Molecular mechanics of the formation of cholic acid micelles

The molecular mechanics of cholic acid micelle formation were simulated using the Sybyl energy minimization program (MAXIMINI), developed by Tripos Associates, interfaced with micro-Vax.Before energy minimization, the molecular dimensions of the cholic acid dodecamer C₂₄H₄₀O₆, in terms of the unit cell axes a, b, and c in the cubic crystal class, had values of 13, 18, and 6.7 Å, respectively. After energy minimization, at 9370 kcalsl dodecamer, these values had increased to 21.6, 42.8 and 20.9 Å. At an energy minimization level of 21 626 kcalsl dodecamer, the micelle structure is stabilized by Hydrophobic interaction, forming distinct horizontal channels along the b-axis, directing the carboxyl and hydroxyl groups toward the surface. These structural changes remain relatively constant as the process of energy minimization continues, down to the lowest energy level we considered, 9370 kcalsl dodecamer. The cholic acid layers are highly dissimilar, forming channels of irregular size and shape in a somewhat helical structure. The carboxyl groups and phenanthrene rings are in a puckered orientation, which permits compact packing of the sandwiched multilayers.From the dimension of the channels, it is apparent that guest molecules, such as phospholipid, cholesterol, or inorganic calcium, can be incorporated into the micelle through more than one channel, forming inclusion complexes, such as gallstones.     

Inclusion of solvation free energy with molecular mechanics energy: alanyl dipeptide as a test case.

A combined force field of molecular mechanics and solvation free energy is tested by carrying out energy minimization and molecular dynamics on several conformations of the alanyl dipeptide. Our results are qualitatively consistent with previous experimental and computational studies, in that the addition of solvation energy stabilizes the C5 conformation of the alanyl dipeptide relative to the C7.     

New methodology for computer-aided modelling of biomolecular structure and dynamics. 2. Local deformations and cycles

A new methodology for the conformational modelling of biomolecular systems (1) is extended to local deformations of chain molecules and to flexible molecular rings. It is shown that these two cases may be reduced to considering an equivalent molecular model with a regular tree-like topology. A simple procedure is developed to analyze any flexible rings (the five- and six-membered sugar rings of carbohydrates and nucleic acids, in particular) and local deformation regions by energy minimization. Dynamic equations are also derived for such molecular systems. As a result, a unified approach is proposed for the efficient energy minimization and simulation of dynamic behavior of multimolecular systems having any set of variable internal coordinates, local deformation regions and cycles. Advantages and domains of applicability of the approach are discussed.     

The combinatorial distance geometry method for the calculation of molecular conformation. II. Sample problems and computational statistics

The performance of a branch and bound algorithm for molecular energy minimization is evaluated on a variety of test problems. Although not at present efficient enough for use in most practical situations, we show that it has distinct advantages over more conventional methods of global minimization. In addition, this study illustrates the technique on which the present algorithm is based, and the problems which must be overcome in developing an efficient algorithm based on similar principles.     

New Methodology for Computer-Aided Modelling of Biomolecular Structure and Dynamics 2. Local Deformations and Cycles

Abstract

A new methodology for the conformational modelling of biomolecular systems (1) is extended to local deformations of chain molecules and to flexible molecular rings. It is shown that these two cases may be reduced to considering an equivalent molecular model with a regular tree-like topology. A simple procedure is developed to analyze any flexible rings (the five- and six-membered suguar rings of carbohydrates and nucleic acids, in particular) and local deformation regions by energy minimization. Dynamic equations are also derived for such molecular systems. As a result, a unified approach is proposed for the efficient energy minimization and simulation of dynamic behavior of multimolecular systems having any set of variable internal coordinates, local deformation regions and cycles. Advantages and domains of applicability of the approach are discussed.     

Conformational analysis of phosphatides: Mapping and minimization of the intramolecular energy

Empirical intramolecular energy calculations were carried out on molecular fragments related to phosphatides in order to find the preferred conformations. The energy was mapped as a function of several pairs of torsional angles in progressively larger molecular fragments, with energy minimization being carried out at each map point with respect to other significant variables. The energy mapping results were used as starting points for energy minimization on diheptanoyl L-α-phosphatidic acid-C, which consisted of the named molecule plus a carbon atom attached to one of the phosphate oxygens. It was found that there are 6 pairs of values for 2 of the torsional angles at the 3-way branch point in the glyceryl group which give sterically acceptable conformations; only 4 of these are compatible with lipid bilayer structure in that they can give a parallel arrangement of the acyl chains. The several acceptable conformations of the phosphate and acyl ester groups within each of these conformational classes are enumerated. The results obtained may be used as a guide for further experimental and theoretical work on phosphatide structures.     

