Replica exchange simulation of reversible folding/unfolding of the Trp-cage miniprotein in explicit solvent: On the structure and possible role of internal water

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

Transferable and Polarizable Coarse Grained Model for Proteins─ProMPT

The application of classical molecular dynamics (MD) simulations at atomic resolution (fine-grained level, FG), to most biomolecular processes, remains limited because of the associated computational complexity of representing all the atoms. This problem is magnified in the presence of protein-based biomolecular systems that have a very large conformational space, and MD simulations with fine-grained resolution have slow dynamics to explore this space. Current transferable coarse grained (CG) force fields in literature are either limited to only peptides with the environment encoded in an implicit form or cannot capture transitions into secondary/tertiary peptide structures from a primary sequence of amino acids. In this work, we present a transferable CG force field with an explicit representation of the environment for accurate simulations with proteins. The force field consists of a set of pseudoatoms representing different chemical groups that can be joined/associated together to create different biomolecular systems. This preserves the transferability of the force field to multiple environments and simulation conditions. We have added electronic polarization that can respond to environmental heterogeneity/fluctuations and couple it to protein's structural transitions. The nonbonded interactions are parametrized with physics-based features such as solvation and partitioning free energies determined by thermodynamic calculations and matched with experiments and/or atomistic simulations. The bonded potentials are inferred from corresponding distributions in nonredundant protein structure databases. We present validations of the CG model with simulations of well-studied aqueous protein systems with specific protein fold types─Trp-cage, Trpzip4, villin, WW-domain, and β-α-β. We also explore the applications of the force field to study aqueous aggregation of Aβ 16-22 peptides.

Resolution exchange with tunneling for enhanced sampling of protein landscapes

Simulations of protein folding and protein association happen on timescales that are orders of magnitude larger than what can typically be covered in all-atom molecular dynamics simulations. Use of low-resolution models alleviates this problem but may reduce the accuracy of the simulations. We introduce a replica-exchange-based multiscale sampling technique that combines the faster sampling in coarse-grained simulations with the potentially higher accuracy of all-atom simulations. After testing the efficiency of our Resolution Exchange with Tunneling (ResET) in simulations of the Trp-cage protein, an often used model to evaluate sampling techniques in protein simulations, we use our approach to compare the landscape of wild-type and A2T mutant Aβ_{1-42} peptides. Our results suggest a mechanism by that the mutation of a small hydrophobic alanine (A) into a bulky polar threonine (T) may interfere with the self-assembly of Aβ fibrils.

The order of PDZ3 and TrpCage in fusion chimeras determines their properties-a biophysical characterization

Most of the structural proteins known today are composed of domains that carry their own functions while keeping their structural properties. It is supposed that such domains, when taken out of the context of the whole protein, can retain their original structure and function to a certain extent. Information on the specific functional and structural characteristics of individual domains in a new context of artificial fusion proteins may help to reveal the rules of internal and external domain communication. Moreover, this could also help explain the mechanism of such communication and address how the mutual allosteric effect plays a role in a such multi-domain protein system. The simple model system of the two-domain fusion protein investigated in this work consisted of a well-folded PDZ3 domain and an artificially designed small protein domain called Tryptophan Cage (TrpCage). Two fusion proteins with swapped domain order were designed to study their structural and functional features as well as their biophysical properties. The proteins composed of PDZ3 and TrpCage, both identical in amino acid sequence but different in composition (PDZ3-TrpCage, TrpCage-PDZ3), were studied using circualr dichroism (CD) spectrometry, analytical ultracentrifugation, and molecular dynamic simulations. The biophysical analysis uncovered different structural and denaturation properties of both studied proteins, revealing their different unfolding pathways and dynamics.

Sampling of the conformational landscape of small proteins with Monte Carlo methods

Computer simulation provides an increasingly realistic picture of large-scale conformational change of proteins, but investigations remain fundamentally constrained by the femtosecond timestep of molecular dynamics simulations. For this reason, many biologically interesting questions cannot be addressed using accessible state-of-the-art computational resources. Here, we report the development of an all-atom Monte Carlo approach that permits the modelling of the large-scale conformational change of proteins using standard off-the-shelf computational hardware and standard all-atom force fields. We demonstrate extensive thermodynamic characterization of the folding process of the α-helical Trp-cage, the Villin headpiece and the β-sheet WW-domain. We fully characterize the free energy landscape, transition states, energy barriers between different states, and the per-residue stability of individual amino acids over a wide temperature range. We demonstrate that a state-of-the-art intramolecular force field can be combined with an implicit solvent model to obtain a high quality of the folded structures and also discuss limitations that still remain.

Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy

The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.

Protein thermal stability

Proteins, in general, fold to a well-organized three-dimensional structure in order to function. The stability of this functional shape can be perturbed by external environmental conditions, such as temperature. Understanding the molecular factors underlying the resistance of proteins to the thermal stress has important consequences. First of all, it can aid the design of thermostable enzymes able to perform efficient catalysis in the high-temperature regime. Second, it is an essential brick of knowledge required to decipher the evolutionary pathways of life adaptation on Earth. Thanks to the development of atomistic simulations and ad hoc enhanced sampling techniques, it is now possible to investigate this problem in silico, and therefore provide support to experiments. After having described the methodological aspects, the chapter proposes an extended discussion on two problems. First, we focus on thermophilic proteins, a perfect model to address the issue of thermal stability and molecular evolution. Second, we discuss the issue of how protein thermal stability is affected by crowded in vivo-like conditions.

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Distinct and Nonadditive Effects of Urea and Guanidinium Chloride on Peptide Solvation

Using enhanced-sampling replica exchange fully atomistic molecular dynamics simulations, we show that, individually, urea and guanidinium chloride (GdmCl) denature the Trpcage protein, but remarkably, the helical segment ¹NLYIQWL⁷ of the protein is stabilized in mixed denaturant solutions. GdmCl induces protein denaturation via a combination of direct and indirect effects involving dehydration of the protein and destabilization of stabilizing salt bridges. In contrast, urea denatures the protein through favorable protein-urea preferential interactions, with peptide-specific indirect effects of urea on the water structure around the protein. In the case of the helical segment of Trpcage, urea "oversolvates" the peptide backbone by reorganizing water molecules from the peptide side chains to the peptide backbone. An intricate nonadditive thermodynamic balance between GdmCl-induced dehydration of the peptide and the urea-induced changes in solvation structure triggers partial counteraction to urea denaturation and stabilization of the helix.

Peptide and Protein Structure Prediction with a Simplified Continuum Solvent Model

A continuum solvent model based on screened Coulomb potentials has been simplified and parametrized to sample native-like structures in replica-exchange simulations of each of six different peptides and miniproteins. Low-energy, native, and non-native structures were used to iteratively refine 11 parameter values. The centroid of the largest cluster of structures sampled in simulations initiated from an extended conformation represents the predicted structure. The main-chain rms deviation of this prediction from the experimental structure was 0.47 Å for the 12-residue Trp-zip2, 0.86 Å for the 14-residue MBH12, 2.53 Å for the 17-residue U(1-17)T9D, 2.03 Å for the 20-residue BS1, 1.08 Å for the 20-residue Trp-cage, and 3.64 Å for the 35-residue villin headpiece subdomain HP35. The centroid of the sixth largest cluster sampled for HP35 deviated by 0.91 Å. The CHARMM22/CMAP force field was used, with an additional ψ torsion term for residues other than glycine and proline. Six parameters govern the dielectric response of the continuum solvent, and four values of surface tension approximate nonpolar effects. An atom's self-energy and interaction energies are screened independently, each depending on whether the atom is part of a charged group, a neutral hydrogen-bonding main-chain group, or any other neutral group. The parameters inferred result in strong main-chain hydrogen bonds, consistent with the view that protein folding is dominated by the formation of these bonds. (1,2) Conformations of MBH12 and BS1 were excluded from the energy-function refinement, suggesting the parameters, referred to as SCP18, are transferable. An efficient estimate of solvent-accessible surface area is also described.

Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations

Replica-exchange molecular dynamics (REMD) and their variants have been widely used in simulations of the biomolecular structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temperature of a pre-defined solute molecule is exchanged between replicas, while solvent temperatures in all the replicas are kept constant. REST greatly reduces the number of replicas compared to the temperature REMD, while replicas at low temperatures are often trapped under their conditions, interfering with the conformational sampling. Here, we introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a molecule or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. We applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the number of replicas necessary for good random walks in the solute-temperature space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Replica-exchange-with-tunneling for fast exploration of protein landscapes

While the use of replica-exchange molecular dynamics in protein simulations has become ubiquitous, its utility is limited in many practical applications. We propose to overcome some shortcomings that hold back its use in settings such as multi-scale or explicit solvent simulations by integrating ideas of hybrid MC/MD into the replica-exchange protocol. This Replica-Exchange-with-Tunneling method is tested by simulating the Trp-cage protein, a system often used in molecular biophysics for testing sampling techniques.

