Stable and metastable states of human amylin in solution

Patients with type II diabetes exhibit fibrillar deposits of human amylin protein in the pancreas. It has been proposed that amylin oligomers arising along the aggregation or fibril-formation pathways are important in the genesis of the disease. In a step toward understanding these aggregation pathways, in this work we report the conformational preferences of human amylin monomer in solution using molecular simulations and infrared experiments. In particular, we identify a stable conformer that could play a key role in aggregation. We find that amylin adopts three stable conformations: one with an α-helical segment comprising residues 9-17 and a short antiparallel β-sheet comprising residues 24-28 and 31-35; one with an extended antiparallel β-hairpin with the turn region comprising residues 20-23; and one with no particular structure. Using detailed calculations, we determine the relative stability of these various conformations, finding that the β-hairpin conformation is the most stable, followed by the α-helical conformation, and then the unstructured coil. To test our predicted structure, we calculate its infrared spectrum in the amide I stretch regime, which is sensitive to secondary structure through vibrational couplings and linewidths, and compare it to experiment. We find that theoretically predicted spectra are in good agreement with the experimental line shapes presented herein. The implications of the monomer secondary structures on its aggregation pathway and on its interaction with cell membranes are discussed.     

Effect of Proline Mutations on the Monomer Conformations of Amylin

The formation of human islet amyloid polypeptide (hIAPP) is implicated in the loss of pancreatic β-cells in type II diabetes. Rat amylin, which differs from human amylin at six residues, does not lead to formation of amyloid fibrils. Pramlintide is a synthetic analog of human amylin that shares three proline substitutions with rat amylin. Pramlintide has a much smaller propensity to form amyloid aggregates and has been widely prescribed in amylin replacement treatment. It is known that the three prolines attenuate β-sheet formation. However, the detailed effects of these proline substitutions on full-length hIAPP remain poorly understood. In this work, we use molecular simulations and bias-exchange metadynamics to investigate the effect of proline substitutions on the conformation of the hIAPP monomer. Our results demonstrate that hIAPP can adopt various β-sheet conformations, some of which have been reported in experiments. The proline substitutions perturb the formation of long β-sheets and reduce their stability. More importantly, we find that all three proline substitutions of pramlintide are required to inhibit β conformations and stabilize the α-helical conformation. Fewer substitutions do not have a significant inhibiting effect.     

Monte carlo simulations of protein folding. II. Application to protein A,ROP, and crambin

The hierarchy of lattice Monte Carlo models described in the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 18:338–352, 1994) is applied to the simulation of protein folding and the prediction of 3-dimensional structure. Using sequence information alone, three proteins have been successfully folded: the B domain of staphylococcal protein A, a 120 residue, monomeric version of ROP dimer, and crambin. Starting from a random expanded conformation, the model proteins fold along relatively well-defined folding pathways. These involve a collection of early intermediates, which are followed by the final (and rate-determining) transition from compact intermediates closely resembling the molten globule state to the native-like state. The predicted structures are rather unique, with native-like packing of the side chains. The accuracy of the predicted native conformations is better than those obtained in previous folding simulations. The best (but by no means atypical) folds of protein A have a coordinate rms of 2.25 Å from the native Cα trace, and the best coordinate rms from crambin is 3.18 Å. For ROP monomer, the lowest coordinate rms from equivalent Cαs of ROP dimer is 3.65 Å. Thus, for two simple helical proteins and a small α/β protein, the ability to predict protein structure from sequence has been demonstrated. © 1994 John Wiley & Sons, Inc.     

Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes

Conformational transitions between open/closed or free/bound states in proteins possess functional importance. We propose a technique in which the collective modes obtained from an anisotropic network model (ANM) are used in conjunction with a Monte Carlo (MC) simulation approach, to investigate conformational transition pathways and pathway intermediates. The ANM-MC technique is applied to adenylate kinase (AK) and hemoglobin. The iterative method, in which normal modes are continuously updated during the simulation, proves successful in accomplishing the transition between open-closed conformations of AK and tense-relaxed forms of hemoglobin (C^α− root mean square deviations between two end structures of 7.13 Å and 3.55 Å, respectively). Target conformations are reached by root mean-square deviations of 2.27 Å and 1.90 Å for AK and hemoglobin, respectively. The intermediate conformations overlap with crystal structures from the AK family within a 3.0-Å root mean-square deviation. In the case of hemoglobin, the transition of tense-to-relaxed passes through the relaxed state. In both cases, the lowest-frequency modes are effective during transitions. The targeted Monte Carlo approach is used without the application of collective modes. Both the ANM-MC and targeted Monte Carlo techniques can explore sequences of events in transition pathways with an efficient yet realistic conformational search.     

