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public 01:34:42

Johannes Reiter : Minimal intratumoral heterogeneity in untreated cancers

  -   Mathematical Biology ( 219 Views )

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.

public 01:29:51

Franziska Michor : Evolutionary dynamics of cancer

  -   Mathematical Biology ( 135 Views )

Cancer emerges due to an evolutionary process in somatic tissue. The fundamental laws of evolution can best be formulated as exact mathematical equations. Therefore, the process of cancer initiation and progression is amenable to mathematical investigation. Of special importance are changes that occur early during malignant transformation because they may result in oncogene addiction and represent promising targets for therapeutic intervention. Here we describe a mathematical approach, called Retracing the Evolutionary Steps in Cancer (RESIC), to deduce the temporal sequence of genetic events during tumorigenesis from crosssectional genomic data of tumors at their fully transformed stage. When applied to a dataset of 70 advanced colorectal cancers, our algorithm accurately predicts the sequence of APC, KRAS, and TP53 mutations previously defined by analyzing tumors at different stages of colon cancer formation. We further validate the method with glioblastoma and leukemia sample data and then apply it to complex integrated genomics databases, finding that high-level EGFR amplification appears to be a late event in primary glioblastomas. RESIC represents the first evolutionary mathematical approach to identify the temporal sequence of mutations driving tumorigenesis and may be useful to guide the validation of candidate genes emerging from cancer genome surveys.

public 01:29:52

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

  -   Mathematical Biology ( 133 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 01:14:49

Mark Alber : Multi-scale Modeling of Bacterial Swarming

  -   Mathematical Biology ( 129 Views )

The ability of animals to self-organize into remarkable patterns of movement is seen throughout nature from herds of large mammals, to flocks of birds, schools of fish, and swarms of insects. Remarkably, patterns of collective movement can be seen even in the simplest forms of life such as bacteria. M. xanthus are common soil bacteria that are among the most “social" bacteria in nature. In this talk clustering mechanism of swarming M. xanthus will be described using combination of experimental movies and stochastic model simulations. Continuous limits of discrete stochastic dynamical systems simulating cell aggregation will be described in the form of reaction-diffusion and nonlinear diffusion equations. Surface motility such as swarming is thought to precede biofilm formation during infection. Population of bacteria P. aeruginosa, major infection in hospitals, will be shown to efficiently propagate as high density waves that move symmetrically as rings within swarms towards the extending tendrils. Multi-scale model simulations suggest a mechanism of wave propagation as well as branched tendril formation at the edge of the population that depend upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. This collective mechanism of cell- cell coordination was recently shown to moderate swarming direction of individual bacteria to avoid a toxic environment. In the last part of the talk a three-dimensional multiscale modeling approach will be described for studying fluid–viscoelastic cell interaction during blood clot formation.