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PubMed2006

Ab initio computational modeling of loops in G-protein-coupled receptors: lessons from the crystal structure of rhodopsin.

With the help of the crystal structure of rhodopsin an ab initio method has been developed to calculate the three-dimensional structure of the loops that connect the transmembrane helices (TMHs). The goal of this procedure is to calculate the loop structures in other G-protein coupled receptors (GPCRs) for which only model coordinates of the TMHs are available. To mimic this situation a construct of rhodopsin was used that only includes the experimental coordinates of the TMHs while the rest of the structure, including the terminal domains, has been removed. To calculate the structure of the loops a method was designed based on Monte Carlo (MC) simulations which use a temperature annealing protocol, and a scaled collective variables (SCV) technique with proper structural constraints. Because only part of the protein is used in the calculations the usual approach of modeling loops, which consists of finding a single, lowest energy conformation of the system, is abandoned because such a single structure may not be a representative member of the native ensemble. Instead, the method was designed to generate structural ensembles from which the single lowest free energy ensemble is identified as representative of the native folding of the loop. To find the native ensemble a successive series of SCV-MC simulations are carried out to allow the loops to undergo structural changes in a controlled manner. To increase the chances of finding the native funnel for the loop, some of the SCV-MC simulations are carried out at elevated temperatures. The native ensemble can be identified by an MC search starting from any conformation already in the native funnel. The hypothesis is that native structures are trapped in the conformational space because of the high-energy barriers that surround the native funnel. The existence of such ensembles is demonstrated by generating multiple copies of the loops from their crystal structures in rhodopsin and carrying out an extended SCV-MC search. For the extracellular loops e1 and e3, and the intracellular loop i1 that were used in this work, the procedure resulted in dense clusters of structures with Calpha-RMSD approximately 0.5 angstroms. To test the predictive power of the method the crystal structure of each loop was replaced by its extended conformations. For e1 and i1 the procedure identifies native clusters with Calpha-RMSD approximately 0.5 angstroms and good structural overlap of the side chains; for e3, two clusters were found with Calpha-RMSD approximately 1.1 angstroms each, but with poor overlap of the side chains. Further searching led to a single cluster with lower Calpha-RMSD but higher energy than the two previous clusters. This discrepancy was found to be due to the missing elements in the constructs available from experiment for use in the calculations. Because this problem will likely appear whenever parts of the structural information are missing, possible solutions are discussed.

Computer Simulation↗

PubMed2006

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20.

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.

Algorithms↗

PubMed2001

FlexE: efficient molecular docking considering protein structure variations.

Side-chain or even backbone adjustments upon docking of different ligands to the same protein structure, a phenomenon known as induced fit, are frequently observed. Sometimes point mutations within the active site influence the ligand binding of proteins. Furthermore, for homology derived protein structures there are often ambiguities in side-chain placement and uncertainties in loop modeling which may be critical for docking applications. Nevertheless, only very few molecular docking approaches have taken into account such variations in protein structures. We present the new software tool FlexE which addresses the problem of protein structure variations during docking calculations. FlexE can dock flexible ligands into an ensemble of protein structures which represents the flexibility, point mutations, or alternative models of a protein. The FlexE approach is based on a united protein description generated from the superimposed structures of the ensemble. For varying parts of the protein, discrete alternative conformations are explicitly taken into account, which can be combinatorially joined to create new valid protein structures.FlexE was evaluated using ten protein structure ensembles containing 105 crystal structures from the PDB and one modeled structure with 60 ligands in total. For 50 ligands (83 %) FlexE finds a placement with an RMSD to the crystal structure below 2.0 A. In all cases our results are of similar quality to the best solution obtained by sequentially docking the ligands into all protein structures (cross docking). In most cases the computing time is significantly lower than the accumulated run times for the single structures. FlexE takes about five and a half minutes on average for placing one ligand into the united protein description on a common workstation. The example of the aldose reductase demonstrates the necessity of considering protein structure variations for docking calculations. We docked three potent inhibitors into four protein structures with substantial conformational changes within the active site. Using only one rigid protein structure for screening would have missed potential inhibitors whereas all inhibitors can be docked taking all protein structures into account.

Aldehyde Reductase↗

PubMedDate not supplied

Root mean square deviation probability analysis of molecular dynamics trajectories on DNA.

The comparison and detection of the commonalities and differences in multiple structural ensembles is an important step in the use of molecular simulations to gain insight into the conformation and dynamics of complex biomacromolecules. While the average structure is often employed as the representative of an ensemble of structures in such comparisons, dynamic molecular systems with multiple conformational substates call for a more accurate representation that captures the complete dynamical range of the ensemble. We present a probability analysis procedure based on the root-mean-square differences among the structural ensembles that efficiently and accurately performs the relevant comparison.

