Structural model of the anti-snake-toxin antibody,Mα2,3

We present results of structural modeling of the variable fragment of Mα2,3, an antibody capable of neutralizing all short snake toxins. Three different methods were used to model the hypervariable loops: the conformational search algorithm CONGEN (Bruccoleri and Karplus, Biopolymers 26:137–168, 1987), high-temperature molecular dynamics (Bruccoleri and Karplus, Biopolymers 29:1847–1862, 1990), and a combined knowledge-based and energy-based algorithm (Martin et al., Proc. Natl. Acad. Sci. USA 86:9268–9272, 1989). Ninety plausible conformations were generated and were clustered into 13 classes. The clustering results indicate that there was little overlap of the conformational space explored by the different methods. Canonical loop structures were found by all methods for two of the loops, in agreement with previously established empirical modeling criteria. Nine of the 13 classes of structure were rejected on the ground of their lacking common features of antibody combining-site structure. The remaining four models were refined using restrained molecular dynamics. It was found that interconversion between the four resulting structures is possible with no significant energy barriers, suggesting that they are in thermodynamic equilibrium at 300 K. Features of the combining-site structure likely to be particularly important for antigen binding are discussed. © 1996 Wiley-Liss, Inc.     

Conformational regions of Boc-Ala-Aib-Ala-OMe. Sampling with molecular dynamics simulations using time averaging of distance restraints.

The method of time averaging of distance restraints in molecular dynamics simulations is applied to Boc-Ala-Aib-Ala-OMe in order to demonstrate the improved sampling properties of this method compared to conventional distance restraining. Two conformational regions, beta-turn type II and gamma-turn, are seen during MD runs at a simulation temperature of 500 K, while in simulations with conventional distance restraining, no conformational transitions could be observed for temperatures up to 1000 K.     

A comparative molecular dynamics study of thermophilic and mesophilic ribonuclease HI enzymes

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Targeted molecular dynamics: A new approach for searching pathways of conformational transitions

Molecular dynamics simulations have proven to be a valuable tool to investigate the dynamic behavior of stable macromolecules at finite temperatures. However, considerable conformational transitions take place during a simulation only accidentally or at exceptionally high temperatures far from the range of experimental conditions. Targeted molecular dynamics (TMD) is a method to induce a conformational change to a known target structure at ordinary temperature by applying a time-dependent, purely geometrical constraint. The transition is enforced independently of the height of energy barriers, while the dynamics of the molecule is only minimally influenced by the constraint. Simulations of decaalanine and insulin show the ability of the method to explore the configurational space for pathways accessible at a given temperature. The transitions studied at insulin comprise unfolding of an α-helical portion and, in the reverse direction, refolding from an extended conformation. A possible application of TMD is the search for energy barriers and stable intermediates from rather local changes up to protein denaturation.     

A Comparative Molecular Dynamics Study of Thermophilic and Mesophilic Ribonuclease HI Enzymes

Abstract

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Protein flexibility: multiple molecular dynamics simulations of insulin chain B

Multiple molecular dynamics simulations totaling more than 100 ns were performed on chain B of insulin in explicit solvent at 300 K and 400 K. Despite some individual variations, a comparison of the protein dynamics of each simulation showed similar trends and most structures were consistent with NMR experimental values, even at the elevated temperature. The importance of packing interactions in determining the conformational transitions of the protein was observed, sometimes resulting in conformations induced by localized hydrophobic interactions. The high temperature simulation generated a more diverse range of structures with similar elements of secondary structure and populated conformations to the simulations at room temperature. A broad sampling of the conformational space of insulin chain B illustrated a wide range of conformational states with many transitions at room temperature in addition to the conformational states observed experimentally. The T-state conformation associated with insulin activity was consistently present and a possible mechanism of behavior was suggested.     

Adaptive conformational sampling based on replicas

Computer simulations of biomolecules such as molecular dynamics simulations are limited by the time scale of conformational rearrangements. Several sampling techniques are available to search the multi-minima free energy landscape but most efficient, time-dependent methods do generally not produce a canonical ensemble. A sampling algorithm based on a self-regulating ladder of searching copies in the dihedral subspace is developped in this paper. The learning process using short- and long-term memory functions allows an efficient search in phase space while combining a deterministic dynamics and stochastic swaps with the searching copies conserves a canonical limit. The sampling efficiency and accuracy are indicated by comparing the ansatz with conventional molecular dynamics and replica exchange simulations.     

Anti-insulin antibody structure and conformation. II. Molecular dynamics with explicit solvent.

