Olaf S. Andersen

Energetics of Inclusion-Induced Bilayer Deformations

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning proteins perturb the structure of the surrounding bilayer. This coupling between the protein and the bilayer arises from hydrophobic interactions between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between the length of the proteins hydrophobic exterior surface and the average thickness of the bilayers hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deformation is described as the sum of three contributions: compression-expansion, splay-distortion, and surface tension. When evaluating the interdependence among the energy components, one modulus renormalizes the other: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion energy. The surface tension contribution always is negligible in thin solvent-free bilayers. When evaluating the energy per unit distance (away from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion component is more prominent further away from the boundary. Despite this complexity, the bilayer deformation energy in many cases can be described by a linear spring formalism. The results show that, for a protein embedded in a membrane with an initial hydrophobic mismatch of only 1 A, an increase in hydrophobic mismatch to 1.3 A can increase the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.

Energetics of ion conduction through the gramicidin channel

The free energy governing K+ conduction through gramicidin A channels is characterized by using over 0.1 μs of all-atom molecular dynamics simulations with explicit solvent and membrane. The results provide encouraging agreement with experiments and insights into the permeation mechanism. The free energy surface of K+, as a function of both axial and radial coordinates, is calculated. Correcting for simulation artifacts due to periodicity and the lack of hydrocarbon polarizability, the calculated single-channel conductance for K+ ions is 0.8 pS, closer to experiment than any previous calculation. In addition, the estimated single ion dissociation constants are within the range of experimental determinations. The relatively small free energy barrier to ion translocation arises from a balance of large opposing contributions from protein, single-file water, bulk electrolyte, and membrane. Mean force decomposition reveals a remarkable ability of the single-file water molecules to stabilize K+ by –40 kcal/mol, roughly half the bulk solvation free energy. The importance of the single-file water confirms the conjecture of Mackay et al. [Mackay, D. H. J., Berens, P. H., Wilson, K. R. & Hagler, A. T. (1984) Biophys. J. 46, 229–248]. Ion association with the channel involves gradual dehydration from approximately six to seven water molecules in the first shell, to just two inside the narrow pore. Ion permeation is influenced by the orientation of the single-file water column, which can present a barrier to conduction and give rise to long-range coupling of ions on either side of the pore. Small changes in the potential function, including contributions from electronic polarization, are likely to be sufficient to obtain quantitative agreement with experiments.

Bilayer-dependent inhibition of mechanosensitive channels by neuroactive peptide enantiomers

The peptide GsMTx4, isolated from the venom of the tarantula Grammostola spatulata, is a selective inhibitor of stretch-activated cation channels (SACs). The mechanism of inhibition remains unknown; but both GsMTx4 and its enantiomer, enGsMTx4, modify the gating of SACs, thus violating a trademark of the traditional lock-and-key model of ligand–protein interactions. Suspecting a bilayer-dependent mechanism, we examined the effect of GsMTx4 and enGsMTx4 on gramicidin A (gA) channel gating. Both peptides are active, and the effect increases with the degree of hydrophobic mismatch between bilayer thickness and channel length, meaning that GsMTx4 decreases the energy required to deform the boundary lipids adjacent to the channel. GsMTx4 decreases inward SAC single-channel currents but has no effect on outward currents, suggesting it is located within a Debye length of the outer vestibule of the SACs, but significantly farther from the inner vestibule. Likewise, GsMTx4 decreases gA single-channel currents. Our results suggest that modulation of membrane proteins by amphipathic peptides—mechanopharmacology—involves not only the protein itself but also the surrounding lipids. The surprising efficacy of the d form of GsMTx4 peptide has important therapeutic implications, because d peptides are not hydrolysed by endogenous proteases and may be administered orally.

