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

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.

Analysis of Protein Folding Simulation with Moving Root Mean Square Deviation

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

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.

Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins

There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.

Hydrophobicity-driven unfolding of Trp-cage encapsulated between graphene sheets

Understanding the interaction between proteins and graphene not only helps elucidate the behaviors of proteins in confined geometries, but is also imperative to the development of a plethora of graphene-based biotechnologies, such as the graphene liquid cell transmission electron microscopy. To discuss the overall geometrical-thermal effects on proteins, we performed molecular dynamics simulations of hydrated Trp-cage miniprotein sandwiched between two graphene sheets and in the bulk environment at the temperatures below and above its unfolding temperature. The structural fluctuations of Trp-cage were characterized using the backbone root mean square displacement and the radius of gyration, from which the free energy landscape of Trp-cage was further constructed. We observed that at both temperatures the confined protein became adsorbed to the graphene surfaces and exhibited unfolded structures. Residue-specific analyses clearly showed the preference for the graphene to interact with the hydrophobic regions of Trp-cage. These results suggested that the conformation space accessible to the protein results from the competition between the thermodynamic driving forces and the geometrical restraints. While confinement usually tends to restrict the conformation of proteins by volume exclusion, it may also induce the unfolding of proteins by hydrophobic interactions.

Real-Time Conformational Changes and Controlled Orientation of Native Proteins Inside a Protein Nanoreactor

Protein conformations play crucial roles in most, if not all, biological processes. Here we show that the current carried through a nanopore by ions allows monitoring conformational changes of single and native substrate-binding domains (SBD) of an ATP-Binding Cassette importer in real-time. Comparison with single-molecule Förster Resonance Energy Transfer and ensemble measurements revealed that proteins trapped inside the nanopore have bulk-like properties. Two ligand-free and two ligand-bound conformations of SBD proteins were inferred and their kinetic constants were determined. Remarkably, internalized proteins aligned with the applied voltage bias, and their orientation could be controlled by the addition of a single charge to the protein surface. Nanopores can thus be used to immobilize proteins on a surface with a specific orientation, and will be employed as nanoreactors for single-molecule studies of native proteins. Moreover, nanopores with internal protein adaptors might find further practical applications in multianalyte sensing devices.

Temperature evolution of Trp-cage folding pathways: An analysis by dividing the probability flux field into stream tubes

Owing to its small size and very fast folding rate, the Trp-cage miniprotein has become a benchmark system to study protein folding. Two folding pathways were found to be characteristic of this protein: pathway I, in which the hydrophobic collapse precedes the formation of α-helix, and pathway II, in which the events occur in the reverse order. At the same time, the relative contribution of these pathways at different temperatures as well as the nature of transition from one pathway to the other remain unclear. To gain insight into this issue, we employ a recently proposed hydrodynamic description of protein folding, in which the process of folding is considered as a motion of a "folding fluid" (Chekmarev et al., Phys. Rev. Lett. 100(1), 018107 2008). Using molecular dynamics simulations, we determine the field of probability fluxes of transitions in a space of collective variables and divide it into stream tubes. Each tube contains a definite fraction of the total folding flow and can be associated with a certain pathway. Specifically, three temperatures were considered, T = 285K, T = 315K, and T = 325K. We have found that as the temperature increases, the contribution of pathway I, which is approximately 90% of the total folding flow at T = 285K, decreases to approximately 10% at T = 325K, i.e., pathway II becomes dominant. At T = 315K, both pathways contribute approximately equally. All these temperatures are found below the calculated melting point, which suggests that the Trp-cage folding mechanism is determined by kinetic factors rather than thermodynamics.

