Two-stage folding of HP-35 from ab initio simulations

Soluble State of Villin Headpiece Protein as a Tool in the Assessment of MD Force Fields

Protein self-assembly plays an important role in cellular processes. Whereas molecular dynamics (MD) represents a powerful tool in studying assembly mechanisms, its predictions depend on the accuracy of underlying force fields, which are known to overly promote protein assembly. We here examine villin headpiece domain, HP36, which remains soluble at concentrations amenable to MD studies. The experimental characterization of soluble HP36 at concentrations of 0.05 to 1 mM reveals concentration-independent 90% monomeric and 10% dimeric populations. Extensive all-atom MD simulations at two protein concentrations, 0.9 and 8.5 mM, probe the HP36 dimer population, stability, and kinetics of dimer formation within two MD force fields, Amber ff14SB and CHARMM36m. MD results demonstrate that whereas CHARMM36m captures experimental HP36 monomer populations at the lower concentration, both force fields overly promote HP36 association at the higher concentration. Moreover, contacts stabilizing HP36 dimers are force-field-dependent. CHARMM36m produces consistently higher HP36 monomer populations, lower association rates, and weaker dependence of these quantities on the protein concentration than Amber ff14SB. Nonetheless, the highest monomer populations and dissociation constants are observed when the TIP3P water model in Amber ff14SB is replaced by TIP4P/2005, showcasing the critical role of the water model in addressing the protein solubility problem in MD.

Pathway regulation mechanism revealed by cotranslational folding of villin headpiece subdomain HP35

Cotranslational folding is one of the most important features of protein folding in vivo. Although many studies have shown that the folding pathways of cotranslational folding are different from free folding in vitro, the detailed mechanism of folding dynamics is lacking. Here we combine all-atom molecular simulations with an ideal ribosome tunnel model to investigate the cotranslational folding of villin headpiece subdomain HP35. By comparing the folding dynamics between cotranslational folding and free folding, we found that cotranslational folding tends to fold along the pathway that is easier to fold into native state in the latter. In addition, the roles of the ribosome tunnel and sequential folding are analyzed separately. Our results show that the ribosome can prevent the untimely folding of the C segment of HP35 to reduce the non-native interactions, while the translation speed can regulate the amounts of native and non-native interactions and the balance between them. Overall, these results give insights into the general mechanisms of cotranslational protein folding.

A novel multiscale scheme to accelerate atomistic simulations of bio-macromolecules by adaptively driving coarse-grained coordinates

All-atom molecular dynamics (MD) simulations of bio-macromolecules can yield relatively accurate results while suffering from the limitation of insufficient conformational sampling. On the other hand, the coarse-grained (CG) MD simulations efficiently accelerate conformational changes in biomolecules but lose atomistic details and accuracy. Here, we propose a novel multiscale simulation method called the adaptively driving multiscale simulation (ADMS)-it efficiently accelerates biomolecular dynamics by adaptively driving virtual CG atoms on the fly while maintaining the atomistic details and focusing on important conformations of the original system with irrelevant conformations rarely sampled. Herein, the "adaptive driving" is based on the short-time-averaging response of the system (i.e., an approximate free energy surface of the original system), without requiring the construction of the CG force field. We apply the ADMS to two peptides (deca-alanine and Ace-GGPGGG-Nme) and one small protein (HP35) as illustrations. The simulations show that the ADMS not only efficiently captures important conformational states of biomolecules and drives fast interstate transitions but also yields, although it might be in part, reliable protein folding pathways. Remarkably, a ∼100-ns explicit-solvent ADMS trajectory of HP35 with three CG atoms realizes folding and unfolding repeatedly and captures the important states comparable to those from a 398-µs standard all-atom MD simulation.

Using the generalized Born surface area model to fold proteins yields more effective sampling while qualitatively preserving the folding landscape

Protein folding is a long-standing problem and has been widely investigated using molecular dynamics simulations with both explicit and implicit solvents. However, to what extent the folding mechanisms observed in two water models agree remains an open question. In this study, ab initio folding simulations of ten proteins with different topologies are performed in two combinations of force fields and water models (ff14SB+TIP3P and ff14SBonlysc+GB-Neck2). Interestingly, the latter combination not only folds more proteins but also provides a better balance of different secondary structures than the former in the same number of integration time steps. More importantly, the folding pathways found in the two types of simulations are conserved and they may only differ in their weights. Our results suggest that simulations with an implicit solvent may also be suitable for the investigation of the mechanism of protein folding.

