Random Initial Conformations Research Articles

Accelerating Kinetics with Time-Reversal Path Sampling.

In comparison to numerous enhanced sampling methods for equilibrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here, we derive a time-reversal path sampling (tRPS) method based on time reversibility to accelerate simulations for determining the transition rates between free-energy basins. It converts the difficult uphill path sampling into an easy downhill problem. This method is easy to implement, i.e., forward and backward shooting simulations with opposite initial velocities are conducted from random initial conformations within a transition-state region until they reach the basin minima, which are then assembled to give the distribution of transition paths efficiently. The effects of tRPS are demonstrated using a comparison with direct simulations of protein folding and unfolding, where tRPS is shown to give results consistent with direct simulations and increase the efficiency by up to five orders of magnitude. This approach is generally applicable to stochastic processes with microscopic reversibility, regardless of whether the variables are continuous or discrete.

Reverse Micelles As Antioxidant Carriers: An Experimental and Molecular Dynamics Study

Water-in-oil microemulsions with biocompatible components were formulated to be used as carriers of natural antioxidants, such as hydroxytyrosol (HT) and gallic acid (GA). The system was composed of a mixture of natural surfactants, lecithin and monoglycerides, medium chain triglycerides, and aqueous phase. A dual approach was undertaken to study the structure and dynamics of these complicated systems. First, experimental data were collected by using adequate techniques, such as dynamic light scattering (DLS) and electron paramagnetic resonance (EPR) spectroscopy. Following this, a coarse-grained molecular dynamics (CGMD) study based on the experimental composition using the MARTINI force field was conducted. The simulations revealed the spontaneous formation of reverse micelles (RMs) starting from completely random initial conformations, underlying their enhanced thermodynamic stability. The location of the bioactive molecules, as well as the structure of the RM, were in accordance with the experimental findings. Furthermore, GA molecules were found to be located inside the water core, in contrast to the HT ones, which seem to lie at the surfactant interfacial layer. The difference in the antioxidants' molecular location was only revealed in detail from the computational analysis and explains the RM's swelling observed by GA in DLS measurements.

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β-sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3-94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α-helices and a five stranded β-sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two-state behavior commonly seen in natural single domain proteins. In our all-atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native-like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non-native states with high native-like secondary structure.

De novo Folding of Two-Helix Potassium Channel Blockers with Free-Energy Models and Molecular Dynamics.

We report the predictive de novo folding of three two-helix proteins using the free-energy protein forcefield PFF01. Starting from random initial conformations 40-90% of the members of the simulated ensembles converge to near-native conformations. The energetically lowest conformations approach the conserved part of the native conformations to within 1.64, 1.86, and 1.84 Å for 1WQC, 1WQD, and 1WQE, respectively. An analysis of the low-lying conformations predicts the correct topology of the disulfide bridges, which are formed in additional simulations with a constraining potential. The free energy landscapes of these proteins are very simple, suggesting them as candidates for all-atom molecular dynamics simulations. In five independent simulations we find the formation of the correct secondary structure and several folding events into the tertiary structure.

Structural refinement of protein segments containing secondary structure elements: Local sampling, knowledge‐based potentials, and clustering

In this article, we present an iterative, modular optimization (IMO) protocol for the local structure refinement of protein segments containing secondary structure elements (SSEs). The protocol is based on three modules: a torsion-space local sampling algorithm, a knowledge-based potential, and a conformational clustering algorithm. Alternative methods are tested for each module in the protocol. For each segment, random initial conformations were constructed by perturbing the native dihedral angles of loops (and SSEs) of the segment to be refined while keeping the protein body fixed. Two refinement procedures based on molecular mechanics force fields - using either energy minimization or molecular dynamics - were also tested but were found to be less successful than the IMO protocol. We found that DFIRE is a particularly effective knowledge-based potential and that clustering algorithms that are biased by the DFIRE energies improve the overall results. Results were further improved by adding an energy minimization step to the conformations generated with the IMO procedure, suggesting that hybrid strategies that combine both knowledge-based and physical effective energy functions may prove to be particularly effective in future applications.

