Browsing by Subject "Vesicles"

Interfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.

A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface, to obtain optimal rates of convergence we employ a hierarchical local refinement approach to improve the geometrical representation of interface.

In multiple dimensions, a spline basis is obtained as a tensor product of the one-dimensional basis. This necessitates a rectangular grid that cannot be refined locally in regions of embedded interfaces. To address this issue, we develop an adaptive spline-based finite element method that employs hierarchical refinement and coarsening techniques. The process of refinement and coarsening guarantees linear independence and remains the regularity of the basis functions. We further propose an efficient data transfer algorithm during both refinement and coarsening which yields to accurate results.

The adaptive approach is applied to vesicle modeling which allows three-dimensional simulation to proceed efficiently. In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles. The chemical energy is described by a Cahn-Hilliard type density functional that characterizes the line energy between domains of different species. The generalized Canham-Helfrich-Evans model provides a description of the mechanical energy of the vesicle membrane. This coupled model is cast in a diffuse-interface form using the phase-field framework. The effect of coupling is seen through several numerical examples of domain formation coupled to vesicle shape changes.

Outer membrane vesicles (OMVs) are spherical structures that bud from the outer membrane (OM) of bacteria containing OM and periplasmic material. They are known to be produced by all bacteria studied to date and play important roles in inter-bacterial communication, bacterial-host interactions, toxin delivery, survival, nutrient acquisition, and biofilm development. The process of OMV production is known to be genetically regulated and selective cargo packaging into bacterial vesicles has been reported and implicated in many biological processes. While much is known about how cargo gets incorporated into vesicles in eukaryotic systems, the mechanism behind cargo selectivity in bacteria has remained largely unexplored. In this study we aimed to characterize preferential sorting trends in OMV packaging in Escherichia coli under oxidative stress, and investigate the mechanism behind selective sorting into OMVs. Proteomic analysis of outer membrane (OM) and OM vesicle fractions from enterotoxigenic E. coli (ETEC) revealed significant differences in protein abundance in the OMV and OM fractions for cultures shifted to oxidative stress conditions. Analysis of sequences of proteins preferentially packaged into OMVs showed that proteins with oxidizable residues were more packaged into OMVs in comparison with those retained in the membrane. In addition, the results indicated two distinct classes of OM-associated proteins were differentially packaged into OMVs as a function of peroxide treatment and we observed a slight increase in periplasmic content. Implementing a Bayesian hierarchical model, OM lipoproteins were determined to be preferentially exported during stress whereas integral OM proteins were preferentially retained in the cell. We first inquired whether this sorting was due to the need of the cell to discard or retain OM proteins and tested oxidative stress sensitivity of mutants of lipoproteins and integral proteins. We hypothesized that mutants of lipoproteins would not be more sensitive than integral proteins however both groups showed increased sensitivity. Therefore, this did not explain this preferential sorting. We next wondered if selectivity was dependent on gene expression. By mining gene expression databases and performing qRT-PCR we found the sorting to be independent of transcriptional regulation of the proteins upon oxidative stress. We were also able to validate these preferential sorting trends of lipoproteins vs integral proteins using randomly selected protein candidates from the different cargo classes. We also observed that a shift to oxidative stress conditions improved the fitness of bacteria to a secondary oxidative challenge, suggesting the differential sorting resulted in an OMV-mediated remodeling of the OM during stress. Together, our data showed that oxidative stress induced a differential sorting of proteins into OMVs and OM of E. coli and that OMV production might serve as a disposal mechanism for the cell to rid itself of oxidized proteins. Since our data revealed that the preferentially retained proteins were those known to have ties to other cell envelope components, a hypothetical functional and mechanistic basis for cargo selectivity was tested using OmpA as a model. A full-length and a truncated version of OmpA were used to test whether physical tethering to the cell is a determinant for protein retention in the OM. Quantifying OMV protein packaging of both OmpA constructs revealed a basic mechanism for cargo selectivity into OMVs. We show that the untethered version of OmpA was more likely to be exported than the tethered version and that this preferential selection was exacerbated under oxidative stress. The findings of this study provide insight into the dynamics of bacterial cargo selection and membrane remodeling during stress as well as propose and test a mechanism for cargo incorporation in E. coli.

The surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation.

In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport, as has been observed in several experimental studies on GUVs. In this study, shape changes are assumed to be instantaneous, while species transport, which is modeled by phase separation and domain coarsening, follows a natural time scale described by the Cahn--Hilliard dynamics.

The curvature energy of the vesicle membrane is defined by the classical Canham--Helfrich--Evans model. Dependence of flexural rigidity and spontaneous curvature on the lipid species is built into the energy functional. The chemical energy is characterized by a Cahn--Hilliard type density function that intrinsically captures the line energy of interfaces between two phases. Both curvature and chemical contributions to the vesicle energetics are consistently non-dimensionalized.

The coupled model is cast in a diffuse-interface form using the phase-field framework. The phase-field form of the governing equations describing shape equilibrium and species transport are both fourth-order and nonlinear. The system of equations is discretized using the finite element method with a uniform cubic-spline basis that satisfies global higher-order continuity. For shape equilibrium, geometric constraints of constant internal volume and constant surface area of the vesicle are imposed weakly using the penalty approach. A time-stepping scheme based on the unconditionally gradient-stable convexity-splitting technique is employed for explicit time integration of nonlocal integrals arising from the geometric constraints.

Numerical examples of axisymmetric stationary shapes of uniform vesicles are presented. Further, two- and three-dimensional numerical examples of domain formation and growth coupled to vesicle shape changes are discussed. Simulations qualitatively depicting curvature-dependent domain sorting and shape changes to minimize line tension are presented. The effect of capturing the difference in time scales is also brought out in a few numerical simulations that predict a starkly different pathway to equilibrium.