Conformational study of a nine residue fragment of the antigenic loop of foot-and-mouth disease virus.

The nine-residue peptide Ac-TASARGDLA-NHMe was selected as model peptide in order to understand the conformational features of the antigenic loop of foot-and-mouth disease virus (FMDV). A throughout exploration of the conformational space has been carried out by means of molecular dynamics (MD) and energy minimization. The calculations have been carried out using the AMBER force field. Solvent effects have been included by an effective dielectric constant of epsilon = 4r. The lowest energy conformation presents a secondary structure constituted by an alpha-helix at the N-terminal end followed by two gamma-turns in the central region. The rest of the accessible minima found present also a high tendency to form gamma-turns. Finally, a 100 ps MD trajectory calculation at 298 K suggest a stability of the secondary structure elements of the lowest energy conformation.     

Molecular dynamics of sickle and normal hemoglobins

Molecular dynamics (MD) simulations have been carried out for 62.5 ps on crystal structures of deoxy sickle cell hemoglobin (HbS) and normal deoxy hemoglobin (HbA) using the CHARMM MD algorithm, with a time step of 0.001 ps. In the trajectory analysis of the 12.5–62.5 (50 ps) simulation, oscillations of the radius of gyration and solvent-accessible surface area were calculated. HbS exhibited a general contraction during the simulation, while HbA exhibited a nearly constant size. The average deviations of simulated structures from the starting structures were found to be 1.8 Å for HbA and 2.3 Å for HbS. The average rms amplitudes of atomic motions (atomic flexibility) were about 0.7 Å for HbA and about 1.0 Å for HbS. The amplitudes of backbone motion correlate well with temperature factors derived from x-ray crystallography. A comparison of flexibility between the α- and β-chains in both HbA and HbS indicates that the β-chains generally exhibited greater flexibility than the α-chains, and that the HbS β-chains exhibit greater flexibility in the N-terminal and D- and F-helix regions than do those of HbA. The average amplitude of backbone torsional oscillations was about 9°, a value comparable with that of other simulations, with enhanced torsional oscillation occurring primarily at the ends of helices or in loop regions between helices. Comparison of atomic flexibility and torsional oscillation results suggests that the increased β-chain flexibility results from relatively concerted motions of secondary structure elements. The increased flexibility may play an important role in HbS polymerization. Time course analysis of conformational energy of association, hydrogen bonding and hydrophobic bonding (as calculated from solvent accessibility) shows that all three of these factors contribute to the stability of subunit association for both hemoglobins. © 1993 John Wiley & Sons, Inc.     

Structural basis of hierarchical multiple substates of a protein. I: Introduction

A computer experiment of protein dynamics is carried out, which consists of two steps: (1) A Monte Carlo simulation of thermal fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor; and (2) a simulation of the quick freezing of fluctuating conformations into energy minima by minimization of the energy of a number of conformations sampled in the Monte Carlo simulation. From the analysis of results of the computer experiment is obtained the following picture of protein dynamics: multiple energy minima exist in the native state, and they are distributed in clusters in the conformational space. The dynamics has a hierarchical structure which has at least two levels. In the first level, dynamics is restricted within one of the clusters of minima. In the second, transitions occur among the clusters. Local parts of a protein molecule, side chains and local main chain segments, can take multiple locally stable conformations in the native state. Many minima result from combinations of these multiple local conformations. The hierarchical structure in the dynamics comes from interactions among the local parts. Protein molecules have two types of flexibility, each associated with elastic and plastic deformations, respectively.     

Structural basis of hierarchical multiple substates of a protein. II: Monte Carlo simulation of native thermal fluctuations and energy minimization

Conformational fluctuations in a globular protein, bovine pancreatic trypsin inhibitor, in the time range between picoseconds and nanoseconds are studied by a Monte Carlo simulation method. Multiple energy minima are derived from sampled conformations by minimizing their energy. They are distributed in clusters in the conformational space. A hierarchical structure is observed in the simulated dynamics. In the time range between 10(-14) and 10(-10) seconds dynamics is well represented by a superposition of vibrational motions within an energy well with transitions among minima within each cluster. Transitions among clusters take place in the time range of nanoseconds or longer.     

Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.     

Energy landscape of a native protein: Jumping-among-minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998. © 1998 Wiley-Liss, Inc.     

Comparison of the dynamical structures of lipoamide dehydrogenase and glutathione reductase by time-resolved polarized flavin fluorescence.