Generalized Born Implicit Solvent Models for Biomolecules

It would often be useful in computer simulations to use an implicit description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation and can be very efficient compared to the explicit treatment of the solvent. Here, we review a particular class of so-called fast implicit solvent models, generalized Born (GB) models, which are widely used for molecular dynamics (MD) simulations of proteins and nucleic acids. These approaches model hydration effects and provide solvent-dependent forces with efficiencies comparable to molecular-mechanics calculations on the solute alone; as such, they can be incorporated into MD or other conformational searching strategies in a straightforward manner. The foundations of the GB model are reviewed, followed by examples of newer, emerging models and examples of important applications. We discuss their strengths and weaknesses, both for fidelity to the underlying continuum model and for the ability to replace explicit consideration of solvent molecules in macromolecular simulations.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Characterizing a partially ordered miniprotein through folding molecular dynamics simulations: Comparison with the experimental data

The villin headpiece helical subdomain (HP36) is one of the best known model systems for computational studies of fast-folding all-α miniproteins. HP21 is a peptide fragment-derived from HP36-comprising only the first and second helices of the full domain. Experimental studies showed that although HP21 is mostly unfolded in solution, it does maintain some persistent native-like structure as indicated by the analysis of NMR-derived chemical shifts. Here we compare the experimental data for HP21 with the results obtained from a 15-μs long folding molecular dynamics simulation performed in explicit water and with full electrostatics. We find that the simulation is in good agreement with the experiment and faithfully reproduces the major experimental findings, namely that (a) HP21 is disordered in solution with <10% of the trajectory corresponding to transiently stable structures, (b) the most highly populated conformer is a native-like structure with an RMSD from the corresponding portion of the HP36 crystal structure of <1 Å, (c) the simulation-derived chemical shifts-over the whole length of the trajectory-are in reasonable agreement with the experiment giving reduced χ(2) values of 1.6, 1.4, and 0.8 for the Δδ(13) C(α) , Δδ(13) CO, and Δδ(13) C(β) secondary shifts, respectively (becoming 0.8, 0.7, and 0.3 when only the major peptide conformer is considered), and finally, (d) the secondary structure propensity scores are in very good agreement with the experiment and clearly indicate the higher stability of the first helix. We conclude that folding molecular dynamics simulations can be a useful tool for the structural characterization of even marginally stable peptides.

Binding of an RNA pol II Ligand to the WW Domain of Pin1 Using Molecular Dynamics Docking Simulations

A novel docking protocol using a long, all atom molecular dynamics (MD) simulation, in an explicit solvent medium, without using any distance constraints is presented. This MD docking protocol is able to dock ligands, based on the C-terminal domain (CTD) of RNA polymerase II, into the tryptophan-tryptophan (WW) domain of Pin1. In this docking process, a significant loop-bending event occurs in order to encircle the ligand into its solvent exposed binding site, which cannot be simulated using current protocols. The simulations were validated structurally and energetically against an X-ray structure to confirm correct sampling of conformational space. Based on these simulations, and justification of the starting structure as a valid intermediate structure, a potential molecular basis for binding was predicted as well as confirming the key residues involved in the formation of the final strong and stable Pin1 WW domain-ligand complex.

Computational evidence that fast translation speed can increase the probability of cotranslational protein folding

Translation speed can affect the cotranslational folding of nascent peptide. Experimental observations have indicated that slowing down translation rates of codons can increase the probability of protein cotranslational folding. Recently, a kinetic modeling indicates that fast translation can also increase the probability of cotranslational protein folding by avoiding misfolded intermediates. We show that the villin headpiece subdomain HP35 is an ideal model to demonstrate this phenomenon. We studied cotranslational folding of HP35 with different fast translation speeds by all-atom molecular dynamics simulations and found that HP35 can fold along a well-defined pathway that passes the on-pathway intermediate but avoids the misfolded off-pathway intermediate in certain case. This greatly increases the probability of HP35 cotranslational folding and the approximate mean first passage time of folding into native state is about 1.67μs. Since we also considered the space-confined effect of the ribosomal exit tunnel on the cotranslational folding, our simulation results suggested alternative mechanism for the increasing of cotranslational folding probability by fast translation speed.