Base Sequence↗

PubMed2005

Reconstruction of the src-SH3 protein domain transition state ensemble using multiscale molecular dynamics simulations.

We use an integrated computational approach to reconstruct accurately the transition state ensemble (TSE) for folding of the src-SH3 protein domain. We first identify putative TSE conformations from free energy surfaces generated by importance sampling molecular dynamics for a fully atomic, solvated model of the src-SH3 protein domain. These putative TSE conformations are then subjected to a folding analysis using a coarse-grained representation of the protein and rapid discrete molecular dynamics simulations. Those conformations that fold to the native conformation with a probability (P(fold)) of approximately 0.5, constitute the true transition state. Approximately 20% of the putative TSE structures were found to have a P(fold) near 0.5, indicating that, although correct TSE conformations are populated at the free energy barrier, there is a critical need to refine this ensemble. Our simulations indicate that the true TSE conformations are compact, with a well-defined central beta sheet, in good agreement with previous experimental and theoretical studies. A structured central beta sheet was found to be present in a number of pre-TSE conformations, however, indicating that this element, although required in the transition state, does not define it uniquely. An additional tight cluster of contacts between highly conserved residues belonging to the diverging turn and second beta-sheet of the protein emerged as being critical elements of the folding nucleus. A number of commonly used order parameters to identify the transition state for folding were investigated, with the number of native Cbeta contacts displaying the most satisfactory correlation with P(fold) values.

Models, Molecular↗

PubMed2006

Single-pair FRET characterization of DNA tweezers.

The self-assembly properties of DNA make it an ideal choice for the construction of nanomachines such as DNA tweezers. Because nanomachines function as individual units, they need to be studied on the single-molecule level. From single-pair FRET investigations, we show that "open" tweezers exist in a single conformation with minimal FRET efficiency, whereas upon addition of a "closing strand", three conformations are observed, which are averaged out in ensemble measurements.

DNA↗

PubMed2003

The effect of the polyproline II (PPII) conformation on the denatured state entropy.

Polyproline II (PPII) is reported to be a dominant conformation in the unfolded state of peptides, even when no prolines are present in the sequence. Here we use isothermal titration calorimetry (ITC) to investigate the PPII bias in the unfolded state by studying the binding of the SH3 domain of SEM-5 to variants of its putative PPII peptide ligand, Sos. The experimental system is unique in that it provides direct access to the conformational entropy change of the substituted amino acids. Results indicate that the denatured ensemble can be characterized by at least two thermodynamically distinct states, the PPII conformation and an unfolded state conforming to the previously held idea of the denatured state as a random collection of conformations determined largely by hard-sphere collision. The probability of the PPII conformation in the denatured states for Ala and Gly were found to be significant, approximately 30% and approximately 10%, respectively, resulting in a dramatic reduction in the conformational entropy of folding.

Alanine↗

PubMed2006

Folding transition-state and denatured-state ensembles of FSD-1 from folding and unfolding simulations.

Characterization of the folding transition-state ensemble and the denatured-state ensemble is an important step toward a full elucidation of protein folding mechanisms. We report herein an investigation of the free-energy landscape of FSD-1 protein by a total of four sets of folding and unfolding molecular dynamics simulations with explicit solvent. The transition-state ensemble was initially identified from unfolding simulations at 500 K and was verified by simulations at 300 K starting from the ensemble structures. The denatured-state ensemble and the early-stage folding were studied by a combination of unfolding simulations at 500 K and folding simulations at 300 K starting from the extended conformation. A common feature of the transition-state ensemble was the substantial formation of the native secondary structures, including both the alpha-helix and beta-sheet, with partial exposure of the hydrophobic core in the solvent. Both the native and non-native secondary structures were observed in the denatured-state ensemble and early-stage folding, consistent with the smooth experimental melting curve. Interestingly, the contact orders of the transition-state ensemble structures were similar to that of the native structure and were notably lower than those of the compact structures found in early-stage folding, implying that chain and topological entropy might play significant roles in protein folding. Implications for FSD-1 folding mechanisms and the rate-limiting step are discussed. Analyses further revealed interesting non-native interactions in the denatured-state ensemble and early-stage folding and the possibility that destabilization of these interactions could help to enhance the stability and folding rate of the protein.

DNA-Binding Proteins↗

PubMed2006

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions.

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.

Algorithms↗

PubMed2005

Recognition of RNA by amide modified backbone nucleic acids: molecular dynamics simulations of DNA-RNA hybrids in aqueous solution.