Refining the structure of the strongly bound actin-myosin complex by protein docking

The structure of the strongly bound complex of the globular myosin head and F-actin is a key for understanding some important details of the mechanism of the actin-myosin motor. Current knowledge about the structure is based on the docking of known atomic structures of actin and myosin heads into low-resolution EM electron density maps. To refine the structure, we suggested a new approach based on energy minimization using the ICM-Pro software. The minimization includes rigid-body movement of protein backbone and side chain optimization on the protein interface. Our best model structure is similar to that obtained from EM. It also provides the highest calculated interaction energy and agrees with a number of mutagenesis experiments. Using the structure, we suggest molecular explanations for actin activation of product release from myosin and actin-induced myosin dissociation.     

Visualization of energetics and conformations from molecular computer simulations

The quantity of data generated from molecular dynamics simulations and energy minimizations of macromolecules is overwhelming. It is an arduous task to extract the relevant and interesting information from the numerous coordinate sets produced. To help solve this problem, the authors have developed a method to aid the visualization of the relevant information from the simulations. This approach combines animation of the results on a high performance graphics device, such as the PS300, with colour-coded atoms based on changes in energy or conformation. The method will be illustrated using as examples: the molecular mechanics minimization of a nonapeptide, the molecular dynamics simulation of the protein myoglobin, including the analysis of the motion of helices during a 300ps trajectory, and changes in sugar puckering that occur during the molecular dynamics simulation of a DNA oligomer. The method is also applicable for analysing energy components and conformational properties of a fixed conformation.     

Molecular mechanics analysis of inhibitor binding to HIV-1 protease.

Crystallographic structures of HIV protease with three different peptide-mimetic inhibitors were subjected to energy minimization using molecular mechanics, the minimized structures analyzed and the inhibitor binding energies calculated. Partial charge assignment for the hydrogen bonded catalytic aspartic acids, Asp25 and -25', was in good agreement with charge calculations using semi-empirical molecular orbital methods. Root mean square deviations on minimization were small and similar for both subunits in the protease dimer. The surface loops, which had the largest B factors, changed most on minimization; the hydrophobic core and the inhibitor binding site showed little change. The distance-dependent dielectric of D(r) = 4r was found to be preferable to D(r) = r. Distance restraints were applied for the intermolecular hydrogen bonds to maintain the conformation of the inhibitor binding site. Using the dielectric of D(r) = 4r, the calculated interaction energy of the three inhibitors with the protease ranged from -53 to -56 kcal/mol. The psi groups of the inhibitors were changed to add or remove a 'transition state analogue' hydroxyl group, and the loss in energy on the removal of this group was calculated to be 0.9-1.7 kcal/mol. This would represent 19-36% of the total measured difference in binding energy between the inhibitors JG365 and MVT-101.     

Molecular modeling of proteins: a strategy for energy minimization by molecular mechanics in the AMBER force field.

Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly alpha-helical) and cardiotoxin (mostly beta-sheet and beta-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70-80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T4 lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (less than 0.3 A root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of 60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation.(ABSTRACT TRUNCATED AT 400 WORDS)     

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly, i.e., no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally, we show that when these structures are used as the initial point of a molecular dynamics energy minimization process, the correct native folds are recovered with high probability.     

Thermitase, a thermostable subtilisin: comparison of predicted and experimental structures and the molecular cause of thermostability

The Subtilisin family of proteases has four members of known sequence and structure: subtilisin Carlsberg, Subtilisin novo, proteinase K, and thermitase. Using thermitase as a test case, we ask two questions. How good are methods for model building a three-dimensional structure of a protein based on sequence homology to a known structure? And what are the molecular causes of thermostability? First, we compare predicted models of thermitase, refined by energy minimization and varied by molecular dynamics, with the preliminary crystal structure. The predictions work best in the conserve structural core and less well in seven loop regions involving insertions and deletions relative to Subtilisin. Here, variation of loop regions by molecular dynamics simulation in vacuo followed by energy minimization does not improve the prediction since we find no correlation between in vacuo energy and correctness of structure when comparing local energy minima. Second, in order to identify the molecular case of thermostability we confront hypotheses erived by calculation of the details of interatomic interactions with inactivation experiments. As a result, we can exclude salt bridges and hydrophobic interactions as main cause of thermostability. Based on a combination of theoretical and experimental evidence, the unusually tight binding of calcium by thermitase emerges as the most likely single influence responsible for its increased thermostability.     

