Monte Carlo calculations of order parameter profiles in models of lipid-protein interactions in bilayers

The Monte Carlo method has been utilized to calculate lipid chain order parameters in model monomolecular layers (half-bilayers) containing several different model polypeptides. The systems all consist of a periodic array of identical cells, each containing 35 hydrocarbon chains and 1 "perturbant" (a small model polypeptide or protein). The lipid chains are each 10 CH2 subunits long, have one end constrained to lie in the bilayer plane, and interact via van der Waals forces between all subunits. The chains also interact with the perturbant via van der Waals forces. With standard Monte Carlo procedures order parameter profiles are calculated for chains that are close to the perturbant and for the nonneighboring chains. In order to examine a wide range of possibilities, several different model polypeptides are considered: (i) a rigid smooth cylinder, (ii) a cylinder with identical side chains at alpha-helical positions, (iii) a cylinder with nonidentical side chains at alpha-helical positions, and (iv) a cylinder identical with (ii) but which only extends about halfway through the monolayer. Although results differ for the different systems studied, in all cases only slight conformational differences between the bulk chains and the chains that are nearest the perturbants are found, and it is not possible to characterize the boundary chains as "more ordered" or "less ordered" than the nonboundary chains.     

Monte Carlo studies of lipid chains and gramicidin A in a model membrane

The Monte Carlo method has been used to simulate the equilibrium properties of a planar array of 94 saturated lipid chains and one monomer of Gramicidin A. Chains are free to move laterally in the layer plane and to change conformation via gauche rotations and long axis rotations in a continuum. All non-hydrogen atoms on chains and on the Gramicidin A monomer interact via 6-12 potentials, and periodic boundary conditions are imposed. Calculated results consist of order parameter profiles for C-14 and C-16 chains. Profiles are calculated for chains which are neighbors to the Gramicidin A molecule and for chains which are not neighbors to the peptide. The main conclusion is that the average conformations of the chains neighboring the Gramicidin A monomer are very similar to those of the bulk chains.     

Monte Carlo simulation of diffusion of adsorbed proteins

We present the results of three-dimensional lattice Monte Carlo simulations of protein diffusion on the liquid-solid interface in a wide temperature range including the most interesting temperatures (from slightly below T(f) and up to T(c), where T(f) and T(c) are the folding and collapse temperatures). For the model under consideration (27 monomers of two types), the temperature dependence of the diffusion coefficient is found to obey the Arrhenius law with the normal value (approximately 10(-2)-10(-3) cm(2)/s) of the preexponential factor. Proteins 2000;39:76-81.     

Monte Carlo simulation of lipid mixtures: finding phase separation.

The nonideal mixing of phosphatidylserine (PS) and phosphatidylcholine (PC) binary lipid mixtures was studied by computer simulation based on a model wherein the excess energy of mixing is divided between an electrostatic term and one adjustable term delta Em that includes all other nonideal interactions. The lateral distribution of the lipids and the energy of the mixtures were obtained by using Kawasaki relaxation in a canonical ensemble. The Gibbs free energies were calculated by Kirkwood's coupling parameter method. The simulation results are strongly dependent on simulation size for sizes smaller than about 1000 lipids. Nonideal interaction between lipids can result in large scale separation of lipid phases of different composition at reasonable delta Em values as well as clustering of like lipids. In plots of total Gibbs free energy of mixing versus PS mole fraction in PS/PC, the boundaries of the two phase region could be accurately determined. The electrostatic interaction influences cluster size and shape, and also the composition of phases in the two-phase region.     

Monte Carlo simulation of denaturation of adsorbed proteins

Denaturation of model proteinlike molecules at the liquid–solid interface is simulated over a wide temperature range by employing the lattice Monte Carlo technique. Initially, the molecule containing 27 monomers of two types (A and B) is assumed to be adsorbed in the native folded state (a 3 × 3 × 3 cube) so that one of its sides is in contact with the surface. The details of the denaturation kinetics are found to be slightly dependent on the choice of the side, but the main qualitative conclusions hold for all the sides. In particular, the kinetics obey approximately the conventional first-order law at T > T_c (T_c is the collapse temperature for solution). With decreasing temperature, below T_c but above T_f (T_f is the folding temperature for solution), deviations appear from the first-order kinetics. For the most interesting temperatures, that is, below T_f, the denaturation kinetics are shown to be qualitatively different from the conventional ones. In particular, the denaturation process occurs via several intermediate steps due to trapping in metastable states. Mathematically, this means that (i) the transition to the denatured state of a given molecule is nonexponential, and (ii) the denaturation process cannot be described by a single rate constant k_r. One should rather introduce a distribution of values of this rate constant (different values of k_r correspond to the transitions to the altered state via different metastable states). Proteins 30:168–176, 1998. © 1998 Wiley-Liss, Inc.     

