A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations

Machine learning. Clustering by fast search and find of density peaks

Cluster analysis is aimed at classifying elements into categories on the basis of their similarity. Its applications range from astronomy to bioinformatics, bibliometrics, and pattern recognition. We propose an approach based on the idea that cluster centers are characterized by a higher density than their neighbors and by a relatively large distance from points with higher densities. This idea forms the basis of a clustering procedure in which the number of clusters arises intuitively, outliers are automatically spotted and excluded from the analysis, and clusters are recognized regardless of their shape and of the dimensionality of the space in which they are embedded. We demonstrate the power of the algorithm on several test cases.

Folding simulation of Trp-cage utilizing a new AMBER compatible force field with coupled main chain torsions

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity Cvis only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032Dis an accurate force field that can be used for protein folding simulations.

Statistical mechanics of the denatured state of a protein using replica-averaged metadynamics

The characterization of denatured states of proteins is challenging because the lack of permanent structure in these states makes it difficult to apply to them standard methods of structural biology. In this work we use all-atom replica-averaged metadynamics (RAM) simulations with NMR chemical shift restraints to determine an ensemble of structures representing an acid-denatured state of the 86-residue protein ACBP. This approach has enabled us to reach convergence in the free energy landscape calculations, obtaining an ensemble of structures in relatively accurate agreement with independent experimental data used for validation. By observing at atomistic resolution the transient formation of native and non-native structures in this acid-denatured state of ACBP, we rationalize the effects of single-point mutations on the folding rate, stability, and transition-state structures of this protein, thus characterizing the role of the unfolded state in determining the folding process.

Thermodynamics of Deca-alanine Folding in Water

The determination of the folding dynamics of polypeptides and proteins is critical in characterizing their functions in biological systems. Numerous computational models and methods have been developed for studying structure formation at the atomic level. Due to its small size and simple structure, deca-alanine is used as a model system in molecular dynamics (MD) simulations. The free energy of unfolding in vacuum has been studied extensively using the end-to-end distance of the peptide as the reaction coordinate. However, few studies have been conducted in the presence of explicit solvent. Previous results show a significant decrease in the free energy of extended conformations in water, but the α-helical state is still notably favored over the extended state. Although sufficient in vacuum, we show that end-to-end distance is incapable of capturing the full complexity of deca-alanine folding in water. Using α-helical content as a second reaction coordinate, we deduce a more descriptive free-energy landscape, one which reveals a second energy minimum in the extended conformations that is of comparable free energy to the α-helical state. Equilibrium simulations demonstrate the relative stability of the extended and α-helical states in water as well as the transition between the two states. This work reveals both the necessity and challenge of determining a proper reaction coordinate to fully characterize a given process.

Molecular recognition of DNA by ligands: roughness and complexity of the free energy profile

Understanding the molecular mechanism by which probes and chemotherapeutic agents bind to nucleic acids is a fundamental issue in modern drug design. From a computational perspective, valuable insights are gained by the estimation of free energy landscapes as a function of some collective variables (CVs), which are associated with the molecular recognition event. Unfortunately the choice of CVs is highly non-trivial because of DNA's high flexibility and the presence of multiple association-dissociation events at different locations and/or sliding within the grooves. Here we have applied a modified version of Locally-Scaled Diffusion Map (LSDMap), a nonlinear dimensionality reduction technique for decoupling multiple-timescale dynamics in macromolecular systems, to a metadynamics-based free energy landscape calculated using a set of intuitive CVs. We investigated the binding of the organic drug anthramycin to a DNA 14-mer duplex. By performing an extensive set of metadynamics simulations, we observed sliding of anthramycin along the full-length DNA minor groove, as well as several detachments from multiple sites, including the one identified by X-ray crystallography. As in the case of equilibrium processes, the LSDMap analysis is able to extract the most relevant collective motions, which are associated with the slow processes within the system, i.e., ligand diffusion along the minor groove and dissociation from it. Thus, LSDMap in combination with metadynamics (and possibly every equivalent method) emerges as a powerful method to describe the energetics of ligand binding to DNA without resorting to intuitive ad hoc reaction coordinates.

