Accelerated simulation of unfolding and refolding of a large single chain globular protein

We have developed novel strategies for contracting simulation times in protein dynamics that enable us to study a complex protein with molecular weight in excess of 34 kDa. Starting from a crystal structure, we produce unfolded and then refolded states for the protein. We then compare these quantitatively using both established and new metrics for protein structure and quality checking. These include use of the programs Concoord and Darvols. Simulation of protein-folded structure well beyond the molten globule state and then recovery back to the folded state is itself new, and our results throw new light on the protein-folding process. We accomplish this using a novel cooling protocol developed for this work.     

Determination of the transition state ensemble for the folding of ubiquitin from a combination of Phi and Psi analyses

Protein engineering techniques have emerged as powerful tools for characterizing transition states (TSs) for protein folding. Recently, the Ψ analysis, in which double-histidine mutations create the possibility of reversible crosslinking in the native state, has been proposed as an additional approach to the well-established Φ analysis. We present here a combination of these two procedures for defining the structure of the TS of ubiquitin, a small α/β protein that has been used extensively as a model system for both experimental and computational studies of the protein-folding process. We performed a series of molecular dynamics simulations in which Φ and Ψ values were used as ensemble-averaged structural restraints to determine an ensemble of structures representing the TS of ubiquitin. Although the available Ψ values for ubiquitin did not, by themselves, generate well-defined TS ensembles, the inclusion of the restricted set of zero or unity values, but not fractional ones, provided useful complementary information to the Φ analysis. Our results show that the TS of ubiquitin is formed by a relatively narrow ensemble of structures exhibiting an overall native-like topology in which the N-terminal and C-terminal regions are in close proximity.     

Molecular Dynamics Study of the Opening Mechanism for DNA Polymerase I

During DNA replication, DNA polymerases follow an induced fit mechanism in order to rapidly distinguish between correct and incorrect dNTP substrates. The dynamics of this process are crucial to the overall effectiveness of catalysis. Although X-ray crystal structures of DNA polymerase I with substrate dNTPs have revealed key structural states along the catalytic pathway, solution fluorescence studies indicate that those key states are populated in the absence of substrate. Herein, we report the first atomistic simulations showing the conformational changes between the closed, open, and ajar conformations of DNA polymerase I in the binary (enzyme∶DNA) state to better understand its dynamics. We have applied long time-scale, unbiased molecular dynamics to investigate the opening process of the fingers domain in the absence of substrate for B. stearothermophilis DNA polymerase in silico. These simulations are biologically and/or physiologically relevant as they shed light on the transitions between states in this important enzyme. All closed and ajar simulations successfully transitioned into the fully open conformation, which is known to be the dominant binary enzyme-DNA conformation from solution and crystallographic studies. Furthermore, we have detailed the key stages in the opening process starting from the open and ajar crystal structures, including the observation of a previously unknown key intermediate structure. Four backbone dihedrals were identified as important during the opening process, and their movements provide insight into the recognition of dNTP substrate molecules by the polymerase binary state. In addition to revealing the opening mechanism, this study also demonstrates our ability to study biological events of DNA polymerase using current computational methods without biasing the dynamics.     

Probing the wild-type HRas activation mechanism using steered molecular dynamics,understanding the energy barrier and role of water in the activation

Ras is one of the most common oncogenes in human cancers. It belongs to a family of GTPases that functions as binary conformational switches by timely switching of their conformations from GDP to GTP and vice versa. It attains the final active state structure via an intermediate GTP-bound state. The transition between these states is a millisecond-time-scale event. This makes studying this mechanism beyond the scope of classical molecular dynamics. In the present study, we describe the activation pathway of the HRas protein complex along the distance-based reaction coordinate using steered molecular dynamics. Approximately ~720 ns of MD simulations using CMD and SMD was performed. We demonstrated the change in orientation and arrangement of the two switch regions and the role of various hydrogen bonds during the activation process. The weighted histogram analysis method was also performed, and the potential of mean force was calculated between the inactive and active via the intermediate state (state 1) of HRas. The study indicates that water seems to play a crucial role in the activation process and to transfer the HRas protein from its intermediate state to the fully active state. The implications of our study hereby suggest that the HRas activation mechanism is a multistep process. It starts from the inactive state to an intermediate state 1 followed by trapping of water molecules and flipping of the Thr35 residue to form a fully active state (state 2). This state 2 also comprises Gly60, Thr35, GTP, Mg²⁺ and water-forming stable interactions.     

