Regions Of Conformational Space Research Articles

Conformational Space Sampled by Domain Reorientation of Linear Diubiquitin Reflected in Its Binding Mode for Target Proteins.

Linear polyubiquitin chains regulate diverse signaling proteins, in which the chains adopt various conformations to recognize different target proteins. Thus, the structural plasticity of the chains plays an important role in controlling the binding events. Herein, paramagnetic NMR spectroscopy is employed to explore the conformational space sampled by linear diubiquitin, a minimal unit of linear polyubiquitin, in its free state. Rigorous analysis of the data suggests that, regarding the relative positions of the ubiquitin units, particular regions of conformational space are preferentially sampled by the molecule. By combining these results with further data collected for charge-reversal derivatives of linear diubiquitin, structural insights into the factors underlying the binding events of linear diubiquitin are obtained.

Controlled-advancement rigid-body optimization of nanosystems.

In this study, we propose a novel optimization algorithm, with application to the refinement of molecular complexes. Particularly, we consider optimization problem as the calculation of quasi-static trajectories of rigid bodies influenced by the inverse-inertia-weighted energy gradient and introduce the concept of advancement region that guarantees displacement of a molecule strictly within a relevant region of conformational space. The advancement region helps to avoid typical energy minimization pitfalls, thus, the algorithm is suitable to work with arbitrary energy functions and arbitrary types of molecular complexes without necessary tuning of its hyper-parameters. Our method, called controlled-advancement rigid-body optimization of nanosystems (Carbon), is particularly useful for the large-scale molecular refinement, as for example, the putative binding candidates obtained with protein-protein docking pipelines. Implementation of Carbon with user-friendly interface is available in the SAMSON platform for molecular modeling at https://www.samson-connect.net. © 2019 Wiley Periodicals, Inc.

Conformation of Ethylene Glycol in the Liquid State: Intra- versus Intermolecular Interactions.

Ethylene glycol is a typical rotor molecule with the three dihedral angles that allow for a number of possible conformers. The geometry of the molecule in the liquid state brings into sharp focus the competition between intra- and inter-molecular interactions in deciding conformation. Here, we report a conformational analysis of ethylene glycol in the liquid state from ab initio molecular dynamics simulations. Our results highlight the importance of intermolecular hydrogen bonding over intramolecular interactions in the liquid, with the central OCCO linkage adopting both gauche and trans geometries in contrast to the gas phase, wherein only the gauche has been reported. The influence of intermolecular interactions on the conformation of the terminal CCOH moieties is even more striking, with certain regions of conformational space, wherein the ethylene glycol molecule cannot participate with its full complement of intermolecular hydrogen bonds, excluded. The results are in agreement with Raman and NMR spectroscopic studies of liquid ethylene glycol, but at the same time they are able to provide new insights into how intermolecular interactions favor certain conformations while excluding others.

Charting molecular free-energy landscapes with an atlas of collective variables.

Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and β-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies.

Insights into Unfolded Proteins from the Intrinsic ϕ/ψ Propensities of the AAXAA Host-Guest Series

Various host-guest peptide series are used by experimentalists as reference conformational states. One such use is as a baseline for random-coil NMR chemical shifts. Comparison to this random-coil baseline, through secondary chemical shifts, is used to infer protein secondary structure. The use of these random-coil data sets rests on the perception that the reference chemical shifts arise from states where there is little or no conformational bias. However, there is growing evidence that the conformational composition of natively and nonnatively unfolded proteins fail to approach anything that can be construed as random coil. Here, we use molecular dynamics simulations of an alanine-based host-guest peptide series (AAXAA) as a model of unfolded and denatured states to examine the intrinsic propensities of the amino acids. We produced ensembles that are in good agreement with the experimental NMR chemical shifts and confirm that the sampling of the 20 natural amino acids in this peptide series is be far from random. Preferences toward certain regions of conformational space were both present and dependent upon the environment when compared under conditions typically used to denature proteins, i.e., thermal and chemical denaturation. Moreover, the simulations allowed us to examine the conformational makeup of the underlying ensembles giving rise to the ensemble-averaged chemical shifts. We present these data as an intrinsic backbone propensity library that forms part of our Structural Library of Intrinsic Residue Propensities to inform model building, to aid in interpretation of experiment, and for structure prediction of natively and nonnatively unfolded states.