Molecular dynamics of the proline switch and its role in Crk signaling

The Crk adaptor proteins play a central role as a molecular timer for the formation of protein complexes including various growth and differentiation factors. The loss of regulation of Crk results in many kinds of cancers. A self-regulatory mechanism for Crk was recently proposed, which involves domain–domain rearrangement. It is initiated by a cis–trans isomerization of a specific proline residue (Pro238 in chicken Crk II) and can be accelerated by Cyclophilin A. To understand how the proline switch controls the autoinhibition at the molecular level, we performed large-scale molecular dynamics and metadynamics simulations in the context of short peptides and multidomain constructs of chicken Crk II. We found that the equilibrium and kinetic properties of the macrostates are regulated not only by the local environments of specified prolines but also by the global organization of multiple domains. We observe the two macrostates (cis closed/autoinhibited and trans open/uninhibited) consistent with NMR experiments and predict barriers. We also propose an intermediate state, the trans closed state, which interestingly was reported to be a prevalent state in human Crk II. The existence of this macrostate suggests that the rate of switching off the autoinhibition by Cyp A may be limited by the relaxation rate of this intermediate state.

Following easy slope paths on a free energy landscape: the case study of the Trp-cage folding mechanism

In this work a new method for the automatic exploration and calculation of multidimensional free energy landscapes is proposed. Inspired by metadynamics, it uses several collective variables that are relevant for the investigated process and a bias potential that discourages the sampling of already visited configurations. The latter potential allows escaping a local free energy minimum following the direction of slow motions. This is different from metadynamics in which there is no specific direction of the biasing force and the computational effort increases significantly with the number of collective variables. The method is tested on the Ace-Ala3-Nme peptide, and then it is applied to investigate the Trp-cage folding mechanism. For this protein, within a few hundreds of nanoseconds, a broad range of conformations is explored, including nearly native ones, initiating the simulation from a completely unfolded conformation. Finally, several folding/unfolding trajectories give a systematic description of the Trp-cage folding pathways, leading to a unified view for the folding mechanisms of this protein. The proposed mechanism is consistent with NMR chemical shift data at increasing temperature and recent experimental observations pointing to a pivotal role of secondary structure elements in directing the folding process toward the native state.

Achieving Rigorous Accelerated Conformational Sampling in Explicit Solvent

Molecular dynamics simulations can provide valuable atomistic insights into biomolecular function. However, the accuracy of molecular simulations on general-purpose computers depends on the time scale of the events of interest. Advanced simulation methods, such as accelerated molecular dynamics, have shown tremendous promise in sampling the conformational dynamics of biomolecules, where standard molecular dynamics simulations are nonergodic. Here we present a sampling method based on accelerated molecular dynamics in which rotatable dihedral angles and nonbonded interactions are boosted separately. This method (RaMD-db) is a different implementation of the dual-boost accelerated molecular dynamics, introduced earlier. The advantage is that this method speeds up sampling of the conformational space of biomolecules in explicit solvent, as the degrees of freedom most relevant for conformational transitions are accelerated. We tested RaMD-db on one of the most difficult sampling problems - protein folding. Starting from fully extended polypeptide chains, two fast folding α-helical proteins (Trpcage and the double mutant of C-terminal fragment of Villin headpiece) and a designed β-hairpin (Chignolin) were completely folded to their native structures in very short simulation time. Multiple folding/unfolding transitions could be observed in a single trajectory. Our results show that RaMD-db is a promisingly fast and efficient sampling method for conformational transitions in explicit solvent. RaMD-db thus opens new avenues for understanding biomolecular self-assembly and functional dynamics occurring on long time and length scales.

Activation pathway of Src kinase reveals intermediate states as targets for drug design

Unregulated activation of Src kinases leads to aberrant signaling, uncontrolled growth, and differentiation of cancerous cells. Reaching a complete mechanistic understanding of large scale conformational transformations underlying the activation of kinases could greatly help in the development of therapeutic drugs for the treatment of these pathologies. In principle, the nature of conformational transition could be modeled in silico via atomistic molecular dynamics simulations, although this is very challenging due to the long activation timescales. Here, we employ a computational paradigm that couples transition pathway techniques and Markov state model-based massively distributed simulations for mapping the conformational landscape of c-src tyrosine kinase. The computations provide the thermodynamics and kinetics of kinase activation for the first time, and help identify key structural intermediates. Furthermore, the presence of a novel allosteric site in an intermediate state of c-src that could be potentially utilized for drug design is predicted.

Reconstructing the free-energy landscape of Met-enkephalin using dihedral principal component analysis and well-tempered metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers, however, from the same limitation, i.e., the non-trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachandran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates, and does not depend on the alignment to an arbitrarily chosen reference structure as usual in Cartesian PCA. We illustrate the robustness of this method in the case of a reference model protein, the small and very diffusive Met-enkephalin pentapeptide. We propose a justification a posteriori of the considered number of CVs necessary to bias the metadynamics simulation in terms of the one-dimensional free-energy profiles associated with Ramachandran dihedral angles along the amino-acid sequence.

