Grace Brannigan

Implicit solvent simulation models for biomembranes

Fully atomic simulation strategies are infeasible for the study of many processes of interest to membrane biology, biophysics and biochemistry. We review various coarse-grained simulation methodologies with special emphasis on methods and models that do not require the explicit simulation of water. Examples from our own research demonstrate that such models have potential for simulating a variety of biologically relevant phenomena at the membrane surface.

Solvent-free simulations of fluid membrane bilayers

A molecular level model for lipid bilayers is presented. Lipids are represented by rigid, asymmetric, soft spherocylinders in implicit solvent. A simple three parameter potential between pairs of lipids gives rise to a rich assortment of phases including (but not limited to) micelles, fluid bilayers, and gel-like bilayers. Monte Carlo simulations have been carried out to verify self-assembly, characterize the phases corresponding to different potential parametrizations, and to quantify the physical properties associated with those parameter sets corresponding to fluid bilayer behavior. The studied fluid bilayers have compressibility moduli in agreement with experimental systems, but display bending moduli at least three times larger than typical biological membranes without cholesterol.

The role of molecular shape in bilayer elasticity and phase behavior

A previously developed molecular level model for lipid bilayers [G. Brannigan and F. L. H. Brown, J. Chem. Phys. 120, 1059 (2004)] is extended to allow for variations in lipid length and simulations under constant surface tension conditions. The dependence of membrane elasticity on bilayer thickness is obtained by adjusting lipid length at constant temperature and surface tension. Additionally, bilayer fluidity at various lipid lengths is quantified by analysis of a length versus temperature phase diagram at vanishing tension. Regions of solid, gel-like (hexatic) and fluid bilayer behavior are established by identification of phase boundaries. The main melting transition is found to be density driven; the melting temperature scales inversely with lipid length since thermal expansion increases with lipid aspect ratio.

Composition dependence of bilayer elasticity

A previously developed molecular level model for homogeneous lipid bilayers [Brannigan and Brown, J. Chem. Phys 120, 1059 (2004)] is extended to allow for multiple lipid species. Monte Carlo simulations (including species exchange moves for efficient sampling) reveal a variety of mixing behaviors in binary systems. Two species are identified that maintain stable, randomly mixed fluid membranes at vanishing tension over all possible binary compositions. The thermal and elastic properties of membranes formed by these lipids are characterized over the full composition range. Equilibrium area at constant tension is nonmonotonic with respect to composition, but consistent with that of a quadratic mixture. In the constant tension ensemble, the bending rigidity of the bilayer is minimized at an intermediate composition. The observed functional form of bending rigidity vs composition is fit to a simple expression motivated by linear elasticity theory; this expression accounts for membrane heterogeneity through a single parameter.

A streamlined, general approach for computing ligand binding free energies and its application to GPCR-bound cholesterol

The theory of receptor-ligand binding equilibria has long been well-established in biochemistry, and was primarily constructed to describe dilute aqueous solutions. Accordingly, few computational approaches have been developed for making quantitative predictions of binding probabilities in environments other than dilute isotropic solution. Existing techniques, ranging from simple automated docking procedures to sophisticated thermodynamics-based methods, have been developed with soluble proteins in mind. Biologically and pharmacologically relevant protein-ligand interactions often occur in complex environments, including lamellar phases like membranes and crowded, nondilute solutions. Here, we revisit the theoretical bases of ligand binding equilibria, avoiding overly specific assumptions that are nearly always made when describing receptor-ligand binding. Building on this formalism, we extend the asymptotically exact Alchemical Free Energy Perturbation technique to quantifying occupancies of sites on proteins in a complex bulk, including phase-separated, anisotropic, or nondilute solutions, using a thermodynamically consistent and easily generalized approach that resolves several ambiguities of current frameworks. To incorporate the complex bulk without overcomplicating the overall thermodynamic cycle, we simplify the common approach for ligand restraints by using a single distance-from-bound-configuration (DBC) ligand restraint during AFEP decoupling from protein. DBC restraints should be generalizable to binding modes of most small molecules, even those with strong orientational dependence. We apply this approach to compute the likelihood that membrane cholesterol binds to known crystallographic sites on three GPCRs (β2-adrenergic, 5HT-2B, and μ-opioid) at a range of concentrations. Nonideality of cholesterol in a binary cholesterol:phosphatidylcholine (POPC) bilayer is characterized and consistently incorporated into the interpretation. We find that the three sites exhibit very different affinities for cholesterol: The site on the adrenergic receptor is predicted to be high affinity, with 50% occupancy for 1:109 CHOL:POPC mixtures. The sites on the 5HT-2B and μ-opioid receptor are predicted to be lower affinity, with 50% occupancy for 1:103 CHOL:POPC and 1:102 CHOL:POPC, respectively. These results could not have been predicted from the crystal structures alone.