MTS-MD of Biomolecules Steered with 3D-RISM-KH Mean Solvation Forces Accelerated with Generalized Solvation Force Extrapolation

We developed a generalized solvation force extrapolation (GSFE) approach to speed up multiple time step molecular dynamics (MTS-MD) of biomolecules steered with mean solvation forces obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model with the Kovalenko-Hirata closure). GSFE is based on a set of techniques including the non-Eckart-like transformation of coordinate space separately for each solute atom, extension of the force-coordinate pair basis set followed by selection of the best subset, balancing the normal equations by modified least-squares minimization of deviations, and incremental increase of outer time step in motion integration. Mean solvation forces acting on the biomolecule atoms in conformations at successive inner time steps are extrapolated using a relatively small number of best (closest) solute atomic coordinates and corresponding mean solvation forces obtained at previous outer time steps by converging the 3D-RISM-KH integral equations. The MTS-MD evolution steered with GSFE of 3D-RISM-KH mean solvation forces is efficiently stabilized with our optimized isokinetic Nosé-Hoover chain (OIN) thermostat. We validated the hybrid MTS-MD/OIN/GSFE/3D-RISM-KH integrator on solvated organic and biomolecules of different stiffness and complexity: asphaltene dimer in toluene solvent, hydrated alanine dipeptide, miniprotein 1L2Y, and protein G. The GSFE accuracy and the OIN efficiency allowed us to enlarge outer time steps up to huge values of 1-4 ps while accurately reproducing conformational properties. Quasidynamics steered with 3D-RISM-KH mean solvation forces achieves time scale compression of conformational changes coupled with solvent exchange, resulting in further significant acceleration of protein conformational sampling with respect to real time dynamics. Overall, this provided a 50- to 1000-fold effective speedup of conformational sampling for these systems, compared to conventional MD with explicit solvent. We have been able to fold the miniprotein from a fully denatured, extended state in about 60 ns of quasidynamics steered with 3D-RISM-KH mean solvation forces, compared to the average physical folding time of 4-9 μs observed in experiment.

Computational investigation of cold denaturation in the Trp-cage miniprotein

The functional native states of globular proteins become unstable at low temperatures, resulting in cold unfolding and impairment of normal biological function. Fundamental understanding of this phenomenon is essential to rationalizing the evolution of freeze-tolerant organisms and developing improved strategies for long-term preservation of biological materials. We present fully atomistic simulations of cold denaturation of an α-helical protein, the widely studied Trp-cage miniprotein. In contrast to the significant destabilization of the folded structure at high temperatures, Trp-cage cold denatures at 210 K into a compact, partially folded state; major elements of the secondary structure, including the α-helix, are conserved, but the salt bridge between aspartic acid and arginine is lost. The stability of Trp-cage's α-helix at low temperatures suggests a possible evolutionary explanation for the prevalence of such structures in antifreeze peptides produced by cold-weather species, such as Arctic char. Although the 310-helix is observed at cold conditions, its position is shifted toward Trp-cage's C-terminus. This shift is accompanied by intrusion of water into Trp-cage's interior and the hydration of buried hydrophobic residues. However, our calculations also show that the dominant contribution to the favorable energetics of low-temperature unfolding of Trp-cage comes from the hydration of hydrophilic residues.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

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.

Intrinsic Localized Modes in Proteins

Protein dynamics is essential for proteins to function. Here we predicted the existence of rare, large nonlinear excitations, termed intrinsic localized modes (ILMs), of the main chain of proteins based on all-atom molecular dynamics simulations of two fast-folder proteins and of a rigid α/β protein at 300 K and at 380 K in solution. These nonlinear excitations arise from the anharmonicity of the protein dynamics. The ILMs were detected by computing the Shannon entropy of the protein main-chain fluctuations. In the non-native state (significantly explored at 380 K), the probability of their excitation was increased by a factor between 9 and 28 for the fast-folder proteins and by a factor 2 for the rigid protein. This enhancement in the non-native state was due to glycine, as demonstrated by simulations in which glycine was mutated to alanine. These ILMs might play a functional role in the flexible regions of proteins and in proteins in a non-native state (i.e. misfolded or unfolded states).