Lipid bilayer regulation of membrane protein function: gramicidin channels as molecular force probes

Membrane protein function is regulated by the host lipid bilayer composition. This regulation may depend on specific chemical interactions between proteins and individual molecules in the bilayer, as well as on non-specific interactions between proteins and the bilayer behaving as a physical entity with collective physical properties (e.g. thickness, intrinsic monolayer curvature or elastic moduli). Studies in physico-chemical model systems have demonstrated that changes in bilayer physical properties can regulate membrane protein function by altering the energetic cost of the bilayer deformation associated with a protein conformational change. This type of regulation is well characterized, and its mechanistic elucidation is an interdisciplinary field bordering on physics, chemistry and biology. Changes in lipid composition that alter bilayer physical properties (including cholesterol, polyunsaturated fatty acids, other lipid metabolites and amphiphiles) regulate a wide range of membrane proteins in a seemingly non-specific manner. The commonality of the changes in protein function suggests an underlying physical mechanism, and recent studies show that at least some of the changes are caused by altered bilayer physical properties. This advance is because of the introduction of new tools for studying lipid bilayer regulation of protein function. The present review provides an introduction to the regulation of membrane protein function by the bilayer physical properties. We further describe the use of gramicidin channels as molecular force probes for studying this mechanism, with a unique ability to discriminate between consequences of changes in monolayer curvature and bilayer elastic moduli.

Regulation of Sodium Channel Function by Bilayer Elasticity: The Importance of Hydrophobic Coupling. Effects of Micelle-forming Amphiphiles and Cholesterol

Membrane proteins are regulated by the lipid bilayer composition. Specific lipid–protein interactions rarely are involved, which suggests that the regulation is due to changes in some general bilayer property (or properties). The hydrophobic coupling between a membrane-spanning protein and the surrounding bilayer means that protein conformational changes may be associated with a reversible, local bilayer deformation. Lipid bilayers are elastic bodies, and the energetic cost of the bilayer deformation contributes to the total energetic cost of the protein conformational change. The energetics and kinetics of the protein conformational changes therefore will be regulated by the bilayer elasticity, which is determined by the lipid composition. This hydrophobic coupling mechanism has been studied extensively in gramicidin channels, where the channel–bilayer hydrophobic interactions link a “conformational” change (the monomer↔dimer transition) to an elastic bilayer deformation. Gramicidin channels thus are regulated by the lipid bilayer elastic properties (thickness, monolayer equilibrium curvature, and compression and bending moduli). To investigate whether this hydrophobic coupling mechanism could be a general mechanism regulating membrane protein function, we examined whether voltage-dependent skeletal-muscle sodium channels, expressed in HEK293 cells, are regulated by bilayer elasticity, as monitored using gramicidin A (gA) channels. Nonphysiological amphiphiles (β-octyl-glucoside, Genapol X-100, Triton X-100, and reduced Triton X-100) that make lipid bilayers less “stiff”, as measured using gA channels, shift the voltage dependence of sodium channel inactivation toward more hyperpolarized potentials. At low amphiphile concentration, the magnitude of the shift is linearly correlated to the change in gA channel lifetime. Cholesterol-depletion, which also reduces bilayer stiffness, causes a similar shift in sodium channel inactivation. These results provide strong support for the notion that bilayer–protein hydrophobic coupling allows the bilayer elastic properties to regulate membrane protein function.

Spring Constants for Channel-Induced Lipid Bilayer Deformations Estimates Using Gramicidin Channels

Hydrophobic interactions between a bilayer and its embedded membrane proteins couple protein conformational changes to changes in the packing of the surrounding lipids. The energetic cost of a protein conformational change therefore includes a contribution from the associated bilayer deformation energy (DeltaGdef0), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies based on an elastic liquid-crystal model of the bilayer deformation show that DeltaGdef0 should be quantifiable by a phenomenological linear spring model, in which the bilayer mechanical characteristics are lumped into a single spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurements of the spring constant and thereby evaluate quantitatively the DeltaGdef0 associated with protein conformational changes. Gramicidin channels can be used as such reporter proteins because the channels form by the transmembrane assembly of two nonconducting monomers. The monomerleft arrow over right arrow dimer reaction thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant describing the channel-induced bilayer deformation by examining how DeltaGdef0 varies as a function of a mismatch between the hydrophobic channel length and the unperturbed bilayer thickness. We show this is possible by analyzing experimental studies on the relation between bilayer thickness and gramicidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclusion-induced bilayer deformations using independently measured material constants.