Absolute Affinity Calculations for Cholesterol Binding to G-Protein Coupled Receptors (GPCR)

Cholesterol is an essential constituent of most eukaryotic plasma membranes, and is critical for native function of many membrane proteins, including pentameric ligand gated ion channels (pLGICs) and G-protein coupled receptors (GPCRs). GPCRs are a family of integral membrane proteins that play a critical role in signal transduction across the membrane and are estimated to be the target for more than a third of all drugs. Although the number of available crystal structures for GPCRs in complex with various agonists, antagonists, and G proteins has expanded rapidly, the physiological relevance of direct and indirect interactions of GPCRs with cholesterol and other lipids in mixed membranes is poorly understood. For instance, resolved cholesterol is a common feature of most GPCR crystal structures, indicating a potentially significant structural role. The ubiquity of the resolved cholesterol in GPCR structures, even across GPCRs with a range of cholesterol sensitivities, largely precludes interpretation of the directly bound cholesterol molecule in the context of known functional effects of cholesterol. In the simplest mechanism, differential affinities of cholesterol for the cholesterol binding site on a range of GPCRs could predict differential sensitivities, but testing such a mechanism is complicated by numerous challenges in experimental measurements of lipid binding affinity. We recently developed a framework for calculating absolute binding affinity of lipophilic ligands for transmembrane proteins, which we used to predict cholesterol occupation ratio of intersubunit cavities of GluCl, a eukaryotic pLGIC, at physiological membrane concentrations of cholesterol. Here we employ this approach to calculate absolute cholesterol binding free energies and estimate average binding site occupancies for a range of GPCRs.

Transmembrane Domain Packing in Cys-Loop Receptors: What Can we Learn from Prokaryotes?

The significance of large gaps in protein density observed in the cryo-EM structure (2BG9) of the nicotinic acetylcholine receptor (nAChR) transmembrane domain remains a pressing question. Although it was originally proposed that the gaps were filled with water, water-filled pockets are not stable under simulation, causing collapse of the transmembrane domain. Alternative explanations include the possibility that the gaps are filled with cholesterol or other lipid, as proposed by our group, or that the gaps are an artifact of the experimental method. Recent crystal structures of prokaryotic homologues, including GLIC, do not include such gaps, supporting the latter scenario. However, here we show through homology modeling that models of the nAChR based on GLIC still retain low protein density in the extracellular half of the TM domain, due to consistently smaller residue volume in that region of the nAChR compared to GLIC. Simulations of this model over the 100ns time scale also display collapse that increases amino acid density in this region of the protein, although for this model collapse largely proceeds by significant widening of the pore rather than reduction in the overall footprint. An analysis of residue volume, determined from sequence, is presented across identified prokaryotic, eukaryotic anionic, and eukaryotic cationic members of the pentameric ligand-gated ion channels family, demonstrating that residue volume has been consistently lost as channels become less primitive, and that a tightly-packed nAChR would require a substantially tighter packing of backbone helices than what is observed in prokaryotic channels.