Browsing by Subject "Electrodiffusion"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Multiscale models of antimicrobial peptides.
    (2010-12) Bolintineanu, Dan
    Antimicrobial peptides (AMPs) are small proteins that constitute a first line of defense against invading pathogens in the innate immune systems of countless plant and animal species. Their mechanism of action relies to a large extent on selectively disrupting the cell membranes of bacteria, which makes them promising therapeutic agents in the fight against infectious pathogens, including antibiotic-resistant bacterial strains. However, AMPs also exhibit toxicity towards mammalian cells, which presents a significant bottleneck in the development of AMPs for antibiotic treatment in humans. Thus, before the full potential of AMPs as therapeutic agents can be unlocked, their fundamental mechanism of action must be understood in order to identify targets for mutation that can improve activity and ameliorate toxic effects. To this end, we carry out computer simulations and modeling studies in order to understand the interactions of protegrin, a particularly potent and well-studied AMP, with lipid bilayers that mimic the compositions of bacterial and mammalian cell membranes. In particular, we attempt to connect molecular-level thermodynamic information to biologically relevant membrane association equilibria; we elucidate the ion transport characteristics of protegrin pores, and show how the atomistic structure leads to experimentally observed conductance behavior; we provide multi-scale models that can quantitatively link the structure of protegrin and protegrin pores to the leakage of potassium ions from bacterial cells, which appears to be an essential element in the bactericidal mechanism of action of protegrin; finally, we investigate the structure of protegrin pores using molecular dynamics simulations with atomistic resolution. Our work reveals this link for the first time, and provides a united, quantitative connection between molecular-level structural and thermodynamic information and mesoscopic, measurable quantities. Our modeling tools can be easily extended to other AMPs, and protein-membrane systems in general.
  • Thumbnail Image
    Item
    Volume transitions in gels with biomedical applications: Mechanics and electrodiffusion.
    (2010-07) Micek, Catherine Ann
    In this thesis, mathematical models for gels are developed and analyzed using both analytical and numerical approaches. The work is motivated by two biomedical applications: body implantable devices such as artificial bone implants and a drug delivery device designed by Siegel et al. [14, 41, 42, 62]. The mathematical structure of the models depends on the device being studied: the former application is an equilibrium problem focusing on mechanical effects, whereas the latter is a dynamical problem focusing on chemomechanical effects. Both types of models are considered in this work. The mechanical equilibrium model presented is suitable for gel problems in both the mixing or separating regime. For mixing regime problems, the existence of minimizers for a convex energy is established. The Euler-Lagrange equilibrium equations for this model are equations of nonlinear elasticity, and the Stokes elasticity mixed finite element method is developed for the linearized Euler-Lagrange equations. The Stokes formulation is used to numerically simulate the effects of confinement and temperature changes with the software FEniCs for an artificial bone implant. For the separating regime model, the existence of minimizers for a non-convex energy is established following the proof first presented in [61]. The dynamical model presented is an electrochemical model derived from balance laws for mechanics and chemistry. The primary goal in the analysis of this model is to model a cyclic gel volume phase transition using chemomechanical coupling. Two issues are addressed: the origin of the volume phase transition and modeling a mechanically realistic cycling mechanism. Following the studies of Horkay et al. in physiology [34, 35], the volume phase transition is formulated as higher order terms from the Flory-Huggins mixing energy. After a careful examination of the chemical and mechanical governing equations, the cycling mechanism is modeled as a non-monotone mechanical stress for which hysteresis is inherently present. The mechanical emphasis of the model is an alternative approach to the chemical emphasis found in the models of Siegel et al.