Reaction Coordinates and Pathways of Mechanochemical Transformations.

The notions of a reaction path and a reaction coordinate are central to chemistry as they provide low-dimensional descriptions of complex molecular processes. Here we discuss how to define, compute, and use the reaction paths for chemical transformations in molecules that are subjected to mechanical stress and thus driven toward regions of conformational space that are otherwise inaccessible both in computational studies and in reality. We further show that the circuitous nature of mechanochemical pathways often makes their one-dimensional description impossible and describe how multidimensional effects can be detected experimentally.

Predictive Atomic Resolution Descriptions of Intrinsically Disordered hTau40 and α-Synuclein in Solution from NMR and Small Angle Scattering

The development of molecular descriptions of intrinsically disordered proteins (IDPs) is essential for elucidating conformational transitions that characterize common neurodegenerative disorders. We use nuclear magnetic resonance, small angle scattering, and molecular ensemble approaches to characterize the IDPs Tau and α-synuclein. Ensemble descriptions of IDPs are highly underdetermined due to the inherently large number of degrees of conformational freedom compared with available experimental measurements. Using extensive cross-validation we show that five different types of independent experimental parameters are predicted more accurately by selected ensembles than by statistical coil descriptions. The improvement increases in regions whose local sampling deviates from statistical coil, validating the derived conformational description. Using these approaches we identify enhanced polyproline II sampling in aggregation-nucleation sites, supporting suggestions that this region of conformational space is important for aggregation.

Glycan synthesis, structure, and dynamics: A selection

Glycan structural information is a prerequisite for elucidation of carbohydrate function in biological systems. To this end we employ a tripod approach for investigation of carbohydrate 3D structure and dynamics based on organic synthesis; different experimental spectroscopy techniques, NMR being of prime importance; and molecular simulations using, in particular, molecular dynamics (MD) simulations. The synthesis of oligosaccharides in the form of glucosyl fluorides is described, and their use as substrates for the Lam16A E115S glucosyl synthase is exemplified as well as a conformational analysis of a cyclic β-(1→3)-heptaglucan based on molecular simulations. The flexibility of the N-acetyl group of aminosugars is by MD simulations indicated to function as a gatekeeper for transitions of glycosidic torsion angles to other regions of conformational space. A novel approach to visualize glycoprotein (GP) structures is presented in which the protein is shown by, for example, ribbons, but instead of stick or space-filling models for the carbohydrate portion it is visualized by the colored geometrical figures known as CFG representation in a 3D way, which we denote 3D-CFG, thereby effectively highlighting the sugar residues of the glycan part of the GP and the position(s) on the protein.

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (ϕ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed ϕ/ψ combinations. The "bridge region" (ϕ ≤ 0° and -20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of ϕ/ψ angles in 850 non-homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B-factor less than 30 Ų. We show that the distribution of ϕ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.

The molecular structure and conformational characteristics of some specific benzodiazepine receptor ligands: A molecular orbital study of C3-substituted betacarboline derivatives

The molecular structures of the benzodiazepine receptor ligands {beta}-carboline-3-carboxylic acid (BCCA), its methyl, ethyl, and propyl esters (BCCM, BCCE, and BCCP, respectively), and 3-CN-{beta}-carboline (BC-3-CN) have been investigated on a minimal basis STO-3G level of accuracy. For BCCM, BCCE, and BCCP semiempirical AM 1 calculations have also been performed. Fully optimized molecular geometries are reported. Comparisons with available experimental structures indicate that minimal basis results may have a useful predictive value. For the mobile ester side chains, a study of chosen points on the conformational surface was made. Both the STO-3G and the AM 1 results give the planar conformers is the most stable structures with small barriers to internal rotation, provided the ester side chain remains extended. The calculated STO-3G rotational barriers are higher than are the corresponding AM 1 barriers. Partial optimization, i.e., of side-chain structure parameters only, seems sufficient to map the conformational characteristics of these compounds. The orientation of the dipole moment vector and its magnitude may have consequences for possible interaction with a receptor. On the basis of the sidechain internal dynamics, the intramolecular flexibility tends to be confined to certain regions of conformational space.

