Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation

Integrated Design of a Membrane-Lytic Peptide-Based Intravenous Nanotherapeutic Suppresses Triple-Negative Breast Cancer

Membrane-lytic peptides offer broad synthetic flexibilities and design potential to the arsenal of anticancer therapeutics, which can be limited by cytotoxicity to noncancerous cells and induction of drug resistance via stress-induced mutagenesis. Despite continued research efforts on membrane-perforating peptides for antimicrobial applications, success in anticancer peptide therapeutics remains elusive given the muted distinction between cancerous and normal cell membranes and the challenge of peptide degradation and neutralization upon intravenous delivery. Using triple-negative breast cancer as a model, the authors report the development of a new class of anticancer peptides. Through function-conserving mutations, the authors achieved cancer cell selective membrane perforation, with leads exhibiting a 200-fold selectivity over non-cancerogenic cells and superior cytotoxicity over doxorubicin against breast cancer tumorspheres. Upon continuous exposure to the anticancer peptides at growth-arresting concentrations, cancer cells do not exhibit resistance phenotype, frequently observed under chemotherapeutic treatment. The authors further demonstrate efficient encapsulation of the anticancer peptides in 20 nm polymeric nanocarriers, which possess high tolerability and lead to effective tumor growth inhibition in a mouse model of MDA-MB-231 triple-negative breast cancer. This work demonstrates a multidisciplinary approach for enabling translationally relevant membrane-lytic peptides in oncology, opening up a vast chemical repertoire to the arms race against cancer.

Predicting Membrane-Active Peptide Dynamics in Fluidic Lipid Membranes

Understanding the interactions between peptides and lipid membranes could not only accelerate the development of antimicrobial peptides as treatments for infections but also be applied to finding targeted therapies for cancer and other diseases. However, designing biophysical experiments to study molecular interactions between flexible peptides and fluidic lipid membranes has been an ongoing challenge. Recently, with hardware advances, algorithm improvements, and more accurate parameterizations (i.e., force fields), all-atom molecular dynamics (MD) simulations have been used as a "computational microscope" to investigate the molecular interactions and mechanisms of membrane-active peptides in cell membranes (Chen et al., Curr Opin Struct Biol 61:160-166, 2020; Ulmschneider and Ulmschneider, Acc Chem Res 51(5):1106-1116, 2018; Dror et al., Annu Rev Biophys 41:429-452, 2012). In this chapter, we describe how to utilize MD simulations to predict and study peptide dynamics and how to validate the simulations by circular dichroism, intrinsic fluorescent probe, membrane leakage assay, electrical impedance, and isothermal titration calorimetry. Experimentally validated MD simulations open a new route towards peptide design starting from sequence and structure and leading to desirable functions.

Applications of Molecular Dynamics Simulation in Structure Prediction of Peptides and Proteins

Compared with rapid accumulation of protein sequences from high-throughput DNA sequencing, obtaining experimental 3D structures of proteins is still much more difficult, making protein structure prediction (PSP) potentially very useful. Currently, a vast majority of PSP efforts are based on data mining of known sequences, structures and their relationships (informatics-based). However, if closely related template is not available, these methods are usually much less reliable than experiments. They may also be problematic in predicting the structures of naturally occurring or designed peptides. On the other hand, physics-based methods including molecular dynamics (MD) can utilize our understanding of detailed atomic interactions determining biomolecular structures. In this mini-review, we show that all-atom MD can predict structures of cyclic peptides and other peptide foldamers with accuracy similar to experiments. Then, some notable successes in reproducing experimental 3D structures of small proteins through MD simulations (some with replica-exchange) of the folding were summarized. We also describe advancements of MD-based refinement of structure models, and the integration of limited experimental or bioinformatics data into MD-based structure modeling.

Peptide and Protein Structure Prediction with a Simplified Continuum Solvent Model