Thermodynamic and structural properties of a chemically modified DNA-RNA hybrid in which a phosphodiester linkage is replaced by a neutral amide-3 linkage (3'-CH(2)-CONH-5') were investigated using UV melting experiments, molecular dynamics simulations in explicit water, and continuum solvent models. van't Hoff analysis of the experimental UV melting curves suggests that the significant increase of the thermodynamic stability of a 15-mer DNA-RNA with seven alternated amide-3 modifications (+11 degrees C) is mainly due to an increased binding enthalpy. To further evaluate the origin in the observed affinities differences, the electrostatic contribution to the binding free energy was calculated by solving the Poisson-Boltzmann equation numerically. The nonelectrostatic contribution was estimated as the product of a hydrophobic surface tension coefficient and the surface area that is buried upon double strand formation. Structures were taken from 10 ns molecular dynamics simulations computed in a consistent fashion using explicit solvent, counterions, and the particle-mesh Ewald procedure. The present preliminary thermodynamic study suggests that the favorable binding free energy of the amide-3 DNA single strand to the complementary RNA is equally driven by electrostatic and nonpolar contributions to the binding compared to their natural analogues. In addition, molecular dynamics simulations in explicit water were performed on an amide-3 DNA single strand and the corresponding natural DNA. Results from the conformations cluster analysis of the simulated amide-3 DNA single strand ensembles suggest that the 25% of the population sampled within 10 ns has a pre-organized conformation where the sugar C3' endo pucker is favored at the 3'-flanking nucleotides. These structural and thermodynamic features contribute to the understanding of the observed increased affinities of the amide-3 DNA-RNA hybrids at the microscopic level.

Amides↗

PubMed2005

On the salt-induced stabilization of pair and many-body hydrophobic interactions.

Salting-out of hydrophobic solutes in aqueous salt solutions and their relevance to salt effects on biophysical phenomena are now well appreciated. Although salt effects on hydrophobic transfer have been well studied, to our knowledge, no quantitative molecular simulation study of salt-induced strengthening of hydrophobic interactions has yet been reported. Here we present quantitative characterization of salt-induced strengthening of hydrophobic interactions at the molecular and nanoscopic length scales through molecular dynamics simulations. Specifically, we quantify the effect of NaCl on the potential of mean force between molecular hydrophobic solutes (methanes) and on conformational equilibria of a 25-mer hydrophobic polymer that efficiently samples ensembles of compact and extended states in water. In both cases, we observe relative stabilization of compact conformations that is accompanied by a clear depletion of salt density (preferential exclusion) and a slight enhancement of water density (preferential hydration) in the solute vicinity. We show that the structural details of salt exclusion can be related to the salt-induced free energy changes using preferential interaction coefficients. We also test the applicability of surface-area-based models to describe the salt-induced free energy changes. These models provide a useful empirical description that can be used to predict the effects of salt on conformational equilibria of hydrophobic solutes. However, we find that the effective increase in the surface tension of the solute-aqueous solution interface depends on the type and concentration of salt as well as the length-scale (i.e., molecular vs nanoscopic) of the conformational change. These calculations underscore the utility of simulation studies to connect quantitatively structural details at the molecular level (described by preferential hydration/exclusion) to macroscopic solvation thermodynamics. The hydrophobic polymer also provides a useful model for studies of effect of thermodynamic variables (P, T, salt/additives) on many-body hydrophobic interactions at nanometer length scales.

Computer Simulation↗

PubMed2006

Atomic-level description of amyloid beta-dimer formation.

All-atom simulations have been carried out on a monomer and dimer of the aggregation-prone fragment (16-22) of amyloid beta peptide, which is implicated in Alzheimer's disease. The replica exchange molecular dynamics method, which has been successfully applied to peptide folding, is utilized as a means to sample the configurational space with proper Boltzmann weighting so that the structural, motional, and thermodynamic description of self-assembly can be obtained. The free energy landscape showing the delicate balance between different monomer and dimer conformations is mapped along carefully chosen reaction coordinates. The canonical ensembles at 38 different temperatures are used to describe the thermodynamics and the relative stabilities of at least six different dimer conformations including that of parallel and antiparallel orientations. We also delineate the nature of the molecular forces that activate and stabilize these different dimer conformations as a function of temperature, especially as related to secondary structural propensity of monomer. We identify parallel loop dimer conformations that are stabilized due to specific interactions with water molecules.

Amyloid beta-Peptides↗

PubMedDate not supplied

[Distribution of neural memory, loading factor, its regulation and optimization].

Recording and retrieving functions of the neural memory are simulated as a control of local conformational processes in neural synaptic fields. The localization of conformational changes is related to the afferent temporal-spatial pulse pattern flow, the microstructure of connections and a plurality of temporal delays in synaptic fields and afferent pathways. The loci of conformations are described by sets of afferent addresses named address domains. Being superimposed on each other, address domains form a multilayer covering of the address space of the neuron or the ensemble. The superposition factor determines the dissemination of the conformational process, and the fuzzing of memory, and its accuracy and reliability. The engram is formed as detects in the packing of the address space and hence can be retrieved in inverse form. The accuracy of the retrieved information depends on the threshold level of conformational transitions, the distribution of conformational changes in synaptic fields of the neuronal population, and the memory loading factor. The latter is represented in the model by a slow potential. It reflects total conformational changes and displaces the membrane potential to monostable conformational regimes, by governing the exit from the recording regime, the potentiation of the neurone, and the readiness to reproduction. A relative amplitude of the slow potential and the coefficient of postconformational modification of ionic conductivity, which provides maximum reliability, accuracy, and capacity of memory, are calculated.

