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public 01:29:52

Anita Layton : Myogenic Response to Systolic Pressure in the Afferent Arteriole

  -   Mathematical Biology ( 131 Views )

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.

public 01:14:42

Rick Durrett : Overview of the semester

  -   Mathematical Biology ( 120 Views )

public 01:29:50

Katarzyna Rejniak : Fluid dynamics in cancer cell biology

  -   Mathematical Biology ( 119 Views )

Eukaryotic cell microenvironment (inner and outer) is composed in large parts from fluids that interact with solid and elastic bodies, whereas it is the cell cytoplasm, cytoskeleton and basal membrane; the interstitial fluid interpenetrating the stroma and tumor cells; or blood flow carrying the immune or circulating tumor cells. I will discuss the use of two fluid-structure interactions methods, the immersed boundary and the regularized Stokeslets, in applications dealing with the tumor development and treatment. First model operates on the cellular scale and will be used to model various cell processes, such as cell growth, division or death, during the cellular self-organization into a normal mammary acinus, a 3D in vitro structure recapitulating the morphology of breast cysts (acini). I will discuss model development, parameterization and tuning with the experimental data, as well as their subsequent use to investigate the link between morphogenesis of epithelial mutants and molecular alterations of tumor cells. Second model acts on the tissue level, and will be used to investigate the relation between tumor tissue structure and efficacy of anticancer drugs in the context of interstitial fluid flow. I will present simulation results showing non-linear relation between tumor tissue structure and effectiveness of drug penetration. I will also discuss how tumor tissue metabolic state(its oxygenation and acidity) becomes modified due to actions of chemotherapeutic drugs leading to the emergence of tumor zones with potentially drug-resistant cells and/or to tumor areas that are not exposed to drugs at all. Both of these phenomena can contribute to the moderateclinical success of many anticancer drugs.

public 01:29:57

Jim Keener : Mechanisms of length regulation of flagella in Salmonella

  -   Mathematical Biology ( 117 Views )

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

public 01:34:46

Friday is the start of spring break : no talk

  -   Mathematical Biology ( 114 Views )

public 01:14:56

Sylvie Méléard : Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

  -   Mathematical Biology ( 114 Views )

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.