A continuum solvent model based on screened Coulomb potentials has been simplified and parametrized to sample native-like structures in replica-exchange simulations of each of six different peptides and miniproteins. Low-energy, native, and non-native structures were used to iteratively refine 11 parameter values. The centroid of the largest cluster of structures sampled in simulations initiated from an extended conformation represents the predicted structure. The main-chain rms deviation of this prediction from the experimental structure was 0.47 Å for the 12-residue Trp-zip2, 0.86 Å for the 14-residue MBH12, 2.53 Å for the 17-residue U(1-17)T9D, 2.03 Å for the 20-residue BS1, 1.08 Å for the 20-residue Trp-cage, and 3.64 Å for the 35-residue villin headpiece subdomain HP35. The centroid of the sixth largest cluster sampled for HP35 deviated by 0.91 Å. The CHARMM22/CMAP force field was used, with an additional ψ torsion term for residues other than glycine and proline. Six parameters govern the dielectric response of the continuum solvent, and four values of surface tension approximate nonpolar effects. An atom's self-energy and interaction energies are screened independently, each depending on whether the atom is part of a charged group, a neutral hydrogen-bonding main-chain group, or any other neutral group. The parameters inferred result in strong main-chain hydrogen bonds, consistent with the view that protein folding is dominated by the formation of these bonds. (1,2) Conformations of MBH12 and BS1 were excluded from the energy-function refinement, suggesting the parameters, referred to as SCP18, are transferable. An efficient estimate of solvent-accessible surface area is also described.

Enhanced Monte Carlo Methods for Modeling Proteins Including Computation of Absolute Free Energies of Binding

The generation of a complete ensemble of geometrical configurations is required to obtain reliable estimations of absolute binding free energies by alchemical free energy methods. Molecular dynamics (MD) is the most popular sampling method, but the representation of large biomolecular systems may be incomplete owing to energetic barriers that impede efficient sampling of the configurational space. Monte Carlo (MC) methods can possibly overcome this issue by adapting the attempted movement sizes to facilitate transitions between alternative local-energy minima. In this study, we present an MC statistical mechanics algorithm to explore the protein-ligand conformational space with emphasis on the motions of the protein backbone and side chains. The parameters for each MC move type were optimized to better reproduce conformational distributions of 18 dipeptides and the well-studied T4-lysozyme L99A protein. Next, the performance of the improved MC algorithms was evaluated by computing absolute free energies of binding for L99A lysozyme with benzene and seven analogs. Results for benzene with L99A lysozyme from MD and the optimized MC protocol were found to agree within 0.6 kcal/mol, while a mean unsigned error of 1.2 kcal/mol between MC results and experiment was obtained for the seven benzene analogs. Significant advantages in computation speed are also reported with MC over MD for similar extents of configurational sampling.

Segmenting Proteins into Tripeptides to Enhance Conformational Sampling with Monte Carlo Methods

This paper presents an approach to enhance conformational sampling of proteins employing stochastic algorithms such as Monte Carlo (MC) methods. The approach is based on a mechanistic representation of proteins and on the application of methods originating from robotics. We outline the general ideas of our approach and detail how it can be applied to construct several MC move classes, all operating on a shared representation of the molecule and using a single mathematical solver. We showcase these sampling techniques on several types of proteins. Results show that combining several move classes, which can be easily implemented thanks to the proposed approach, significantly improves sampling efficiency.

Inverse kinematic solutions of 6-D.O.F. biopolymer segments

We present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

Designing peptide sequences in flexible chain conformations to bind RNA: a search algorithm combining Monte Carlo, self-consistent mean field and concerted rotation techniques

A search algorithm combining Monte Carlo, self-consistent mean field, and concerted rotation techniques was developed to discover peptide sequences that are reasonable HIV drug candidates due to their exceptional binding to human tRNAUUU(Lys3), the primer of HIV replication. The search algorithm allows for iteration between sequence mutations and conformation changes during sequence evolution. Searches conducted for different classes of peptides identified several potential peptide candidates. Analysis of the energy revealed that the asparagine and cysteine at residues 11 and 12 play important roles in "recognizing" tRNA(Lys3) via van der Waals interactions, contributing to binding specificity. Arginines preferentially attract the phosphate linkage via charge-charge interaction, contributing to binding affinity. Evaluation of the RNA/peptide complex's structure revealed that adding conformation changes to the search algorithm yields peptides with better binding affinity and specificity to tRNA(Lys3) than a previous mutation-only algorithm.

Modifying the OPLS-AA force field to improve hydration free energies for several amino acid side chains using new atomic charges and an off-plane charge model for aromatic residues

The hydration free energies of amino acid side chains are an important determinant of processes that involve partitioning between different environments, including protein folding, protein complex formation, and protein-membrane interactions. Several recent papers have shown that calculated hydration free energies for polar and aromatic residues (Trp, His, Tyr, Asn, Gln, Asp, Glu) in several common molecular dynamics force fields differ significantly from experimentally measured values. We have attempted to improve the hydration energies for these residues by modifying the partial charges of the OPLS-AA force field based on natural population analysis of density functional theory calculations. The resulting differences between calculated hydration free energies and experimental results for the seven side chain analogs are less than 0.1 kcal/mol. Simulations of the synthetic Trp-rich peptide Trpzip2 show that the new charges lead to significantly improved geometries for interacting Trp-side chains. We also investigated an off-plane charge model for aromatic rings that more closely mimics their electronic configuration. This model results in an improved free energy of hydration for Trp and a somewhat altered benzene-sodium potential of mean force with a more favorable energy for direct benzene-sodium contact.