Role of tryptophan side chain dynamics on the Trp-cage mini-protein folding studied by molecular dynamics simulations

The 20 residue Trp-cage mini-protein is one of smallest proteins that adopt a stable folded structure containing also well-defined secondary structure elements. The hydrophobic core is arranged around a single central Trp residue. Despite several experimental and simulation studies the detailed folding mechanism of the Trp-cage protein is still not completely understood. Starting from fully extended as well as from partially folded Trp-cage structures a series of molecular dynamics simulations in explicit solvent and using four different force fields was performed. All simulations resulted in rapid collapse of the protein to on average relatively compact states. The simulations indicate a significant dependence of the speed of folding to near-native states on the side chain rotamer state of the central Trp residue. Whereas the majority of intermediate start structures with the central Trp side chain in a near-native rotameric state folded successfully within less than 100 ns only a fraction of start structures reached near-native folded states with an initially non-native Trp side chain rotamer state. Weak restraining of the Trp side chain dihedral angles to the state in the folded protein resulted in significant acceleration of the folding both starting from fully extended or intermediate conformations. The results indicate that the side chain conformation of the central Trp residue can create a significant barrier for controlling transitions to a near native folded structure. Similar mechanisms might be of importance for the folding of other protein structures.

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

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

Effects of a disulfide bridge prior to amyloid formation of the ABRI peptide

Computational studies characterize remarkable differences between the most probable structures of the monomeric amyloidogenic peptide, ABRI, with and without a single disulfide bond; the peptide is compact and alpha-helical with the bond, otherwise it is partially extended with slight β-bridges and an exposed hydrophobic surface area.

From metadynamics to dynamics

Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables it can explore complex free energy surfaces characterized by several metastable states separated by large free energy barriers. Here we extend its scope by introducing a simple yet powerful method for calculating the rates of transition between different metastable states. The method does not rely on a previous knowledge of the transition states or reaction coordinates, as long as collective variables are known that can distinguish between the various stable minima in free energy space. We demonstrate that our method recovers the correct escape rates out of these stable states and also preserves the correct sequence of state-to-state transitions, with minimal extra computational effort needed over ordinary metadynamics. We apply the formalism to three different problems and in each case find excellent agreement with the results of long unbiased molecular dynamics runs.

Assessment of local friction in protein folding dynamics using a helix cross-linker

Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.

Predicting the Thermodynamics and Kinetics of Helix Formation in a Cyclic Peptide Model

The peptide Ac-(cyclo-2,6)-R[KAAAD]-NH2 (cyc-RKAAAD) is a short cyclic peptide known to adopt a remarkably stable single turn α-helix in water. Due to its simplicity and the availability of thermodynamic and kinetic experimental data, cyc-RKAAAD poses as an ideal model for evaluating the aptness of current molecular dynamics (MD) simulation methodologies to accurately sample conformations that reproduce experimentally observed properties. In this work, we extensively sample the conformational space of cyc-RKAAAD using microsecond-timescale MD simulations. We characterize the peptide conformational preferences in terms of secondary structure propensities and, using Cartesian-coordinate principal component analysis (cPCA), construct its free energy landscape, thus obtaining a detailed weighted discrimination between the helical and nonhelical subensembles. The cPCA state discrimination, together with a Markov model built from it, allowed us to estimate the free energy of unfolding (-0.57 kJ/mol) and the relaxation time (∼0.435 μs) at 298.15 K, which are in excellent agreement with the experimentally reported values (-0.22 kJ/mol and 0.42 μs, Serrano, A. L.; Tucker, M. J.; Gai, F. J. Phys. Chem. B, 2011, 115, 7472-7478.). Additionally, we present simulations conducted using two enhanced sampling methods: replica-exchange molecular dynamics (REMD) and bias-exchange metadynamics (BE-MetaD). We compare the free energy landscape obtained by these two methods with the results from MD simulations and discuss the sampling and computational gains achieved. Overall, the results obtained attest to the suitability of modern simulation methods to explore the conformational behavior of peptide systems with a high level of realism.

