Electroelastic coupling between membrane surface fluctuations and membrane-embedded charges: continuum multidielectric treatment

Heterogeneous Dielectric Implicit Membrane Model for the Calculation of MMPBSA Binding Free Energies

Membrane-bound protein receptors are a primary biological drug target, but the computational analysis of membrane proteins has been limited. In order to improve molecular mechanics Poisson-Boltzmann surface area (MMPBSA) binding free energy calculations for membrane protein-ligand systems, we have optimized a new heterogeneous dielectric implicit membrane model, with respect to free energy simulations in explicit membrane and explicit water, and implemented it into the Amber software suite. This new model supersedes our previous uniform, single dielectric implicit membrane model by allowing the dielectric constant to vary with depth within the membrane. We calculated MMPBSA binding free energies for the human purinergic platelet receptor (P2Y₁₂R) and two of the muscarinic acetylcholine receptors (M2R and M3R) bound to various antagonist ligands using both membrane models, and we found that the heterogeneous dielectric membrane model has a stronger correlation with experimental binding affinities compared to the older model under otherwise identical conditions. This improved membrane model increases the utility of MMPBSA calculations for the rational design and improvement of future drug candidates.

Coarse-grained model of titrating peptides interacting with lipid bilayers

Molecular-level computer simulations of peptide aggregation, translocation, and protonation at and in biomembranes are impeded by the large time and length scales involved. We present a computationally efficient, coarse-grained, and solvent-free model for the interaction between lipid bilayers and peptides. The model combines an accurate description of mechanical membrane properties with a new granular representation of the dielectric mismatch between lipids and the aqueous phase. All-atom force fields can be easily mapped onto the coarse-grained model, and parameters for coarse-grained monopeptides accurately extrapolate to membrane permeation free energies for the corresponding dipeptides and tripeptides. Acid-base equilibria of titratable amino acid residues are further studied using a constant-pH ensemble, capturing protonation state changes upon membrane translocation. Important differences between histidine, lysine, and arginine are observed, which are in good agreement with experimental observations.

Changes in lipid membrane mechanics induced by di- and tri-phenyltins

Organotin compounds, being biologically active, affect a variety of cellular functions due to their ability to accumulate in and penetrate biological membranes. These compounds influence the distribution of electrostatic charges, alter organization, disrupt molecular dynamics and change mechanical properties of biological membranes. It was found that the membrane/water partition coefficient equals 4, a value significantly higher than octanol/water partition coefficient. In addition, the effect of di- and tri-phenyltin chlorides on the mechanics of model lipid membranes was measured for the first time. It has been determined that phenyltins affect the global model lipid bilayer properties by reducing the membrane expansion modulus, when measured using micromanipulation technique, and elevating the bending rigidity coefficient of the lipid bilayer, as determined with the flickering noise spectroscopy. In addition, the elevated water permeability shows that phenyltins also cause the local defects formation in the lipid bilayer, i.e. lipid pores. These data shows that phenyltins may interfere indirectly with variety cellular processes by altering non-specifically the entire cellular membrane system. Accordingly, when phenyltins are added to macrophages in culture, they inflict massive alterations of cell morphology and interfere with membrane-associated processes, as visualized using fluorescence labelling of selected subcellular compartments.

Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

Models of membrane electrostatics

Formulas are derived for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the distribution of ions near cell membranes more accurately than by using Poisson-Boltzmann theory or its linearized version. Here I use them to discuss the electric field of a uniformly charged membrane, the image charges of an ion, the distribution of salt ions near a charged membrane, the energy of a zwitterion near a lipid slab, and the effect of including the phosphate head groups as thin layers of high electric permittivity.

The role of membrane thickness in charged protein-lipid interactions

Charged amino acids are known to be important in controlling the actions of integral and peripheral membrane proteins and cell disrupting peptides. Atomistic molecular dynamics studies have shed much light on the mechanisms of membrane binding and translocation of charged protein groups, yet the impact of the full diversity of membrane physico-chemical properties and topologies has yet to be explored. Here we have performed a systematic study of an arginine (Arg) side chain analog moving across saturated phosphatidylcholine (PC) bilayers of variable hydrocarbon tail length from 10 to 18 carbons. For all bilayers we observe similar ion-induced defects, where Arg draws water molecules and lipid head groups into the bilayers to avoid large dehydration energy costs. The free energy profiles all exhibit sharp climbs with increasing penetration into the hydrocarbon core, with predictable shifts between bilayers of different thickness, leading to barrier reduction from 26 kcal/mol for 18 carbons to 6 kcal/mol for 10 carbons. For lipids of 10 and 12 carbons we observe narrow transmembrane pores and corresponding plateaus in the free energy profiles. Allowing for movements of the protein and side chain snorkeling, we argue that the energetic cost for burying Arg inside a thin bilayer will be small, consistent with recent experiments, also leading to a dramatic reduction in pK(a) shifts for Arg. We provide evidence that Arg translocation occurs via an ion-induced defect mechanism, except in thick bilayers (of at least 18 carbons) where solubility-diffusion becomes energetically favored. Our findings shed light on the mechanisms of ion movement through membranes of varying composition, with implications for a range of charged protein-lipid interactions and the actions of cell-perturbing peptides. This article is part of a Special Issue entitled: Membrane protein structure and function.