Development of softcore potential functions for overcoming steric barriers in molecular dynamics simulations

In this work, we describe the development of softcore potential functions that permit occasional “tunneling” through the regions of conformational space during molecular dynamics (MD) simulations, which would otherwise be sterically prohibited. The modification consists of a truncation of the nonbonded interaction before the steeply repulsive region encountered at short interatomic distances. This modification affects both Lennard-Jones and Coulomb parts of the nonbonded potential. Critical to success is the choice of appropriate pairwise switching distances at which this modification should be made. In the present work, these are calculated based on potential of mean force functions extracted from model system molecular dynamics simulations. We believe that these functions describe the dynamic short-range interactions much better than mean force potentials derived from an ensemble of static structures (e.g. protein data bank (PDB)). Once a set of mean force potentials is obtained, a single empirical parameter, effective barrier height, is employed to determine switching distances for all pairwise atomic interactions. Changing this single parameter allows adjustment of the “softness” of the whole system. We tested the applicability of the new softcore potentials in a loop structure optimization study. The H1 loop in the antibody 17/9 was selected as our test case because substantial repacking of loop residues in the dense protein environment is necessary for successful relaxation of random initial conformations. Softcore simulations converted to correct loop conformations, in contrast to standard simulations which never sampled this structure even after 10 ns. The resulting root mean square deviation (RMSD) values (below 1.3 A for all heavy atoms of the loop) demonstrate the usefulness of the approach based on mean force derived softcore functions.

Tertiary Structure Prediction of C-Peptide of Ribonuclease A by Multicanonical Algorithm

We have performed multicanonical Monte Carlo simulations of C-peptide of ribonuclease A. It is known by CD and NMR experiments that this peptide has high α-helix content in aqueous solution and that the side-chain charges of residues Glu-2- and His-12+ play an important role in the stability of the α-helix. To confirm these experimental implications, we have used two analogues of the peptide with charged and neutral side chains of Glu-2 and His-12. Two dielectric functions, distance-dependent and constant, are considered to study the effects of solvent contributions. All the simulations were started from random initial conformations. Various thermodynamic quantities such as average helicity as a function of residue number and average distance between two side chains as a function of temperature are calculated. The results are found to be in accord with the implications of CD and NMR experiments. The lowest-energy conformation obtained has an α-helix from Ala-4 to Gln-11 in complete agreement with the corresponding structure deduced from an X-ray crystallography experiment of ribonuclease A. It is shown that the salt bridge between the side chains of Glu-2- and Arg-10+, which is known to exist from both NMR and X-ray experiments, is formed only when the side chains are properly charged. Its formation is greatly enhanced when the distance-dependent dielectric function is used.

Thermodynamics of helix-coil transitions in amino-acid homopolymers studied by multicanonical algorithms

Thermodynamics of helix-coil transitions in amino-acid homopolymers are studied by the multicanonical algorithms. Homopolymers of length 10 are considered for three characteristic amino acids, alanine (helix former), valine (helix indifferent), and glycine (helix breaker). For alanine other lengths (15 and 20) are also considered in order to examine the length dependence. From one multicanonical production run with completely random initial conformations, we have obtained various thermodynamic quantities (average helix length, specific heat, etc.) as functions of temperature. The results, though preliminary, suggest that the helix-coil transition for poly-alanine is second-order, while the nature of phase transition is not clear for poly-valine and poly-glycine.

Thermodynamics of Helix-Coil Transitions Studied by Multicanonical Algorithms

Thermodynamics of helix-coil transitions in amino acid homo-oligomers are studied by the recently proposed multicanonical algorithms. Homo-oligomers of length 10 are considered for three characteristic amino acids, alanine (helix former), valine (helix indifferent), and glycine (helix breaker). For alanine other lengths (15 and 20) are also considered in order to examine the length dependence. From one multicanonical production run with completely random initial conformations, we have obtained the lowest-energy conformations and various thermodynamic quantities (average helicity, Zimm-Bragg s and {sigma} parameters, free energy differences between helix and coil states, etc.) as functions of temperature. The results confirm the fact that alanine is helix-forming, valine is helix-indifferent, and glycine is helix-breaking. 36 refs., 10 figs., 5 tabs.

α-Helix Propensities of Amino Acids Studied by Multicanonical Algorithm

Abstract We report the results of multicanonical simulations on α-helix propensities of homo-oligomers of nonpolar amino acids. Three characteristic amino acids are considered: alanine (helix former), glycine (helix breaker), and valine (helix indifferent). Starting simulations from completely random initial conformations, we have calculated the average % helix, free energy differences of helix-coil transitions, and the Zimm-Bragg s parameters over a wide range of temperatures. The results are shown to be in good agreement with experiments.

Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing.