Unusual Temperature Dependence of Photosynthetic Electron Transfer due to Protein Dynamics

The initial electron transfer rate and protein dynamics in wild type and five mutant reaction centers from Rhodobacter sphaeroides have been studied as a function of temperature (10-295 K). Detailed kinetic measurements of initial electron transfer in Rhodobacter sphaeroides reaction centers can be quantitatively described by a reaction diffusion formalism at all temperatures from 10 to 295 K. In this model, the time course of electron transfer is determined by the ability of the protein to interconvert between conformations until one is found where the activation energy for electron transfer is near zero. In reaction centers with a free energy for electron transfer similar to wild type, the reaction proceeds at least as fast at cryogenic temperatures as at room temperature. This may be because interconversion between conformations at low temperature is restricted to conformations with near zero activation energy (it is not possible to diffuse away from this region of conformational space). In contrast, mutants with a decreased free energy initially find themselves in conformations unfavorable for electron transfer and require more extensive conformational diffusion to achieve a low activation energy conformation. They therefore undergo electron transfer more slowly at 10 K vs 295 K.

Dinucleotide TpT and Its 2‘-O-Me Analogue Possess Different Backbone Conformations and Flexibilities but Similar Stacked Geometries

UV irradiation at 254 nm of 2'-O,5-dimethyluridylyl(3'-5')-2'-O,5-dimethyluridine (1a) and of natural thymidylyl(3'-5')thymidine (1b) generates the same photoproducts (CPD and (6-4)PP; responsible for cell death and skin cancer). The ratios of quantum yields of photoproducts obtained from 1a (determined herein) to that from 1b are in a proportion close to the approximately threefold increase of stacked dinucleotides for 1a compared with those of 1b (from previous circular dichroism results). 1a and 1b however are endowed with different predominant sugar conformations, C3'-endo (1a) and C2'-endo (1b). The present investigation of the stacked conformation of these molecules, by unrestrained state-of-the-art molecular simulation in explicit solvent and salt, resolves this apparent paradox and suggests the following main conclusions. Stacked dinucleotides 1a and 1b adopt the main characteristic features of a single-stranded A and B form, respectively, where the relative positions of the backbone and the bases are very different. Unexpectedly, the geometry of the stacking of two thymine bases, within each dinucleotide, is very similar and is in excellent agreement with photochemical and circular dichroism results. Analyses of molecular dynamics trajectories with conformational adiabatic mapping show that 1a and 1b explore two different regions of conformational space and possess very different flexibilities. Therefore, even though their base stacking is very similar, these molecules possess different geometrical, mechanical, and dynamical properties that may account for the discrepancy observed between increased stacking and increased photoproduct formations. The computed average stacked conformations of 1a and 1b are well-defined and could serve as starting models to investigate photochemical reactions with quantum dynamics simulations.

Exploring the relationship between funneled energy landscapes and two‐state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

Validation of a search technique for crystal structure prediction of flexible molecules by application to piracetam

A new approach to the crystal structure prediction of flexible molecules is presented. It is applied to piracetam, whose conformational polymorphs exhibit a variety of hydrogen-bond motifs but lack the intramolecular hydrogen bond found in the gas-phase ab initio optimized conformer. Stable crystal packing can result when favourable intermolecular interactions are made possible when the molecule distorts from the gas-phase conformation. If the resulting intermolecular lattice energy is sufficiently favourable to compensate for the intramolecular energy penalty associated with the suboptimal gas-phase conformation, then the crystal structure may be experimentally feasible. The new approach involves searching for low-energy crystal structures using a large number of rigid conformers, firstly to systematically explore which regions of conformational space could give rise to low-energy hydrogen-bonded crystal structures, and then to refine the search using crystallographic insight to optimize particular intermolecular interactions. The timely discovery of a new polymorph (form IV) by an independent experimental team allowed this approach to be validated by way of a ;blind test' of crystal structure prediction. Form IV was successfully identified as the most favourable computed crystal structure with a conformation very distinct from that in the previously known polymorphs.

