Insights into the folding pathway of the Engrailed Homeodomain protein using replica exchange molecular dynamics simulations

Learned Reconstruction of Protein Folding Trajectories from Noisy Single-Molecule Time Series

Single-molecule Förster resonance energy transfer (smFRET) is an experimental methodology to track the real-time dynamics of molecules using fluorescent probes to follow one or more intramolecular distances. These distances provide a low-dimensional representation of the full atomistic dynamics. Under mild technical conditions, Takens' Delay Embedding Theorem guarantees that the full three-dimensional atomistic dynamics of a system are diffeomorphic (i.e., related by a smooth and invertible transformation) to a time-delayed embedding of one or more scalar observables. Appealing to these theoretical guarantees, we employ manifold learning, artificial neural networks, and statistical mechanics to learn from molecular simulation training data the a priori unknown transformation between the atomic coordinates and delay-embedded intramolecular distances accessible to smFRET. This learned transformation may then be used to reconstruct atomistic coordinates from smFRET time series data. We term this approach Single-molecule TAkens Reconstruction (STAR). We have previously applied STAR to reconstruct molecular configurations of a C24H50 polymer chain and the mini-protein Chignolin with accuracies better than 0.2 nm from simulated smFRET data under noise free and high time resolution conditions. In the present work, we investigate the role of signal-to-noise ratio, data volume, and time resolution in simulated smFRET data to assess the performance of STAR under conditions more representative of experimental realities. We show that STAR can reconstruct the Chignolin and Villin mini-proteins to accuracies of 0.12 and 0.42 nm, respectively, and place bounds on these conditions for accurate reconstructions. These results demonstrate that it is possible to reconstruct dynamical trajectories of protein folding from time series in noisy, time binned, experimentally measurable observables and lay the foundations for the application of STAR to real experimental data.

Visualizing Protein Folding and Unfolding

Protein folding/unfolding is a complicated process that defies high-resolution characterization by experimental methods. As an alternative, atomistic molecular dynamics simulations are now routinely employed to elucidate and magnify the accompanying conformational changes and the role of solvent in the folding process. However, the level of detail necessary to map the process at high spatial-temporal resolution provides an overwhelming amount of data. As more and better tools are developed for analysis of these large data sets and validation of the simulations, one is still left with the problem of visualizing the results in ways that provide insight into the folding/unfolding process. While viewing and interrogating static crystal structures has become commonplace, more and different approaches are required for dynamic, interconverting, unfolding, and refolding proteins. Here we review a variety of approaches, ranging from straightforward to complex and unintuitive for multiscale analysis and visualization of protein folding and unfolding.

Atomistic molecular dynamics simulations of bioactive engrailed 1 interference peptides (EN1-iPeps)

The neural-specific transcription factor Engrailed 1 - is overexpressed in basal-like breast tumours. Synthetic interference peptides - comprising a cell-penetrating peptide/nuclear localisation sequence and the Engrailed 1-specific sequence from the N-terminus have been engineered to produce a strong apoptotic response in tumour cells overexpressing EN1, with no toxicity to normal or non Engrailed 1-expressing cells. Here scaled molecular dynamics simulations were used to study the conformational dynamics of these interference peptides in aqueous solution to characterise their structure and dynamics. Transitions from disordered to α-helical conformation, stabilised by hydrogen bonds and proline-aromatic interactions, were observed throughout the simulations. The backbone of the wild-type peptide folds to a similar conformation as that found in ternary complexes of anterior Hox proteins with conserved hexapeptide motifs important for recognition of pre-B-cell leukemia Homeobox 1, indicating that the motif may possess an intrinsic preference for helical structure. The predicted NMR chemical shifts of these peptides are consistent with the Hox hexapeptides in solution and Engrailed 2 NMR data. These findings highlight the importance of aromatic residues in determining the structure of Engrailed 1 interference peptides, shedding light on the rational design strategy of molecules that could be adopted to inhibit other transcription factors overexpressed in other cancer types, potentially including other transcription factor families that require highly conserved and cooperative protein-protein partnerships for biological activity.

Ligand induced change of β2 adrenergic receptor from active to inactive conformation and its implication for the closed/open state of the water channel: insight from molecular dynamics simulation, free energy calculation and Markov state model analysis

The reported crystal structures of β2 adrenergic receptor (β2AR) reveal that the open and closed states of the water channel are correlated with the inactive and active conformations of β2AR. However, more details about the process by which the water channel states are affected by the active to inactive conformational change of β2AR remain illusive. In this work, molecular dynamics simulations are performed to study the dynamical inactive and active conformational change of β2AR induced by inverse agonist ICI 118,551. Markov state model analysis and free energy calculation are employed to explore the open and close states of the water channel. The simulation results show that inverse agonist ICI 118,551 can induce water channel opening during the conformational transition of β2AR. Markov state model (MSM) analysis proves that the energy contour can be divided into seven states. States S1, S2 and S5, which represent the active conformation of β2AR, show that the water channel is in the closed state, while states S4 and S6, which correspond to the intermediate state conformation of β2AR, indicate the water channel opens gradually. State S7, which represents the inactive structure of β2AR, corresponds to the full open state of the water channel. The opening mechanism of the water channel is involved in the ligand-induced conformational change of β2AR. These results can provide useful information for understanding the opening mechanism of the water channel and will be useful for the rational design of potent inverse agonists of β2AR.

Important roles of hydrophobic interactions in folding and charge interactions in misfolding of α-helix bundle protein

An enhanced-sampling molecular dynamics simulation is presented to quantitatively demonstrate the important roles of hydrophobic and charge interactions in the folding and misfolding of α-helix bundle protein, respectively.

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.

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.

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 Å in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.