Molecular dynamics at 300 K was used as a conformation searching tool to analyze a knowledge-based structure prediction of an anti-insulin antibody. Solvation effects were modeled by packing water molecules around the antigen binding loops. Some loops underwent backbone and side-chain conformational changes during the 95-ps equilibration, and most of these new, lower potential energy conformations were stable during the subsequent 200-ps simulation. Alterations to the model include changes in the intraloop, main-chain hydrogen bonding network of loop H3, and adjustments of Tyr and Lys side chains of H3 induced by hydrogen bonding to water molecules. The structures observed during molecular dynamics support the conclusion of the previous paper that hydrogen bonding will play the dominant role in antibody-insulin recognition. Determination of the structure of the antibody by x-ray crystallography is currently being pursued to provide an experimental test of these results. The simulation appears to improve the model, but longer simulations at higher temperatures should be performed.     

β‐Hairpin folding and stability: molecular dynamics simulations of designed peptides in aqueous solution

The structural properties of a 10‐residue and a 15‐residue peptide in aqueous solution were investigated by molecular dynamics simulation. The two designed peptides, SYINSDGTWT and SESYINSDGTWTVTE, had been studied previously by NMR at 278 K and the resulting model structures were classified as 3:5 β‐hairpins with a type I + G1 β‐bulge turn. In simulations at 278 K, starting from the NMR model structure, the 3:5 β‐hairpin conformers proved to be stable over the time period evaluated (30 ns). Starting from an extended conformation, simulations of the decapeptide at 278 K, 323 K and 353 K were also performed to study folding. Over the relatively short time scales explored (30 ns at 278 K and 323 K, 56 ns at 353 K), folding to the 3:5 β‐hairpin could only be observed at 353 K. At this temperature, the collapse to β‐hairpin‐like conformations is very fast. The conformational space accessible to the peptide is entirely dominated by loop structures with different degrees of β‐hairpin character. The transitions between different types of ordered loops and β‐hairpins occur through two unstructured loop conformations stabilized by a single side‐chain interaction between Tyr2 and Trp9, which facilitates the changes of the hydrogen‐bond register. In agreement with previous experimental results, β‐hairpin formation is initially driven by the bending propensity of the turn segment. Nevertheless, the fine organization of the turn region appears to be a late event in the folding process. Copyright © 2004 European Peptide Society and John Wiley & Sons, Ltd.     

Conformational dynamics of cytochrome c: correlation to hydrogen exchange.

We study the dynamical fluctuations of horse heart cytochrome c by molecular dynamics (MD) simulations in aqueous solution, at four temperatures: 300 K, 360 K, 430 K, and 550 K. Each simulation covers a production time of at least 1.5 nanoseconds (ns). The conformational dynamics of the system is analyzed in terms of collective motions that involve the whole protein, and local motions that involve the formation and breaking of intramolecular hydrogen bonds. The character of the MD trajectories can be described within the framework of rugged energy landscape dynamics. The MD trajectories sample multiple conformational minima, with basins in protein conformational space being sampled for a few hundred picoseconds. The trajectories of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. As a consequence of the hierarchical nature of the dynamics, the mean square displacement autocorrelation function, <|x(t) - x(0)|2>, exhibits a power law dependence on time, with an exponent of around 0.5 for times shorter than 100 ps, and an exponent of 1.75 for longer times. This power law behavior indicates that the system exhibits suppressed diffusion (sub-diffusion) in sampling of configurational space at time scales shorter than 100 ps, and enhanced (super-diffusion) at longer time scales. The multi-basin feature of the trajectories is present at all temperatures simulated. Structural changes associated with inter-basin displacements correspond to collective motions of the Omega loops and coiled regions and relative motions of the alpha-helices as rigid bodies. Similar motions may be involved in experimentally observed amide hydrogen exchange. However, some groups showing large correlated motions do not expose the amino hydrogens to the solvent. We show that large fluctuations are not necessarily correlated to hydrogen exchange. For example, regions of the proteins forming alpha helices and turns show significant fluctuations, but as rigid bodies, and the hydrogen bonds involved in the formation of these structures do not break in proportion to these fluctuations. Proteins 1999;36:175-191. Published 1999 Wiley-Liss, Inc.     

Enhanced sampling of molecular dynamics simulation of peptides and proteins by double coupling to thermal bath

Low sampling efficiency in conformational space is the well-known problem for conventional molecular dynamics. It greatly increases the difficulty for molecules to find the transition path to native state, and costs amount of CPU time. To accelerate the sampling, in this paper, we re-couple the critical degrees of freedom in the molecule to environment temperature, like dihedrals in generalized coordinates or nonhydrogen atoms in Cartesian coordinate. After applying to ALA dipeptide model, we find that this modified molecular dynamics greatly enhances the sampling behavior in the conformational space and provides more information about the state-to-state transition, while conventional molecular dynamics fails to do so. Moreover, from the results of 16 independent 100?ns simulations by the new method, it shows that trpzip2 has one-half chances to reach the naive state in all the trajectories, which is greatly higher than conventional molecular dynamics. Such an improvement would provide a potential way for searching the conformational space or predicting the most stable states of peptides and proteins.     

