Ab initio folding simulation of Trpcage by replica exchange with hybrid Hamiltonian

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Folding Thermodynamics and Mechanism of Five Trp-Cage Variants from Replica-Exchange MD Simulations with RSFF2 Force Field

To test whether our recently developed residue-specific force field RSFF2 can reproduce the mutational effect on the thermal stability of Trp-cage mini-protein and decipher its detailed folding mechanism, we carried out long-time replica-exchange molecular dynamics (REMD) simulations on five Trp-cage variants, including TC5b and TC10b. Initiated from their unfolded structures, the simulations not only well-reproduce their experimental structures but also their melting temperatures and folding enthalpies reasonably well. For each Trp-cage variant, the overall folding free energy landscape is apparently two-state, but some intermediate states can be observed when projected on more detailed coordinates. We also found different variants have the same major folding pathway, including the well formed PII-helix in the unfolded state, the formation of W6-P12/P18/P19 contacts and the α-helix before the transition state, the following formation of most native contacts, and the final native loop formation. The folding mechanism derived here is consistent with many previous simulations and experiments.

Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage

The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.

Folding dynamics and pathways of the trp-cage miniproteins

Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.

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.

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.

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.

Effect of self-assembly of fullerene nano-particles on lipid membrane

Carbon nanoparticles can penetrate the cell membrane and cause cytotoxicity. The diffusion feature and translocation free energy of fullerene through lipid membranes is well reported. However, the knowledge on self-assembly of fullerenes and resulting effects on lipid membrane is poorly addressed. In this work, the self-assembly of fullerene nanoparticles and the resulting influence on the dioleoylphosphtidylcholine (DOPC) model membrane were studied by using all-atom molecular dynamics simulations with explicit solvents. Our simulation results confirm that gathered small fullerene cluster can invade lipid membrane. Simulations show two pathways: 1) assembly process is completely finished before penetration; 2) assembly process coincides with penetration. Simulation results also demonstrate that in the membrane interior, fullerene clusters tend to stay at the position which is 1.0 nm away from the membrane center. In addition, the diverse microscopic stacking mode (i.e., equilateral triangle, tetrahedral pentahedral, trigonal bipyramid and octahedron) of these small fullerene clusters are well characterized. Thus our simulations provide a detailed high-resolution characterization of the microscopic structures of the small fullerene clusters. Further, we found the gathered small fullerene clusters have significant adverse disturbances to the local structure of the membrane, but no great influence on the global integrity of the lipid membrane, which suggests the prerequisite of high-content fullerene for cytotoxicity.

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.

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.

Dynamic folding pathway models of the Trp-cage protein

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

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.

Dynamical stability and assembly cooperativity of β-sheet amyloid oligomers--effect of polarization

The soluble intermediate oligomers of amyloidogenic proteins are suspected to be more cytotoxic than the mature fibrils in neurodegenerative disorders. Here, the dynamic stability and assembly cooperativity of a model oligomer of human islet amyloid polypeptide (hIAPP) segments were explored by means of all-atom molecular dynamics (MD) simulations under different force fields including AMBER99SB, OPLS, and polarized protein-specific charge (PPC) model. Simulation results show that the dynamic stability of β-sheet oligomers is seriously impacted by electrostatic polarization. Without inclusion of polarization (simulation under standard AMBER and OPLS force field), the β-sheet oligomers are dynamically unstable during MD simulation. For comparison, simulation results under PPC give significantly more stable dynamical structures of the oligomers. Furthermore, calculation of electrostatic interaction energy between the neighboring β strands with an approximate polarizable method produces energetic evidence for cooperative assembly of β-strand oligomers. This result supports a picture of downhill-like cooperative assembly of β strands during fibrillation process. The present study demonstrates the critical role of polarization in dynamic stability and assembly cooperativity of β-sheet-rich amyloid oligomers.