Unfolding crystallins: The destabilizing role of a β‐hairpin cysteine in βB2‐crystallin by simulation and experiment

The thermodynamic and kinetic stabilities of the eye lens family of betagamma-crystallins are important factors in the etiology of senile cataract. They control the chance of proteins unfolding, which can lead to aggregation and loss of transparency. betaB2-Crystallin orthologs are of low stability and comprise two typical betagamma-crystallin domains, although, uniquely, the N-terminal domain has a cysteine in one of the conserved folded beta-hairpins. Using high-temperature (500 K) molecular dynamics simulations with explicit solvent on the N-terminal domain of rodent betaB2-crystallin, we have identified in silico local flexibility in this folded beta-hairpin. We have shown in vitro using two-domain human betaB2-crystallin that replacement of this cysteine with a more usual aromatic residue (phenylalanine) results in a gain in conformational stability and a reduction in the rate of unfolding. We have used principal components analysis to visualize and cluster the coordinates from eight separate simulated unfolding trajectories of both the wild-type and the C50F mutant N-terminal domains. These data, representing fluctuations around the native well, show that although the mutant and wild-type appear to behave similarly over the early time period, the wild type appears to explore a different region of conformational space. It is proposed that the advantage of having this low-stability cysteine may be correlated with a subunit-exchange mechanism that allows betaB2-crystallin to interact with a range of other beta-crystallin subunits.

Temperature Weighted Histogram Analysis Method, Replica Exchange, and Transition Paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.

Protein folding and the organization of the protein topology universe

The mechanism by which proteins fold to their native states has been the focus of intense research in recent years. The rate-limiting event in the folding reaction is the formation of a conformation in a set known as the transition-state ensemble. The structural features present within such ensembles have now been analysed for a series of proteins using data from a combination of biochemical and biophysical experiments together with computer-simulation methods. These studies show that the topology of the transition state is determined by a set of interactions involving a small number of key residues and, in addition, that the topology of the transition state is closer to that of the native state than to that of any other fold in the protein universe. Here, we review the evidence for these conclusions and suggest a molecular mechanism that rationalizes these findings by presenting a view of protein folds that is based on the topological features of the polypeptide backbone, rather than the conventional view that depends on the arrangement of different types of secondary-structure elements. By linking the folding process to the organization of the protein structure universe, we propose an explanation for the overwhelming importance of topology in the transition states for protein folding.

Sweetening Cyclic Peptide Libraries

Enzymatic macrolactamization of linear glycosidated peptides provides access to an important class of drug-like molecules. The work presented in this issue [1] shows that it may be possible to make complex libraries of glycosidated cyclic peptides by incorporating glycosidated amino acids into linear peptides via solid-phase peptide synthesis followed by thioesterase-mediated peptide cyclization.

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.

Designing refoldable model molecules.

We report a numerical study of the design of lattice heteropolymers that can refold when the properties of only a few monomers are changed. If we assume that the effect of an external agent on a heteropolymer is to alter the interactions between its constituent monomers, our simulations provide a description of a simple allosteric transition. We characterize the free energy surfaces of the initial and the modified chain molecule. We find that there is a region of conformation space where molecules can be made to refold with minimal free energy cost. This region is accessible by thermal fluctuations. The efficiency of a motor based on such an allosteric transition would be enhanced by "borrowing" heat from the environment in the initial stages of the refolding, and "paying back" later. In fact, the power cycle of many real molecular motors does involve such a borrowing activation step.