Structural insights into the cellular retinaldehyde-binding protein (CRALBP)

Cellular retinaldehyde-binding protein (CRALBP) is an essential protein in the human visual cycle without a known three-dimensional structure. Previous studies associate retinal pathologies to specific mutations in the CRALBP protein. Here we use homology modeling and molecular dynamics methods to investigate the structural mechanisms by which CRALBP functions in the visual cycle. We have constructed two conformations of CRALBP representing two states in the process of ligand association and dissociation. Notably, our homology models map the pathology-associated mutations either directly in or adjacent to the putative ligand-binding cavity. Furthermore, six novel residues have been identified to be crucial for the hinge movement of the lipid-exchange loop in CRALBP. We conclude that the binding and release of retinoid involve large conformational changes in the lipid-exchange loop at the entrance of the ligand-binding cavity.     

Molecular dynamics simulations of ethanol binding to the transmembrane domain of the glycine receptor: implications for the channel potentiation mechanism

The glycine receptor (GlyR) is potentiated by ethanol and other anesthetics. The potentiation mechanism at the molecular level is unknown and remains elusive, but mutagenic studies have shown that ethanol and other volatile anesthetics bind to a pocket between TM1, TM2, and TM3. The present study extends previous studies (Cheng et al., Proteins 2007;68:581-593) wherein we conducted homology modeling and molecular dynamics (MD) simulations to construct models of the homopentameric alpha1 subunits of the GlyR transmembrane domain in open and closed states. To understand the potentiation of GlyR by ethanol we compare the binding of ethanol molecules to the channel in these different states. We observe that ethanol stably resides inside solvent-accessible cavities found in the open state of GlyR that are formed by I229 (of TM1) in one subunit and S267 and A288 (of TM2 and TM3, respectively) in the adjacent subunit. The volume of these putative binding pockets is state-dependent. Selective binding to the open states of receptors has been proposed to explain the potentiating actions of this class of anesthetics. In accordance with this model, our MD simulations suggest that the potentiation of ethanol on GlyR may be effected through preferential binding of ethanol molecules to an inter-subunit binding pocket in the open state.     

Structural interpretation of hydrogen exchange protection factors in proteins: characterization of the native state fluctuations of CI2

Protection factors obtained from equilibrium hydrogen exchange experiments are an important source of structural information on both native and nonnative states of proteins. We present a method for determining ensembles of protein structures by using hydrogen exchange data as restraints in molecular dynamics simulations in conjunction with an empirical force-field. The method is applied to determine the ensemble of structures representing the native state of chymotrypsin inhibitor 2 (CI2), including the rare, large fluctuations responsible for hydrogen exchange.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

SPINFAST: using structure alignment profiles to enhance the accuracy and assess the reliability of protein side-chain modeling

We present a novel, knowledge-based method for the side-chain addition step in protein structure modeling. The foundation of the method is a conditional probability equation, which specifies the probability that a side-chain will occupy a specific rotamer state, given a set of evidence about the rotamer states adopted by the side-chains at aligned positions in structurally homologous crystal structures. We demonstrate that our method increases the accuracy of homology model side-chain addition when compared with the widely employed practice of preserving the side-chain conformation from the homology template to the target at conserved residue positions. Furthermore, we demonstrate that our method accurately estimates the probability that the correct rotamer state has been selected. This interesting result implies that our method can be used to understand the reliability of each and every side-chain in a protein homology model.     

