Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Rule-Based Cell Systems Model of Aging using Feedback Loop Motifs Mediated by Stress Responses

Investigating the complex systems dynamics of the aging process requires integration of a broad range of cellular processes describing damage and functional decline co-existing with adaptive and protective regulatory mechanisms. We evolve an integrated generic cell network to represent the connectivity of key cellular mechanisms structured into positive and negative feedback loop motifs centrally important for aging. The conceptual network is casted into a fuzzy-logic, hybrid-intelligent framework based on interaction rules assembled from a priori knowledge. Based upon a classical homeostatic representation of cellular energy metabolism, we first demonstrate how positive-feedback loops accelerate damage and decline consistent with a vicious cycle. This model is iteratively extended towards an adaptive response model by incorporating protective negative-feedback loop circuits. Time-lapse simulations of the adaptive response model uncover how transcriptional and translational changes, mediated by stress sensors NF-κB and mTOR, counteract accumulating damage and dysfunction by modulating mitochondrial respiration, metabolic fluxes, biosynthesis, and autophagy, crucial for cellular survival. The model allows consideration of lifespan optimization scenarios with respect to fitness criteria using a sensitivity analysis. Our work establishes a novel extendable and scalable computational approach capable to connect tractable molecular mechanisms with cellular network dynamics underlying the emerging aging phenotype

Oral Carriage of Candida Species and Coliforms in Patients with Burning Mouth Syndrome

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The effect of indigenous bacterial populations on buccal epithelial cells on subsequent microbial adhesion in vitro

Despite the numerous investigations on the adhesion of microorganisms to buccal epithelial cells, it is difficult to correlate different results, as disparate adherence values have been reported for a given organism. As one reason for this disparity may be the indigenous or natural bacterial populations on human buccal epithelial cells, the effect of the latter on subsequent microbial adherence in vitro was examined. There was a highly significant correlation between the degree of natural bacterial colonization on pooled buccal epithelial cells from 8 healthy donors and the adhesion of a single isolate each of Streptococcus mitis, Escherichia coli and Actinomyces naeslundii. However, no such relationship could be established for Candida albicans, Streptococcus milleri and another isolate of Streptococcus mitis. As in previous studies, variation in adherence values was found, both between samples from different donors, and from the same donor over time, but to a far lesser degree in pooled samples from different donors. These results imply that natural bacterial populations on buccal epithelial cells may affect the adhesion values derived from laboratory experimentation, and hence such data should be interpreted with caution.link_to_subscribed_fulltex