Strong Electrostatic Interactions Lead to Entropically Favorable Binding of Peptides to Charged Surfaces

Thermodynamic analyses can provide key insights into the origins of protein self-assembly on surfaces, protein function, and protein stability. However, obtaining quantitative measurements of thermodynamic observables from unbiased classical simulations of peptide or protein adsorption is challenging because of sampling limitations brought on by strong biomolecule/surface binding forces as well as time scale limitations. We used the parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) enhanced sampling method to study the adsorption behavior and thermodynamics of several explicitly solvated model peptide adsorption systems, providing new molecular-level insight into the biomolecule adsorption process. Specifically studied were peptides LKα14 and LKβ15 and trpcage miniprotein adsorbing onto a charged, hydrophilic self-assembled monolayer surface functionalized with a carboxylic acid/carboxylate headgroup and a neutral, hydrophobic methyl-terminated self-assembled monolayer surface. Binding free energies were calculated as a function of temperature for each system and decomposed into their respective energetic and entropic contributions. We investigated how specific interfacial features such as peptide/surface electrostatic interactions and surface-bound ion content affect the thermodynamic landscape of adsorption and lead to differences in surface-bound conformations of the peptides. Results show that upon adsorption to the charged surface, configurational entropy gains of the released solvent molecules dominate the configurational entropy losses of the bound peptide. This behavior leads to an apparent increase in overall system entropy upon binding and therefore to the surprising and seemingly nonphysical result of an apparent increased binding free energy at elevated temperatures. Opposite effects and conclusions are found for the neutral surface. Additional simulations demonstrate that by adjusting the ionic strength of the solution, results that show the expected physical behavior, i.e., peptide binding strength that decreases with increasing temperature or is independent of temperature altogether, can be recovered on the charged surface. On the basis of this analysis, an overall free energy for the entire thermodynamic cycle for peptide adsorption on charged surfaces is constructed and validated with independent simulations.

Phospholipid and Hydrocarbon Interactions with a Charged Electrode Interface

Using a combination of molecular dynamics simulations and experiments we examined the interactions of alkanes and phospholipids at charged interfaces in order to understand how interfacial charge densities affect the association of these two representative molecules with electrodes. Consistent with theory and experiment, these model systems reveal interfacial associations mediated through a combination of Coulombic and van der Waals forces. van der Waals forces, in particular, mediate rapid binding of decane to neutral electrodes. No decane binding was observed at high surface charge densities because of interfacial water polarization, which screens hydrophobic attractions. The positively charged choline moiety of the phospholipid palmitoyloleoylphosphatidylcholine (POPC) is primarily responsible for POPC attraction by a moderately negatively charged electrode. The hydrocarbon tails of POPC interact with the hydrophobic electrode interface similarly to decane. Previously reported electrochemical results confirm these findings by demonstrating bipolar displacement currents from PC vesicles adhering to moderately negatively charged interfaces, originating from the choline interactions observed in simulations. At more negatively charged interfaces, choline-to-surface binding was stronger. In both simulations and experiments the maximal interaction of anionic PS occurs with a positively charged interface, provided that the electrostatic forces outweigh local Lennard-Jones interactions. Direct comparisons between the binding affinities measured in experiments and those obtained in simulations reveal previously unobserved atomic interactions that facilitate lipid vesicle adhesion to charged interfaces. Moreover, the implementation of a charged interface in molecular dynamics simulations provides an alternative method for the generation of large electric fields across phospholipid bilayers, especially for systems with periodic boundary conditions, and may be useful for simulations of membrane electropermeabilization.

Comparison of hydration behavior and conformational preferences of the Trp-cage mini-protein in different rigid-body water models

Trp-cage unfolds at different temperatures in different water models revealing the sensitivity of conformational order metrics to the choice of water models.

A hydrodynamic view of the first-passage folding of Trp-cage miniprotein

We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential.

Parallel continuous simulated tempering and its applications in large-scale molecular simulations

In this paper, we introduce a parallel continuous simulated tempering (PCST) method for enhanced sampling in studying large complex systems. It mainly inherits the continuous simulated tempering (CST) method in our previous studies [C. Zhang and J. Ma, J. Chem. Phys. 130, 194112 (2009); C. Zhang and J. Ma, J. Chem. Phys. 132, 244101 (2010)], while adopts the spirit of parallel tempering (PT), or replica exchange method, by employing multiple copies with different temperature distributions. Differing from conventional PT methods, despite the large stride of total temperature range, the PCST method requires very few copies of simulations, typically 2-3 copies, yet it is still capable of maintaining a high rate of exchange between neighboring copies. Furthermore, in PCST method, the size of the system does not dramatically affect the number of copy needed because the exchange rate is independent of total potential energy, thus providing an enormous advantage over conventional PT methods in studying very large systems. The sampling efficiency of PCST was tested in two-dimensional Ising model, Lennard-Jones liquid and all-atom folding simulation of a small globular protein trp-cage in explicit solvent. The results demonstrate that the PCST method significantly improves sampling efficiency compared with other methods and it is particularly effective in simulating systems with long relaxation time or correlation time. We expect the PCST method to be a good alternative to parallel tempering methods in simulating large systems such as phase transition and dynamics of macromolecules in explicit solvent.

