The folding funnel landscape for the peptide Met-enkephalin

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Protein structure predictions by enhanced conformational sampling methods

In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō's 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.

The conformation of enkephalin bound to its receptor: an "elusive goal" becoming reality

The availability of solid state structures of opioid receptors has prompted us to reconsider a crucial question concerning bioactive peptides: can their conformation be studied without any knowledge of the structure of their receptors? The possibility of giving a meaningful answer to this query rests ultimately on the ease of dealing with the flexibility of bioactive peptides, and amongst them one of the most flexible bioactive peptides, enkephalin. All solution studies of enkephalin hint at an inextricable mixture of quasi isoenergetic conformers. In this study we refer to the only NMR work that yielded inter-residue NOEs, performed at very low temperature. In the present work, we have used the simplest possible docking methods to check the consistency of the main conformers of enkephalin with the steric requirements of the active site of the receptor, as provided by the crystal structure of its complex with naltrindole, a rigid antagonist. We show that the conformers found in the equilibrium mixture at low temperature are indeed compatible with a good fit to the receptor active site. The possible uncertainties linked to the different behavior of agonists and antagonists do not diminish the relevance of the finding.

The free energy landscape in translational science: how can somatic mutations result in constitutive oncogenic activation?

The free energy landscape theory has transformed the field of protein folding. The significance of perceiving function in terms of conformational heterogeneity is gradually shifting the interest in the community from folding to function. From the free energy landscape standpoint the principles are unchanged: rather than considering the entire protein conformational landscape, the focus is on the ensemble around the bottom of the folding funnel. The protein can be viewed as populating one of two states: active or inactive. The basins of the two states are separated by a surmountable barrier, which allows the conformations to switch between the states. Unless the protein is a repressor, under physiological conditions it typically populates the inactive state. Ligand binding (or post-translational modification) triggers a switch to the active state. Constitutive allosteric mutations work by shifting the population from the inactive to the active state and keeping it there. This can happen by either destabilizing the inactive state, stabilizing the active state, or both. Identification of the mechanism through which they work is important since it may assist in drug discovery. Here we spotlight the usefulness of the free energy landscape in translational science, illustrating how oncogenic mutations can work in key proteins from the EGFR/Ras/Raf/Erk/Mek pathway, the main signaling pathway in cancer. Finally, we delineate the key components which are needed in order to trace the mechanism of allosteric events.

Reconstructing the free-energy landscape of Met-enkephalin using dihedral principal component analysis and well-tempered metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers, however, from the same limitation, i.e., the non-trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachandran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates, and does not depend on the alignment to an arbitrarily chosen reference structure as usual in Cartesian PCA. We illustrate the robustness of this method in the case of a reference model protein, the small and very diffusive Met-enkephalin pentapeptide. We propose a justification a posteriori of the considered number of CVs necessary to bias the metadynamics simulation in terms of the one-dimensional free-energy profiles associated with Ramachandran dihedral angles along the amino-acid sequence.

Multiple replica repulsion technique for efficient conformational sampling of biological systems

Here, we propose a technique for sampling complex molecular systems with many degrees of freedom. The technique, termed "multiple replica repulsion" (MRR), does not suffer from poor scaling with the number of degrees of freedom associated with common replica exchange procedures and does not require sampling at high temperatures. The algorithm involves creation of multiple copies (replicas) of the system, which interact with one another through a repulsive potential that can be applied to the system as a whole or to portions of it. The proposed scheme prevents oversampling of the most populated states and provides accurate descriptions of conformational perturbations typically associated with sampling ground-state energy wells. The performance of MRR is illustrated for three systems of increasing complexity. A two-dimensional toy potential surface is used to probe the sampling efficiency as a function of key parameters of the procedure. MRR simulations of the Met-enkephalin pentapeptide, and the 76-residue protein ubiquitin, performed in presence of explicit water molecules and totaling 32 ns each, investigate the ability of MRR to characterize the conformational landscape of the peptide, and the protein native basin, respectively. Results obtained for the enkephalin peptide reflect more closely the extensive conformational flexibility of this peptide than previously reported simulations. Those obtained for ubiquitin show that conformational ensembles sampled by MRR largely encompass structural fluctuations relevant to biological recognition, which occur on the microsecond timescale, or are observed in crystal structures of ubiquitin complexes with other proteins. MRR thus emerges as a very promising simple and versatile technique for modeling the structural plasticity of complex biological systems.