Dynamical Phase Transitions Reveal Amyloid-like States on Protein Folding Landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.     

A method for predicting protein structure from sequence

BACKGROUND: The ability to predict the native conformation of a globular protein from its amino-acid sequence is an important unsolved problem of molecular biology. We have previously reported a method in which reduced representations of proteins are folded on a lattice by Monte Carlo simulation, using statistically-derived potentials. When applied to sequences designed to fold into four-helix bundles, this method generated predicted conformations closely resembling the real ones. RESULTS: We now report a hierarchical approach to protein-structure prediction, in which two cycles of the above-mentioned lattice method (the second on a finer lattice) are followed by a full-atom molecular dynamics simulation. The end product of the simulations is thus a full-atom representation of the predicted structure. The application of this procedure to the 60 residue, B domain of staphylococcal protein A predicts a three-helix bundle with a backbone root mean square (rms) deviation of 2.25-3 A from the experimentally determined structure. Further application to a designed, 120 residue monomeric protein, mROP, based on the dimeric ROP protein of Escherichia coli, predicts a left turning, four-helix bundle native state. Although the ultimate assessment of the quality of this prediction awaits the experimental determination of the mROP structure, a comparison of this structure with the set of equivalent residues in the ROP dime- crystal structure indicates that they have a rms deviation of approximately 3.6-4.2 A. CONCLUSION: Thus, for a set of helical proteins that have simple native topologies, the native folds of the proteins can be predicted with reasonable accuracy from their sequences alone. Our approach suggest a direction for future work addressing the protein-folding problem.     

Hierarchical Modeling of Activation Mechanisms in the ABL and EGFR Kinase Domains: Thermodynamic and Mechanistic Catalysts of Kinase Activation by Cancer Mutations

Structural and functional studies of the ABL and EGFR kinase domains have recently suggested a common mechanism of activation by cancer-causing mutations. However, dynamics and mechanistic aspects of kinase activation by cancer mutations that stimulate conformational transitions and thermodynamic stabilization of the constitutively active kinase form remain elusive. We present a large-scale computational investigation of activation mechanisms in the ABL and EGFR kinase domains by a panel of clinically important cancer mutants ABL-T315I, ABL-L387M, EGFR-T790M, and EGFR-L858R. We have also simulated the activating effect of the gatekeeper mutation on conformational dynamics and allosteric interactions in functional states of the ABL-SH2-SH3 regulatory complexes. A comprehensive analysis was conducted using a hierarchy of computational approaches that included homology modeling, molecular dynamics simulations, protein stability analysis, targeted molecular dynamics, and molecular docking. Collectively, the results of this study have revealed thermodynamic and mechanistic catalysts of kinase activation by major cancer-causing mutations in the ABL and EGFR kinase domains. By using multiple crystallographic states of ABL and EGFR, computer simulations have allowed one to map dynamics of conformational fluctuations and transitions in the normal (wild-type) and oncogenic kinase forms. A proposed multi-stage mechanistic model of activation involves a series of cooperative transitions between different conformational states, including assembly of the hydrophobic spine, the formation of the Src-like intermediate structure, and a cooperative breakage and formation of characteristic salt bridges, which signify transition to the active kinase form. We suggest that molecular mechanisms of activation by cancer mutations could mimic the activation process of the normal kinase, yet exploiting conserved structural catalysts to accelerate a conformational transition and the enhanced stabilization of the active kinase form. The results of this study reconcile current experimental data with insights from theoretical approaches, pointing to general mechanistic aspects of activating transitions in protein kinases.     