Introducing folding stability into the score function for computational design of RNA-binding peptides boosts the probability of success

A computational strategy that integrates our peptide search algorithm with atomistic molecular dynamics simulation was used to design rational peptide drugs that recognize and bind to the anticodon stem and loop domain (ASL(Lys3)) of human tRNAUUULys3 for the purpose of interrupting HIV replication. The score function of the search algorithm was improved by adding a peptide stability term weighted by an adjustable factor λ to the peptide binding free energy. The five best peptide sequences associated with five different values of λ were determined using the search algorithm and then input in atomistic simulations to examine the stability of the peptides' folded conformations and their ability to bind to ASL(Lys3). Simulation results demonstrated that setting an intermediate value of λ achieves a good balance between optimizing the peptide's binding ability and stabilizing its folded conformation during the sequence evolution process, and hence leads to optimal binding to the target ASL(Lys3). Thus, addition of a peptide stability term significantly improves the success rate for our peptide design search.

Folding Simulations of the Transmembrane Helix of Virus Protein U in an Implicit Membrane Model

Vpu is an 81-amino-acid auxiliary membrane protein encoded by human immunodeficiency virus type 1 (HIV-1). One of its roles is to amplify viral release by self-assembling in homo-oligomers to form functional water-filled pores enabling the flux of ions across the membrane. Various NMR and CD studies have shown that the transmembrane domain of Vpu has a helical conformation. With a recently developed implicit membrane model and an efficient Monte Carlo (MC) algorithm using concerted backbone rotations, we simulate the folding of the transmembrane domain of Vpu at atomic resolution. The implicit membrane environment is based on the generalized Born theory and enables very long time scale events, such as folding to be observed using detailed all-atom representation of the protein. Such studies are currently computationally unfeasible with fully explicit lipid bilayer molecular dynamics simulations. The correct helical transmembrane structure of Vpu is predicted from extended conformations and remains stably inserted. Tilt and kink angles agree well with experimental estimates from NMR measurements. The experimentally observed change in tilt angle in membranes of varying hydrophobic width is accurately reproduced. The extensive simulation of a pentamer of the Vpu transmembrane domain in the implicit membrane gives results similar to the ones reported previously for fully explicit bilayer simulations.

Efficient Generalized Born Models for Monte Carlo Simulations

The Generalized Born Surface Area theory (GBSA) has become a popular method to model the solvation of biomolecules. While efficient in the context of molecular dynamics simulations, GBSA calculations do not integrate well with Monte Carlo simulations because of the nonlocal nature of the Generalized Born energy. We present a method by which Monte Carlo Generalized Born simulations can be made seven to eight times faster on a protein-ligand binding free energy calculation with little or no loss of accuracy. The method can be employed in any type of Monte Carlo or Hybrid Monte Carlo-molecular dynamics simulation and should prove useful in numerous applications.

PACE Force Field for Protein Simulations. 2. Folding Simulations of Peptides

We present the application of our recently developed PACE force field to the folding of peptides. These peptides include α-helical (AK17 and Fs), β-sheet (GB1m2 and Trpzip2), and mixed helical/coil (Trp-cage) peptides. With replica exchange molecular dynamics (REMD), our force field can fold the five peptides into their native structures while maintaining their stabilities reasonably well. Our force field is also able to capture important thermodynamic features of the five peptides that have been observed in previous experimental and computational studies, such as different preferences for a helix-turn-helix topology for AK17 and Fs, the relative contribution of four hydrophobic side chains of GB1p to the stability of β-hairpin, and the distinct role of a hydrogen bond involving Trp-Hε and a D9/R16 salt bridge in stabilizing the Trp-cage native structure. Furthermore, multiple folding and unfolding events are observed in our microsecond-long normal MD simulations of AK17, Trpzip2, and Trp-cage. These simulations provide mechanistic information such as a "zip-out" pathway of the folding mechanism of Trpzip2 and the folding times of AK17 and Trp-cage, which are estimated to be about 51 ± 43 ns and 270 ± 110 ns, respectively. A 600 ns simulation of the peptides can be completed within one day. These features of our force field are potentially applicable to the study of thermodynamics and kinetics of real protein systems.

A hybrid MD-kMC algorithm for folding proteins in explicit solvent

We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.