MOLS sampling and its applications in structural biophysics

This review describes the MOLS method and its applications. This computational method has been developed in our laboratory primarily to explore the conformational space of small peptides and identify features of interest, particularly the minima, i.e., the low energy conformations. A systematic "brute-force" search through the vast conformational space for such features faces the insurmountable problem of combinatorial explosion, whilst other techniques, e.g., Monte Carlo searches, are somewhat limited in their region of exploration and may be considered inexhaustive. The MOLS method, on the other hand, uses a sampling technique commonly employed in experimental design theory to identify a small sample of the conformational space that nevertheless retains information about the entire space. The information is extracted using a technique that is a variant of the self-consistent mean field technique, which has been used to identify, for example, the optimal set of side-chain conformations in a protein. Applications of the MOLS method to understand peptide structure, predict the structures of loops in proteins, predict three-dimensional structures of small proteins, and arrive at the best conformation, orientation, and positions of a small molecule ligand in a protein receptor site have all yielded satisfactory results.

NCAD, a database integrating the intrinsic conformational preferences of non-coded amino acids

Peptides and proteins find an ever-increasing number of applications in the biomedical and materials engineering fields. The use of non-proteinogenic amino acids endowed with diverse physicochemical and structural features opens the possibility to design proteins and peptides with novel properties and functions. Moreover, non-proteinogenic residues are particularly useful to control the three-dimensional arrangement of peptidic chains, which is a crucial issue for most applications. However, information regarding such amino acids--also called non-coded, non-canonical, or non-standard--is usually scattered among publications specialized in quite diverse fields as well as in patents. Making all these data useful to the scientific community requires new tools and a framework for their assembly and coherent organization. We have successfully compiled, organized, and built a database (NCAD, Non-Coded Amino acids Database) containing information about the intrinsic conformational preferences of non-proteinogenic residues determined by quantum mechanical calculations, as well as bibliographic information about their synthesis, physical and spectroscopic characterization, conformational propensities established experimentally, and applications. The architecture of the database is presented in this work together with the first family of non-coded residues included, namely, alpha-tetrasubstituted alpha-amino acids. Furthermore, the NCAD usefulness is demonstrated through a test-case application example.

Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables

A new implementation of the adaptive biasing force (ABF) method is described. This implementation supports a wide range of collective variables and can be applied to the computation of multidimensional energy profiles. It is provided to the community as part of a code that implements several analogous methods, including metadynamics. ABF and metadynamics have not previously been tested side by side on identical systems. Here, numerical tests are carried out on processes including conformational changes in model peptides and translocation of a halide ion across a lipid membrane through a peptide nanotube. On the basis of these examples, we discuss similarities and differences between the ABF and metadynamics schemes. Both approaches provide enhanced sampling and free energy profiles in quantitative agreement with each other in different applications. The method of choice depends on the dimension of the reaction coordinate space, the height of the barriers, and the relaxation times of degrees of freedom in the orthogonal space, which are not explicitly described by the chosen collective variables.

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.

Exploring conformational space using a mean field technique with MOLS sampling

The computational identification of all the low energy structures of a peptide given only its sequence is not an easy task even for small peptides,due to the multiple-minima problem and combinatorial explosion. We have developed an algorithm, called the MOLS technique,that addresses this problem, and have applied it to a number of different aspects of the study of peptide and protein structure. Conformational studies of oligopeptides, including loop sequences in proteins have been carried out using this technique. In general the calculations identified all the folds determined by previous studies,and in addition picked up other energetically favorable structures. The method was also used to map the energy surface of the peptides. In another application, we have combined the MOLS technique, using it to generate a library of low energy structures of an oligopeptide, with a genetic algorithm to predict protein structures. The method has also been applied to explore the conformational space of loops in protein structures.Further, it has been applied to the problem of docking a ligand in its receptor site, with encouraging results.