Variational Bayes Analysis of a Photon-Based Hidden Markov Model for Single-Molecule FRET Trajectories

Single-molecule fluorescence resonance energy transfer (smFRET) measurement is a powerful technique for investigating dynamics of biomolecules, for which various efforts have been made to overcome significant stochastic noise. Time stamp (TS) measurement has been employed experimentally to enrich information within the signals, while data analyses such as the hidden Markov model (HMM) have been successfully applied to recover the trajectories of molecular state transitions from time-binned photon counting signals or images. In this article, we introduce the HMM for TS-FRET signals, employing the variational Bayes (VB) inference to solve the model, and demonstrate the application of VB-HMM-TS-FRET to simulated TS-FRET data. The same analysis using VB-HMM is conducted for other models and the previously reported change point detection scheme. The performance is compared to other analysis methods or data types and we show that our VB-HMM-TS-FRET analysis can achieve the best performance and results in the highest time resolution. Finally, an smFRET experiment was conducted to observe spontaneous branch migration of Holliday-junction DNA. VB-HMM-TS-FRET was successfully applied to reconstruct the state transition trajectory with the number of states consistent with the nucleotide sequence. The results suggest that a single migration process frequently involves rearrangement of multiple basepairs.     

Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

Morphogenesis of a protein: folding pathways and the energy landscape

Current knowledge on the reaction whereby a protein acquires its native three-dimensional structure was obtained by and large through characterization of the folding mechanism of simple systems. Given the multiplicity of amino acid sequences and unique folds, it is not so easy, however, to draw general rules by comparing folding pathways of different proteins. In fact, quantitative comparison may be jeopardized not only because of the vast repertoire of sequences but also in view of a multiplicity of structures of the native and denatured states. We have tackled the problem of the relationships between the sequence information and the folding pathway of a protein, using a combination of kinetics, protein engineering and computational methods, applied to relatively simple systems. Our strategy has been to investigate the folding mechanism determinants using two complementary approaches, i.e. (i) the study of members of the same family characterized by a common fold, but substantial differences in amino acid sequence, or (ii) heteromorphic pairs characterized by largely identical sequences but with different folds. We discuss some recent data on protein-folding mechanisms by presenting experiments on different members of the PDZ domain family and their circularly permuted variants. Characterization of the energetics and structures of intermediates and TSs (transition states), obtained by Φ-value analysis and restrained MD (molecular dynamics) simulations, provides a glimpse of the malleability of the dynamic states and of the role of the topology of the native states and of the denatured states in dictating folding and misfolding pathways.     

Molecular dynamics simulations of folding processes of a beta-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.     

A directed essential dynamics simulation of peptide folding

We present a directed essential dynamics (DED) method for peptide and protein folding. DED is a molecular dynamics method based on the essential dynamics sampling and the principal component analysis. The main idea of DED is to use principal component analysis to determine the direction of the most active collective motion of peptides at short intervals of time (20 fs) during the folding process and then add an additional force along it to adjust the folding direction. This method can make the peptides avoid being trapped in the local minima for a long time and enhance the sampling efficiency in conformational space during the simulation. An S-peptide with 15 amino acids is used to demonstrate the DED method. The results show that DED can lead the S-peptide to fold quickly into the native state, whereas traditional molecular dynamics needs more time to do this.     

Determination of the protonation state of the Asp dyad: conventional molecular dynamics versus thermodynamic integration

The protonation state of the Asp dyad is important as it can reveal enzymatic mechanisms, and the information this provides can be used in the development of drugs for proteins such as memapsin 2 (BACE-1), HIV-1 protease, and rennin. Conventional molecular dynamics (MD) simulations have been successfully used to determine the preferred protonation state of the Asp dyad. In the present work, we demonstrate that the results obtained from conventional MD simulations can be greatly influenced by the particular force field applied or the values used for control parameters. In principle, free-energy changes between possible protonation states can be used to determine the protonation state. We show that protonation state prediction by the thermodynamic integration (TI) method is insensitive to force field version or to the cutoff for calculating nonbonded interactions (a control parameter). In the present study, the protonation state of the Asp dyad predicted by TI calculations was the same regardless of the force field and cutoff value applied. Contrary to the intuition that conventional MD is more efficient, our results clearly show that the TI method is actually more efficient and more reliable for determining the protonation state of the Asp dyad.