Functional assembly of protein fragments induced by spatial confinement

Natural proteins are often confined within their local microenvironments, such as three-dimensional confinement in organelles or two-dimensional confinement in lipid rafts on cytoplasmic membrane. Spatial confinement restricts proteins' entropic freedom, forces their lateral interaction, and induces new properties that the same proteins lack at the soluble state. So far, the phenomenon of environment-induced protein functional alteration still lacks a full illustration. We demonstrate here that engineered protein fragments, although being non-functional in solution, can be re-assembled within the nanometer space to give the full activity of the whole protein. Specific interaction between hexahistidine-tag (His-tag) and NiO surface immobilizes protein fragments on NiO nanoparticles to form a self-assembled protein "corona" on the particles inside the nanopores of mesoporous silica. Site-specific assembly forces a shoulder-by-shoulder orientation and promotes fragment-fragment interaction; this interaction together with spatial confinement of the mesopores results in functional re-assembly of the protein half fragments. To our surprise, a single half fragment of luciferase (non-catalytic in solution) exhibited luciferase activity when immobilized on NiO in the mesopores, in the absence of the complimentary half. This shows for the first time that spatial confinement can induce the folding of a half fragment, reconstitute the enzyme active site, and re-gain the catalytic capability of the whole protein. Our work thereby highlights the under-documented notion that aside from the chemical composition such as primary sequence, physical environment of a protein also determines its function.

Competition between surface adsorption and folding of fibril-forming polypeptides

Self-assembly of polypeptides into fibrillar structures can be initiated by planar surfaces that interact favorably with certain residues. Using a coarse-grained model, we systematically studied the folding and adsorption behavior of a β-roll forming polypeptide. We find that there are two different folding pathways depending on the temperature: (i) at low temperature, the polypeptide folds in solution into a β-roll before adsorbing onto the attractive surface; (ii) at higher temperature, the polypeptide first adsorbs in a disordered state and folds while on the surface. The folding temperature increases with increasing attraction as the folded β-roll is stabilized by the surface. Surprisingly, further increasing the attraction lowers the folding temperature again, as strong attraction also stabilizes the adsorbed disordered state, which competes with folding of the polypeptide. Our results suggest that to enhance the folding, one should use a weakly attractive surface. They also explain the recent experimental observation of the nonmonotonic effect of charge on the fibril formation on an oppositely charged surface [C. Charbonneau et al., ACS Nano 8, 2328 (2014)].

Entropy and enthalpy of interaction between amino acid side chains in nanopores

Understanding the stabilities of proteins in nanopores requires a quantitative description of confinement induced interactions between amino acid side chains. We use molecular dynamics simulations to study the nature of interactions between the side chain pairs ALA-PHE, SER-ASN, and LYS-GLU in bulk water and in water-filled nanopores. The temperature dependence of the bulk solvent potentials of mean force and the interaction free energies in cylindrical and spherical nanopores is used to identify the corresponding entropic and enthalpic components. The entropically stabilized hydrophobic interaction between ALA and PHE in bulk water is enthalpically dominated upon confinement depending on the relative orientations between the side chains. In the case of SER-ASN, hydrogen bonded configurations that are similar in bulk water are thermodynamically distinct in a cylindrical pore, thus making rotamer distributions different from those in the bulk. Remarkably, salt bridge formation between LYS-GLU is stabilized by entropy in contrast to the bulk. Implications of our findings for confinement-induced alterations in protein stability are briefly outlined.

