Subdiffusion of proteins and oligomers on membranes

Diffusion in heterogeneous discs and spheres: New closed-form expressions for exit times and homogenization formulas

Mathematical models of diffusive transport underpin our understanding of chemical, biochemical, and biological transport phenomena. Analysis of such models often focuses on relatively simple geometries and deals with diffusion through highly idealized homogeneous media. In contrast, practical applications of diffusive transport theory inevitably involve dealing with more complicated geometries as well as dealing with heterogeneous media. One of the most fundamental properties of diffusive transport is the concept of mean particle lifetime or mean exit time, which are particular applications of the concept of first passage time and provide the mean time required for a diffusing particle to reach an absorbing boundary. Most formal analysis of mean particle lifetime applies to relatively simple geometries, often with homogeneous (spatially invariant) material properties. In this work, we present a general framework that provides exact mathematical insight into the mean particle lifetime, and higher moments of particle lifetime, for point particles diffusing in heterogeneous discs and spheres with radial symmetry. Our analysis applies to geometries with an arbitrary number and arrangement of distinct layers, where transport in each layer is characterized by a distinct diffusivity. We obtain exact closed-form expressions for the mean particle lifetime for a diffusing particle released at an arbitrary location, and we generalize these results to give exact, closed-form expressions for any higher-order moment of particle lifetime for a range of different boundary conditions. Finally, using these results, we construct new homogenization formulas that provide an accurate simplified description of diffusion through heterogeneous discs and spheres.

New homogenization approaches for stochastic transport through heterogeneous media

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative jump coefficients can arise when transport operators are discretized on heterogeneous domains. Often this is dealt with through homogenization approximations by replacing the heterogeneous medium with an effective homogeneous medium. In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates. We derive closed form solutions for the kth moment of particle lifetime, carefully explaining how to deal with the internal interfaces between layers. These general tools allow us to derive simple formulae for the effective transport coefficients, leading to significant generalisations of previous homogenization approaches. Here, we find that different jump rates in the layers give rise to a net bias, leading to a non-zero advection, for the entire homogenized system. Example calculations show that our generalized approach can lead to very different outcomes than traditional approaches, thereby having the potential to significantly affect simulation studies that use homogenization approximations.

Characterization of a Biomimetic Mesophase Composed of Nonionic Surfactants and an Aqueous Solvent

We have investigated the physical and biomimetic properties of a sponge (L₃) phase composed of pentaethylene glycol monododecyl ether (C₁₂E₅), a nonionic surfactant, an aqueous solvent, and a cosurfactant. The following cosurfactants, commonly used for solubilizing membrane proteins, were incorporated: n-octyl-β-d-glucopyranoside (β-OG), n-dodecyl-β-d-maltopyranoside (DDM), 4-cyclohexyl-1-butyl-β-d-maltoside (CYMAL-4), and 5-cyclohexyl-1-pentyl-β-d-maltoside (CYMAL-5). Partial phase diagrams of these systems were created. The L₃ phase was characterized using crossed polarizers, diffusion of a fluorescent probe by fluorescence recovery after pattern photobleaching (FRAPP), and freeze fracture electron microscopy (FFEM). By varying the hydration of the phase, we were able to tune the distance between adjacent bilayers. The characteristic distance (d_b) of the phase was obtained from small angle scattering (SAXS/SANS) as well as from FFEM, which yielded complementary d_b values. These d_b values were neither affected by the nature of the cosurfactant nor by the addition of membrane proteins. These findings illustrate that a biomimetic surfactant sponge phase can be created in the presence of several common membrane protein-solubilizing detergents, thus making it a versatile medium for membrane protein studies.

Surfactant bilayers maintain transmembrane protein activity

In vitro studies of membrane proteins are of interest only if their structure and function are significantly preserved. One approach is to insert them into the lipid bilayers of highly viscous cubic phases rendering the insertion and manipulation of proteins difficult. Less viscous lipid sponge phases are sometimes used, but their relatively narrow domain of existence can be easily disrupted by protein insertion. We present here a sponge phase consisting of nonionic surfactant bilayers. Its extended domain of existence and its low viscosity allow easy insertion and manipulation of membrane proteins. We show for the first time, to our knowledge, that transmembrane proteins, such as bacteriorhodopsin, sarcoplasmic reticulum Ca(2+)ATPase (SERCA1a), and its associated enzymes, are fully active in a surfactant phase.