Prediction of conformation of rat galanin in the presence and absence of water with the use of monte Carlo methods and the ECEPP/3 force field

The conformation of the 29-residue rat galanin neuropeptide was studied using the Monte Carlo with energy minimization (MCM) and electrostatically driven Monte Carlo (EDMC) methods. According to a previously elaborated procedure, the polypeptide chain was first treated in a united-residue approximation, in order to enable extensive exploration of the conformational space to be carried out (with the use of MCM), Then the low-energy united-residue conformations were converted to the all-atom representations, and EDMC simulations were carried out for the all-atom polypeptide chains, using the ECEPP/3 force field with hydration included. In order to estimate the effect of environment on galanin conformation, the low-energy conformations obtained as a result of these simulations were taken as starting structures for further EDMC runs that did not include hydration. The lowest-energy conformation obtained in aqueous solution calculations had a nonhelical N-terminal part packed against the nonpolar face of a residual helix that extended from Pro¹³ toward the C-terminus. One next lowest-energy structure was a nearly-all-helical conformation, but with a markedly higher energy. In contrast, all of the low-energy conformations in the absence of water were all-helical differing only by the extent to which the helix was kinked around Pro¹³. These results are in qualitative agreement with the available NMR and CD data of galanin in aqueous and nonaqueous solvents.     

The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Calculated pH-dependent population and protonation of carbon-monoxy-myoglobin conformers

X-ray structures of carbonmonoxymyoglobin (MbCO) are available for different pH values. We used conventional electrostatic continuum methods to calculate the titration behavior of MbCO in the pH range from 3 to 7. For our calculations, we considered five different x-ray structures determined at pH values of 4, 5, and 6. We developed a Monte Carlo method to sample protonation states and conformations at the same time so that we could calculate the population of the considered MbCO structures at different pH values and the titration behavior of MbCO for an ensemble of conformers. To increase the sampling efficiency, we introduced parallel tempering in our Monte Carlo method. The calculated population probabilities show, as expected, that the x-ray structures determined at pH 4 are most populated at low pH, whereas the x-ray structure determined at pH 6 is most populated at high pH, and the population of the x-ray structures determined at pH 5 possesses a maximum at intermediate pH. The calculated titration behavior is in better agreement with experimental results compared to calculations using only a single conformation. The most striking feature of pH-dependent conformational changes in MbCO-the rotation of His-64 out of the CO binding pocket-is reproduced by our calculations and is correlated with a protonation of His-64, as proposed earlier.     

Effect of Proline Mutations on the Monomer Conformations of Amylin

The formation of human islet amyloid polypeptide (hIAPP) is implicated in the loss of pancreatic β-cells in type II diabetes. Rat amylin, which differs from human amylin at six residues, does not lead to formation of amyloid fibrils. Pramlintide is a synthetic analog of human amylin that shares three proline substitutions with rat amylin. Pramlintide has a much smaller propensity to form amyloid aggregates and has been widely prescribed in amylin replacement treatment. It is known that the three prolines attenuate β-sheet formation. However, the detailed effects of these proline substitutions on full-length hIAPP remain poorly understood. In this work, we use molecular simulations and bias-exchange metadynamics to investigate the effect of proline substitutions on the conformation of the hIAPP monomer. Our results demonstrate that hIAPP can adopt various β-sheet conformations, some of which have been reported in experiments. The proline substitutions perturb the formation of long β-sheets and reduce their stability. More importantly, we find that all three proline substitutions of pramlintide are required to inhibit β conformations and stabilize the α-helical conformation. Fewer substitutions do not have a significant inhibiting effect.     