Monte Carlo studies of lipid / water interfaces

The results of a series of numerical simulations of the aqueous interface near several types of lipid bilayer headgroups are presented. The Monte Carlo method was used to study 172 water molecules located between two lipid bilayers separated by 24.5 Å. The types of headgroups used in the studies include phosphorylcholine, -ethanolamine and -serine. The quantities calculated were molecular density, dipolar orientation and number of hydrogen bonds as functions of the distance from the interfacial regions. The data point out important differences in the organization of the interfacial water for each of the three different lipids.     

Experimental and Monte Carlo simulation studies of the thermodynamics of polyethyleneglycol chains grafted to lipid bilayers.

Experimental measurements of the affinity of binding of fluorescent acylated polyethyleneglycol (PEG) conjugates to bilayers containing varying levels of phosphatidylethanolamine-PEGs (PE-PEGs) have been combined with Monte Carlo simulations to investigate the properties of the polymer chains at a PEG-grafted lipid interface. The affinity of binding of such conjugates to large unilamellar phosphatidylcholine/phosphatidylethanolamine (9:1) vesicles decreases 27-fold as the size of the coupled PEG chain increases from 1 to 114 monomer units. Incorporation of increasing amounts of PE-PEG2000 or PE-PEG5000 into the vesicles progressively reduces the affinity of binding of acylpeptide-PEG2000 or -PEG5000 conjugates. Monte Carlo simulations of surfaces with grafted PEG chains revealed no significant dependence of several characteristic properties of the polymer chains, including the average internal energy per polymer and the radii of gyration, on the grafting density in the range examined experimentally. The average conformation of a surface-grafted PEG2000 or PEG5000 chain was calculated to be fairly extended even at low grafting densities, and the projected cross-sectional areas of the grafted PEG chains are considerably smaller than those predicted on the basis of the estimated Flory radius. The experimental variation of the binding affinity of acylated conjugates for bilayers containing varying mole fractions of PE-PEG2000 or -PEG5000 is well explained by expressions treating the surface-grafted PEG polymers either as a van der Waals gas or as a system of rigid discs described by scaled particle theory. From the combined results of our experimental and simulation studies we conclude that the grafted PEG chains exist in a "mushroom" regime throughout the range of polymer densities examined experimentally and that the diminished affinity of binding of acylated-PEG conjugates to bilayers containing PE-PEGs results from occlusion of the surface area accessible for conjugate binding by the mobile PE-PEG polymer chains.     

Monte Carlo simulation of protein-induced lipid demixing in a membrane with interactions derived from experiment

Lipid domain formation induced by annexin was investigated in mixtures of phosphatidylcholine (PC), phosphatidylserine (PS), and cholesterol (Chol), which were selected to mimic the inner leaflet of a eukaryotic plasma membrane. Annexins are ubiquitous and abundant cytoplasmic, peripheral proteins, which bind to membranes containing PS in the presence of calcium ions (Ca²⁺), but whose function is unknown. Prompted by indications of interplay between the presence of cholesterol in PS/PC mixtures and the binding of annexins, we used Monte Carlo simulations to investigate protein and lipid domain formation in these mixtures. The set of interaction parameters between lipids and proteins was assigned by matching experimental observables to corresponding variables in the calculations. In the case of monounsaturated phospholipids, the PS-PC and PC-Chol interactions are weakly repulsive. The interaction between protein and PS was determined based on experiments of annexin binding to PC/PS mixtures in the presence of Ca²⁺. Based on the proposal that PS and cholesterol form a complex in model membranes, a favorable PS-Chol interaction was postulated. Finally, protein-protein favorable interactions were also included, which are consistent with observations of large, two-dimensional, regular arrays of annexins on membranes. Those net interactions between pairs of lipids, proteins and lipids, and between proteins are all small, of the order of the average kinetic energy. We found that annexin a5 can induce formation of large PS domains, coincident with protein domains, but only if cholesterol is present.     