Folding dynamics of the Trp-cage miniprotein: evidence for a native-like intermediate from combined time-resolved vibrational spectroscopy and molecular dynamics simulations

Trp-cage is a synthetic 20-residue miniprotein which folds rapidly and spontaneously to a well-defined globular structure more typical of larger proteins. Due to its small size and fast folding, it is an ideal model system for experimental and theoretical investigations of protein folding mechanisms. However, Trp-cage's exact folding mechanism is still a matter of debate. Here we investigate Trp-cage's relaxation dynamics in the amide I' spectral region (1530-1700 cm(-1)) using time-resolved infrared spectroscopy. Residue-specific information was obtained by incorporating an isotopic label ((13)C═(18)O) into the amide carbonyl group of residue Gly11, thereby spectrally isolating an individual 310-helical residue. The folding-unfolding equilibrium is perturbed using a nanosecond temperature-jump (T-jump), and the subsequent re-equilibration is probed by observing the time-dependent vibrational response in the amide I' region. We observe bimodal relaxation kinetics with time constants of 100 ± 10 and 770 ± 40 ns at 322 K, suggesting that the folding involves an intermediate state, the character of which can be determined from the time- and frequency-resolved data. We find that the relaxation dynamics close to the melting temperature involve fast fluctuations in the polyproline II region, whereas the slower process can be attributed to conformational rearrangements due to the global (un)folding transition of the protein. Combined analysis of our T-jump data and molecular dynamics simulations indicates that the formation of a well-defined α-helix precedes the rapid formation of the hydrophobic cage structure, implying a native-like folding intermediate, that mainly differs from the folded conformation in the orientation of the C-terminal polyproline II helix relative to the N-terminal part of the backbone. We find that the main free-energy barrier is positioned between the folding intermediate and the unfolded state ensemble, and that it involves the formation of the α-helix, the 310-helix, and the Asp9-Arg16 salt bridge. Our results suggest that at low temperature (T ≪ Tm) a folding path via formation of α-helical contacts followed by hydrophobic clustering becomes more important.

Effect of proline mutations on the monomer conformations of amylin

The formation of human islet amyloid polypeptide (hIAPP) is implicated in the loss of pancreatic β-cells in type II diabetes. Rat amylin, which differs from human amylin at six residues, does not lead to formation of amyloid fibrils. Pramlintide is a synthetic analog of human amylin that shares three proline substitutions with rat amylin. Pramlintide has a much smaller propensity to form amyloid aggregates and has been widely prescribed in amylin replacement treatment. It is known that the three prolines attenuate β-sheet formation. However, the detailed effects of these proline substitutions on full-length hIAPP remain poorly understood. In this work, we use molecular simulations and bias-exchange metadynamics to investigate the effect of proline substitutions on the conformation of the hIAPP monomer. Our results demonstrate that hIAPP can adopt various β-sheet conformations, some of which have been reported in experiments. The proline substitutions perturb the formation of long β-sheets and reduce their stability. More importantly, we find that all three proline substitutions of pramlintide are required to inhibit β conformations and stabilize the α-helical conformation. Fewer substitutions do not have a significant inhibiting effect.

Two-state dynamics of the SH3-SH2 tandem of Abl kinase and the allosteric role of the N-cap

The regulation and localization of signaling enzymes is often mediated by accessory modular domains, which frequently function in tandems. The ability of these tandems to adopt multiple conformations is as important for proper regulation as the individual domain specificity. A paradigmatic example is Abl, a ubiquitous tyrosine kinase of significant pharmacological interest. SH3 and SH2 domains inhibit Abl by assembling onto the catalytic domain, allosterically clamping it in an inactive state. We investigate the dynamics of this SH3-SH2 tandem, using microsecond all-atom simulations and differential scanning calorimetry. Our results indicate that the Abl tandem is a two-state switch, alternating between the conformation observed in the structure of the autoinhibited enzyme and another configuration that is consistent with existing scattering data for an activated form. Intriguingly, we find that the latter is the most probable when the tandem is disengaged from the catalytic domain. Nevertheless, an amino acid stretch preceding the SH3 domain, the so-called N-cap, reshapes the free-energy landscape of the tandem and favors the interaction of this domain with the SH2-kinase linker, an intermediate step necessary for assembly of the autoinhibited complex. This allosteric effect arises from interactions between N-cap and the SH2 domain and SH3-SH2 connector, which involve a phosphorylation site. We also show that the SH3-SH2 connector plays a determinant role in the assembly equilibrium of Abl, because mutations thereof hinder the engagement of the SH2-kinase linker. These results provide a thermodynamic rationale for the involvement of N-cap and SH3-SH2 connector in Abl regulation and expand our understanding of the principles of modular domain organization.

Using D-Amino Acids to Delineate the Mechanism of Protein Folding: Application to Trp-cage

Using the miniprotein Trp-cage as a model, we show that D-amino acids can be used to facilitate the delineation of protein folding mechanism. Specifically, we study the folding-unfolding kinetics of three Trp-cage mutants where the native glycine residue near the C-terminus of the α-helix is replaced by a D-amino acid. A previous study showed that these mutations increase the Trp-cage stability, due to a terminal capping effect. Our results show that the stabilizing effect of D-asparagine and D-glutamine originates almost exclusively from a decrease in the unfolding rate, while the D-alanine mutation results in a similar decrease in the unfolding rate, but it also increases the folding rate. Together, these results support a folding mechanism wherein the α-helix formation in the transition state is nucleated at the N-terminus, whereas those long-range native interactions stabilizing this helix are developed at the downhill side of the folding free energy barrier.