Search for the stable state of a short chain in a molecular field.

A general approach is developed to search for stable structures of short chain fragments (e.g. of loops or bound oligopeptides) in a given molecular field. This molecular field is produced by the remaining part of a globule or by any other surface with a defined spatial structure. The fragment must be short enough to have no pronounced long-range interactions within itself. The method is illustrated by calculation of the 3-D structures of two loops of bovine pancreatic trypsin inhibitor (BPTI). Computations are based on a lattice model of conformational space and on strict and fast algorithms of 1-D statistical mechanics and dynamic programming (which are very similar in essence). This makes a search of oligopeptide structures only several times (and not several orders of magnitude) longer than that of a dipeptide.     

Simulation of peptide folding with explicit water--a mean solvation method

A new approach to efficiently calculate solvent effect in computer simulation of macromolecular systems has been developed. Explicit solvent molecules are included in the simulation to provide a mean solvation force for the solute conformational search. Simulations of an alanine dipeptide in aqueous solution showed that the new approach is significantly more efficient than conventional molecular dynamics method in conformational search, mainly because the mean solvation force reduced the solvent damping effect. This approach allows the solute and solvent to be simulated separately with different methods. For the macromolecule, the rigid fragment constraint dynamics method we developed previously allows large time-steps. For the solvent, a combination of a modified force-bias Monte Carlo method and a preferential sampling can efficiently sample the conformational space. A folding simulation of a 16-residue peptide in water showed high efficiency of the new approach.     

A theoretical study of pentacyclo-undecane cage peptides of the type [Ac-X-Y-NHMe].

The conformational preferences of peptides of the type, Ac-X-Y-NHMe, where X and Y = Ala, cage and Pro, were studied by means of computational techniques within the framework of a molecular mechanics approach. For each of the eight peptide analogues, extensive conformational searches were carried out using molecular dynamics (MD) and simulated annealing (SA) protocols in an iterative fashion. Both results are in good agreement and complement each other. The conformational search indicates that the cage residue restricts the conformational freedom of the dipeptide considerably in comparison with the other model residues used. This study revealed that proline exhibits a greater tendency in promoting reverse-turn characteristics in comparison to the cage peptides, which show promising beta-turn characteristics. It was also found that 300-500 K is not sufficient to overcome rotational barriers for cage peptides. In all cases, the low-energy conformers have a tendency to form bent structures.     

Analysis of the dynamics of rhizomucor miehei lipase at different temperatures.

The dynamics of Rhizomucor miehei lipase has been studied by molecular dynamics simulations at temperatures ranging from 200-500K. Simulations carried out in periodic boundary conditions and using explicit water molecules were performed for 400 ps at each temperature. Our results indicate that conformational changes and internal motions in the protein are significantly influenced by the temperature increase. With increasing temperature, the number of internal hydrogen bonds decreases, while surface accessibility, radius of gyration and the number of residues in random coil conformation increase. In the temperature range studied, the motions can be described in a low dimensional subspace, whose dimensionality decreases with increasing temperature. Approximately 80% of the total motion is described by the first (i) 80 eigenvectors at T=200K, (ii) 30 eigenvectors at T=300K and (iii) 10 eigenvectors at T=400K. At high temperature, the alpha-helix covering the active site in the native Rhizomucor miehei lipase, the helix at which end the active site is located, and in particular, the loop (Gly35-Lys50) show extensive flexibility.     

Characterization of the conformational domains of bradykinin by computational methods

The AMBER 4.0 force field was used to perform a characterization of the conformational profile of the nonapeptide bradykinin. A thorough conformational search was carried out using molecular dynamics as sampling technique, by computing cycles of high (900 K) and low (300 K) temperature trajectories. A total of 2400 minima were generated and subsequently clustered using the root-mean-square of the backbone dihedral angles as criterium. After the use of a tolerance value of 20deg;, the conformations were clustered in 233 unique conformations with energies up to 40 kcal/mol above the lowest minimum. The analysis of the low-energy conformations indicate that the peptide exhibits a high tendency to adopt a β-turn at the C-terminus and a propensity to adopt a bent structure at the N-terminus. These results are in agreement with the experimental evidence reported in the literature and provide detailed information necessary to understand the conformational preferences of the peptide.     