A Modified Valley Restrained Monte Carlo Method to Efficiently Search the Low Energy Structures of Peptides

Abstract

A new Monte Carlo sampling scheme, namely the Modified Valley Restrained Monte Carlo procedure, is used to obtain the global energy minimum conformations for polypeptides, such as Met-enkephalin and Melittin. For each peptide, we found close agreement with previous results from both theoretical and experimental studies. The simple idea for controlling the step size according to the Valley Function, provides useful suggestions in searching the global energy minimum structures, and furthermore helps solve the multiple minima problem.     

Characterizing aqueous solution conformations of a peptide backbone using Raman optical activity computations

Mounting spectroscopic evidence indicates that alanine predominantly adopts extended polyproline II (PPII) conformations in short polypeptides. Here we analyze Raman optical activity (ROA) spectra of N-acetylalanine-N′-methylamide (Ala dipeptide) in H₂O and D₂O using density functional theory on Monte Carlo (MC) sampled geometries to examine the propensity of Ala dipeptide to adopt compact right-handed (α_R) and left-handed (α_L) helical conformations. The computed ROA spectra based on MC-sampled α_R and PPII peptide conformations contain all the key spectral features found in the measured spectra. However, there is no significant similarity between the measured and computed ROA spectra based on the α_L- and β-conformations sampled by the MC methods. This analysis suggests that Ala dipeptide populates the α_R and PPII conformations but no substantial population of α_L- or β-structures, despite sampling α_L- and β-structures in our MC simulations. Thus, ROA spectra combined with the theoretical analysis allow us to determine the dominant populated structures. Including explicit solute-solvent interactions in the theoretical analysis is essential for the success of this approach.     

Rapid generation of a representative ensemble of N-glycan conformations

Glycosylated proteins are ubiquitous components of extracellular matrices and cellular surfaces where their oligosaccharide moieties are implicated in a wide range of cell-cell and cell-matrix recognition events. Glycans constitute highly flexible molecules. Only a small number of glycan X-ray structures is available for which sufficient electron density for an entire oligosaccharide chain has been observed. An unambiguous structure determination based on NMR-derived geometric constraints alone is often not possible. Time consuming computational approaches such as Monte Carlo calculations and molecular dynamics simulations have been widely used to explore the conformational space accessible to complex carbohydrates. The generation of a comprehensive data base for N-glycan fragments based on long time molecular dynamics simulations is presented. The fragments are chosen in such a way that the effects of branched N-glycan structures are taken into account. The prediction database constitutes the basis of a procedure to generate a complete set of all possible conformations for a given N-glycan. The constructed conformations are ranked according to their energy content. The resulting conformations are in reasonable agreement with experimental data. A web interface has been established (http://www.dkfz.de/spec/glydict/), which enables to input any N-glycan of interest and to receive an ensemble of generated conformations within a few minutes.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. I. Backbone structure of enkephalin

A new methodology for theoretically predicting the native, three-dimensional structure of a polypeptide is presented. Based on equilibrium statistical mechanics, an algorithm has been designed to determine the probable conformation of a polypeptide by calculating conditional free-energy maps for each residue of the macromolecule. The conditional free-energy map of each residue is computed from a set of probability integrals, obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. By locating the region(s) of lowest free energy for each map, the probable conformation for each residue can be identified. The native structure of the polypeptide is assumed to be the combination of the probable conformations of the individual residues. All multidimensional probability integrals are evaluated by an adaptive Monte Carlo algorithm (SMAPPS —Statistical-Mechanical Algorithm for Predicting Protein Structure). The Monte Carlo algorithm searches the entire conformational space, adjusting itself automatically to concentrate its sampling in regions where the magnitude of the integrand is largest (“importance sampling”). No assumptions are made about the native conformation. The only prior knowledge necessary for the prediction of the native conformation is the amino acid sequence of the polypeptide. To test the effectiveness of the algorithm, SMAPPS was applied to the prediction of the native conformation of the backbone of Met-enkephalin, a pentapeptide. In the calculations, only the backbone dihedral angles (? and ψ) were allowed to vary; all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to the alleged global minimum energy previously determined by direct energy minimization. For each conformation generated randomly by the Monte Carlo algorithm, the total conformational energy of the polypeptide was obtained from established empirical potential energy functions. Solvent effects were not included in the computations. With this initial application of SMAPPS , three distinct low-free-energy β-bend structures of Met-enkephalin were found. In particular, one of the structures has a conformation remarkably similar to the one associated with the previously alleged global minimum energy. The two additional structures of the pentapeptide have conformational energies lower than the previously computed low-energy structure. However, the Monte Carlo results are in agreement with an improved energy-minimization procedure. These initial results on the backbone structure of Met-enkephalin indicate that an equilibrium statistical-mechanical procedure, coupled with an adaptive Monte Carlo algorithm, can overcome many of the problems associated with the standard methods of direct energy minimization.     