Elucidation of the Aggregation Pathways of Helix-Turn-Helix Peptides: Stabilization at the Turn Region Is Critical for Fibril Formation

Aggregation of proteins to fiberlike aggregates often involves a transformation of native monomers to β-sheet-rich oligomers. This general observation underestimates the importance of α-helical segments in the aggregation cascade. Here, using a combination of experimental techniques and accelerated molecular dynamics simulations, we investigate the aggregation of a 43-residue, apolipoprotein A-I mimetic peptide and its E21Q and D26N mutants. Our study indicates a strong propensity of helical segments not to adopt cross-β-fibrils. The helix-turn-helix monomeric conformation of the peptides is preserved in the mature fibrils. Furthermore, we reveal opposite effects of mutations on and near the turn region in the self-assembly of these peptides. We show that the E21-R24 salt bridge is a major contributor to helix-turn-helix folding, subsequently leading to abundant fibril formation. On the other hand, the K19-D26 interaction is not required to fold the native helix-turn-helix peptide. However, removal of the charged D26 residue decreases the stability of the helix-turn-helix monomer and consequently reduces the level of aggregation. Finally, we provide a more refined assembly model for the helix-turn-helix peptides from apolipoprotein A-I based on the parallel stacking of helix-turn-helix dimers.

A compact native 24-residue supersecondary structure derived from the villin headpiece subdomain

Many small proteins fold highly cooperatively in an all-or-none fashion and thus their native states are well protected from thermal fluctuations by an extensive network of interactions across the folded structure. Because protein structures are stabilized by local and nonlocal interactions among distal residues, dissecting individual substructures from the context of folded proteins results in large destabilization and loss of unique three-dimensional structure. Thus, mini-protein substructures can only rarely be derived from natural templates. Here, we describe a compact native 24-residues-long supersecondary structure derived from the hyperstable villin headpiece subdomain consisting of helices 2 and 3 (HP24). Using a combination of experimental techniques, including NMR and small-angle x-ray scattering, as well as all-atom replica exchange molecular-dynamics simulations, we show that a variant with stabilizing substitutions (HP24stab) forms a densely packed and compact conformation. In HP24stab, interactions between helices 2 and 3 are similar to those observed in native folded HP35, and the two helices cooperatively stabilize each other by completing the hydrophobic core lining the central part of HP35. Interestingly, even though the HP24wt fragment shows a more expanded and less structured conformation, NMR and simulations demonstrate a preference for a native-like topology. Thus, the two stabilizing residues in HP24stab shift the energy balance toward the native state, leading to a minimal folding motif.

Equilibrium kinetic network of the villin headpiece in implicit solvent

We applied the single-replica multiple-state transition-interface sampling method to elucidate the equilibrium kinetic network of the 35-residue-fragment (HP-35) villin headpiece in implicit water at room temperature. Starting from the native Protein Data Bank structure, nine (meta)stable states of the system were identified, from which the kinetic network was built by sampling pathways between these states. Application of transition path theory allowed analysis of the (un)folding mechanism. The resulting (un)folding rates agree well with experiments. This work demonstrates that high (un)folding barriers can now be studied.

Structural characterization of MG and pre-MG states of proteins by MD simulations, NMR, and other techniques

Almost all proteins fold via a number of partially structured intermediates such as molten globule (MG) and pre-molten globule states. Understanding the structure of these intermediates at atomic level is often a challenge, as these states are observed under extreme conditions of pH, temperature, and chemical denaturants. Furthermore, several other processes such as chemical modification, site-directed mutagenesis (or point mutation), and cleavage of covalent bond of natural proteins often lead to MG like partially unfolded conformation. However, the dynamic nature of proteins in these states makes them unsuitable for most structure determination at atomic level. Intermediate states studied so far have been characterized mostly by circular dichroism, fluorescence, viscosity, dynamic light scattering measurements, dye binding, infrared techniques, molecular dynamics simulations, etc. There is a limited amount of structural data available on these intermediate states by nuclear magnetic resonance (NMR) and hence there is a need to characterize these states at the molecular level. In this review, we present characterization of equilibrium intermediates by biophysical techniques with special reference to NMR.