Animals↗

PubMed2006

A novel high resolution Calpha--Calpha distance dependent force field based on a high quality decoy set.

This work presents a novel C(alpha)--C(alpha) distance dependent force field which is successful in selecting native structures from an ensemble of high resolution near-native conformers. An enhanced and diverse protein set, along with an improved decoy generation technique, contributes to the effectiveness of this potential. High quality decoys were generated for 1489 nonhomologous proteins and used to train an optimization based linear programming formulation. The goal in developing a set of high resolution decoys was to develop a simple, distance-dependent force field that yields the native structure as the lowest energy structure and assigns higher energies to decoy structures that are quite similar as well as those that are less similar. The model also includes a set of physical constraints that were based on experimentally observed physical behavior of the amino acids. The force field was tested on two sets of test decoys not in the training set and was found to excel on all the metrics that are widely used to measure the effectiveness of a force field. The high resolution force field was successful in correctly identifying 113 native structures out of 150 test cases and the average rank obtained for this test was 1.87. All the high resolution structures (training and testing) used for this work are available online and can be downloaded from http://titan.princeton.edu/HRDecoys.

Algorithms↗

PubMed1998

The changing nature of the protein folding transition state: implications for the shape of the free-energy profile for folding.

According to landscape theory proteins do not fold by localised pathways, but find their native conformation by a progressive organisation of an ensemble of partly folded structures down a folding funnel. Here, we use kinetics and protein engineering to investigate the shape of the free-energy profile for two-state folding, which is the macroscopic view of the funnel process for small and rapidly folding proteins. Our experiments are based mainly on structural changes of the transition state of chymotrypsin inhibitor 2 (CI2) upon destabilisation with temperature and GdnHCl. The transition state ensemble of CI2 is a localised feature in the free-energy profile that is sharply higher than the other parts of the activation barrier. The relatively fixed position of the CI2 transition state on the reaction coordinate makes it easy to characterise but contributes also to overshadow the rest of the free-energy profile, the shape of which is inaccessible for analysis. Results from mutants of CI2 and comparison with other two-state proteins, however, point at the possibility that the barrier for folding is generally broad and that localised transition states result from minor ripples in the free-energy profile. Accordingly, variabilities in the folding kinetics may not indicate different folding mechanisms, but could be accounted for by various degrees of ruggedness on top of very broad activation barriers for folding. The concept is attractive since it summarises a wide range of folding data which have previously seemed unrelated. It is also supported by theory. Consistent with experiment, broad barriers predict that new transition state ensembles are exposed upon extreme destabilisation or radical mutations.

Chymotrypsin↗

PubMed2004

The protein folding network.

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.

Models, Molecular↗

PubMed2005

Structural dissection of ATP turnover in the prototypical GHL ATPase TopoVI.

GHL proteins are functionally diverse enzymes defined by the presence of a conserved ATPase domain that self-associates to trap substrate upon nucleotide binding. The structural states adopted by these enzymes during nucleotide hydrolysis and product release, and their consequences for enzyme catalysis, have remained unclear. Here, we have determined a complete structural map of the ATP turnover cycle for topoVI-B, the ATPase subunit of the archaeal GHL enzyme topoisomerase VI. With this ensemble of structures, we show that significant conformational changes in the subunit occur first upon ATP binding, and subsequently upon release of hydrolyzed P(i). Together, these data provide a structural framework for understanding the role of ATP hydrolysis in the type II topoisomerase reaction. Our results also suggest that the GHL ATPase module is a molecular switch in which ATP hydrolysis serves as a prerequisite but not a driving force for substrate-dependent structural transitions in the enzyme.

Adenosine Triphosphatases↗

PubMed2001

A self-consistent knowledge-based approach to protein design.

A simple and very efficient protein design strategy is proposed by developing some recently introduced theoretical tools which have been successfully applied to exactly solvable protein models. The design approach is implemented by using three amino acid classes and it is based on the minimization of an appropriate energy function. For a given native state the results of the design procedure are compared, through a statistical analysis, with the properties of an ensemble of sequences folding in the same conformation. If the success rate is computed on those sites designed with high confidence, it can be as high as 80%. The method is also able to identify key sites for the folding process: results for 2ci2 and barnase are in very good agreement with experimental results.

Amino Acid Sequence↗