Structural properties of small semiconductor-binding synthetic peptides

We have performed exhaustive multicanonical Monte Carlo simulations of three 12-residue synthetic peptides in order to investigate the thermodynamic and structural properties as well as the characteristic helix-coil transitions. In these studies, we employ a realistic model where the interactions between all atoms are taken into account. Effects of solvation are also simulated by using an implicit-solvent model.

Conformational study of Met-enkephalin based on the ECEPP force fields

We report a computational study of the small peptide Met-enkephalin based on the ECEPP/2 and ECEPP/3 force fields using the basin paving method. We have located a new global minimum when using the ECEPP/3 force field with peptide angles omega fixed at 180 degrees. With this new result, we can conclude that the lowest energy configurations of Met-enkephalin predicted based on all four versions of ECEPP have a classic gamma-turn centered at residue Gly3 and a beta-turn at residues Gly3-Phe4. However, minor differences between the structures also exist.

Molecular mechanism for stabilizing a short helical peptide studied by generalized-ensemble simulations with explicit solvent

We study the folding mechanism of an analog of the C-peptide of ribonuclease A in explicit water by a replica-exchange multicanonical molecular dynamics simulation based on all-atom models. The multicanonical weight factor was determined by the combined use of the multicanonical replica-exchange method and the replica-exchange multicanonical algorithm. Using statistically reliable data thus obtained, we have examined the free-energy landscape of the peptide system. The global-minimum free-energy state in the landscape at room temperature has an alpha-helix structure with a distortion near the N-terminus. The state also has a salt bridge between Glu(-)-2 and Arg(+)-10 and an aromatic-aromatic interaction between Phe-8 and His(+)-12, both of which have been observed in x-ray and other experimental measurements. Principal component analysis clearly shows the different roles of these side-chain interactions in the peptide folding. The side-chain interaction between Phe-8 and His(+)-12 greatly enhances the stability of helical structure toward the C-terminal end, whereas the salt bridge between Glu(-)-2 and Arg(+)-10 mainly works as a restraint to prevent the alpha-helix structure from extending to the N-terminus. The free-energy landscape of C-peptide reveals a funnel-like shape where all of these interactions consistently exist only in the global-minimum state. This is the major reason why the native structure of the short helical peptide shows significant stability at low temperatures.

A structural model of polyglutamine determined from a host-guest method combining experiments and landscape theory

Modeling the structure of natively disordered peptides has proved difficult due to the lack of structural information on these peptides. In this work, we use a novel application of the host-guest method, combining folding theory with experiments, to model the structure of natively disordered polyglutamine peptides. Initially, a minimalist molecular model (C(alpha)C(beta)) of CI2 is developed with a structurally based potential and captures many of the folding properties of CI2 determined from experiments. Next, polyglutamine "guest" inserts of increasing length are introduced into the CI2 "host" model and the polyglutamine is modeled to match the resultant change in CI2 thermodynamic stability between simulations and experiments. The polyglutamine model that best mimics the experimental changes in CI2 thermodynamic stability has 1), a beta-strand dihedral preference and 2), an attractive energy between polyglutamine atoms 0.75-times the attractive energy between the CI2 host Go-contacts. When free-energy differences in the CI2 host-guest system are correctly modeled at varying lengths of polyglutamine guest inserts, the kinetic folding rates and structural perturbation of these CI2 insert mutants are also correctly captured in simulations without any additional parameter adjustment. In agreement with experiments, the residues showing structural perturbation are located in the immediate vicinity of the loop insert. The simulated polyglutamine loop insert predominantly adopts extended random coil conformations, a structural model consistent with low resolution experimental methods. The agreement between simulation and experimental CI2 folding rates, CI2 structural perturbation, and polyglutamine insert structure show that this host-guest method can select a physically realistic model for inserted polyglutamine. If other amyloid peptides can be inserted into stable protein hosts and the stabilities of these host-guest mutants determined, this novel host-guest method may prove useful to determine structural preferences of these intractable but biologically relevant protein fragments.