REMD and umbrella sampling simulations to probe the energy barrier of the folding pathways of engrailed homeodomain

Proteins fold by diverse pathways which depend on the energy barriers involved in reaching different intermediates. There has been a lot of development in the theoretical aspects of protein folding, from force-field to simulation techniques. One such simulation approach is replica exchange molecular dynamics simulation (REMD), which provides an efficient conformational sampling method to understand the events involved in protein folding. In this study, an attempt is made to explore the folding funnel of engrailed homeodomain protein (EnHD) using REMD simulations. EnHD is a 54 residue long helix bundle protein which has a folding time of about 15 μs. The protein was represented using the Amber United atom model in order to reduce the system size which helped to speed up the simulation. Individual replicas were simulated for 1.4-2 μs making cumulative time of more than 100 μs of REMD simulations. Free energy analysis was carried out to understand the folding behavior of EnHD protein. Effects of temperature range and exchange frequency in REMD simulations have been explored. In addition to this, multiple umbrella sampling (US) simulations of a total of 320 ns were also carried out, followed by weighted histogram analysis method (WHAM) to investigate the energy barriers involved during the folding of various intermediates. US studies were also carried on mutational variants of EnHD protein to see effect of the mutations on the folding pathway of the protein. The use of US technique may be helpful for predicting fast folding mutants or protein engineering. The combination of REMD with US may help in understanding the energetics between multiple pathways of fast folding proteins and their mutant counterparts.

Ultrafast folding kinetics and cooperativity of villin headpiece in single-molecule force spectroscopy

In this study we expand the accessible dynamic range of single-molecule force spectroscopy by optical tweezers to the microsecond range by fast sampling. We are able to investigate a single molecule for up to 15 min and with 300-kHz bandwidth as the protein undergoes tens of millions of folding/unfolding transitions. Using equilibrium analysis and autocorrelation analysis of the time traces, the full energetics as well as real-time kinetics of the ultrafast folding of villin headpiece 35 and a stable asparagine 68 alanine/lysine 70 methionine variant can be measured directly. We also performed Brownian dynamics simulations of the response of the bead-DNA system to protein-folding fluctuations. All key features of the force-dependent deflection fluctuations could be reproduced: SD, skewness, and autocorrelation function. Our measurements reveal a difference in folding pathway and cooperativity between wild-type and stable variant of headpiece 35. Autocorrelation force spectroscopy pushes the time resolution of single-molecule force spectroscopy to ∼10 µs thus approaching the timescales accessible for all atom molecular dynamics simulations.

Soliton driven relaxation dynamics and protein collapse in the villin headpiece

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen's thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.

Binding free-energy calculation of an ion-peptide complex by constrained dynamics

Binding free energy is the most important physical parameter that describes the binding affinity of a receptor-ligand complex. Conventionally, it was obtained based on the thermodynamic cycle or alchemical reaction. These strategies have been widely used, but they would be problematic if the receptors and/or ligands have large conformational changes during the binding processes. In this paper, we present a way to calculate the binding free energy: constrained dynamics along a fragmental and high-dimensional transition path. This method directly considers unbound states in the simulation. The application to the calmodulin loop-calcium complexes shows that it is practical and the calculated relative binding affinities are in good agreement with experimental results.

Simulation study of the role of the ribosomal exit tunnel on protein folding

To investigate the role of the ribosomal exit tunnel on protein folding, we simulate the initial-stage folding behavior of the protein villin headpiece subdomain HP35 (PDB id: 1yrf) with and without prefolding in the exit tunnel by using an all-atom model and find that prefolding in the exit tunnel could effectively help the protein form native secondary structures. Furthermore, our results show that, after releasing from the exit tunnel, the prefolded chains may have a tendency to form more native contacts than those only in free space and this reduces the conformational space of sampling. Our results may provide an alternative way to explain the fast folding mechanism of proteins in vivo.

MOLECULAR DYNAMICS SIMULATIONS OF HELIX BUNDLE PROTEINS USING UNRES FORCE FIELD AND ALL-ATOM FORCE FIELD

We have investigated the folding of two helix-bundle proteins, 36-residue Villin headpiece and 56-residue E-domain of Staphylococcal protein A, by combining molecular dynamics (MD) simulations with Coarse-Grained United-Residue (UNRES) Force Field and all-atom force field. Starting from extended structures, each of the proteins was folded to a stable structure within a short time frame using the UNRES model. However, the secondary structures of helices were not well formed. Further refinement using MD simulations with the all-atom force field was able to fold the protein structure into the native-like state with the smallest main-chain root-mean-square deviation of around 3 Å. Detailed analysis of the folding trajectories was presented and the performance of GPU-based MD simulations was also discussed.