Characterization by NMR and molecular modeling of the binding of polyisoprenols and polyisoprenyl recognition sequence peptides: 3D structure of the complexes reveals sites of specific interactions

The objective of these studies was to test the hypothesis that proteins that contain potential polyisoprenyl recognition sequences (PIRSs) in their transmembrane-spanning domain can bind to the polyisoprenyl (PI) glycosyl carrier lipids undecaprenyl phosphate (C55-P) and dolichyl phosphate (C95-P). A number of prokaryotic and eukaryotic glycosyltransferases that utilize PI coenzymes contain a conserved PIRS postulated to be the active PI binding domain. To study this problem, we first determined the 3D structure of a PIRS peptide, NeuE, by homonuclear 2D 1H-nuclear magnetic resonance (NMR) spectroscopy. Experimentally generated distance constraints derived from nuclear Overhauser enhancement and torsion angle constraints derived from coupling constants were used for restrained molecular dynamics and energy minimization calculations. Molecular models of the NeuE peptide were built based on calculations of energy minimization using the DGII program NMRchitect. 3D models of dolichol (C95) and C95-P were built based on our 2D 1H-NMR nuclear Overhauser enhancement spectroscopy (NOESY) results and refined by energy minimization with respect to all atoms using the AMBER (assisted modeling with energy refinements) force field. Our energy minimization studies were carried out on a conformational model of dolichol that was originally derived from small-angle X-ray scattering and molecular mechanics methods. These results revealed that the PIs are conformationally nearly identical tripartite molecules, with their three domains arranged in a coiled, helical structure. Analyses of the intermolecular cross-peaks in the 2D NOESY spectra of PIRS peptides in the presence of PIs confirmed a highly specific interaction and identified key contact amino acids in the NeuE peptide that constituted a binding motif for interacting with the PIs. These studies also showed that subtle conformational changes occurred within both the PIs and the NeuE peptide after binding. 3D structures of the resulting molecular complexes revealed that each PI could bind more than one PIRS peptide. These studies thus represent the first evidence for a direct physical interaction between specific contact amino acids in the PIRS peptides and the PIs and supports the hypothesis of a bifunctional role for the PIs. The central idea is that these superlipids may serve as a structural scaffold to organize and stabilize in functional domains PIRS-containing proteins within multiglycosyltransferase complexes that participate in biosynthetic and translocation processes.     

Substrate binding and catalytic mechanism in phospholipase C from Bacillus Cereus: A molecular mechanics and molecular dynamics study

For the first time a consistent catalytic mechanism of phospholipase C from Bacillus cereus is reported based on molecular mechanics calculations. We have identified the position of the nucleophilic water molecule, which is directly involved in the hydrolysis of the natural substrate, phosphatidylcholine, in phospholipase C. This catalytically essential water molecule, after being activated by an acidic residue (Asp55), performs the nucleophilic attack on the phosphorus atom in the substrate, leading to a trigonal bipyramidal pentacoordinated intermediate (and structurally similar transition state). The subsequent collapse of the intermediate, regeneration of the enzyme, and release of the products has to involve a not yet identified second water molecule. The catalytic mechanism reported here is based on a series of molecular mechanics calculations. First, the x-ray structure of phospholipase C from B. cereus including a docked substrate molecule was subjected to a stepwise molecular mechanics energy minimization. Second, the location of the nucleophilic water molecule in the active site of the fully relaxed enzyme–substrate complex was determined by evaluation of nonbonded interaction energies between the complex and a water molecule. The nucleophilic water molecule is positioned at a distance (3.8 Å) from the phosphorus atom in the substrate, which is in good agreement with experimentally observed distances. Finally, the stability of the complex between phospholipase C, the substrate, and the nucleophilic water molecule was verified during a 100 ps molecular dynamics simulation. During the simulation the substrate undergoes a conformational change, but retains its localization in the active site. The contacts between the enzyme, the substrate, and the nucleophilic water molecule display some fluctuations, but remain within reasonable limits, thereby confirming the stability of the enzyme–substrate–water complex. The protocol developed for energy minimization of phospholipase C containing three zinc ions located closely together at the bottom of the active site cleft is reported in detail. In order to handle the strong electrostatic interactions in the active site realistically during energy minimization, delocalization of the charges from the three zinc ions was considered. Therefore, quantum mechanics calculations on the zinc ions and the zinc-coordinating residues were carried out prior to the molecular mechanics calculations, and two different sets of partial atomic charges (MNDO-Mulliken and AM1-ESP) were applied. After careful assignment of partial atomic charges, a complete energy minimization of the protein was carried out by a stepwise procedure without explicit solvent molecules. Energy minimization with either set of charges yielded structures, which were very similar both to the x-ray structure and to each other, although using AM1-ESP partial atomic charges and a dielectric constant of 4, yielded the best protein structure. © 1997 John Wiley and Sons, Inc. Biopoly 42: 319–336, 1997     