Time-resolved polarized fluorescence spectroscopy has been applied to the bound FAD in the structurally related flavoproteins lipoamide dehydrogenase from Azotobacter vinelandii (LipDH-AV) and glutathione reductase (GR) from human erythrocytes. The fluorescence parameters as obtained from the maximum entropy analysis differ considerably in both enzymes, reflecting the unique properties of the flavin microenvironment. Three conformational substates are revealed in LipDH-AV and five in GR. Almost 90% of the population of GR molecules has a fluorescence lifetime in the order of 30 ps which originates from efficient exciplex formation with Tyr197. Equilibrium fluctuations between conformational substates are observed for LipDH-AV on a nanosecond time scale in the temperature range 277-313 K. Interconversion between conformational substates in GR is slow, indicating that large activation barriers exist between the states. In agreement with these results, a model is postulated which ascribes a role in catalysis to equilibrium fluctuations between conformational substates in GR and LipDH-AV. From time-resolved fluorescence anisotropy as a function of temperature, distinction can be made between flavin reorientational motion and interflavin energy transfer. In both proteins intersubunit energy transfer between the prosthetic groups is observed. Furthermore, it is revealed that only the flavin in glutathione reductase exhibits rapid restricted reorientational motion. Geometric information concerning the relative orientation and distance of the flavins can be extracted from the parameters describing the energy-transfer process. The obtained spatial arrangement of the flavins is in excellent agreement with crystallographic data.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

RNA loop structure prediction via bond scaling and relaxation

We have developed a method for predicting the structure of small RNA loops that can be used to augment already existing RNA modeling techniques. The method requires no input constraints on loop configuration other than end-to-end distance. Initial loop structures are generated by randomizing the torsion angles, beginning at one end of the polynucleotide chain and correlating each successive angle with the previous. The bond lengths of these structures are then scaled to fit within the known end constraints and the equilibrium bond lengths of the potential energy function are scaled accordingly. Through a series of rescaling and minimization steps the structures are allowed to relax to lower energy configurations with standard bond lengths and reduced van der Waals clashes. This algorithm has been tested on the variable loops of yeast tRNA-Asp and yeast tRNA-Phe, as well as the sarcin-ricin tetraloop and the anticodon loop of yeast tRNA-Phe. The results indicate good correlation between potential energy and the loop structure predictions that are closest to the variable loop crystal structures, but poorer correlation for the more isolated stem loops. The number of stacking interactions has proven to be a good objective measure of the best loop predictions. Selecting on the basis of energy and stacking, we obtain two structures with 0.65 and 0.75 Å all-atom rms deviations (RMSD) from the crystal structure for the tRNA-Asp variable loop. The best structure prediction for the tRNA-Phe variable loop has an all-atom RMSD of 2.2 Å and a backbone RMSD of 1.6 Å, with a single base responsible for most of the deviation. For the sarcin-ricin loop from 28S ribosomal RNA, the predicted structure's all-atom RMSD from the nmr structure is 1.0 Å. We obtain a 1.8 Å RMSD structure for the tRNA-Phe anticodon loop. © 1996 John Wiley & Sons, Inc.     

Consequences of Sequential Ca2+ Occupancy for the Structure and Dynamics of CalbindinD9K: Computational Simulations and Comparison to Experimental Determinations in Solution (10, 309, (1993))

Abstract

Due to the slow convergence of the atomic rms fluctuations with the length of time for which they are calculated, the entropic contribution to the cooperativity of Ca²⁺ binding to calbindin_D9k, discussed on pp. 329–330, has to be evaluated for a longer interval than used for the rms values given in Table 5. The value of ΔΔG obtained from the rms fluctuations given in Table 5 is about 0.5 Kcal/mole. For the longer interval of 179 ps the average rms values calculated for CAB₀, CAB₁ and CAB₂ (see original article for definitions) are 4.5 Å, 0.9 Å and 0.8 Å, respectively. The value of ΔΔG calculated from these rms fluctuations according to the equations in the the original article is about 1.0 Kcal/mole. It is noted that these trends do not affect the interpretation or conclusions regarding the significance of the configurational entropy for the cooperativity of binding in calbindin_D9k.     