Crystal and NMR structures of a Trp-cage mini-protein benchmark for computational fold prediction

To provide high-resolution X-ray crystallographic structures of a peptide with the Trp-cage fold, we prepared a cyclized version of this motif. Cyclized Trp-cage is remarkably stable and afforded two crystal forms suitable for X-ray diffraction. The resulting higher resolution crystal structures validate the prior NMR models and provide explanations for experimental observations that could not be rationalized by NMR structural data, including the structural basis for the increase in fold stability associated with motif cyclization and the manner in which a polar serine side chain is accommodated in the hydrophobic interior. A hexameric oligomer of the cyclic peptide is found in both crystal forms and indicates that under appropriate conditions, this minimized system may also serve as a model for protein-protein interactions.

Influence of water-protein hydrogen bonding on the stability of Trp-cage miniprotein. A comparison between the TIP3P and TIP4P-Ew water models

We report extensive replica exchange molecular dynamics (REMD) simulations on the folding/unfolding equilibrium of Trp-cage miniprotein using the Amber ff99SB all atom forcefield and TIP3P and TIP4P-Ew explicit water solvent models. REMD simulation-lengths in the 500 ns to the microsecond regime per replica are required to adequately sample the folding/unfolding equilibrium. We observe that this equilibrium is significantly affected by the choice of the water model. Compared with experimental data, simulations using the TIP3P solvent describe the stability of the Trp-cage quite realistically, providing a melting point which is just a few Kelvins above the experimental transition temperature of 317 K. The TIP4P-Ew model shifts the equilibrium towards the unfolded state and lowers the free energy of unfolding by about 3 kJ mol(-1) at 280 K, demonstrating the need to fine-tune the protein-forcefield depending on the chosen water model. We report evidence that the main difference between the two water models is mostly due to the different solvation of polar groups of the peptide. The unfolded state of the Trp-cage is stabilized by an increasing number of hydrogen bonds, destabilizing the α-helical part of the molecule and opening the R-D salt bridge. By reweighting the strength of solvent-peptide hydrogen bonds by adding a hydrogen bond square well potential, we can fully recover the effect of the different water models and estimate the shift in population as due to a difference in hydrogen bond-strength of about 0.4 kJ mol(-1) per hydrogen bond.

Optimal salt bridge for Trp-cage stabilization

Gai and co-workers [Bunagan, M. R., et al. (2006) J. Phys. Chem. B 110, 3759-3763] reported computational design studies suggesting that a D9E mutation would stabilize the Trp-cage. Experimental studies for this mutation were reported in 2008 [Hudaky, P., et al. (2008) Biochemistry 47, 1007-1016]; the authors suggested that [D9E]-TC5b presented a more compact and melting resistant structure because of the "optimal distance between the two sides of the molecule". Nonetheless, the authors reported essentially the same circular dichroism (CD) melting temperature, 38 ± 0.3 °C, for TC5b and its [D9E] mutant. In this study, a more stable Trp-cage, DAYAQ WLKDG GPSSG RPPPS, was examined by nuclear magnetic resonance and CD with the following mutations: [D9E], [D9R,R16E], [R16O], [D9E,R16O], [R16K], and [D9E,R16K]. Of these, the [D9E] mutant displayed the smallest acidification-induced change in the apparent T(m). In analogy to the prior study, the CD melts of TC10b and its [D9E] mutant were, however, very similar; all of the other mutations were significantly fold destabilizing by all measures. A detailed analysis indicates that the original D9-R16 salt bridge is optimal with regard to fold cooperativity and fold stabilization. Evidence of salt bridge formation is also provided for a swapped pair, the [D9R,R16E] mutant. Model systems reveal that an ionized aspartate at the C-terminus of a helix significantly decreases intrinsic helicity, a requirement for Trp-cage fold stability. The CD evidence that was cited as supporting increased fold stability for [D9E]-TC5b at higher temperatures appears to be a reflection of increased helix stability in both the folded and unfolded states rather than a more favorable salt bridge. Our study also provides evidence of other Trp-cage stabilizing roles of the R16 side chain.