Metropolis simulations of Met-Enkephalin with solvent-accessible area parametrizations

We investigate the solvent-accessible area method by means of Metropolis simulations of the brain peptide Met-Enkephalin at 300 K. For the energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied. The simulations are compared with one another, with simulations with a distance dependent electrostatic permittivity epsilon(r), and with vacuum simulations (epsilon=2). Parallel tempering and the biased Metropolis techniques RM1 are employed and their performance is evaluated. The measured observables include energy and dihedral probability densities, integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other systems selected configurations are minimized in the search for global energy minima, which are found for vacuum and the epsilon(r) system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, we find three ASP sets for which the autocorrelations at 300 K are considerably smaller than those for vacuum simulations.

Multioverlap simulations for transitions between reference configurations

We introduce a procedure to construct weight factors, which flatten the probability density of the overlap with respect to some predefined reference configuration. This allows one to overcome free-energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brain peptide Met-enkephalin with the ECEPP/2 (Empirical Conformational Energy Program for Peptides) energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free-energy barrier.

Metropolis importance sampling for rugged dynamical variables

A funnel transformation is introduced, which acts recursively from higher towards lower temperatures. It biases the a priori probabilities of a canonical or generalized ensemble Metropolis simulation, so that they zoom in on the global energy minimum, if a funnel exists indeed. A first, crude approximation to the full transformation, called rugged Metropolis one (RM1), is tested for Met-Enkephalin. At 300 K the computational gain is a factor of 2 and, due to its simplicity, RM1 is well suited to replace the conventional Metropolis updating for these kinds of systems.

Efficiency of the multicanonical simulation method as applied to peptides of increasing size: the heptapeptide deltorphin

The advantage of the multicanonical (MUCA) simulation method of Berg and coworkers over the conventional Metropolis method is in its ability to move a system effectively across energy barriers thereby providing results for a wide range of temperatures. However, a MUCA simulation is based on weights (related to the density of states) that should be determined prior to a production run and their calculation is not straightforward. To overcome this difficulty a procedure has been developed by Berg that calculates the MUCA weights automatically. In a previous article (Yaşar et al. J Comput Chem 2000, 14, 1251-1261) we extended this procedure to continuous systems and applied it successfully to the small pentapeptide Leu-enkephalin. To investigate the performance of the automated MUCA procedure for larger peptides, we apply it here to deltorphin, a linear heptapeptide with bulky side chains (H-Tyr(1)-D-Met(2)-Phe(3)-His(4)-Leu(5)-Met(6)-Asp(7)-NH(2)). As for Leu-enkephalin, deltorphin is modeled in vacuum by the potential energy function ECEPP. MUCA is found to perform well. A weak second peak is seen for the specific heat, which is given a special attention. By minimizing the energy of structures along the trajectory it is found that MUCA provides a good conformational coverage of the low energy region of the molecule. These latter results are compared with conformational coverage obtained by the Monte Carlo minimization method of Li and Scheraga.

Structure of Met-enkephalin in explicit aqueous solution using replica exchange molecular dynamics

Replica exchange molecular dynamics (MD) simulations of Met-enkephalin in explicit solvent reveal helical and nonhelical structures. Four predominant structures of Met-enkephalin are sampled with comparable probabilities (two helical and two nonhelical). The energy barriers between these configurations are low, suggesting that Met-enkephalin switches easily between configurations. This is consistent with the requirement that Met-enkephalin be sufficiently flexible to bind to several different receptors. Replica exchange simulations of 32 ns are shown to sample approximately five times more configurational space than constant temperature MD simulations of the same duration. The energy landscape for the replica exchange simulation is presented. A detailed study of replica trajectories demonstrates that the significant increases in temperature provided by the replica exchange technique enable transitions from nonhelical to helical structures that would otherwise be prevented by kinetic trapping. Met-enkephalin (Type Entrez Proteins; Value A61445; Service Entrez Proteins).