Oligomerization of integral membrane proteins under lipid peroxidation

Using polyacrylamide gel electrophoresis in the presence of Na-SDS, the oligomerization of membrane proteins of the retinal rod outer segments of the frog and the wall-eyed pollock and of rabbit skeletal muscle sarcoplasmic reticulum was studied. It was shown that under storage of the retinal rod outer segments the rhodopsin oligomerization is inhibited by the lipid peroxidation inhibitor--ionol. Similar oligomerization was observed under induction of lipid peroxidation in the membranes; the accumulation of the lipid peroxidation product--malonic dialdehyde--was accompanied by disappearance of the rhodopsin monomeric form in the outer segments. The cross-linking agent--glutaric dialdehyde--also causes oligomerization of the rhodopsins. Similar aggregation is also characteristic of the major protein of the sarcoplasmic reticulum fragments, i. e. Ca2+-dependent ATP-ase. Thus, one of the main changes in the protein content of biomembranes under lipid peroxidation is the oligomerization of integral proteins due to their interaction with bifunctional reagents, i. e. lipid peroxidation products.     

Reconstitution of membrane proteins. Spontaneous association of integral membrane proteins with preformed unilamellar lipid bilayers

We have developed a simple method for reconstituting pure, integral membrane proteins into phospholipid-protein vesicles. The method does not depend on use of detergents or sonication. It has been used successfully with three different types of integral membrane proteins: UDPglucuronosyltransferase (EC 2.4.1.17) from pig liver microsomes, cytochrome oxidase (EC 1.9.3.1) from pig heart, and bacteriorhodopsin from Halobacterium halobium. The method depends on preparing unilamellar vesicles of dimyristoylphosphatidylcholine (DMPC) that contain a small amount of myristate as fusogen. Under conditions that the vesicles of DMPC have the property of fusing, all of the above proteins incorporated into bilayers. Two events appear to be involved in forming the phospholipid-protein complexes. The first is a rapid insertion of all proteins into a small percentage of total vesicles. The second is slower but continued fusion of the remaining phospholipid-protein vesicles, or proteoliposomes, with small unilamellar vesicles of DMPC. This latter process was inhibited by conditions under which vesicles of DMPC themselves would not fuse. On the basis of proton pumping by bacteriorhodopsin and negative staining, the vesicles were unilamellar and large. The data suggest that insertion of the above integral membrane proteins into vesicles occurred independently of fusion between vesicles.     

Monte Carlo studies of the hydrocarbon region of lipid bilayers

We present the results of a Monte Carlo study of systems of hydrocarbon chains attached to a plane interface and interacting through hard core repulsive forces only. The chain-order parameters which we find in our studies are compared to experimental results (NMR and ESR). The role of “kink” states and the relevance of our studies to theoretical models are also discussed.     

Insertion and hairpin formation of membrane proteins: a Monte Carlo study.

Some particular effects of a lipid membrane on the partitioning and the concomitant folding processes of model proteins have been investigated using Monte Carlo methods. It is observed that orientational order and lateral density fluctuations of the lipid matrix stabilize the orientation of helical proteins and induce a tendency of spontaneous formation of helical hairpins for helices longer than the width of the membrane. The lateral compression of the lipids on a hairpin leads to the extrusion of a loop at the trans side of the membrane. The stability of the hairpin can be increased by the design of appropriate groups of hydrophilic and hydrophobic residues at the extruded loop. It is shown that in the absence of lipids the orientation of proteins is not stable and the formation of hairpins is absent. Some analogies between the formation of helical hairpins in membranes and the formation of hairpins in polymer liquid crystals are discussed. The simulations indicate that the insertion process follows a well-defined pattern of kinetic steps.     

