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

Quantitative Analysis of Protein Unfolded State Energetics: Experimental and Computational Studies Demonstrate That Non-Native Side-Chain Interactions Stabilize Local Native Backbone Structure

Proteins fold on relatively smooth free energy landscapes which are biased toward the native state, but even simple topologies which fold rapidly can experience roughness on their free energy landscape. The details of these interactions are difficult to elucidate experimentally. Closely related to the problem of deciphering the details of the free energy landscape is the problem of defining the interactions in the denatured state ensemble (DSE) which is populated under native conditions, that is, under conditions where the native state is stable. The DSE of many proteins deviates from random coil models, but quantifying and defining the energetics of the transiently populated interactions in this ensemble is extremely challenging. Characterization of the DSE of proteins which fold to compact structures is also relevant to studies of intrinsically disordered proteins (IDPs) since interactions in the dynamic ensemble populated by IDPs can modulate their behavior. Here we show how experimental thermodynamic and pK_a measurements can be combined with computational thermodynamic integration to quantify interactions in the DSE. We show that non-native side chain interactions can stabilize native backbone structure in the DSE and demonstrate that that even rapidly folding proteins can form energetically significant non-native interactions in their DSE. As an example, we characterize a non-native salt bridge that stabilizes local native backbone structure in the DSE of a widely studied fast-folding protein, the villin headpiece helical domain. The combined computational experimental approach is applicable to other protein unfolded states and provides insight that is impossible to obtain with either method alone.

Heterogeneity in the Folding of Villin Headpiece Subdomain HP36

Small single domain proteins that fold on the microsecond time scale have been the subject of intense interest as models for probing the complexity of folding energy landscapes. The villin headpiece subdomain (HP36) has been extensively studied because of its simple three helix structure, ultrafast folding lifetime of a few microseconds, and stable native fold. We have previously shown that folding as measured by a single ¹³C═¹⁸O isotopic label on residue A57 in helix 2 occurs at a different rate than that measured by global probes of folding, indicating noncooperative complexity in the folding of HP36. In order to determine whether this complexity reflects intermediates or parallel pathways over a small activation barrier, ¹³C═¹⁸O labels were individually incorporated at six different positions in HP36, including into all 3 helices. The equilibrium thermal unfolding transitions and the folding/unfolding dynamics were monitored using the unique IR signature of the ¹³C═¹⁸O label by temperature dependent FTIR and temperature jump IR spectroscopy, respectively. Equilibrium experiments reveal that the ¹³C═¹⁸O labels at different positions in HP36 show drastic differences in the midpoint of their transitions ( T_m), ranging from 45 to 67 °C. Heterogeneity is also observed in the relaxation kinetics; there are differences in the microsecond phase when different labeled positions are probed. At a final temperature of 45 °C, the relaxation rate for ¹³C═¹⁸O A57 is 2.4e + 05 s^-1 whereas for ¹³C═¹⁸O L69 HP36 the relaxation rate is 5.1e + 05 s^-1, two times faster. The observation of site-dependent midpoints for the equilibrium unfolding transitions and differences in the relaxation rates of the labeled positions enables us to probe the progressive accumulation of the folded structure, providing insight into the microscopic details of the folding mechanism.

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.

A Folding Pathway Model of Mini-Protein BBA5

We present the folding pathway model of mini-protein BBA5, a bundle of secondary structures, α-helix and β-hairpin, by using action-derived molecular dynamics (ADMD) simulations. From ten independent ADMD simulations, we extracted common features of the folding pathway of BBA5, from which we found that the early stage chain compaction was followed by the formation of C-terminal α-helix. The N-terminal β-hairpin was observed to form only after α-helix was stabilized. This result is in good agreement with the experimental observation that BBA5 mutants were moderately cooperative folders, and their C-terminal helical fragments were of higher secondary structure propensity while the N-terminal hairpin fragments were of a random coil spectrum. We found that the most flexible part of BBA5 is the N-terminal four residues. Although both are made of the identical ββα motif, the secondary structure formation sequence of BBA5 is found to be different from that of FSD-1. Finally, a description of the folding pathway in terms of principal component analysis is presented to characterize the folding dynamics in reduced dimensions. With only three principal components, we were able to describe 83.4% of the pathway.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

Transition pathway and its free-energy profile: a protocol for protein folding simulations

We propose a protocol that provides a systematic definition of reaction coordinate and related free-energy profile as the function of temperature for the protein-folding simulation. First, using action-derived molecular dynamics (ADMD), we investigate the dynamic folding pathway model of a protein between a fixed extended conformation and a compact conformation. We choose the pathway model to be the reaction coordinate, and the folding and unfolding processes are characterized by the ADMD step index, in contrast to the common a priori reaction coordinate as used in conventional studies. Second, we calculate free-energy profile as the function of temperature, by employing the replica-exchange molecular dynamics (REMD) method. The current method provides efficient exploration of conformational space and proper characterization of protein folding/unfolding dynamics from/to an arbitrary extended conformation. We demonstrate that combination of the two simulation methods, ADMD and REMD, provides understanding on molecular conformational changes in proteins. The protocol is tested on a small protein, penta-peptide of met-enkephalin. For the neuropeptide met-enkephalin system, folded, extended, and intermediate sates are well-defined through the free-energy profile over the reaction coordinate. Results are consistent with those in the literature.

Dynamic folding pathway models of the Trp-cage protein

Using action-derived molecular dynamics (ADMD), we study the dynamic folding pathway models of the Trp-cage protein by providing its sequential conformational changes from its initial disordered structure to the final native structure at atomic details. We find that the numbers of native contacts and native hydrogen bonds are highly correlated, implying that the native structure of Trp-cage is achieved through the concurrent formations of native contacts and native hydrogen bonds. In early stage, an unfolded state appears with partially formed native contacts (~40%) and native hydrogen bonds (~30%). Afterward, the folding is initiated by the contact of the side chain of Tyr3 with that of Trp6, together with the formation of the N-terminal α -helix. Then, the C-terminal polyproline structure docks onto the Trp6 and Tyr3 rings, resulting in the formations of the hydrophobic core of Trp-cage and its near-native state. Finally, the slow adjustment processes of the near-native states into the native structure are dominant in later stage. The ADMD results are in agreement with those of the experimental folding studies on Trp-cage and consistent with most of other computational studies.

Folding models of mini-protein FSD-1

We have carried out all-atom action-derived molecular dynamics (ADMD) folding simulations of the full-size FSD-1. FSD-1 is a designed mini-protein of 28 residues containing both α and β secondary structure elements. Multiple folding pathways are found for FSD-1, which is consistent with existing computational studies. Hydrophobic collapse is observed first, and then subsequent folding events proceeds by forming either α-helix or β-hairpin. Concurrent formation of the full tertiary structure and the secondary structure elements of α-helix and β-hairpin is observed. The folding pathway of FSD-1 elucidated by ADMD simulations does not follow the scenario of the framework model. ADMD simulations provide significant insights for the general mechanisms of protein folding and conformational changes.

Combining optimal control theory and molecular dynamics for protein folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages.

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.

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.

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.

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.