Separability between overall and internal motion: a protein folding problem

The separability between overall and internal motions is evaluated over multiple folding trajectories of the villin headpiece subdomain. The analysis, which relies on the Prompers-Brüschweiler separability index, offers a potentially useful perspective on protein folding. The protein is considered folded in this study, not when it reaches some static target, but rather when it tumbles as a dynamically constrained object. The analysis also demonstrates how the separability index, when applied to protein folding simulations, can facilitate the analysis of NMR relaxation data.

Correlation between protein secondary structure, backbone bond angles, and side-chain orientations

We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C(α) carbon of a protein backbone, and for this we develop new visualization techniques to analyze high-resolution x-ray structures in the Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse-grained energy function to describe the ensuing side-chain geometry in terms of the C(β) carbon orientations. The energy function can model the side-chain geometry with a subatomic precision. As an example we construct the C(α)-C(β) structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 Å in root-mean-square distance from the experimental x-ray structure.

Microsecond scale replica exchange molecular dynamic simulation of villin headpiece: an insight into the folding landscape

Reaching the experimental time scale of millisecond is a grand challenge for protein folding simulations. The development of advanced Molecular Dynamics techniques like Replica Exchange Molecular Dynamics (REMD) makes it possible to reach these experimental timescales. In this study, an attempt has been made to reach the multi microsecond simulation time scale by carrying out folding simulations on a three helix bundle protein, Villin, by combining REMD and Amber United Atom model. Twenty replicas having different temperatures ranging from 295 K to 390 K were simulated for 1.5 µs each. The lowest Root Mean Square Deviation (RMSD) structure of 2.5 Å was obtained with respect to native structure (PDB code 1VII), with all the helices formed. The folding population landscapes were built using segment-wise RMSD and Principal Components as reaction coordinates. These analyses suggest the two-stage folding for Villin. The combination of REMD and Amber United Atom model may be useful to understand the folding mechanism of various fast folding proteins.

Discrete Frenet frame, inflection point solitons, and curve visualization with applications to folded proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three-dimensional space. Our approach is based on the concept of an intrinsically discrete curve. This enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation reproduces the generalized Frenet equation. In particular, we draw attention to the conceptual similarity between inflection points where the curvature vanishes and topologically stable solitons. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of C(β) carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this C(β) framing relates intimately to the discrete Frenet framing. We also explain how inflection points (a.k.a. soliton centers) can be located in the loops and clarify their distinctive rôle in determining the loop structure of folded proteins.

Computational model for protein unfolding simulation

The protein folding problem is one of the fundamental and important questions in molecular biology. However, the all-atom molecular dynamics studies of protein folding and unfolding are still computationally expensive and severely limited by the time scale of simulation. In this paper, a simple and fast protein unfolding method is proposed based on the conformational stability analyses and structure modeling. In this method, two structure-based conditions are considered to identify the unstable regions of proteins during the unfolding processes. The protein unfolding trajectories are mimicked through iterative structure modeling according to conformational stability analyses. Two proteins, chymotrypsin inhibitor 2 (CI2) and α -spectrin SH3 domain (SH3) were simulated by this method. Their unfolding pathways are consistent with the previous molecular dynamics simulations. Furthermore, the transition states of the two proteins were identified in unfolding processes and the theoretical Φ values of these transition states showed significant correlations with the experimental data (the correlation coefficients are >0.8). The results indicate that this method is effective in studying protein unfolding. Moreover, we analyzed and discussed the influence of parameters on the unfolding simulation. This simple coarse-grained model may provide a general and fast approach for the mechanism studies of protein folding.

The protein folding network indicates that the ultrafast folding mutant of villin headpiece subdomain has a deeper folding funnel

Protein folding is a dynamic process with continuous transitions among different conformations. In this work, the dynamics in the protein folding network of villin headpiece subdomain (HP35) has been investigated based on multiple reversible folding trajectories of HP35 and its ultrafast folding mutant where sub-angstrom folding was achieved. The four folding states were clearly separated on the network, validating the classification of the states. Examination of the eight conformers with different formation of the individual helices revealed high plasticity of the three helices in all the four states. A consistent feature between the wild type and mutant protein is the dominant conformer 111 (all three helices formed) in the folded state and conformers 111 and 011 (helices II and III formed) in the major intermediate state, indicating the critical role of helices II and III in the folding mechanism. When compared to the wild type, the folding landscape of the ultrafast folding mutant exhibited a deeper folding funnel towards the folded state. The very beginning of the folding (0-10 ns) was very similar for both protein variants but it soon diverged and displayed different folding pathways. Although going through the major intermediate state is the dominant pathway for both, it was also observed that some folding went through the minor intermediate state for the mutant. The intriguing difference resulting from the mutation at two residues in helix III has been carefully analyzed and discussed in details.