Characterization of folding mechanisms of Trp-cage and WW-domain by network analysis of simulations with a hybrid-resolution model

In this study, we apply a hybrid-resolution model, namely, PACE, to characterize the free energy surfaces (FESs) of Trp-cage and a WW-domain variant along with the respective folding mechanisms. Unbiased, independent simulations with PACE are found to achieve together multiple folding and unfolding events for both proteins, allowing us to perform network analysis of the FESs to identify folding pathways. PACE reproduces for both proteins expected complexity hidden in the folding FESs, in particular metastable non-native intermediates. Pathway analysis shows that some of these intermediates are, actually, on-pathway folding intermediates and that intermediates kinetically closest to the native states can be either critical on-pathway or off-pathway intermediates, depending on the protein. Apart from general insights into folding, specific folding mechanisms of the proteins are resolved. We find that Trp-cage folds via a dominant pathway in which hydrophobic collapse occurs before the N-terminal helix forms; full incorporation of Trp6 into the hydrophobic core takes place as the last step of folding, which, however, may not be the rate-limiting step. For the WW-domain variant studied, we observe two main folding pathways with opposite orders of formation of the two hairpins involved in the structure; for either pathway, formation of hairpin 1 is more likely to be the rate-limiting step. Altogether, our results suggest that PACE combined with network analysis is a computationally efficient and valuable tool for the study of protein folding.

How kinetics within the unfolded state affects protein folding: an analysis based on markov state models and an ultra-long MD trajectory

Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤40 ns, compared with the folding time of ∼5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 μs of the ultralong MD trajectory, which on average explores ∼27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.

Mapping the Native Conformational Ensemble of Proteins from a Combination of Simulations and Experiments: New Insight into the src-SH3 Domain

The biological function of a protein is strongly tied to the ensemble of three-dimensional conformations populated at physiological temperature, and dynamically transforming into each other. Experimental techniques such as nuclear magnetic resonance spectroscopy (NMR) provide a wealth of structural and dynamical information, which, in combination with an accurate atomic-level computational modeling, can disclose the details of protein behavior. We here propose a fast and efficient protocol employing molecular dynamics (MD) simulations and NMR chemical shifts, which allows one to reconstruct the detailed conformational ensemble of small globular proteins. In the case of the well-studied src-SH3 domain, we are able to obtain new important insight including the existence of a helical state in the RT loop and a pathway for single-file water diffusion in and out of the core.

NMR relaxation in proteins with fast internal motions and slow conformational exchange: model-free framework and Markov state simulations

Calculating NMR relaxation effects for proteins with dynamics on multiple time scales generally requires very long trajectories based on conventional molecular dynamics simulations. In this report, we have built Markov state models from multiple MD trajectories and used the resulting MSM to capture the very fast internal motions of the protein within a free energy basin on a time scale up to hundreds of picoseconds and the more than 3 orders of magnitude slower conformational exchange between macrostates. To interpret the relaxation data, we derive new equations using the model-free framework which includes two slowly exchanging macrostates, each of which also exhibits fast local motions. Using simulations of HIV-1 protease as an example, we show how the populations of slowly exchanging conformational states as well as order parameters for the different states can be determined from the NMR relaxation data.

Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics

The use of free-energy landscapes rationalizes a wide range of aspects of protein behavior by providing a clear illustration of the different states accessible to these molecules, as well as of their populations and pathways of interconversion. The determination of the free-energy landscapes of proteins by computational methods is, however, very challenging as it requires an extensive sampling of their conformational spaces. We describe here a technique to achieve this goal with relatively limited computational resources by incorporating nuclear magnetic resonance (NMR) chemical shifts as collective variables in metadynamics simulations. As in this approach the chemical shifts are not used as structural restraints, the resulting free-energy landscapes correspond to the force fields used in the simulations. We illustrate this approach in the case of the third Ig-binding domain of protein G from streptococcal bacteria (GB3). Our calculations reveal the existence of a folding intermediate of GB3 with nonnative structural elements. Furthermore, the availability of the free-energy landscape enables the folding mechanism of GB3 to be elucidated by analyzing the conformational ensembles corresponding to the native, intermediate, and unfolded states, as well as the transition states between them. Taken together, these results show that, by incorporating experimental data as collective variables in metadynamics simulations, it is possible to enhance the sampling efficiency by two or more orders of magnitude with respect to standard molecular dynamics simulations, and thus to estimate free-energy differences among the different states of a protein with a k(B)T accuracy by generating trajectories of just a few microseconds.