Reconstitution of membrane proteins: sequential incorporation of integral membrane proteins into preformed lipid bilayers

Several integral membrane proteins can be inserted sequentially into preformed unilamellar vesicles (ULV's) composed of dimyristoylphosphatidylcholine (DMPC) and cholesterol in a gel phase. Thus, proteoliposomes of DMPC, cholesterol, and bacteriorhodopsin from Halobacterium halobium rapidly incorporate UDPglucuronosyltransferase (EC 2.4.1.17) from pig liver microsomes, cytochrome oxidase from beef heart mitochondria, and additional bacteriorhodopsin, added sequentially. This process of spontaneous incorporation can be regulated to produce complex artificial membranes that contain phospholipids and proteins at ratios (mol/mol) equivalent to what is found in biological membranes. The ability of the lipid-protein bilayers to incorporate additional integral membrane proteins is not affected by annealing of the proteoliposomes at 37 degrees C nor by the order of addition of the proteins. Bacteriorhodopsin-containing vesicles formed by the sequential addition of integral membrane proteins demonstrate light-driven proton pumping. Therefore, they have retained a vesicular structure. Vesicles containing one or two different proteins will fuse with each other at 21 degrees C or with ULV's devoid of proteins. Incorporation of bacteriorhodopsin or UDPglucuronosyltransferase into proteoliposomes containing DMPC, with or without cholesterol as impurity, also occurs above the phase transition for DMPC. The presence of a protein in a liquid-crystalline bilayer provides the necessary condition for promoting the spontaneous incorporation of other membrane proteins into preformed bilayers.     

Monte Carlo docking of oligopeptides to proteins.

A new two-step procedure has been developed for the docking of flexible oligopeptide chains of unknown conformation to static proteins of known structure. In the first step positions and conformations are sampled and the association energy minimized starting from an approximate preselected docking position. The resulting conformations are further optimized in the second step by a Metropolis Monte Carlo minimization, which optimizes each of these structures. The method has been tested on the HIV-1 aspartic proteinase complex with an inhibitor, whose crystallographic structure is known at 2.3 A resolution. Furthermore, the application of this method to the docking of the hendecapeptide 58-68 of the influenza A virus matrix protein to the HLA-A2 molecule produced results which are in agreement with experimental observations in identifying side chains critical for T cell recognition and residues responsible of MHC protein binding.     

A Monte Carlo model of fd and Pf1 coat proteins in lipid membranes.

A Monte Carlo Dynamics simulation was used to investigate the behavior of filamentous bacteriophage coat proteins in a model membrane environment. Our simulation agrees with the previous experimental observations that despite the low sequence similarity between the major coat proteins of Pf1 and fd bacteriophages, their structure in the membrane environment is very similar. These results support the hypothesis that the hydrophobic effect exerts an important influence on membrane protein structure. The model may also be used for modeling the insertion and transport processes in protein-membrane systems. The example of fd protein was also used as a test of sensitivity of our model to temperature, thickness of the hydrocarbon phase, and simulation time. In all cases, the results were independent (over the tested range) of the particular values of the parameters.     

Overexpression of mammalian integral membrane proteins for structural studies

Recent successes in the determination of atomic resolution structures of integral membrane proteins have relied on purifying the proteins from abundant natural sources. In contrast, the majority of mammalian receptors, ion channels and transporters need to be overexpressed to obtain sufficient material for structural studies. This has often proved to be very difficult. Overexpression studies on a wide range of mammalian membrane proteins have shown that a few can be expressed functionally in bacteria, but many others require an insect or mammalian cell host for activity or high level expression. The serotonin transporter, which has been expressed in all the major hosts available, is a good example that has given insights into the problem of overexpressing mammalian membrane proteins for structural studies.     

Efficient Monte Carlo method for simulation of fluctuating conformations of native proteins

A powerful Monte Carlo method is described to simulate thermal conformational fluctuations in native proteins by using an empirical conformational energy function in which bond lengths and bond angles are kept fixed and only dihedral angles are independent variables. In this method, collective variables corresponding to eigenvectors of the second-derivative matrix of the energy function at its minimum point are scaled according to corresponding eigenvalues in such a way that the energy function in terms of the scaled collective variables is isotropic at the minimum point. Simulation is carried out with an isotropic step size in the space of these scaled collective variables. This simulation method is applied to a small protein, bovine pancreatic trypsin inhibitor (BPTI), and its model harmonic system defined by a quadratic energy function with the same second-derivative matrix as that of BPTI at its minimum point. Efficiency of the simulation method with an isotropic step size in the space of the scaled collective variables is found to be about 500–50 times greater than the conventional method with with an isotropic step in the space of the usual nonscaled variables. One step of this new method generates conformational changes that occur in the real-time range of 0.05 ps. In a record of 5 × 10⁵ step simulation, the BPTI molecule is observed to migrate beyond a single minimum-energy region.