Polar transmembrane interactions drive formation of ligand-specific and signal pathway-biased family B G protein-coupled receptor conformations

Recently, the concept of ligand-directed signaling--the ability of different ligands of an individual receptor to promote distinct patterns of cellular response--has gained much traction in the field of drug discovery, with the potential to sculpt biological response to favor therapeutically beneficial signaling pathways over those leading to harmful effects. However, there is limited understanding of the mechanistic basis underlying biased signaling. The glucagon-like peptide-1 receptor is a major target for treatment of type-2 diabetes and is subject to ligand-directed signaling. Here, we demonstrate the importance of polar transmembrane residues conserved within family B G protein-coupled receptors, not only for protein folding and expression, but also in controlling activation transition, ligand-biased, and pathway-biased signaling. Distinct clusters of polar residues were important for receptor activation and signal preference, globally changing the profile of receptor response to distinct peptide ligands, including endogenous ligands glucagon-like peptide-1, oxyntomodulin, and the clinically used mimetic exendin-4.

Folding of small proteins using constrained molecular dynamics

The focus of this paper is to examine whether conformational search using constrained molecular dynamics (MD) method is more enhanced and enriched toward "native-like" structures compared to all-atom MD for the protein folding as a model problem. Constrained MD methods provide an alternate MD tool for protein structure prediction and structure refinement. It is computationally expensive to perform all-atom simulations of protein folding because the processes occur on a time scale of microseconds. Compared to the all-atom MD simulation, constrained MD methods have the advantage that stable dynamics can be achieved for larger time steps and the number of degrees of freedom is an order of magnitude smaller, leading to a decrease in computational cost. We have developed a generalized constrained MD method that allows the user to "freeze and thaw" torsional degrees of freedom as fit for the problem studied. We have used this method to perform all-torsion constrained MD in implicit solvent coupled with the replica exchange method to study folding of small proteins with various secondary structural motifs such as, α-helix (polyalanine, WALP16), β-turn (1E0Q), and a mixed motif protein (Trp-cage). We demonstrate that constrained MD replica exchange method exhibits a wider conformational search than all-atom MD with increased enrichment of near-native structures. "Hierarchical" constrained MD simulations, where the partially formed helical regions in the initial stretch of the all-torsion folding simulation trajectory of Trp-cage were frozen, showed a better sampling of near-native structures than all-torsion constrained MD simulations. This is in agreement with the zipping-and-assembly folding model put forth by Dill and co-workers for folding proteins. The use of hierarchical "freeze and thaw" clustering schemes in constrained MD simulation can be used to sample conformations that contribute significantly to folding of proteins.

RNA Conformational Sampling: II. Arbitrary Length Multinucleotide Loop Closure

In this paper, we describe how the inverse kinematic solution to the loop closure problem may be generalized to reclose a RNA segment of arbitrary length containing any number of nucleotides without disturbing the atomic positions of the rest of the molecule. This generalization is made possible by representing the boundary conditions of the closure in terms of a set of virtual coordinates called RETO, allowing the inverse kinematics to be reduced from the original six-variable/six-constraint problem to a four-variable/four-constraint problem. Based on this generalized closure solution, a new Monte Carlo algorithm has been formulated and implemented in a fully atomistic RNA simulation capable of moving loops of arbitrary lengths using torsion angle updates exclusively. Combined with other conventional Monte Carlo moves, this new algorithm is able to sample large-scale RNA chain conformations much more efficiently. The utility of this new class of Monte Carlo moves in generating large-loop conformational rearrangements is demonstrated in the simulated unfolding of the full-length hammerhead ribozyme with a bound substrate.

Conformational analysis of a nitroxide side chain in an α-helix with density functional theory

In site directed spin labeling, a nitroxide side chain is introduced at a selected site in a protein; the most commonly used is a disulfide-linked side chain designated R1. The electron paramagnetic resonance (EPR) spectra of R1, and the interspin distance between pairs of R1 residues as determined by dipolar EPR spectroscopy, encode a wealth of information on the protein structure and dynamics. However, extracting this information requires structural and dynamical models of the R1 side chain, that is, the favored rotamers, the intraresidue interactions that stabilize them, and the internal modes of motion. X-ray crystal structures of R1 in proteins have revealed a set of preferred rotamers in the crystal lattice. To identify the intraresidue interactions that stabilize particular rotamers of R1 in the absence of interactions with nearby side chains in a helix, and to evaluate models for the internal motion of the side chain, quantum mechanical calculations were performed on a relevant fragment of R1 in a 10-residue α-helix. Relative rotamer energies were determined in the gas phase, and solvation energies were estimated from a continuum solvent model that includes both electrostatic and hydrophobic contributions. The results identified preferred rotamers that are in agreement with the X-ray crystallographic studies. The rotamers are apparently stabilized by intraresidue sulfur-backbone interactions, suggesting that the preferred rotamers may be the same at all solvent-exposed helix sites.