Nucleation process of a fibril precursor in the C-terminal segment of amyloid-β

By extended atomistic simulations in explicit solvent and bias-exchange metadynamics, we study the aggregation process of 18 chains of the C-terminal segment of amyloid-β, an intrinsically disordered protein involved in Alzheimer's disease and prone to form fibrils. Starting from a disordered aggregate, we are able to observe the formation of an ordered nucleus rich in beta sheets. The rate limiting step in the nucleation pathway involves crossing a barrier of approximately 40 kcal/mol and is associated with the formation of a very specific interdigitation of the side chains belonging to different sheets. This structural pattern is different from the one observed experimentally in a microcrystal of the same system, indicating that the structure of a "nascent" fibril may differ from the one of an "extended" fibril.

The molecular mechanism of substrate engagement and immunosuppressant inhibition of calcineurin

Ser/thr phosphatases dephosphorylate their targets with high specificity, yet the structural and sequence determinants of phosphosite recognition are poorly understood. Calcineurin (CN) is a conserved Ca(2+)/calmodulin-dependent ser/thr phosphatase and the target of immunosuppressants, FK506 and cyclosporin A (CSA). To investigate CN substrate recognition we used X-ray crystallography, biochemistry, modeling, and in vivo experiments to study A238L, a viral protein inhibitor of CN. We show that A238L competitively inhibits CN by occupying a critical substrate recognition site, while leaving the catalytic center fully accessible. Critically, the 1.7 Å structure of the A238L-CN complex reveals how CN recognizes residues in A238L that are analogous to a substrate motif, "LxVP." The structure enabled modeling of a peptide substrate bound to CN, which predicts substrate interactions beyond the catalytic center. Finally, this study establishes that "LxVP" sequences and immunosuppressants bind to the identical site on CN. Thus, FK506, CSA, and A238L all prevent "LxVP"-mediated substrate recognition by CN, highlighting the importance of this interaction for substrate dephosphorylation. Collectively, this work presents the first integrated structural model for substrate selection and dephosphorylation by CN and lays the groundwork for structure-based development of new CN inhibitors.

Structural insights into the Trp-cage folding intermediate formation

The 20 residue long Trp-cage is the smallest protein known, and thus has been the subject of several in vitro and in silico folding studies. Here, we report the multistate folding scenario of the miniprotein in atomic detail. We detected and characterized different intermediate states by temperature dependent NMR measurements of the (15)N and (13)C/(15)N labeled protein, both at neutral and acidic pH values. We developed a deconvolution technique to characterize the invisible--fully folded, unfolded and intermediate--fast exchanging states. Using nonlinear fitting methods we can obtain both the thermodynamic parameters (ΔH(F-I), T(m)(F-I), ΔC(p)(F-I) and ΔH(I-U), T(m)(I-U), ΔC(p)(I-U)) and the NMR chemical shifts of the conformers of the multistate unfolding process. During the unfolding of Trp-cage distinct intermediates evolve: a fast-exchanging intermediate is present under neutral conditions, whereas a slow-exchanging intermediate-pair emerges at acidic pH. The fast-exchanging intermediate has a native-like structure with a short α-helix in the G(11)-G(15) segment, whereas the slow-exchanging intermediate-pair presents elevated dynamics, with no detectable native-like residue contacts in which the G(11)-P(12) peptide bond has either cis or trans conformation. Heteronuclear relaxation studies combined with MD simulations revealed the source of backbone mobility and the nature of structural rearrangements during these transitions. The ability to detect structural and dynamic information about folding intermediates in vitro provides an excellent opportunity to gain new insights into the energetic aspects of the energy landscape of protein folding. Our new experimental data offer exceptional testing ground for further computational simulations.

Circular Permutation of the Trp-cage: Fold Rescue upon Addition of a Hydrophobic Staple

The Trp-cage, at 20 residues in length, is generally acknowledged as the smallest fully protein-like folding motif. Linking the termini by a two-residue unit and excising one residue affords circularly permuted sequences that adopt the same structure. This represents the first successful circular permutation of any fold of less than 50-residue length. As was observed for the original topology, a hydrophobic staple near the chain termini is required for enhanced fold stability.