Proteinlike behavior of a spin system near the transition between a ferromagnet and a spin glass

A simple spin system is studied as an analog for proteins. We investigate how the introduction of randomness and frustration into the system affects the designability and stability of ground-state configurations. We observe that the spin system exhibits proteinlike behavior in the vicinity of the transition between a ferromagnet and a spin glass. Our results illuminate some guiding principles in protein evolution.

Generalized-ensemble algorithms for molecular simulations of biopolymers

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.

Identification and ab initio simulations of early folding units in proteins

The location of protein subunits that form early during folding, constituted of consecutive secondary structure elements with some intrinsic stability and favorable tertiary interactions, is predicted using a combination of threading algorithms and local structure prediction methods. Two folding units are selected among the candidates identified in a database of known protein structures: the fragment 15-55 of 434 cro, an all-alpha protein, and the fragment 1-35 of ubiquitin, an alpha/beta protein. These units are further analyzed by means of Monte Carlo simulated annealing using several database-derived potentials describing different types of interactions. Our results suggest that the local interactions along the chain dominate in the first folding steps of both fragments, and that the formation of some of the secondary structures necessarily occurs before structure compaction. These findings led us to define a prediction protocol, which is efficient to improve the accuracy of the predicted structures. It involves a first simulation with a local interaction potential only, whose final conformation is used as a starting structure of a second simulation that uses a combination of local interaction and distance potentials. The root mean square deviations between the coordinates of predicted and native structures are as low as 2-4 A in most trials. The possibility of extending this protocol to the prediction of full proteins is discussed. Proteins 2001;42:164-176.

Modeling the third loop of short-chain snake venom neurotoxins: roles of the short-range and long-range interactions

The influence of long-range interactions on local structures is an important issue in understanding protein folding process and protein structure stability. Using short-chain snake venom neurotoxin as a model system, we have studied the conformational properties of eight different loop III sequences either in the environment of one of the short-chain neurotoxin, erabutoxin b (PDB ID 1nxb), or in free state by Monte Carlo simulated annealing method. The surrounding protein structure was found to be crucial in stabilizing the loop conformation. Although all the eight peptides prefer type V beta turn in solution, three of them (KPGI, KPGV, KSGI) turn to type II beta turn and the other five (KKGI, KKGV, KNGI, KQGI, and KRGV) are confined to more rigid type V beta turn conformation in the protein structure. Using flexible tetra-glycine-peptide to screen the backbone conformational space in the protein environment also validates the results. This study shows that long-range interactions do contribute to the stability and the types of conformation for a surface loop in protein, while short-range interactions may only provide candidate conformations, which then have to be filtered by the long-range interactions further.

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.

New Monte Carlo algorithms for protein folding

Over the past three decades, a number of powerful simulation algorithms have been introduced to the protein folding problem. For many years, the emphasis has been placed on how to both overcome the multiple minima problem and find the conformation with the global minimum potential energy. Since the new view of the protein folding mechanism (based on the free energy landscape of the protein system) arose in the past few years, however, it is now of interest to obtain a global knowledge of the phase space, including the intermediate and denatured states of proteins. Monte Carlo methods have proved especially valuable for these purposes. As well as new, powerful optimization techniques, novel algorithms that can sample much a wider phase space than conventional methods have been established.

Temperature dependence of distributions of conformations of a small peptide

Multicanonical Monte Carlo simulations of the pentapeptide Met-enkephalin were used to study its low-energy conformations in detail. The resulting conformations are classified into six categories of similar structures based on the pattern of intrachain hydrogen bonds. Several thermodynamic quantities such as the distributions of hydrogen bonds and those of backbone dihedral angles were obtained as a function of temperature. From these results, it was concluded that at least four of the six categories are well-defined local minimum energy states. These four categories are in agreement with our prior results based on root-mean-square interatomic distances.