Thermodynamic stability of beta-peptide helices and the role of cyclic residues

Beta-peptides are emerging as an attractive class of peptidomimetic molecules. In contrast to naturally occurring alpha-peptides, short oligomers of beta-amino acids (comprising just 4-6 monomers) exhibit stable secondary structures that make them amenable for quantitative, concerted experimental and theoretical studies of the effects of particular chemical interactions on structure. In this work, molecular simulations are used to study the thermodynamic stability of helical conformations formed by beta-peptides containing varying proportions of acyclic (beta(3)) and cyclic (ACH) residues. More specifically, several beta-peptides differing only in their content of cyclic residues are considered in this work. Previous computational studies of beta-peptides have relied mostly on energy minimization of molecular dynamics simulations. In contrast, our study relies on density-of-states based Monte Carlo simulations to calculate the free energy and examine the stability of various folded structures of these molecules along a well-defined order parameter. By resorting to an expanded-ensemble formalism, we are able to determine the free energy required to unfold specific molecules, a quantity that could be measured directly through single-molecule force spectroscopy. Simulations in both implicit and explicit solvents have permitted a systematic study of the role of cyclic residues and electrostatics on the stability of secondary structures. The molecules considered in this work are shown to exhibit stable H-14 helical conformations and, in some cases, relatively stable H-12 conformations, thereby suggesting that solvent quality may be used to manipulate the hydrogen-bonding patterns and structure of these peptides.     

Monte Carlo docking of oligopeptides to proteins.

A new two-step procedure has been developed for the docking of flexible oligopeptide chains of unknown conformation to static proteins of known structure. In the first step positions and conformations are sampled and the association energy minimized starting from an approximate preselected docking position. The resulting conformations are further optimized in the second step by a Metropolis Monte Carlo minimization, which optimizes each of these structures. The method has been tested on the HIV-1 aspartic proteinase complex with an inhibitor, whose crystallographic structure is known at 2.3 A resolution. Furthermore, the application of this method to the docking of the hendecapeptide 58-68 of the influenza A virus matrix protein to the HLA-A2 molecule produced results which are in agreement with experimental observations in identifying side chains critical for T cell recognition and residues responsible of MHC protein binding.     

Using robotics to fold proteins and dock ligands

The problems of protein folding and ligand docking have been explored largely using molecular dynamics or Monte Carlo methods. These methods are very compute intensive because they often explore a much wider range of energies, conformations and time than necessary. In addition, Monte Carlo methods often get trapped in local minima. We initially showed that robotic motion planning permitted one to determine the energy of binding and dissociation of ligands from protein binding sites (Singh et al., 1999). The robotic motion planning method maps complicated three-dimensional conformational states into a much simpler, but higher dimensional space in which conformational rearrangements can be represented as linear paths. The dimensionality of the conformation space is of the same order as the number of degrees of conformational freedom in three-dimensional space. We were able to determine the relative energy of association and dissociation of a ligand to a protein by calculating the energetics of interaction for a few thousand conformational states in the vicinity of the protein and choosing the best path from the roadmap. More recently, we have applied roadmap planning to the problem of protein folding (Apaydin et al., 2002a). We represented multiple conformations of a protein as nodes in a compact graph with the edges representing the probability of moving between neighboring states. Instead of using Monte Carlo simulation to simulate thousands of possible paths through various conformational states, we were able to use Markov methods to calculate the steady state occupancy of each conformation, needing to calculate the energy of each conformation only once. We referred to this Markov method of representing multiple conformations and transitions as stochastic roadmap simulation or SRS. We demonstrated that the distribution of conformational states calculated with exhaustive Monte Carlo simulations asymptotically approached the Markov steady state if the same Boltzman energy distribution was used in both methods. SRS permits one to calculate contributions from all possible paths simultaneously with far fewer energy calculations than Monte Carlo or molecular dynamics methods. The SRS method also permits one to represent multiple unfolded starting states and multiple, near-native, folded states and all possible paths between them simultaneously. The SRS method is also independent of the function used to calculate the energy of the various conformational states. In a paper to be presented at this conference (Apaydin et al., 2002b) we have also applied SRS to ligand docking in which we calculate the dynamics of ligand-protein association and dissociation in the region of various binding sites on a number of proteins. SRS permits us to determine the relative times of association to and dissociation from various catalytic and non-catalytic binding sites on protein surfaces. Instead of just following the best path in a roadmap, we can calculate the contribution of all the possible binding or dissociation paths and their relative probabilities and energies simultaneously.     

