Abstract : Advances in our understanding of complex problems in biology are aided by mathematical modeling. A common challenge in this effort is incorporating a wide range of temporal and spatial scales into a single model. This symposium will explore a variety of biological systems, such as microtubule polymerization and blood coagulation, and the diversity of methods used to examine them, such as dynamical systems theory and numerical methods. Our proposed speakers from the US and Canada represent various stages in academia and highlight the versatility of modeling as a tool to answer active biological questions.
[04951] A Spatially Averaged Model for Platelet Cohesion by vWF
Format : Talk at Waseda University
Author(s) :
Keshav Bhavesh Patel (University of Utah)
Aaron Fogelson (University of Utah)
Abstract : Platelet aggregation in high shear rate environments, in both healthy and stenotic arterioles, is mediated by Von Willebrand Factor (vWF). Computational fluid dynamics (CFD) models can study this process but are time-intensive and unable to explore sets of physiologically relevant parameters. In this talk, we will discuss a spatially averaged dynamical systems model of platelet aggregation. We quantify how vWF reduces aggregation time at high shear rates and determine essential parameters involved in aggregate formation.
[04400] Investigating traveling waves in biophysical models of cardiac dynamics
Format : Talk at Waseda University
Author(s) :
Stephanie Dodson (Colby College)
Timothy Lewis (University of California Davis)
Abstract : Regular cardiac function is characterized by coherent traveling waves of electrical activity that drive heart beats. When this process goes awry, the ensuing irregular rhythms are known as arrhythmias, which can be life-threatening. Hence, it is crucial to understand conditions that influence arrhythmia onset. In previous work, these traveling waves have been mathematically investigated in qualitative models of excitable media. We investigate traveling wave properties and arrhythmia onset using biophysically realistic models of cardiac dynamics.
[05165] Modeling and Simulation of Mucin-like Polyelectrolyte Gels
Format : Talk at Waseda University
Author(s) :
Owen Lewis (University of New Mexico)
Jian Du (Florida Institute of Technology)
Aaron L Fogelson (University of Utah)
James P Keener (University of Utah)
Abstract : Volume phase transitions in polyeletrolyte gels play important roles in many biophysical processes such as mucus secretion, DNA packaging, nerve excitation, and cellular secretion. The swelling and deswelling of these charged polymer gels depend strongly on their ionic environment. In this paper, we present an extension to our previous two-fluid model for ion-binding-mediated gel swelling. The model treats the polyeletrolyte gel as a mixture of two continuum materials, the network and the solvent. We use mean-field arguments to derive the force densities that nano-scale species (ions and individual solvent particles) exert on these two species. The resulting model is suitable for the investigation of a large family of biologically relevant problems.
[04304] Adaptive IMEX method for fractional PDE in viscoelastic fluids
Format : Talk at Waseda University
Author(s) :
Dipa Ghosh (IIIT DELHI)
Abstract : Fractional PDEs have emerged as a powerful tool for modelling multiphysics and multiscale processes in numerical simulations ranging from physics and biology to quantitative finance. We propose a novel family of time-asymptotically stable, implicit-explicit, adaptive time integration methods for the solution of the fractional advection-diffusion-reaction equations. The fractional diffusion equation (2D) and the incompressible, subdiffusive dynamics of the Rouse chain melts (α = 1/2) and the Zimm chain solution (α = 2/3) are used to assess the method.
[04322] A mathematical model of microtubule assembly and polarity in dendrites
Format : Talk at Waseda University
Author(s) :
Anna Nelson (Duke University)
Veronica Ciocanel (Duke University)
Scott McKinley (Tulane University)
Abstract : The microtubule cytoskeleton is responsible for sustained transport of cellular cargo inside neurons. However, microtubules must also be dynamic and rearrange their orientation in response to injuries. We introduce a spatially-explicit mathematical model of dendritic microtubule growth dynamics using parameters informed by experimental data. We explore several hypotheses of microtubule growth using both a stochastic model and a continuum model, and use fluorescence microscopy experiments to validate mechanisms such as limited tubulin and length-dependent catastrophe.
[04441] Parameter Estimation for Mechanistic Models of Tear Film Breakup
Format : Talk at Waseda University
Author(s) :
Rayanne A Luke (George Mason University)
Richard J Braun (University of Delaware)
Tobin A Driscoll (University of Delaware)
Deborah Awisi-Gyau (Alcon Research LLC)
Carolyn G Begley (Indiana University)
Abstract : Tear film breakup is related to dry eye disease. Breakup causes include evaporation and divergent flow; related quantities cannot be directly measured during breakup. We determine such variables by fitting thin film fluid dynamics models for breakup to experimental data. Our results suggest that evaporation and divergent flow cooperate to drive faster breakup; purely evaporative cases exhibit slower thinning. These results are the first to make a tight comparison between such models and experimental data.
[05183] Modelling Glucose Regulation: Lipotoxicity and the Progression to Type 2 Diabetes
Format : Talk at Waseda University
Author(s) :
Katharine R Faulkner (University of British Columbia)
Abstract : As an individual moves from healthy to pre-diabetic to diabetic, there are many physiological changes that occur, but it is not known which of these changes are the main drivers of the progression to type II diabetes. In this talk, I will describe a simple model for glucose regulation and how modeling can help determine which of these physiological changes are capable of pushing an individual from healthy to diseased. By framing this problem in terms of bifurcations, we can find models that create qualitative changes to the system that allow for movement between healthy and diseased states. We will examine a model that includes the toxicity of lipids in the pancreas, and find a bifurcation that describes the progression to type II diabetes.
[04351] PIEZO1 regulates cellular coordination during collective cell migration
Format : Talk at Waseda University
Author(s) :
Jinghao Chen (University of California, Irvine)
Jesse Holt (University of California, Irvine)
Beth Evans (University of California, Irvine)
John Lowengrub (University of California, Irvine)
Medha Pathak (University of California, Irvine)
Abstract : The mechanically-activated ion channel PIEZO1 was recently identified to play an inhibitory role during wound healing. Through an integrative experimental and mathematical modeling approach, we elucidate PIEZO1’s contributions to keratinocyte collective migration, an essential component of the healing process. Here, through a 2D-multiscale model of wound closure which links observations at both the single and multicell scales, and subsequent experimental validation, we identify cell directionality as being impacted by PIEZO1 activity during wound closure.