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

PACE Force Field for Protein Simulations. 2. Folding Simulations of Peptides

We present the application of our recently developed PACE force field to the folding of peptides. These peptides include α-helical (AK17 and Fs), β-sheet (GB1m2 and Trpzip2), and mixed helical/coil (Trp-cage) peptides. With replica exchange molecular dynamics (REMD), our force field can fold the five peptides into their native structures while maintaining their stabilities reasonably well. Our force field is also able to capture important thermodynamic features of the five peptides that have been observed in previous experimental and computational studies, such as different preferences for a helix-turn-helix topology for AK17 and Fs, the relative contribution of four hydrophobic side chains of GB1p to the stability of β-hairpin, and the distinct role of a hydrogen bond involving Trp-Hε and a D9/R16 salt bridge in stabilizing the Trp-cage native structure. Furthermore, multiple folding and unfolding events are observed in our microsecond-long normal MD simulations of AK17, Trpzip2, and Trp-cage. These simulations provide mechanistic information such as a "zip-out" pathway of the folding mechanism of Trpzip2 and the folding times of AK17 and Trp-cage, which are estimated to be about 51 ± 43 ns and 270 ± 110 ns, respectively. A 600 ns simulation of the peptides can be completed within one day. These features of our force field are potentially applicable to the study of thermodynamics and kinetics of real protein systems.

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.

New Insights into Protein (Un)Folding Dynamics

A fundamental open problem in biophysics is how the folded structure of the main chain (MC) of a protein is determined by the physics of the interactions between the side chains (SCs). All-atom molecular dynamics simulations of a model protein (Trp-cage) revealed that strong correlations between the motions of the SCs and the MC occur transiently at 380 K in unfolded segments of the protein and during the simulations of the whole amino-acid sequence at 450 K. The high correlation between the SC and MC fluctuations is a fundamental property of the unfolded state and is also relevant to unstructured proteins as intrinsically disordered proteins (IDPs), for which new reaction coordinates are introduced. The presented findings may open a new door as to how functions of IDPs are related to conformations, which play a crucial role in neurodegenerative diseases.

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.

Tackling sampling challenges in biomolecular simulations

Molecular dynamics (MD) simulations are a powerful tool to give an atomistic insight into the structure and dynamics of proteins. However, the time scales accessible in standard simulations, which often do not match those in which interesting biological processes occur, limit their predictive capabilities. Many advanced sampling techniques have been proposed over the years to overcome this limitation. This chapter focuses on metadynamics, a method based on the introduction of a time-dependent bias potential to accelerate sampling and recover equilibrium properties of a few descriptors that are able to capture the complexity of a process at a coarse-grained level. The theory of metadynamics and its combination with other popular sampling techniques such as the replica exchange method is briefly presented. Practical applications of these techniques to the study of the Trp-Cage miniprotein folding are also illustrated. The examples contain a guide for performing these calculations with PLUMED, a plugin to perform enhanced sampling simulations in combination with many popular MD codes.

Folding and self-assembly of a small heterotetramer

Designed miniproteins offer a possibility to study folding and association of protein complexes, both experimentally and in silico. Using replica exchange molecular dynamics and the coarse-grain UNRES force field, we have simulated the folding and self-assembly of the heterotetramer BBAThet1, comparing it with that of the homotetramer BBAT1 which has the same size and ββα-fold. For both proteins, association of the tetramer precedes and facilitates folding of the individual chains.

Protein structure prediction: assembly of secondary structure elements by basin-hopping

The prediction of protein tertiary structure from primary structure remains a challenging task. One possible approach to this problem is the application of basin-hopping global optimization combined with an all-atom force field. In this work, the efficiency of basin-hopping is improved by introducing an approach that derives tertiary structures from the secondary structure assignments of individual residues. This approach is termed secondary-to-tertiary basin-hopping and benchmarked for three miniproteins: trpzip, trp-cage and ER-10. For each of the three miniproteins, the secondary-to-tertiary basin-hopping approach successfully and reliably predicts their three-dimensional structure. When it is applied to larger proteins, correctly folded structures are obtained. It can be concluded that the assembly of secondary structure elements using basin-hopping is a promising tool for de novo protein structure prediction.

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.

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.

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.