Effect of denaturant and protein concentrations upon protein refolding and aggregation: a simple lattice model.

We present a study of the competition between protein refolding and aggregation for simple lattice model proteins. The effect of solvent conditions (i.e., the denaturant concentration and the protein concentration) on the folding and aggregation behavior of a system of simple, two-dimensional lattice protein molecules has been investigated via (dynamic Monte Carlo simulations. The population profiles and aggregation propensities of the nine most populated intermediate configurations exhibit a complex dependence on the solution conditions that can be understood by considering the competition between intra- and interchain interactions. Some of these configurations are not even seen in isolated chain simulations; they are observed to be highly aggregation prone and are stabilized primarily by the aggregation reaction in multiple-chain systems. Aggregation arises from the association of partially folded intermediates rather than from the association of denatured random-coil states. The aggregation reaction dominates over the folding reaction at high protein concentration and low denaturant concentration, resulting in low refolding yields at those conditions. However, optimum folding conditions exist at which the refolding yield is a maximum, in agreement with some experimental observations.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Using a FRET Library with Multiple Probe Pairs To Drive Monte Carlo Simulations of α-Synuclein

We describe a strategy for experimentally-constraining computational simulations of intrinsically disordered proteins (IDPs), using α-synuclein, an IDP with a central role in Parkinson’s disease pathology, as an example. Previously, data from single-molecule Förster Resonance Energy Transfer (FRET) experiments have been effectively utilized to generate experimentally constrained computational models of IDPs. However, the fluorophores required for single-molecule FRET experiments are not amenable to the study of short-range (<30 Å) interactions. Using ensemble FRET measurements allows one to acquire data from probes with multiple distance ranges, which can be used to constrain Monte Carlo simulations in PyRosetta. To appropriately employ ensemble FRET data as constraints, we optimized the shape and weight of constraining potentials to afford ensembles of structures that are consistent with experimental data. We also used this approach to examine the structure of α-synuclein in the presence of the compacting osmolyte trimethylamine-N-oxide. Despite significant compaction imparted by 2 M trimethylamine-N-oxide, the underlying ensemble of α-synuclein remains largely disordered and capable of aggregation, also in agreement with experimental data. These proof-of-concept experiments demonstrate that our modeling protocol enables one to efficiently generate experimentally constrained models of IDPs that incorporate atomic-scale detail, allowing one to study an IDP under a variety of conditions.     

Folding of gas-phase polyalanines in a static electric field: alignment, deformations, and polarization effects

Monte Carlo simulations of the temperature-induced unfolding of small gas-phase polyalanines in a static, homogeneous electric field are reported, based on the AMBER ff96 force field. The peptides exhibit a structural transition from the native α-helix state to entropically favored β-sheet conformations, before eventually turning to extended coil at higher temperatures. Upon switching the electric field, the molecules undergo preferential alignment of their dipole moment vector toward the field axis and a shift of the α-β transition to higher temperatures. At higher field strengths (>10⁸ V/m) the molecules stretch and the α-β and β-coil transitions merge. A simple three-state model is shown to account for the observed behavior. Under even higher fields, density functional theory calculations and a polarizable force field both show that electronic rearrangements tend to further increase the dipole moment, polarization effects being approximately half in magnitude with respect to stretching effect. Finally a tentative (temperature, field-strength) phase diagram is sketched.