Monte Carlo simulated annealing is applied to the tertiary structure prediction of a 17-residue synthetic peptide, which is known by experiment to exhibit high helical content at low pH. Two dielectric models are considered: sigmoidal distance-dependent dielectric function and a constant dielectric function (epsilon = 2). Starting from completely random initial conformations, our simulations for both dielectric models at low pH gave many helical conformations. The obtained low-energy conformations are compared with the nuclear Overhauser effect spectroscopy cross-peak data for both main chain and side chains, and it is shown that the results for the sigmoidal dielectric function are in remarkable agreement with the experimental data. The results predict the existence of two disjoint helices around residues 5-9 and 11-16, while nmr experiments imply significant alpha-helix content between residues 5 and 14. Simulations with high pH, on the other hand, hardly gave a helical conformation, which is also in accord with the experiment. These findings indicate that when side chains are charged, electrostatic interactions due to these changes play a major role in the helix stability. Our results are compared with the previous 500 ps molecular dynamics simulations of the same peptide. It is argued that simulated annealing is superior to molecular dynamics in two respects: (1) direct folding of alpha-helix from completely random initial conformations is possible for the former, whereas only unfolding of an alpha-helix can be studied by the latter; (2) while both methods predict high helix content for low pH, the results for high pH agree with experiment (low helix content) only for the former method.

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 A for a 5-residue alpha-helical segment, 1.11 A for a 5-residue beta-strand segment, and 1.03, 1.61, and 1.87 A 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.

Prediction of α-Helix Folding of Isolated C-Peptide of Ribonuclease A by Monte Carlo Simulated Annealing

Abstract Conformation of the C-peptide fragment of RNase A is calculated by Monte Carlo simulated annealing. Starting from completely random initial conformations and minimizing the total potential energy without any bias, we obtained partial α-helix structure with a high probability (≈ 40%). The energetically most favourable structure exhibits a 2.5-turn α-helix. The results of simulation are consistent with the experimental implication for the role of charged residues for α-helix stability in this peptide.

α-Helix folding by Monte Carlo simulated annealing in isolated C-peptide of ribonuclease A

Conformation of the C-peptide fragment of RNase A is calculated by Monte Carlo simulated annealing. We adopt the total potential energy as given by the sum of generic interatomic energies whose parameters are determined separately for each amino acid without referring to the empirical structure of the C-peptide. The simulation is carried out in a completely unrestricted way without imposing any weight towards given final destinations. Starting from completely random initial conformations and minimizing the total potential energy with respect to main-chain dihedral angles and side-chain torsion angles, we have obtained partial alpha-helix structure with a high probability (approximately 40%). The energetically most favourable structure exhibits a 2.5-turn alpha-helix at the location identical with that of the 3-turn alpha-helix in the native enzyme molecule. Classification of conformations obtained in the simulation into clusters of similar structure shows that our simulation indeed predicts the alpha-helix structure for the isolated C-peptide with specific charged residues. The results of simulation with various amino acid substitutions are also found to be consistent with the experimental implication for the importance of intramolecular ionic interactions for alpha-helix stability for this peptide.

Conformation in solution of porcine brain natriuretic peptide determined by combined use of nuclear magnetic resonance and distance geometry

The conformation in solution of porcine brain natriuretic peptide was determined by combined use of NMR spectroscopy and distance geometry. A set of 157 inter-proton-distance constraints was derived from the two-dimensional NOE spectra, and further a set of three hydrogen bond constraints was obtained from analysis of the temperature dependence of labile protons. The five structures with minimal violations were selected after performing distance-geometry calculations starting from 40 random initial conformations. The distance-geometry structures were further refined by the use of restrained energy minimization and restrained molecular dynamics. This structure shows a compact conformation with the carboxy-terminal region, Asn21-Tyr26, folded back to the disulfide-linked loop region, Cys4-Cys20. The characteristics of the conformation determined are as follows: conformations of the three segments interposed by glycine residues, which are Arg7-Ile12, Ser14-Leu18 and Cys20-Arg25, were well defined and the segments Arg7-Ile12 and Cys20-Arg25 are rather close to each other and nearly parallel. The biological significance of these local conformations is discussed on the basis of comparisons with those of atrial natriuretic peptide reported by Kobayashi et al.

Structure and free energy of complex thermodynamic systems

Biological systems are intrinsically complex, involving many degrees of freedom, heterogeneity, and strong interactions among components. For the simplest of biological substances, e.g., biomolecules, which obey the laws of thermodynamics, we may try to investigate them by means of a statistical mechanical approach. Even for these simplest many-body systems, assuming all microscopic interactions are completely known, current physical and chemical methods of characterizing the overall structure and free energy face the fundamental challenge of an exponential amount of computations as the number of degrees of freedom of these systems increases. As a response to this problem, two general procedures have been developed to compute the structure (Monte Carlo-minimization method) and free energy (Monte Carlo recursion method) of a complex thermodynamic system. The Monte Carlo-minimization procedure has been applied to determine the structure of a pentapeptide Met-enkephalin, leading consistently to a stable β-bend structure, starting from random initial conformations. The Monte Carlo recursion method has been applied to a Lennard-Jones fluid, with results in agreement with previously published values of the free energy obtained from other procedures.