Optimization of Monte Carlo trial moves for protein simulations

Closed rigid-body rotations of residue segments under bond-angle restraints are simple and effective Monte Carlo moves for searching the conformational space of proteins. The efficiency of these moves is examined here as a function of the number of moving residues and the magnitude of their displacement. It is found that the efficiency of folding and equilibrium simulations can be significantly improved by tailoring the distribution of the number of moving residues to the simulation temperature. In general, simulations exploring compact conformations are more efficient when the average number of moving residues is smaller. It is also demonstrated that the moves do not require additional restrictions on the magnitude of the rotation displacements and perform much better than other rotation moves that do not restrict the bond angles a priori. As an example, these results are applied to the replica exchange method. By assigning distributions that generate a smaller number of moving residues to lower temperature replicas, the simulation times are decreased as long as the higher temperature replicas are effective.

Modeling peptide-protein interactions

Peptide-protein interactions are prevalent in the living cell and form a key component of the overall protein-protein interaction network. These interactions are drawing increasing interest due to their part in signaling and regulation, and are thus attractive targets for computational structural modeling. Here we report an overview of current techniques for the high resolution modeling of peptide-protein complexes. We dissect this complicated challenge into several smaller subproblems, namely: modeling the receptor protein, predicting the peptide binding site, sampling an initial peptide backbone conformation and the final refinement of the peptide within the receptor binding site. For each of these conceptual stages, we present available tools, approaches, and their reported performance. We summarize with an illustrative example of this process, highlighting the success and current challenges still facing the automated blind modeling of peptide-protein interactions. We believe that the upcoming years will see considerable progress in our ability to create accurate models of peptide-protein interactions, with applications in binding-specificity prediction, rational design of peptide-mediated interactions and the usage of peptides as therapeutic agents.

Conformational preferences of a 14-residue fibrillogenic peptide from acetylcholinesterase

A 14-residue fragment from near the C-terminus of the enzyme acetylcholinesterase (AChE) is believed to have a neurotoxic/neurotrophic effect acting via an unknown pathway. While the peptide is α-helical in the full-length enzyme, the structure and association mechanism of the fragment are unknown. Using multiple molecular dynamics simulations, starting from a tetrameric complex of the association domain of AChE and systematically disassembled subsets that include the peptide fragment, we show that the fragment is incapable of retaining its helicity in solution. Extensive replica exchange Monte Carlo folding and unfolding simulations in implicit solvent with capped and uncapped termini failed to converge to any consistent cluster of structures, suggesting that the fragment remains largely unstructured in solution under the conditions considered. Furthermore, extended molecular dynamics simulations of two steric zipper models show that the peptide is likely to form a zipper with antiparallel sheets and that peptides with mutations known to prevent fibril formation likely do so by interfering with this packing. The results demonstrate how the local environment of a peptide can stabilize a particular conformation.

A fast method for large-scale de novo peptide and miniprotein structure prediction

Although peptides have many biological and biomedical implications, an accurate method predicting their equilibrium structural ensembles from amino acid sequences and suitable for large-scale experiments is still missing. We introduce a new approach-PEP-FOLD-to the de novo prediction of peptides and miniproteins. It first predicts, in the terms of a Hidden Markov Model-derived structural alphabet, a limited number of local conformations at each position of the structure. It then performs their assembly using a greedy procedure driven by a coarse-grained energy score. On a benchmark of 52 peptides with 9-23 amino acids, PEP-FOLD generates lowest-energy conformations within 2.8 and 2.3 A Calpha root-mean-square deviation from the full nuclear magnetic resonance structures (NMR) and the NMR rigid cores, respectively, outperforming previous approaches. For 13 miniproteins with 27-49 amino acids, PEP-FOLD reaches an accuracy of 3.6 and 4.6 A Calpha root-mean-square deviation for the most-native and lowest-energy conformations, using the nonflexible regions identified by NMR. PEP-FOLD simulations are fast-a few minutes only-opening therefore, the door to in silico large-scale rational design of new bioactive peptides and miniproteins.

