Browsing by Subject "random walk"

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    Experimental and simulated cell migration in 1D and 2D nanofiber microenvironments
    (2017-03) Estabridis, Horacio
    Understanding how cells migrate in fibrous environments is important in wound healing, immune function, and cancer progression. A key question is how fiber orientation and network geometry influence cell movement. Here we describe a quantitative, modeling-based approach toward identifying the mechanisms by which glioblastoma cells migrate in fibrous geometries having well controlled orientation. Specifically, U251 glioblastoma cells were seeded onto STEP Fiber substrates that consist of networks of suspended 400 nm diameter nanofibers. Cells were classified based on the local fiber geometry and live cell migration was tracked, quantified and parameterized. Cells were found in three distinct geometries: adhering two a single fiber, adhering to two parallel fibers, and adhering to a network of orthogonal fibers. Cells adhering to a single fiber or two parallel fibers can only move in one dimension along the fiber axis, whereas cells on a network of orthogonal fibers can move in two dimensions. We found that cells move faster and more persistently in 1D geometries than in 2D, with cell migration being faster on parallel fibers than on single fibers. To explain these behaviors mechanistically, we simulated cell migration in the three different geometries using a motor-clutch based model for cell traction forces. Using nearly identical parameter sets for each of the three cases, we found that the simulated cells naturally replicated the reduced migration in 2D relative to 1D geometries. In addition, the modestly faster 1D migration on parallel fibers relative to single fibers was captured using a modest increase in the number of clutches to reflect increased surface area of adhesion on parallel fibers. Overall, the integrated modeling and experimental analysis indicates that cell migration response to varying fibrous geometries can be explained by a simple mechanical readout of geometry via a motor-clutch mechanism.
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    Geometric ergodicity of a random-walk Metropolis algorithm for a transformed density
    (2010-11-22) Johnson, Leif; Geyer, Charles J.
    Curvature conditions on a target density in R^k for the geometric ergodicity of a random-walk Metropolis algorithm have previously been established (Mengersen and Tweedie(1996), Roberts and Tweedie(1996), Jarner and Hansen(2000)). However, the conditions for target densities in R^k that have exponentially light tails, but are not super-exponential are difficult to apply. In this paper I establish a variable transformation to apply to such target densities, that along with a regularity condition on the target density, ensures that a random-walk Metropolis algorithm for the transformed density is geometrically ergodic. Inference can be drawn for the original target density using Markov chain Monte Carlo estimates based on the transformed density. An application to inference on the regression parameter in multinomial logit regression with a conjugate prior is given.