Models of permeation in ion channels

Ion channels are formed by specific proteins embedded in the cell membrane and provide pathways for fast and controlled flow of selected ions down their electrochemical gradient. This activity generates action potentials in nerves, muscles and other excitable cells, and forms the basis of all movement, sensation and thought processes in living beings. While the functional properties of ion channels are well known from physiological studies, lack of structural knowledge has hindered development of realistic theoretical models necessary for understanding and interpretation of these properties. Recent determination of the molecular structures of potassium and mechanosensitive channels from x-ray crystallography has finally broken this impasse, heralding a new age in ion channel studies where study of structure– function relationships takes a central stage. In this paper, we present a critical review of various approaches to modelling of ion transport in membrane channels, including continuum theories, Brownian dynamics, and classical and ab initio molecular dynamics. Strengths and weaknesses of each approach are discussed and illustrated with applications to some specific ion channels.

On the Importance of Atomic Fluctuations, Protein Flexibility, and Solvent in Ion Permeation

Proteins, including ion channels, often are described in terms of some average structure and pictured as rigid entities immersed in a featureless solvent continuum. This simplified view, which provides for a convenient representation of the proteins overall structure, incurs the risk of deemphasizing important features underlying protein function, such as thermal fluctuations in the atom positions and the discreteness of the solvent molecules. These factors become particularly important in the case of ion movement through narrow pores, where the magnitude of the thermal fluctuations may be comparable to the ion pore atom separations, such that the strength of the ion channel interactions may vary dramatically as a function of the instantaneous configuration of the ion and the surrounding protein and pore water. Descriptions of ion permeation through narrow pores, which employ static protein structures and a macroscopic continuum dielectric solvent, thus face fundamental difficulties. We illustrate this using simple model calculations based on the gramicidin A and KcsA potassium channels, which show that thermal atomic fluctuations lead to energy profiles that vary by tens of kcal/mol. Consequently, within the framework of a rigid pore model, ion-channel energetics is extremely sensitive to the choice of experimental structure and how the space-dependent dielectric constant is assigned. Given these observations, the significance of any description based on a rigid structure appears limited. Creating a conducting channel model from one single structure requires substantial and arbitrary engineering of the model parameters, making it difficult for such approaches to contribute to our understanding of ion permeation at a microscopic level.

Are MD-PhD Programs Meeting Their Goals? An Analysis of Career Choices Made by Graduates of 24 MD-PhD Programs

Purpose MD-PhD training programs provide an integrated approach for training physician-scientists. The goal of this study was to characterize the career path taken by MD-PhD program alumni during the past 40 years and identify trends that affect their success. Method In 2007-early 2008, 24 programs enrolling 43% of current trainees and representing half of the National Institutes of Health-funded MD-PhD training programs submitted anonymous data on 5,969 current and former trainees. Results The average program enrolled 90 trainees, required 8.0 years to complete, and had an attrition rate of 10%. Nearly all (95%) of those who graduated entered residencies. Most (81%) were employed in academia, research institutes, or industry; 16% were in private practice. Of those in academia, 82% were doing research and at least 61% had identifiable research funding. Whereas two-thirds devoted more than 50% effort to research, only 39% devoted more than 75% effort. Many with laboratory-based PhDs reported doing clinical, as well as basic and translational, research. Emerging trends include decreasing numbers of graduates who forego residencies or hold primary appointments in nonclinical departments, increasing time to graduation, and expanding residency choices that include disciplines historically associated with clinical practice rather than research. Conclusions Most MD-PhD program graduates follow career paths generally consistent with their training as physician-scientists. However, the range of their professional options is broad. Further thought should be given to designing their training to anticipate their career choices and maximize their likelihood of success as investigators.

Gramicidin Channel Kinetics under Tension

We have measured the effect of tension on dimerization kinetics of the channel-forming peptide gramicidin A. By aspirating large unilamellar vesicles into a micropipette electrode, we are able to simultaneously monitor membrane tension and electrical activity. We find that the dimer formation rate increases by a factor of 5 as tension ranges from 0 to 4 dyn/cm. The dimer lifetime also increases with tension. This behavior is well described by a phenomenological model of membrane elasticity in which tension modulates the mismatch in thickness between the gramicidin dimer and membrane.