Folding network of villin headpiece subdomain

Protein folding is a complex multidimensional process that is difficult to illustrate by the traditional analyses based on one- or two-dimensional profiles. Analyses based on transition networks have become an alternative approach that has the potential to reveal detailed features of protein folding dynamics. However, due to the lack of successful reversible folding of proteins from conventional molecular-dynamics simulations, this approach has rarely been utilized. Here, we analyzed the folding network from several 10 μs conventional molecular-dynamics reversible folding trajectories of villin headpiece subdomain (HP35). The folding network revealed more complexity than the traditional two-dimensional map and demonstrated a variety of conformations in the unfolded state, intermediate states, and the native state. Of note, deep enthalpic traps at the unfolded state were observed on the folding landscape. Furthermore, in contrast to the clear separation of the native state and the primary intermediate state shown on the two-dimensional map, the two states were mingled on the folding network, and prevalent interstate transitions were observed between these two states. A more complete picture of the folding mechanism of HP35 emerged when the traditional and network analyses were considered together.

Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins

We introduce a novel generalization of the discrete nonlinear Schrödinger equation. It supports solitons that we utilize to model chiral polymers in the collapsed phase and, in particular, proteins in their native state. As an example we consider the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. We use its backbone as a template to explicitly construct a two-soliton configuration. Each of the two solitons describe well over 7.000 supersecondary structures of folded proteins in the Protein Data Bank with sub-angstrom accuracy suggesting that these solitons are common in nature.

Trends in template/fragment-free protein structure prediction

Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.

Protein folding as flow across a network of folding-unfolding pathways. 1. The mid-transition case

Prediction of protein folding rates and folding nuclei is an important problem of protein science. Most of the previously proposed models for protein folding in vitro are based on the nucleation mechanism of this process. Our model considering protein folding as a flow arising in a network of folding-unfolding pathways at a coarse-grained free-energy landscape was described a few years ago, along with an algorithm for calculation of protein folding rates. Here we extend our approach and describe in detail a mathematically strict algorithm for calculating the "folding nuclei", arising as bottlenecks of the flow. Although the proposed physical theory uses no adjustable parameters, its results are in good agreement with experiment. This paper presents (i) the general theory and (ii) the results for the simplest case, i.e., folding/unfolding at the midpoint of thermodynamic equilibrium between the native and unfolded states of a protein; results for "in-water" conditions, i.e., for the case when no denaturant is added and the native state of a protein is much more stable than the unfolded one, will be described in the next paper of the series.

Challenges in protein folding simulations: Timescale, representation, and analysis

Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory

The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Modelling proteins: conformational sampling and reconstruction of folding kinetics

In the last decades biomolecular simulation has made tremendous inroads to help elucidate biomolecular processes in-silico. Despite enormous advances in molecular dynamics techniques and the available computational power, many problems involve long time scales and large-scale molecular rearrangements that are still difficult to sample adequately. In this review we therefore summarise recent efforts to fundamentally improve this situation by decoupling the sampling of the energy landscape from the description of the kinetics of the process. Recent years have seen the emergence of many advanced sampling techniques, which permit efficient characterisation of the relevant family of molecular conformations by dispensing with the details of the short-term kinetics of the process. Because these methods generate thermodynamic information at best, they must be complemented by techniques to reconstruct the kinetics of the process using the ensemble of relevant conformations. Here we review recent advances for both types of methods and discuss their perspectives to permit efficient and accurate modelling of large-scale conformational changes in biomolecules. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe

The four-helix bundle protein Rd-apocyt b(562), a redesigned stable variant of apocytochrome b(562), exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Phi-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Phi-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Phi-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.