Temperature and urea induced denaturation of the TRP-cage mini protein TC5b: A simulation study consistent with experimental observations

The effects of temperature and urea denaturation (6M urea) on the dominant structures of the 20-residue Trp-cage mini-protein TC5b are investigated by molecular dynamics simulations of the protein at different temperatures in aqueous and in 6M urea solution using explicit solvent degrees of freedom and the GROMOS force-field parameter set 45A3. In aqueous solution at 278 K, TC5b is stable throughout the 20 ns of MD simulation and the trajectory structures largely agree with the NMR-NOE atom-atom distance data available. Raising the temperature to 360 K and to 400 K, the protein denatures within 22 ns and 3 ns, showing that the denaturation temperature is well below 360 K using the GROMOS force field. This is 40-90 K lower than the denaturation temperatures observed in simulations using other much used protein force fields. As the experimental denaturation temperature is about 315 K, the GROMOS force field appears not to overstabilize TC5b, as other force fields and the use of continuum solvation models seem to do. This feature may directly stem from the GROMOS force-field parameter calibration protocol, which primarily involves reproduction of condensed phase thermodynamic quantities such as energies, densities, and solvation free energies of small compounds representative for protein fragments. By adding 6M urea to the solution, the onset of denaturation is observed in the simulation, but is too slow to observe a particular side-chain side-chain contact (Trp6-Ile4) that was experimentally observed to be characteristic for the denatured state. Interestingly, using temperature denaturation, the process is accelerated and the experimental data are reproduced.

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.

Folding mechanism of β-hairpin trpzip2: heterogeneity, transition state and folding pathways

We review the studies on the folding mechanism of the β-hairpin tryptophan zipper 2 (trpzip2) and present some additional computational results to refine the picture of folding heterogeneity and pathways. We show that trpzip2 can have a two-state or a multi-state folding pattern, depending on whether it folds within the native basin or through local state basins on the high-dimensional free energy surface; Trpzip2 can fold along different pathways according to the packing order of tryptophan pairs. We also point out some important problems related to the folding mechanism of trpzip2 that still need clarification, e.g., a wide distribution of the computed conformations for the transition state ensemble.

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.

Multiscale Monte Carlo Sampling of Protein Sidechains: Application to Binding Pocket Flexibility

We present a Monte Carlo sidechain sampling procedure and apply it to assessing the flexibility of protein binding pockets. We implemented a multiple "time step" Monte Carlo algorithm to optimize sidechain sampling with a surface generalized Born implicit solvent model. In this approach, certain forces (those due to long-range electrostatics and the implicit solvent model) are updated infrequently, in "outer steps", while short-range forces (covalent, local nonbonded interactions) are updated at every "inner step". Two multistep protocols were studied. The first protocol rigorously obeys detailed balance, and the second protocol introduces an approximation to the solvation term that increases the acceptance ratio. The first protocol gives a 10-fold improvement over a protocol that does not use multiple time steps, while the second protocol generates comparable ensembles and gives a 15-fold improvement. A range of 50-200 inner steps per outer step was found to give optimal performance for both protocols. The resultant method is a practical means to assess sidechain flexibility in ligand binding pockets, as we illustrate with proof-of-principle calculations on six proteins: DB3 antibody, thermolysin, estrogen receptor, PPAR-γ, PI3 kinase, and CDK2. The resulting sidechain ensembles of the apo binding sites correlate well with known induced fit conformational changes and provide insights into binding pocket flexibility.

Site-specific relaxation kinetics of a tryptophan zipper hairpin peptide using temperature-jump IR spectroscopy and isotopic labeling

Two antiparallel beta-strands connected by a turn make beta-hairpins an ideal model system to analyze the interactions and dynamics of beta-sheets. Site-specific conformational dynamics were studied by temperature-jump IR spectroscopy and isotopic labeling in a model based on the tryptophan zipper peptide, Trpzip2, developed by Cochran et al. (Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 5578). The modified Trpzip2C peptides have nearly identical equilibrium spectral behavior as Trpzip2 showing that they also form well-characterized beta-hairpin conformations in aqueous solution. Selective introduction of 13C=O groups on opposite strands lead to distinguishable cross-strand coupling of the labeled residues as monitored in the amide I' band. These frequency patterns reflect theoretical predictions, and the coupled 13C=O band loses intensity with increase in temperature and unfolding of the hairpin. Thermal relaxation kinetics were analyzed for unlabeled and cross-strand isotopically labeled variants. T-jumps of approximately 10 degrees C induce relaxation times of a few microseconds that decrease with increase of the peptide temperature. Differences in kinetic behavior for the loss of beta-strand and gain of disordered structure can be used to distinguish localized structure dynamics by comparison of nonlabeled and labeled amide I' components. Analysis of the data supports multistate dynamic and equilibrium behavior, but because of this process it is not possible to clearly define a folding and unfolding rate. Nonetheless, site-specific relaxation kinetics could be seen to be consistent with a hydrophobic collapse hypothesis for hairpin folding.

