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

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

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

New Continuum Approaches for Determining Protein-Induced Membrane Deformations

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, 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 and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel's orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution

Protons in small spaces:Discrete simulations of vesicle acidification

The lumenal pH of an organelle is one of its defining characteristics and central to its biological function. Experiments have elucidated many of the key pH regulatory elements and how they vary from compartment-to-compartment, and continuum mathematical models have played an important role in understanding how these elements (proton pumps, counter-ion fluxes, membrane potential, buffering capacity, etc.) work together to achieve specific pH setpoints. While continuum models have proven successful in describing ion regulation at the cellular length scale, it is unknown if they are valid at the subcellular level where volumes are small, ion numbers may fluctuate wildly, and biochemical heterogeneity is large. Here, we create a discrete, stochastic (DS) model of vesicular acidification to answer this question. We used this simplified model to analyze pH measurements of isolated vesicles containing single proton pumps and compared these results to solutions from a continuum, ordinary differential equations (ODE)-based model. Both models predict similar parameter estimates for the mean proton pumping rate, membrane permeability, etc., but, as expected, the ODE model fails to report on the fluctuations in the system. The stochastic model predicts that pH fluctuations decrease during acidification, but noise analysis of single-vesicle data confirms our finding that the experimental noise is dominated by the fluorescent dye, and it reveals no insight into the true noise in the proton fluctuations. Finally, we again use the reduced DS model explore the acidification of large, lysosome-like vesicles to determine how stochastic elements, such as variations in proton-pump copy number and cycling between on and off states, impact the pH setpoint and fluctuations around this setpoint