Predicting immunoglobulin-like hypervariable loops

A two-stage method is developed to search the conformational space of small protein segments for low energy structures. Central features of the method are efficient procedures for generating small, eight-backbone atom, local moves in Cartesian coordinates and for introducing geometric constraints in adaptable Monte Carlo procedures. This allows natural implementation of an adaptive simulated annealing algorithm, which achieves an effective trade-off between speed and acceptance ratio. The method is applied to the calculation of various immunoglobulin loops. We also develop data base derived rules for identifying constraint conditions, and show that the incorporation of an identified side-chain constraint allows a 1.2 Å all-backbone atom rms deviation prediction of a 9 residue long L1 loop. © 1994 John Wiley & Sons, Inc.     

Protein conformational dynamics of crambin in crystal, solution and in the trajectories of molecular dynamics simulations

Atomic displacement parameters — B factors of the eight crambin crystal structures obtained at 0.54–1.5 Å resolution and temperatures of 100–293 K have been analyzed. The comparable contributions to the B factor values are the intramolecular motions which are modeled by the harmonic vibration calculations and derived from the molecular dynamics simulation (MD) as well as rigid body changes in the position of a protein molecule as a whole. In solution for the average NMR structure of crambin the amplitudes of the backbone atomic fluctuations of the most residues of the segments with the regular backbone conformations are close to the amplitudes of the small scale harmonic vibrations. For the same residues the probability of the medium scale fluctuations fixed by the hydrogen exchange method is very low. The restricted conformational mobility of those segments is coupled with the depressed amplitudes of the fluctuation changes of the tertiary structure registered by the residue accessibility changes in an ensemble of NMR structures that forms the average NMR structure of crambin. The amplitudes of temperature fluctuations of backbone atoms and the tertiary structure raise in the segment with the irregular conformations, turn and loops. In the same segments the amplitudes of the calculated harmonic vibrations also increase, but to a lesser extent and especially in the interhelical loop with the most strong and complicated fluctuation changes of the backbone conformation. In solution for the NMR structure in this loop the conformational transitions occur between the conformational substates separated by the energy barriers, but they are not observed even in the long 100 ns trajectories from the MD simulation of crambin. These strong local fluctuation changes of the structure may play a key role in the protein functioning and modern performance improvements in the MD simulation techniques are oriented to increase the probability of protein appearance in the trajectories from the MD simulations.     

Frustration‐guided motion planning reveals conformational transitions in proteins

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics‐inspired motion planning procedure called dCC‐RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non‐native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC‐RRT to examine how collective, small‐scale motions of four side‐chains in the active site of cyclophilin A propagate through the protein. dCC‐RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non‐canonical capsid binding site 25 Å away, rationalizing NMR and multi‐temperature crystallography experiments. In all, dCC‐RRT can reveal detailed, all‐atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/ .     

The loop problem in proteins: A monte carlo simulated annealing approach

A Monte Carlo simulated annealing (MCSA) algorithm was used to generate the conformations of local regions in bovine pancreatic trypsin inhibitor (BPTI) starting from random initial conformations. In the approach explored, only the conformation of the segment is computed; the rest of the protein is fixed in the known native conformation. Rather than follow a single simulation exhaustively, computer time is better used by performing multiple independent MCSA simulations in which different starting temperatures are employed and the number of conformations sampled is varied. The best computed conformation is chosen on the basis of lowest total energy and refined further. The total energy used in the annealing is the sum of the intrasegment energy, the interaction energy of the segment with the local surrounding region, and a distance constraint to generate a smooth connection of the initially randomized segment with the rest of the protein. The rms deviations between the main-chain conformations of the computed segments in BPTI and those of the native x-ray structure are 0.94 Å for a 5-residue α-helical segment, 1.11 Å for a 5-residue β-strand segment, and 1.03, 1.61, and 1.87 Ã for 5-, 7-, and 9-residue loop segments. Side-chain deviations are comparable to the main-chain deviations for those side chains that interact strongly with the fixed part of the protein. A detailed view of the deviations at an atom-resolved level is obtained by comparing the predicted segments with their known conformations in the crystal structure of BPTI. These results emphasize the value of predetermined fixed structure against which the computed segment can nest. © 1993 John Wiley & Sons, Inc.     

Effect of anesthetics on the stability of oxyhemoglobin S

The conversion of the serine-195 in α-chymotrypsin to dehydroalanine results in two conformational substates that differ in their extinction coefficients at 240nm. The active site methionine-192 in the substate with lower absorption at 240nm is alkylated by α-bromo-4-nitroacetophenone at a rate of 7.0×10^?4sec^?1, similar to that found for α-chymotrypsin; the substate with higher absorption at 240nm reacts 14 times slower. These two substates are not separated by an affinity resin containing lima bean trypsin inhibitor. These data infer that the serine-195 plays a role in the stabilization of the active site conformation in α-chymotrypsin.     