A simple reference state makes a significant improvement in near-native selections from structurally refined docking decoys

Near-native selections from docking decoys have proved challenging especially when unbound proteins are used in the molecular docking. One reason is that significant atomic clashes in docking decoys lead to poor predictions of binding affinities of near native decoys. Atomic clashes can be removed by structural refinement through energy minimization. Such an energy minimization, however, will lead to an unrealistic bias toward docked structures with large interfaces. Here, we extend an empirical energy function developed for protein design to protein-protein docking selection by introducing a simple reference state that removes the unrealistic dependence of binding affinity of docking decoys on the buried solvent accessible surface area of interface. The energy function called EMPIRE (EMpirical Protein-InteRaction Energy), when coupled with a refinement strategy, is found to provide a significantly improved success rate in near native selections when applied to RosettaDock and refined ZDOCK docking decoys. Our work underlines the importance of removing nonspecific interactions from specific ones in near native selections from docking decoys.     

A classical molecular approach to computer simulation of biological sorting

Steinberg's theory of sorting is modified by replacing the free energy minimization principle with dynamical equations of a molecular nature. Correct cellular sorting then follows in all cases where the mixture is in a liquid or a near-liquid state. Computer examples are described and discussed, primarily for two dimensional, but also for three dimensional, interactions.     

Lysozyme folded in silico according to the limited conformational sub-space

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Lysozyme Folded In Silico According to the Limited Conformational Sub-space

Abstract

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Calculation of binding energies using a robust molecular mechanics technique: Application to an antibody-antigen complex

A novel molecular mechanics technique, which is both computationally efficient and robust, for calculation of relative stability of macromolecules and binding energies is presented. The technique delivers exact results for a number of hypothetical systems; the technique can be used to energy minimize a number of similar macromolecules simultaneously; simultaneous minimization of many structures requires computer time only fractionally over that needed to energy minimize one such structure. The method has been used to successfully calculate the relative stability and binding of two avion lysozymes to the monoclonal antibody D1.3.     

Molecular Mechanics Calculations of Proteins. Comparison of Different Energy Minimization Strategies

Abstract

A general strategy for performing energy minimization of proteins using the SYBYL molecular modelling program has been developed. The influence of several variables including energy minimization procedure, solvation, dielectric function and dielectric constant have been investigated in order to develop a general method, which is capable of producing high quality protein structures. Avian pancreatic polypeptide (APP) and bovine pancreatic phospholipase A2 (BP PLA2) were selected for the calculations, because high quality X-ray structures exist and because all classes of secondary structure are represented in the structures. The energy minimized structures were evaluated relative to the corresponding X-ray structures. The overall similarity was checked by calculating RMS distances for all atom positions. Backbone conformation was checked by Ramachandran plots and secondary structure elements evaluated by the length on hydrogen bonds. The dimensions of active site in BP PLA2 is very dependent on electrostatic interactions, due to the presence of the positively charged calcium ion. Thus, the distances between calcium and the calcium-coordinating groups were used as a quality index for this protein. Energy minimized structures of the trimeric PLA2 from Indian cobra (N.n.n. PLA2) were used for assessing the impact of protein-protein interactions. Based on the above mentioned criteria, it could be concluded that using the following conditions: Dielectric constant ? = 4 or 20; a distance dependent dielectric function and stepwise energy minimization, it is possible to reproduce X-ray structures very accurately without including explicit solvent molecules.