Monte carlo folding of trans-membrane helical peptides in an implicit generalized Born membrane

An efficient Monte Carlo (MC) algorithm using concerted backbone rotations is combined with a recently developed implicit membrane model to simulate the folding of the hydrophobic transmembrane domain M2TM of the M2 protein from influenza A virus and Sarcolipin at atomic resolution. The implicit membrane environment is based on generalized Born theory and has been calibrated against experimental data. The MC sampling has previously been used to fold several small polypeptides and been shown to be equivalent to molecular dynamics (MD). In combination with a replica exchange algorithm, M2TM is found to form continuous membrane spanning helical conformations for low temperature replicas. Sarcolipin is only partially helical, in agreement with the experimental NMR structures in lipid bilayers and detergent micelles. Higher temperature replicas exhibit a rapidly decreasing helicity, in agreement with expected thermodynamic behavior. To exclude the possibility of an erroneous helical bias in the simulations, the model is tested by sampling a synthetic Alanine-rich polypeptide of known helicity. The results demonstrate there is no overstabilization of helical conformations, indicating that the implicit model captures the essential components of the native membrane environment for M2TM and Sarcolipin.

Dehydration-driven solvent exposure of hydrophobic surfaces as a driving force in peptide folding

Recent work has shown that the nature of hydration of pure hydrophobic surfaces changes with the length scale considered: water hydrogen-bonding networks adapt to small exposed hydrophobic species, hydrating or "wetting" them at relatively high densities, whereas larger hydrophobic areas are "dewetted" [Chandler D (2005), Nature 29:640-647]. Here we determine whether this effect is also present in peptides by examining the folding of a beta-hairpin (the 14-residue amyloidogenic prion protein H1 peptide), using microsecond time-scale molecular dynamics simulations. Two simulation models are compared, one explicitly including the water molecules, which may thus adapt locally to peptide configurations, and the other using a popular continuum approximation, the generalized Born/surface area implicit solvent model. The results obtained show that, in explicit solvent, peptide conformers with high solvent-accessible hydrophobic surface area indeed also have low hydration density around hydrophobic residues, whereas a concomitant higher hydration density around hydrophilic residues is observed. This dewetting effect stabilizes the fully folded beta-hairpin state found experimentally. In contrast, the implicit solvent model destabilizes the fully folded hairpin, tending to cluster hydrophobic residues regardless of the size of the exposed hydrophobic surface. Furthermore, the rate of the conformational transitions in the implicit solvent simulation is almost doubled with respect to that of the explicit solvent. The results suggest that dehydration-driven solvent exposure of hydrophobic surfaces may be a significant factor determining peptide conformational equilibria.

Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations

An efficient Monte Carlo (MC) algorithm including concerted rotations is directly compared to molecular dynamics (MD) in all-atom statistical mechanics folding simulations of small polypeptides. The previously reported algorithm "concerted rotations with flexible bond angles" (CRA) has been shown to successfully locate the native state of small polypeptides. In this study, the folding of three small polypeptides (trpzip2/H1/Trp-cage) is investigated using MC and MD, for a combined sampling time of approximately 10(11) MC configurations and 8 micros, respectively. Both methods successfully locate the experimentally determined native states of the three systems, but they do so at different speed, with 2-2.5 times faster folding of the MC runs. The comparison reveals that thermodynamic and dynamic properties can reliably be obtained by both and that results from folding simulations do not depend on the algorithm used. Similar to previous comparisons of MC and MD, it is found that one MD integration step of 2 fs corresponds to one MC scan, revealing the good sampling of MC. The simplicity and efficiency of the MC method will enable its future use in folding studies involving larger systems and the combination with replica exchange algorithms.