Multi-scaled explorations of binding-induced folding of intrinsically disordered protein inhibitor IA3 to its target enzyme

Biomolecular function is realized by recognition, and increasing evidence shows that recognition is determined not only by structure but also by flexibility and dynamics. We explored a biomolecular recognition process that involves a major conformational change - protein folding. In particular, we explore the binding-induced folding of IA3, an intrinsically disordered protein that blocks the active site cleft of the yeast aspartic proteinase saccharopepsin (YPrA) by folding its own N-terminal residues into an amphipathic alpha helix. We developed a multi-scaled approach that explores the underlying mechanism by combining structure-based molecular dynamics simulations at the residue level with a stochastic path method at the atomic level. Both the free energy profile and the associated kinetic paths reveal a common scheme whereby IA3 binds to its target enzyme prior to folding itself into a helix. This theoretical result is consistent with recent time-resolved experiments. Furthermore, exploration of the detailed trajectories reveals the important roles of non-native interactions in the initial binding that occurs prior to IA3 folding. In contrast to the common view that non-native interactions contribute only to the roughness of landscapes and impede binding, the non-native interactions here facilitate binding by reducing significantly the entropic search space in the landscape. The information gained from multi-scaled simulations of the folding of this intrinsically disordered protein in the presence of its binding target may prove useful in the design of novel inhibitors of aspartic proteinases.     

Using enhanced sampling and structural restraints to refine atomic structures into low-resolution electron microscopy maps

For a variety of problems in structural biology, low-resolution maps generated by electron microscopy imaging are often interpreted with the help of various flexible-fitting computational algorithms. In this work, we systematically analyze the quality of final models of various proteins obtained via molecular dynamics flexible fitting (MDFF) by varying the map-resolution, strength of structural restraints, and the steering forces. We find that MDFF can be extended to understand conformational changes in lower-resolution maps if larger structural restraints and lower steering forces are used to prevent overfitting. We further show that the capabilities of MDFF can be extended by combining it with an enhanced conformational sampling method, temperature-accelerated molecular dynamics (TAMD). Specifically, either TAMD can be used to generate better starting configurations for MDFF fitting or TAMD-assisted MDFF (TAMDFF) can be performed to accelerate conformational search in atomistic simulations.     

Molecular dynamics approach to probe the antigenicity of PagN – an outer membrane protein of Salmonella Typhi

PagN is a highly immunogenic 27-kDa outer membrane adhesin present in Salmonella Typhi. It plays a major role in the pathogenesis of typhoid fever and has emerged as a strong vaccine candidate. In this report, we predict the three-dimensional structure of PagN and describe the conformational dynamics associated with its four extracellular loops based on two 100-ns molecular dynamics simulations at 300 and 310 K. The formation and deformation of the secondary structures on these loops were also investigated during the simulations which revealed loops L1 and L2 to be highly flexible, whereas the relative flexibility of loops L3 and L4 was minimal. Essential dynamics and principal component analysis deciphered more realistic dynamic behaviours of the loops, particularly at 310 K. Moreover, our epitope predictions suggest that the antigenic peptides for B-cell recognition are located within the loops L1 and L2, while those for T-cell recognition are located within the loops L3 and L4. The binding specificities of the antigenic peptides towards specific human MHC-I and MHC-II HLA alleles closely resembled the stability of the loops L3 and L4 inferred from the simulations. Finally, we identified potential antigenic peptides in the flexible (L1 and L2) as well as stable (L3 and L4) regions of PagN for both B- and T-cell recognitions, which can help in developing effective sub-unit vaccines.     

Molecular dynamics of the anticodon domain of yeast tRNA(Phe): codon-anticodon interaction

We have studied the effect of codon-anticodon interaction on the structure and dynamics of transfer RNAs using molecular dynamics simulations over a nanosecond time scale. From our molecular dynamical investigations of the solvated anticodon domain of yeast tRNA(Phe) in the presence and absence of the codon trinucleotides UUC and UUU, we find that, although at a gross level the structures are quite similar for the free and the bound domains, there are small but distinct differences in certain parts of the molecule, notably near the Y37 base. Comparison of the dynamics in terms of interatomic or inter-residual distance fluctuation for the free and the bound domains showed regions of enhanced rigidity in the loop region in the presence of codons. Because fluorescence experiments suggested the existence of multiple conformers of the anticodon domain, which interconvert on a much larger time scale than our simulations, we probed the conformational space using five independent trajectories of 500 ps duration. A generalized ergodic measure analysis of the trajectories revealed that at least for this time scale, all the trajectories populated separate parts of the conformational space, indicating a need for even longer simulations or enhanced sampling of the conformational space to give an unequivocal answer to this question.