Folding simulations of a de novo designed protein with a betaalphabeta fold

betaalphabeta structural motifs are commonly used building blocks in protein structures containing parallel beta-sheets. However, to our knowledge, no stand-alone betaalphabeta structure has been observed in nature to date. Recently, for the first time that we know of, a small protein with an independent betaalphabeta structure (DS119) was successfully designed in our laboratory. To understand the folding mechanism of DS119, in the study described here, we carried out all-atom molecular dynamics and coarse-grained simulations to investigate its folding pathways and energy landscape. From all-atom simulations, we successfully observed the folding event and got a stable folded structure with a minimal root mean-square deviation of 2.6 A with respect to the NMR structure. The folding process can be described as a fast collapse phase followed by rapid formation of the central helix, and then slow formation of a parallel beta-sheet. By using a native-centric Gō-like model, the cooperativity of the system was characterized in terms of the calorimetric criterion, sigmoidal transitions, conformation distribution shifts, and free-energy profiles. DS119 was found to be an incipient downhill folder that folds more cooperatively than a downhill folder, but less cooperatively than a two-state folder. This may reflect the balance between the two structural elements of DS119: the rapidly formed alpha-helix and the slowly formed parallel beta-sheet. Folding times estimated from both the all-atom simulations and the coarse-grained model were at microsecond level, making DS119 another fast folder. Compared to fast folders reported previously, DS119 is, to the best of our knowledge, the first that exhibits a parallel beta-sheet.

A critical assessment of putative gatekeeper interactions in the villin headpiece helical subdomain

The helical subdomain of the villin headpiece (HP36) is one of the smallest naturally occurring proteins that folds cooperatively. Its small size, rapid folding, and simple three-helix topology have made it an extraordinary popular model system for computational, theoretical, and experimental studies of protein folding. Aromatic-proline interactions involving Trp64 and Pro62 have been proposed to play a critical role in specifying the subdomain fold by acting as gatekeeper residues. Note that the numbering corresponds to full-length headpiece. Mutation of Pro62 has been shown to lead to a protein that does not fold, but this may arise for two different reasons: The residue may make interactions that are critical for the specificity of the fold or the mutation may simply destabilize the domain. In the first case, the protein cannot fold, while in the second, the small fraction of molecules that do fold adopt the correct structure. The modest stability of the wild type prevents a critical analysis of these interactions because even moderately destabilizing mutations lead to a very small folded state population. Using a hyperstable variant of HP36, denoted DM HP36, as our new wild type, we characterized a set of mutants designed to assess the role of the putative gatekeeper interactions. Four single mutants, DM Pro62Ala, DM Trp64Leu, DM Trp64Lys, and DM Trp64Ala, and a double mutant, DM Pro62Ala Trp64Leu, were prepared. All mutants are less stable than DM HP36, but all are well folded as judged by CD and (1)H NMR. All of the mutants display sigmoidal thermal unfolding and urea-induced unfolding curves. Double-mutant cycle analysis shows that the interactions between Pro62 and Trp64 are weak but favorable. Interactions involving Pro62 and proline-aromatic interactions are, thus, not required for specifying the subdomain fold. The implications for the design and thermodynamics of miniature proteins are discussed.

Detection of a transient intermediate in a rapid protein folding process by solid-state nuclear magnetic resonance

We describe the use of solid-state NMR spectroscopy to characterize a partially folded state of the 35-residue helical protein HP35 created by rapid freeze-quenching from a thermally unfolded state on the 10-20 micros time scale. Two-dimensional solid-state (13)C NMR spectra of (13)C-labeled HP35 in frozen glycerol/water solution exhibit two sets of signals, one corresponding to strongly unfolded protein molecules and the other to an ensemble of molecules having native helical secondary structure but incomplete tertiary structure. The NMR data indicate that secondary structure forms within the freeze-quenching time scale but that full folding involves a slower phase of structural annealing. The approximately 5 micros folding time observed in earlier studies of HP35 by time-resolved optical techniques may not represent the time scale for full folding.

Dynamic folding pathway models of the villin headpiece subdomain (HP-36) structure

We have investigated the folding pathway of the 36-residue villin headpiece subdomain (HP-36) by action-derived molecular dynamics simulations. The folding is initiated by hydrophobic collapse, after which the concurrent formation of full tertiary structure and alpha-helical secondary structure is observed. The collapse is observed to be associated with a couple of specific native contacts contrary to the conventional nonspecific hydrophobic collapse model. Stable secondary structure formation after the collapse suggests that the folding of HP-36 follows neither the framework model nor the diffusion-collision model. The C-terminal helix forms first, followed by the N-terminal helix positioned in its native orientation. The short middle helix is shown to form last. Signs for multiple folding pathways are also observed.