Molecular dynamics simulation of folding of a short helical peptide with many charged residues

A molecular dynamics simulation of the folding of conantokin-T (con-T), a short helical peptide with 5 helical turns of 21 amino acids with 10 charged residues, was carried out to examine folding pathways for this peptide and to predict the folding rate. In the 18 trajectories run at 300 K, 16 trajectories folded, with an averaged folding time of approximately 50 ns. Two trajectories did not fold in up to 200 ns simulation. The folded structure in folded trajectories is in good agreement with experimental structure. An analysis of the trajectories showed that, at the beginning of a few nanoseconds, helix formation started from residues 5-9 with assistance of a hydrophobic clustering involving Tyr5, Met8, and Leu9. The peptide formed a U-shape mainly due to charge-charge interactions between charged residues at the N- and C-terminus segments. In the next approximately 10 ns, several nonnative charge-charge interactions were broken and nonnative Gla10-Lys18 (this denotes a salt bridge between Gal10 and Lys18) and/or Gla10-Lys19 interactions appeared more frequently in this folding step and the peptide became a fishhook J-shape. From this structure, the peptide folded to the folded state in 7 of all 16 folded trajectories in approximately 15 ns. Alternatively, in approximately 30 ns, the con-T went to a conformation in an L-shape with 4 helical turns and a kink at the Arg13 and Gla14 segment in the other 9 trajectories. Con-T in the L-shape then required another approximately 15 ns to fold into the folded state. In addition, in overall folding times, the former 7 trajectories folded faster with the total folding times all shorter than 45 ns, while the latter 9 trajectories folded at a time longer than 45 ns, resulting in an average folding time of approximately 50 ns. Two major folding intermediates found in 2 nonfolded trajectories are stabilized by charge clusters of 5 and 6 charged residues, respectively. With inclusion of friction and solvent-solvent interactions, which were ignored in the present GB/SA solvation model, the folding time obtained above should be multiplied by a factor of 1.25-1.7 according to a previous, similar simulation study. This results in a folding time of 65-105 ns, slightly shorter than the folding time of 127 ns for an alanine-based peptide of the same length. This suggests that the energy barrier of folding for this type of peptides with many charged residues is slightly lower than alanine-based helical peptides by less than 1 kcal/mol.

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains are discussed.

Calculation of the free energy and cooperativity of protein folding

Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.

UV Raman spatially resolved melting dynamics of isotopically labeled polyalanyl peptide: slow alpha-helix melting follows 3(10)-helices and pi-bulges premelting

We used UV resonance Raman (UVRR) to examine the spatial dependence of the T-jump secondary structure relaxation of an isotopically labeled 21-residue mainly Ala peptide, AdP. The AdP penultimate Ala residues were perdeuterated, leaving the central residues hydrogenated, to allow separate monitoring of melting of the middle versus the end peptide bonds. For 5 to 30 degrees C T-jumps, the central peptide bonds show a approximately 2-fold slower relaxation time (189 +/- 31 ns) than do the exterior peptide bonds (97 +/- 15 ns). In contrast, for a 20 to 40 degrees C T-jump, the central peptide bond relaxation appears to be faster (56 +/- 6 ns) than that of the penultimate peptide bonds (131 +/- 46 ns). We show that, if the data are modeled as a two-state transition, we find that only exterior peptide bonds show anti-Arrhenius folding behavior; the middle peptide bonds show both normal Arrhenius-like folding and unfolding. This anti-Arrhenius behavior results from the involvement of pi-bulges/helices and 3(10)-helix states in the melting. The unusual temperature dependence of the (un)folding rates of the interior and exterior peptide bonds is due to the different relative (un)folding rates of 3(10)-helices, alpha-helices, and pi-bulges/helices. Pure alpha-helix unfolding rates are approximately 12-fold slower (approximately 1 micros) than that of pi-bulges and 3(10)-helices. In addition, we also find that the alpha-helix is most stable at the AdP N-terminus where eight consecutive Ala occur, whereas the three hydrophilic Arg located in the middle and at the C-terminus destabilize the alpha-helix in these regions and induce defects such as pi-bulges and 3(10)-helices.

Direct folding simulation of alpha-helices and beta-hairpins based on a single all-atom force field with an implicit solvation model

Recently, we have shown that a modified energy model based on the param99 force field with the generalized Born (GB) solvation model produces reliable free energy landscapes of mini-proteins with a betabetaalpha motif (BBA5, 1FSD, and 1PSV), with the native structures of the mini-proteins located in their lowest free energy minimum states. One of the main features in the modified energy model is a significant improvement for more balanced treatments of alpha and beta strands in proteins. In this study, using the replica exchange molecular dynamics (REMD) simulation method with this new force field, we have carried out extensive ab initio folding studies of several well-known peptides with alpha or beta strands (C-peptide, EK-peptide, le0q, and gbl). Starting from fully extended conformations as the initial conditions, all of the native-like structures of the target peptides were successfully identified by REMD, with reasonable representations of free energy surfaces. The present simulation results with the modified energy model are consistent with experiments, demonstrating an extended applicability of the energy model to folding studies of a variety of alpha-helices, beta-strands, and alpha/beta proteins.