A Computational Model of Protein Induced Membrane Morphology with Geodesic Curvature Driven Protein-Membrane Interface

Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allows a convenient coupling of the morphology of two surfaces. We integrated these two new developments into the energetic model of protein-membrane interactions, and developed the full set of numerical methods for the coupled system. Numerical examples are presented to demonstrate (1) the efficiency and robustness of our methods in locating the curves with minimal total geodesic curvature on highly complicated protein surfaces, (2) the usefulness of these interfaces as interior boundaries for membrane deformation, and (3) the rich morphology of bilayer surfaces for different protein-membrane interfaces

Membrane Protein Properties Revealed through Data-Rich Electrostatics Calculations.

The electrostatic properties of membrane proteins often reveal many of their key biophysical characteristics, such as ion channel selectivity and the stability of charged membrane-spanning segments. The Poisson-Boltzmann (PB) equation is the gold standard for calculating protein electrostatics, and the software APBSmem enables the solution of the PB equation in the presence of a membrane. Here, we describe significant advances to APBSmem, including full automation of system setup, per-residue energy decomposition, incorporation of PDB2PQR, calculation of membrane-induced pKa shifts, calculation of non-polar energies, and command-line scripting for large-scale calculations. We highlight these new features with calculations carried out on a number of membrane proteins, including the recently solved structure of the ion channel TRPV1 and a large survey of 1,614 membrane proteins of known structure. This survey provides a comprehensive list of residues with large electrostatic penalties for being embedded in the membrane, potentially revealing interesting functional information

Introduction

Le terme de theatron, étymologie grecque du mot « théâtre », désignait à l’origine le « lieu d’où le public regarde une action qui lui est présentée dans un autre endroit », comme le rappelle Patrice Pavis. C’est donc par inversion du rapport entre regard et objet regardé que le théâtre a ensuite nommé le lieu même où a lieu une représentation. Les métaphores de theatrum mundi et de « théâtre des opérations », comme désignant le lieu de l’action, prirent un sens renouvelé avec l’avènement d’u..

Investigations of water and tracer movement in covered and uncovered unsaturated waste rock

A better understanding of the hydrogeology of mine waste rock and cover systems is essential for the quantification, prediction and reduction of metals loading to the receiving environment. A series of experiments were conducted on an instrumented intermediate-scale waste rock pile at the Cluff Lake Mine in Saskatchewan to investigate the changes in flow and solute transport within coarse waste rock under three different surface conditions. Following these studies, the waste rock pile was deconstructed, structures were mapped, and samples were collected for physical characterization and pore water extraction. The internal structure of the waste rock pile was more important than the texture and topography under the free-dumped and ripped/leveled surface, while the surface condition was found to be the dominant control on spatial and temporal variability of outflow from the waste rock with the covered surface. Data from a deuterium tracer test, lysimeter outflow, and from TDR probes were used to derive estimates of the maximum and an average pore water velocity through the uncovered and the covered waste rock. An average pore water velocity through the matrix materials of the uncovered waste rock was approximately 1.5 m/yr and maximum preferential flow velocities were as high as 5 m/day. The post-cover pressure wave velocity of 0.1 to 1 m/day is inferred from outflow and TDR data, and average pore water velocities (0.39 m/y and 0.73 m/y) are calculated by the water flux and tracer methods, respectively. The distribution of the tracers in pore water and the internal structure were mapped during a detailed deconstruction of the waste rock pile and attempts were made to link the data to the spatial and temporal patterns of lysimeter outflow. The pore water chloride concentrations and the deuterium values did not provide conclusive data necessary to link the spatial and temporal patterns observed in the lysimeter hydrographs to internal structure; however, it provided insight into the internal flow mechanisms and water residence times.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat

WATER MIGRATION IN COVERED WASTE ROCK, INVESTIGATIONS USING DEUTERIUM AS A TRACER. 1

Abstract. A deuterium tagged rainfall event with a δD of +213 was applied to the top surface of an experimental covered waste rock pile in May of 2003. The tracer experiment was designed to resolve the spatial variability of infiltrating water and to estimate the magnitude and rate of flow within covered waste rock. The five meter high pile was deconstructed one year later and waste rock was sampled along vertical profiles at 10cm increments. Pore waters were extracted from the waste rock using the centrifugal method. The measured δD values range from -90 to background levels of approximately -130 with a few zones of locally high δD values deeper than three meters in the pile. Variability between individual vertical δD profiles are observed within the 8x8 meter area. The combination of the spatial variability and the deep δD values yield strong evidence for intermediate scale (~15 cm) preferential flow

Continuum descriptions of membranes and their interaction with proteins: Towards chemically accurate models

Biological membranes deform in response to resident proteins leading to a coupling between membrane shape and protein localization. Additionally, the membrane influences the function of membrane proteins. Here we review contributions to this field from continuum elastic membrane models focusing on the class of models that couple the protein to the membrane. While it has been argued that continuum models cannot reproduce the distortions observed in fully-atomistic molecular dynamics simulations, we suggest that this failure can be overcome by using chemically accurate representations of the protein. We outline our recent advances along these lines with our hybrid continuum-atomistic model, and we show the model is in excellent agreement with fully-atomistic simulations of the nhTMEM16 lipid scramblase. We believe that the speed and accuracy of continuum-atomistic methodologies will make it possible to simulate large scale, slow biological processes, such as membrane morphological changes, that are currently beyond the scope of other computational approaches. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov

A mathematical model of osteoclast acidification during bone resorption

Bone resorption by osteoclasts occurs through the creation of a sealed extracellular compartment (ECC), or pit, adjacent to the bone that is subsequently acidified through a complex biological process. The low pH of the pit dissolves the bone mineral and activates acid proteases that further break down the bone matrix. There are many ion channels, transporters, and soluble proteins involved in osteoclast mediated resorption, and in the past few years, there has been an increased understanding of the identity and properties of some key proteins such as the ClC-7 Cl-/H+ antiporter and the HV1 proton channel. Here we present a detailed mathematical model of osteoclast acidification that includes the influence of many of the key regulatory proteins. The primary enzyme responsible for acidification is the vacuolar H+-ATPase (V-ATPase), which pumps protons from the cytoplasm into the pit. Unlike the acidification of small lysosomes, the pit is so large that protons become depleted from the cytoplasm. Hence, proton buffering and production in the cytoplasm by carbonic anhydrase II (CAII) is potentially important for proper acidification. We employ an ordinary differential equations (ODE)-based model that accounts for the changes in ionic species in the cytoplasm and the resorptive pit. Additionally, our model tracks ionic flow between the cytoplasm and the extracellular solution surrounding the cell. Whenever possible, the properties of individual channels and transporters are calibrated based on electrophysiological measurements, and physical properties of the cell, such as buffering capacity, surface areas, and volumes, are estimated based on available data. Our model reproduces many of the experimental findings regarding the role of key proteins in the acidification process, and it allows us to estimate, among other things, number of active pumps, protons moved, and the influence of particular mutations implicated in disease