An approach to the multiple-minima problem in protein folding by relaxing dimensionality. Tests on enkephalin

An algorithm for locating the region in conformational space containing the global energy minimum of a polypeptide is described. Distances are used as the primary variables in the minimization of an objective function that incorporates both energetic and distance-geometric terms. The latter are obtained from geometry and energy functions, rather than nuclear magnetic resonance experiments, although the algorithm can incorporate distances from nuclear magnetic resonance data if desired. The polypeptide is generated originally in a space of high dimensionality. This has two important consequences. First, all interatomic distances are initially at their energetically most favorable values; i.e. the polypeptide is initially at a global minimum-energy conformation, albeit a high-dimensional one. Second, the relaxation of dimensionality constraints in the early stages of the minimization removes many potential energy barriers that exist in three dimensions, thereby allowing a means of escaping from three-dimensional local minima. These features are used in an algorithm that produces short trajectories of three-dimensional minimum-energy conformations. A conformation in the trajectory is generated by allowing the previous conformation in the trajectory to evolve in a high-dimensional space before returning to three dimensions. The resulting three-dimensional structure is taken to be the next conformation in the trajectory, and the process is iterated. This sequence of conformations results in a limited but efficient sampling of conformational space. Results for test calculations on Met-enkephalin, a pentapeptide with the amino acid sequence H-Tyr-Gly-Gly-Phe-Met-OH, are presented. A tight cluster of conformations (in three-dimensional space) is found with ECEPP energies (Empirical Conformational Energy Program for Peptides) lower than any previously reported. This cluster of conformations defines a region in conformational space in which the global-minimum-energy conformation of enkephalin appears to lie.     

Correlation between prebiotic amino acid compositions and contemporary proteins.

A method of energy minimization for conformational energy calculations using the least-squares technique has been reported. The method has been tested in the simple case of a pair of alanyl peptide units using the non-bonded potential energy. Starting from any point in the (φ, ψ) energy map (not necessarily near a minimum), convergence to one of the energy minima is achieved rapidly, within a few cycles of iteration.     

Internal dynamics of proteins. Short time and long time motions of aromatic sidechains in PTI.

Theoretical approaches to the internal dynamics of proteins are outlined and illustrated by application to the aromatic sidechain motions of tyrosines in the bovine pancreatic trypsin inhibitor. High frequency torsional oscillations are obtained from a molecular dynamics simulation, while the longer time ring rotations are analyzed by use of adiabatic energy minimization and special transition-state trajectory techniques.     

Optimal protocol and trajectory visualization for conformational searches of peptides and proteins.

Conformational searches by molecular dynamics and different types of Monte Carlo or build-up methods usually aim to find the lowest-energy conformation. However, this is often misleading, as the energy functions used in conformational calculations are imprecise. For instance, though positions of local minima defined by the repulsive part of the Lennard-Jones potential are usually altered only slightly by functional modification, the relative depths of the minima could change significantly. Thus, the purpose of conformational searches and, correspondingly, performance criteria should be reformulated and appropriate methods found to extract different local minima from the search trajectory and allow visualization in the search space. Attempts at convergence to the lowest-energy structure should be replaced with efforts to visit a maximum number of different local energy minima with energies within a certain range. We use this quantitative criterion consistently to evaluate performances of different search procedures. To utilize information generated in the course of simulation, a "stack" of low energy conformations is created and stored. It keeps track of variables and visit numbers for the best representatives of different conformational families. To visualize the search, projection of multidimensional walks onto a principal plane defined by a set of reference structures is used. With Met-enkephalin as a structural example and a Monte Carlo procedure combined with energy minimization (MCM) as a basic search method, we analyzed the influence on search efficiency of different characteristics as temperature schedules, the step size for variable modification, constrained random step and response mechanisms to search difficulties. Simulated annealing MCM had comparable efficiency with MCM at constant and elevated temperature (about 600 K). Constraining the randomized choice of side-chain chi angles to optimal values (rotamers) on every MCM step did not improve, but rather worsened, the search efficiency. Two low-energy Met-enkephalin conformations with parallel Tyr1 and Phe4 rings, a gamma-turn around the Gly2 residue, and Phe4 and Met5 side-chains forming together a compact hydrophobic cluster were found and are suggested as possible structural candidates for interaction with a receptor or a membrane.