Tilting the balance between canonical and noncanonical conformations for the H1 hypervariable loop of a llama VHH through point mutations

Nanobodies are single-domain antibodies found in camelids. These are the smallest naturally occurring binding domains and derive functionality via three hypervariable loops (H1-H3) that form the binding surface. They are excellent candidates for antibody engineering because of their favorable characteristics like small size, high solubility, and stability. To rationally engineer antibodies with affinity for a specific target, the hypervariable loops can be tailored to obtain the desired binding surface. As a first step toward such a goal, we consider the design of loops with a desired conformation. In this study, we focus on the H1 loop of the anti-hCG llama nanobody that exhibits a noncanonical conformation. We aim to "tilt" the stability of the H1 loop structure from a noncanonical conformation to a (humanized) type 1 canonical conformation by studying the effect of selected mutations to the amino acid sequence of the H1, H2, and proximal residues. We use all-atomistic, explicit-solvent, biased molecular dynamic simulations to simulate the wild-type and mutant loops in a prefolded framework. We thus find mutants with increasing propensity to form a stable type 1 canonical conformation of the H1 loop. Free energy landscapes reveal the existence of conformational isomers of the canonical conformation that may play a role in binding different antigenic surfaces. We also elucidate the approximate mechanism and kinetics of transitions between such conformational isomers by using a Markovian model. We find that a particular three-point mutant has the strongest thermodynamic propensity to form the H1 type 1 canonical structure but also to exhibit transitions between conformational isomers, while a different, more rigid three-point mutant has the strongest propensity to be kinetically trapped in such a canonical structure.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).

Effect of surfactant hydrophobicity on the pathway for unfolding of ubiquitin

This paper describes the interaction between ubiquitin (UBI) and three sodium n-alkyl sulfates (SC(n)S) that have the same charge (Z = -1) but different hydrophobicity (n = 10, 12, or 14). Increasing the hydrophobicity of the n-alkyl sulfate resulted in (i) an increase in the number of distinct intermediates (that is, complexes of UBI and surfactant) that form along the pathway of unfolding, (ii) a decrease in the minimum concentrations of surfactant at which intermediates begin to form (i.e., a more negative ΔG(binding) of surfactant for UBI), and (iii) an increase in the number of surfactant molecules bound to UBI in each intermediate or complex. These results demonstrate that small changes in the hydrophobicity of a surfactant can significantly alter the binding interactions with a folded or unfolded cytosolic protein.

Confinement-induced states in the folding landscape of the Trp-cage miniprotein

Although protein folding is typically studied in dilute solution, folding in a cell will be affected by interactions with other biomolecules and excluded volume effects. Here, we examine the effect of hydrophobic confinement on folding of the Trp-cage miniprotein. We used replica exchange molecular dynamics simulations to probe the differences between folding in the bulk, on a hydrophobic surface, and confined between two hydrophobic walls. In addition to promotion of helix formation due to reduced conformational entropy of the unfolded state upon confinement, adsorption of Trp-cage to a hydrophobic surface stabilizes intermediate structures not present in the bulk. These new intermediate structures may alter the folding mechanism and kinetics and show the importance of including environmental effects when studying protein folding.

The impact of small molecule binding on the energy landscape of the intrinsically disordered protein C-myc

Intrinsically disordered proteins are attractive therapeutic targets owing to their prevalence in several diseases. Yet their lack of well-defined structure renders ligand discovery a challenging task. An intriguing example is provided by the oncoprotein c-Myc, a transcription factor that is over expressed in a broad range of cancers. Transcriptional activity of c-Myc is dependent on heterodimerization with partner protein Max. This protein-protein interaction is disrupted by the small molecule 10058-F4 (1), that binds to monomeric and disordered c-Myc. To rationalize the mechanism of inhibition, structural ensembles for the segment of the c-Myc domain that binds to 1 were computed in the absence and presence of the ligand using classical force fields and explicit solvent metadynamics molecular simulations. The accuracy of the computed structural ensembles was assessed by comparison of predicted and measured NMR chemical shifts. The small molecule 1 was found to perturb the composition of the apo equilibrium ensemble and to bind weakly to multiple distinct c-Myc conformations. Comparison of the apo and holo equilibrium ensembles reveals that the c-Myc conformations binding 1 are already partially formed in the apo ensemble, suggesting that 1 binds to c-Myc through an extended conformational selection mechanism. The present results have important implications for rational ligand design efforts targeting intrinsically disordered proteins.

