine to shaving foam and from sand to the snow in Disney's Frozen. I will also talk about some of the practical advantages and disadvantages of hybrid methods and how one of the weaknesses that has long plagued them can now be fixed.
November 14, 2016
12:10 - 1:10 p.m. Surge 268

Venugopala Gonehal, Department of Botany & Plant Sciences, UC Riverside

Title: "Regulation and Interpretation of Stem Cell Promoting Transcription Factor Gradient" 

Abstract:

Stem cells located in growing tips, the shoot apical meristems, of plants provide cells for the development of all above-ground plant parts/biomass. The shoot meristem development and function is being studied for nearly a century. However, recent developments in live imaging have provided unprecedented view of growth patterns at cellular and organ level. These studies have revealed that stem cell number control does not involve mechanisms such as asymmetric cell division, cell death and cell migration. Instead the tissue homeostasis is achieved only through regulated cell expansion, cell division and cell displacement. Recent developments in single cell type genomics are augmenting classical genetics experiments in exploring how cells interpret genetic code to regulate stem cell division, growth and differentiation patterns.   My lab has developed these methods and combining them with transient gene manipulations to understand the molecular and cellular basis of stem cell homeostasis. I will provide overview of our work on transcriptional mechanisms that underlie stem cell control which has taken us into a new area of dose-dependent regulation of gene expression. We have shown that WUSCHEL (WUS), a stem cell promoting transcription factor accumulates at a higher level in the niche and a lower level in stem cells.  This concentration differential allows it to function as a transcriptional repressor at higher level and as an activator at lower levels. I will talk about our work on cis-regulatory logic underlying this behavior. I will also talk about a related topic on how cells regulate WUS concentration. This involves regulation at the level of DNA binding, nuclear-cytoplasmic partitioning and diffusivity of WUS into adjacent cells. I will discuss the importance of dose-dependent transcriptional regulation and the regulation of WUS concentration in the control of stem cell division and the differentiation of stem cell descendants. 

 

November 7, 2016
12:10 - 1:10 p.m. Surge 268

Hoori Ajami, Department of Environmental Sciences, UC Riverside

Title: "A Hydrologist Perspective on Mathematical Modeling of Terrestrial Hydrologic Process" 

Abstract:

Hydrologists often rely on mathematical models to test various hypothesis about watershed response and function at large scales, and make projections about future water availability as a result of climate variability and human use. Increases in greenhouse gas concentrations are expected to impact the terrestrial hydrologic cycle through changes in precipitation and temperature and vegetation dynamics. As a result, projections of future changes in water resources are complex due to the tight coupling between the biosphere and terrestrial hydrologic cycle. In this talk, I will 1) provide an overview of hydrologic model development while focusing on differences in model conceptualization and formulation, 2) discuss issues related to model coupling such as coupling of surface water models with groundwater models and ecologic models, 3) discuss sources of uncertainty in model predictions, and 4) present case studies from USA, Denmark and Australia using different numerical models.

 

October 31, 2016
12:10 - 1:10 p.m. Surge 268

Kurt E. Anderson, Department of Biology, UC Riverside

Title: "Ecological dynamics on river networks" 

Abstract:

I will review current and recent work in my lab exploring dynamics of natural populations and communities on river networks. Using advances in graph theory, we will explore how the structure of river networks influences important ecological outcomes such as population persistence, ecological stability, and community asynchrony

 

October 24, 2016
12:10 - 1:10 p.m. Surge 268

Larry Li, Department of Botany & Plant Sciences, UC Riverside

Title: "Patch invasion: impact of dimensionality on dynamic regimes" 

Abstract:

Spatially explicit models have become widely used in today’s mathematical ecology to study persistence of populations. For the sake of simplicity, population dynamics is often analyzed with 1-D models.

An important question is: how adequate is such 1-D simplification of 2-D (or 3-D) dynamics for predicting species persistence. Here we show that dimensionality of the environment can play a critical role in the persistence of predator–prey interactions.

We consider 1-D and 2-D dynamics of a predator–prey model with the prey growth damped by the Allee effect. We show that adding a second space coordinate into the 1-D model results in a pronounced increase of size of the domain in the parametric space where predator–prey coexistence becomes possible. This result is due to the possibility of formation of a number of 2-D patterns, which is impossible in the 1-D model. The 1-D and the 2-D models exhibit different qualitative responses to variations of system parameters. We show that in ecosystems having a narrow width (e.g. mountain valleys, vegetation patterns along canals in dry areas, etc.), extinction of species is more probable compared to ecosystems having a pronounced second dimension. In particular, the width of a long narrow natural reserve should be large enough to guarantee nonextinction of species via interaction of 2-D population patches.

 

October 17, 2016
12:10 - 1:10 p.m. Surge 268

Richard James Arnott, Department of Economics, UC Riverside

Title: "Solving for Equilibrium in the Basic Bathtub Model" 

Abstract:

The talk will provide background for a paper in progress with Josh Buii, a Ph.D. in mathematics at UCR, which has the same title as the talk. The talk will discuss the state of the art in the transportation economics approach to modeling downtown rush-hour traffic congestion. In the process, it will introduce the method of economic model building.

 

October 10, 2016
12:10 - 1:10 p.m. Surge 268

Mark Alber, Department of Mathematics, UC Riverside

Title: "Stochastic cellular automata"

Abstract:

Cellular automata are mathematical finite state machines which change the state of their cells step by step. Each cell has several possible states: 0,1,...,(p-1). To run cellular automata one needs initial distribution of states for all cells and a set of rules. An example of 2-state cellular automata will be provided as a basic introduction. 


October 3, 2016
12 - 1:30 p.m. Surge 268 *Organization meeting

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