Sampling the equilibrium kinetic network of Trp-cage in explicit solvent

We employed the single replica multiple state transition interface sampling (MSTIS) approach to sample the kinetic (un)folding network of Trp-cage mini-protein in explicit water. Cluster analysis yielded 14 important metastable states in the network. The MSTIS simulation thus resulted in a full 14 × 14 rate matrix. Analysis of the kinetic rate matrix indicates the presence of a near native intermediate state characterized by a fully formed alpha helix, a slightly disordered proline tail, a broken salt-bridge, and a rotated arginine residue. This intermediate was also found in recent IR experiments. Moreover, the predicted rate constants and timescales are in agreement with previous experiments and simulations.

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.

Effect of interactions with the chaperonin cavity on protein folding and misfolding

Recent experimental and computational results have suggested that attractive interactions between a chaperonin and an enclosed substrate can have an important effect on the protein folding rate: it appears that folding may even be slower inside the cavity than under unconfined conditions, in contrast to what we would expect from excluded volume effects on the unfolded state. Here we examine systematically the dependence of the protein stability and folding rate on the strength of such attractive interactions between the chaperonin and substrate, by using molecular simulations of model protein systems in an idealised attractive cavity. Interestingly, we find a maximum in stability, and a rate which indeed slows down at high attraction strengths. We have developed a simple phenomenological model which can explain the variations in folding rate and stability due to differing effects on the free energies of the unfolded state, folded state, and transition state; changes in the diffusion coefficient along the folding coordinate are relatively small, at least for our simplified model. In order to investigate a possible role for these attractive interactions in folding, we have studied a recently developed model for misfolding in multidomain proteins. We find that, while encapsulation in repulsive cavities greatly increases the fraction of misfolded protein, sufficiently strong attractive protein-cavity interactions can strongly reduce the fraction of proteins reaching misfolded traps.

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.

Effects of interactions with the GroEL cavity on protein folding rates

Encapsulation of proteins in chaperonins is an important mechanism by which the cell prevents the accumulation of misfolded species in the cytosol. However, results from theory and simulation for repulsive cavities appear to be inconsistent with recent experimental results showing, if anything, a slowdown in folding rate for encapsulated Rhodanese. We study the folding of Rhodanese in GroEL, using coarse-grained molecular simulations of the complete system including chaperonin and substrate protein. We find that, by approximating the substrate:GroEL interactions as repulsive, we obtain a strong acceleration in rate of between one and two orders of magnitude; a similar result is obtained by representing the chaperonin as a simple spherical cavity. Remarkably, however, we find that using a carefully parameterized, sequence-based potential to capture specific residue-residue interactions between Rhodanese and the GroEL cavity walls induces a very strong reduction of the folding rates. The effect of the interactions is large enough to completely offset the effects of confinement, such that folding in some cases can be even slower than that of the unconfined protein. The origin of the slowdown appears to be stabilization--relative to repulsive confinement--of the unfolded state through binding to the cavity walls, rather than a reduction of the diffusion coefficient along the folding coordinate.

Exhaustively sampling peptide adsorption with metadynamics

Simulating the adsorption of a peptide or protein and obtaining quantitative estimates of thermodynamic observables remains challenging for many reasons. One reason is the dearth of molecular scale experimental data available for validating such computational models. We also lack simulation methodologies that effectively address the dual challenges of simulating protein adsorption: overcoming strong surface binding and sampling conformational changes. Unbiased classical simulations do not address either of these challenges. Previous attempts that apply enhanced sampling generally focus on only one of the two issues, leaving the other to chance or brute force computing. To improve our ability to accurately resolve adsorbed protein orientation and conformational states, we have applied the Parallel Tempering Metadynamics in the Well-Tempered Ensemble (PTMetaD-WTE) method to several explicitly solvated protein/surface systems. We simulated the adsorption behavior of two peptides, LKα14 and LKβ15, onto two self-assembled monolayer (SAM) surfaces with carboxyl and methyl terminal functionalities. PTMetaD-WTE proved effective at achieving rapid convergence of the simulations, whose results elucidated different aspects of peptide adsorption including: binding free energies, side chain orientations, and preferred conformations. We investigated how specific molecular features of the surface/protein interface change the shape of the multidimensional peptide binding free energy landscape. Additionally, we compared our enhanced sampling technique with umbrella sampling and also evaluated three commonly used molecular dynamics force fields.