Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single molecule pulling experiments

We have used kinetic Monte Carlo simulations to study the kinetics of unfolding of cross-linked polymer chains under mechanical loading. As the ends of a chain are pulled apart, the force transmitted by each crosslink increases until it ruptures. The stochastic crosslink rupture process is assumed to be governed by first order kinetics with a rate that depends exponentially on the transmitted force. We have performed random searches to identify optimal crosslink configurations whose unfolding requires a large applied force (measure of strength) and/or large dissipated energy (measure of toughness). We found that such optimal chains always involve cross-links arranged to form parallel strands. The location of those optimal strands generally depends on the loading rate. Optimal chains with a small number of cross-links were found to be almost as strong and tough as optimal chains with a large number of cross-links. Furthermore, optimality of chains with a small number of cross-links can be easily destroyed by adding cross-links at random. The present findings are relevant for the interpretation of single molecule force probe spectroscopy studies of the mechanical unfolding of load-bearing proteins, whose native topology often involves parallel strand arrangements similar to the optimal configurations identified in the study

Axisymmetric deformation of compressible, nearly incompressible, and incompressible thin layers between two rigid surfaces

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson's ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible layers. That classification involves both material and geometric parameters

Generation of a genomic tiling array of the human Major Histocompatibility Complex (MHC) and its application for DNA methylation analysis

Background: The major histocompatibility complex (MHC) is essential for human immunity and is highly associated with common diseases, including cancer. While the genetics of the MHC has been studied intensively for many decades, very little is known about the epigenetics of this most polymorphic and disease-associated region of the genome.Methods: To facilitate comprehensive epigenetic analyses of this region, we have generated a genomic tiling array of 2 Kb resolution covering the entire 4 Mb MHC region. The array has been designed to be compatible with chromatin immunoprecipitation (ChIP), methylated DNA immunoprecipitation (MeDIP), array comparative genomic hybridization (aCGH) and expression profiling, including of non-coding RNAs. The array comprises 7832 features, consisting of two replicates of both forward and reverse strands of MHC amplicons and appropriate controls.Results: Using MeDIP, we demonstrate the application of the MHC array for DNA methylation profiling and the identification of tissue-specific differentially methylated regions (tDMRs). Based on the analysis of two tissues and two cell types, we identified 90 tDMRs within the MHC and describe their characterisation.Conclusion: A tiling array covering the MHC region was developed and validated. Its successful application for DNA methylation profiling indicates that this array represents a useful tool for molecular analyses of the MHC in the context of medical genomics

The default-mode, ego-functions and free-energy: a neurobiological account of Freudian ideas

This article explores the notion that Freudian constructs may have neurobiological substrates. Specifically, we propose that Freud’s descriptions of the primary and secondary processes are consistent with self-organized activity in hierarchical cortical systems and that his descriptions of the ego are consistent with the functions of the default-mode and its reciprocal exchanges with subordinate brain systems. This neurobiological account rests on a view of the brain as a hierarchical inference or Helmholtz machine. In this view, large-scale intrinsic networks occupy supraordinate levels of hierarchical brain systems that try to optimize their representation of the sensorium. This optimization has been formulated as minimizing a free-energy; a process that is formally similar to the treatment of energy in Freudian formulations. We substantiate this synthesis by showing that Freud’s descriptions of the primary process are consistent with the phenomenology and neurophysiology of rapid eye movement sleep, the early and acute psychotic state, the aura of temporal lobe epilepsy and hallucinogenic drug states

Wrinkling of elastic thin films on compliant substrates

textComplex wrinkle patterns have been observed in various thin film systems, typically with integrated hard and soft materials for various technological applications as well as in nature. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. On an elastic substrate, equilibrium and energetics set the critical condition and select the wrinkle wavelength and amplitude. On a viscous substrate, wrinkles grow over time and kinetics select the dominant wavelength. More generally, on a viscoelastic substrate, both energetics and kinetics play important roles in determining the critical condition, the growth rate, and wrinkle patterns. The dynamics of wrinkling, while analogous to other phase ordering phenomena, is rich and distinct under the effects of a variety of stress conditions and nonlocal film-substrate interactions. In this study, a new mathematical model is developed for wrinkling of isotropic and anisotropic elastic films on viscoelastic substrates. Analytic solutions are obtained by a linear perturbation analysis and a nonlinear energy minimization method, which predict the kinetics of wrinkle growth at the initial stage and the equilibrium states at the long-time limit, respectively. In between, a power-law coarsening of the wrinkle wavelength is predicted by a scaling analysis. Numerical simulations confirm the analytical predictions and show diverse wrinkle patterns under various stress conditions. For isotropic elastic films, a transition from parallel wrinkles to zigzag patterns is predicted under anisotropic biaxial stresses. For cubic crystal films, the anisotropic elastic property leads to formation of orthogonal wrinkle patterns under equi-biaxial stresses. In general, the competition between the stress anisotropy and the material anisotropy controls the evolution of wrinkle patterns. Based on the mathematical model, two potential applications of the wrinkling phenomenon are explored, one for surface patterning and the other for estimating viscoelastic properties of thin polymer films. The theoretical and numerical results from this study are compared with experimental observations that are available in literature and through collaborations with experimental groups. The last chapter of this dissertation considers ratcheting-induced wrinkling for an elastic film on an elastoplastic substrate under cyclic temperatures, demonstrating an analogy between plastic ratcheting and viscous creep.Engineering Mechanic

Implementing multiphysics models in FEniCS: Viscoelastic flows, poroelasticity, and tumor growth

The open-source finite element code FEniCS is considered as an alternative to commercial finite element codes for evaluating complex constitutive models of multiphysics phenomena. FEniCS deserves this consideration because it is well-suited for encoding weak forms corresponding to partial differential equations arising from the fundamental balance laws and constitutive equations. It is shown how FEniCS can be adopted for solving boundary-value problems describing viscoelastic flows, poroelasticity, and tumor growth. Those problems span a wide range of models of continuum mechanics, and involve Eulerian, Lagrangian, and combined Eulerian-Lagrangian descriptions. Thus it is demonstrated that FEniCS is a viable computational tool capable of transcending traditional barriers between computational fluid and solid mechanics. Furthermore, it is shown that FEniCS implementations are straightforward, and do not require advanced knowledge of finite element methods and/or coding skills

Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods and Boundary Element Methods

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element methods are used. Error and stability analysis is presented for some of the methods. Numerical examples suggest that all three methods exhibit very similar convergence properties, consistent with available theoretical results.:1. Introduction 2. Model Problem and Background 3. New Coupling Methods 4. Stability and Error Analysis 5. Numerical Examples 6. Summary A. Appendi