A novel approach to the investigation of passive molecular permeation through lipid bilayers from atomistic simulations

Predicting the permeability coefficient (P) of drugs permeating through the cell membrane is of paramount importance in drug discovery. We here propose an approach for calculating P based on bias-exchange metadynamics. The approach allows constructing from atomistic simulations a model of permeation taking explicitly into account not only the "trivial" reaction coordinate, the position of the drug along the direction normal to the lipid membrane plane, but also other degrees of freedom, for example, the torsional angles of the permeating molecule, or variables describing its solvation/desolvation. This allows deriving an accurate picture of the permeation process, and constructing a detailed molecular model of the transition state, making a rational control of permeation properties possible. We benchmarked this approach on the permeation of ethanol molecules through a POPC membrane, showing that the value of P calculated with our model agrees with the one calculated by a long unbiased molecular dynamics of the same system.

Exploration of multi-state conformational dynamics and underlying global functional landscape of maltose binding protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.

A central goal of biology is to understand the function of the organism and its constituent parts at each of its scales of complexity. Function at the molecular level is often realized by changes in conformation. Unfortunately, experimental explorations of global motions critical for functional conformational changes are still challenging. In the present work, we developed a coarse grained triple-well structure-based model to explore the underlying functional landscape of maltose-binding protein (MBP). By quantitative flux analysis, we uncover the underlying mechanism by which the major induced fit and minor population shift pathways co-exist. Though we have previously lent credence to the assertion that dynamical equilibrium between open and minor closed conformations exist for all the free PBPs, the generality of this rule is still a matter of open debate. We found that the hinge flexibility is favorable to population shift mechanism. This finding provides a theoretical explanation of the mechanism discrepancies in PBP protein family. We also simulated the folding dynamics using this functional multi-basin model which successfully reproduced earlier protein melting experiment. This represents an exciting opportunity to characterize the interplay between folding and function, which is a long-standing question in the community. The theoretical approach employed in this study is general and can be applied to other systems.

Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I

Proteins fold and function in the crowded environment of the cell's interior. In the recent years it has been well established that the so-called "macromolecular crowding" effect enhances the folding stability of proteins by destabilizing their unfolded states for selected proteins. On the other hand, chemical and thermal denaturation is often used in experiments as a tool to destabilize a protein by populating the unfolded states when probing its folding landscape and thermodynamic properties. However, little is known about the complicated effects of these synergistic perturbations acting on the kinetic properties of proteins, particularly when large structural fluctuations, such as protein folding, have been involved. In this study, we have first investigated the folding mechanism of Trp-cage dependent on urea concentration by coarse-grained molecular simulations where the impact of urea is implemented into an energy function of the side chain and/or backbone interactions derived from the all-atomistic molecular dynamics simulations with urea through a Boltzmann inversion method. In urea solution, the folding rates of a model miniprotein Trp-cage decrease and the folded state slightly swells due to a lack of contact formation between side chains at the terminal regions. In addition, the equilibrium m-values of Trp-cage from the computer simulations are in agreement with experimental measurements. We have further investigated the combined effects of urea denaturation and macromolecular crowding on Trp-cage's folding mechanism where crowding agents are modeled as hard-spheres. The enhancement of folding rates of Trp-cage is most pronounced by macromolecular crowding effect when the extended conformations of Trp-cast dominate at high urea concentration. Our study makes quantitatively testable predictions on protein folding dynamics in a complex environment involving both chemical denaturation and macromolecular crowding effects.

Evidence for an allosteric mechanism of substrate release from membrane-transporter accessory binding proteins

Numerous membrane importers rely on accessory water-soluble proteins to capture their substrates. These substrate-binding proteins (SBP) have a strong affinity for their ligands; yet, substrate release onto the low-affinity membrane transporter must occur for uptake to proceed. It is generally accepted that release is facilitated by the association of SBP and transporter, upon which the SBP adopts a conformation similar to the unliganded state, whose affinity is sufficiently reduced. Despite the appeal of this mechanism, however, direct supporting evidence is lacking. Here, we use experimental and theoretical methods to demonstrate that an allosteric mechanism of enhanced substrate release is indeed plausible. First, we report the atomic-resolution structure of apo TeaA, the SBP of the Na(+)-coupled ectoine TRAP transporter TeaBC from Halomonas elongata DSM2581(T), and compare it with the substrate-bound structure previously reported. Conformational free-energy landscape calculations based upon molecular dynamics simulations are then used to dissect the mechanism that couples ectoine binding to structural change in TeaA. These insights allow us to design a triple mutation that biases TeaA toward apo-like conformations without directly perturbing the binding cleft, thus mimicking the influence of the membrane transporter. Calorimetric measurements demonstrate that the ectoine affinity of the conformationally biased triple mutant is 100-fold weaker than that of the wild type. By contrast, a control mutant predicted to be conformationally unbiased displays wild-type affinity. This work thus demonstrates that substrate release from SBPs onto their membrane transporters can be facilitated by the latter through a mechanism of allosteric modulation of the former.