Folding and unfolding thermodynamics of the TC10b Trp-cage miniprotein

We examine the folding-unfolding of a variant of the Trp-cage, known as TC10b, and compare structural stability, dynamics, and thermodynamics with that of the TC5b variant, using replica exchange molecular dynamics (REMD). The TC10b variant was designed to have larger helical stability by the substitution of amino acids with greater alpha helical propensities in the N-terminal region. Experiments have shown TC10b to possess larger overall stability than TC5b. Simulations starting from unbiased, unfolded initial conditions are run for 1 μs per replica. The calculations show a higher melting temperature for TC10b than TC5b, and suggest a more ordered folded structure through the elimination of a substate found in the folded ensemble of TC5b. We model the difference in Gibbs free energy, ΔG(P,T), of folding using the bootstrap statistical method, which is used to calculate uncertainties associated with the thermodynamic parameters for both variants of the Trp-cage. We find that while the shape of the area for which the protein is stability folded is elliptical for TC5b, there is a degree of uncertainty associated with that of TC10b, with one model suggesting elliptical and another suggesting hyperbolic. This model suggests that at high pressures, TC5b can experience pressure denaturation, but TC10b may not.

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.

Structure and dynamics of the N-terminal domain of the Cu(I) binding protein CusB

CusCFBA is one of the metal efflux systems in Escherichia coli that is highly specific for its substrates, Cu(I) and Ag(I). It serves to protect the bacteria in environments that have lethal concentrations of these metals. The membrane fusion protein CusB is the periplasmic piece of CusCFBA, which has not been fully characterized by crystallography because of its extremely disordered N-terminal region. This region has both structural and functional importance because it has been experimentally proven to transfer the metal by itself from the metallochaperone CusF and to induce a structural change in the rest of CusB to increase Cu(I)/Ag(I) resistance. Understanding metal uptake from the periplasm is critical to gain insight into the mechanism of the whole CusCFBA pump, which makes resolving a structure for the N-terminal region necessary because it contains the metal binding site. We ran extensive molecular dynamics simulations to reveal the structural and dynamic properties of both the apo and Cu(I)-bound versions of the CusB N-terminal region. In contrast to its functional companion CusF, Cu(I) binding to the N-terminus of CusB causes only a slight, local stabilization around the metal site. The trajectories were analyzed in detail, revealing extensive structural disorder in both the apo and holo forms of the protein. CusB was further analyzed by breaking the protein up into three subdomains according to the extent of the observed disorder: the N- and C-terminal tails, the central beta strand motif, and the M21-M36 loop connecting the two metal-coordinating methionine residues. Most of the observed disorder was traced back to the tail regions, leading us to hypothesize that the latter two subdomains (residues 13-45) may form a functionally competent metal-binding domain because the tail regions appear to play no role in metal binding.

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.

Reliable oligonucleotide conformational ensemble generation in explicit solvent for force field assessment using reservoir replica exchange molecular dynamics simulations

Molecular dynamics force field development and assessment requires a reliable means for obtaining a well-converged conformational ensemble of a molecule in both a time-efficient and cost-effective manner. This remains a challenge for RNA because its rugged energy landscape results in slow conformational sampling and accurate results typically require explicit solvent which increases computational cost. To address this, we performed both traditional and modified replica exchange molecular dynamics simulations on a test system (alanine dipeptide) and an RNA tetramer known to populate A-form-like conformations in solution (single-stranded rGACC). A key focus is on providing the means to demonstrate that convergence is obtained, for example, by investigating replica RMSD profiles and/or detailed ensemble analysis through clustering. We found that traditional replica exchange simulations still require prohibitive time and resource expenditures, even when using GPU accelerated hardware, and our results are not well converged even at 2 μs of simulation time per replica. In contrast, a modified version of replica exchange, reservoir replica exchange in explicit solvent, showed much better convergence and proved to be both a cost-effective and reliable alternative to the traditional approach. We expect this method will be attractive for future research that requires quantitative conformational analysis from explicitly solvated simulations.

Efficient numerical reconstruction of protein folding kinetics with partial path sampling and pathlike variables

Numerically predicting rate constants of protein folding and other relevant biological events is still a significant challenge. We show that the combination of partial path transition interface sampling with the optimal interfaces and free-energy profiles provided by path collective variables makes the rate calculation for practical biological applications feasible and efficient. This methodology can reproduce the experimental rate constant of Trp-cage miniprotein folding with the same level of accuracy as transition path sampling at a fraction of the cost.

Generating reservoir conformations for replica exchange through the use of the conformational space annealing method

Temperature replica exchange molecular dynamics (T-REM) has been successfully used to improve the conformational search for model peptides and small proteins. However, for larger and more complicated systems, the use of T-REM is computationally intensive since the complexity of the free energy landscape and number of replicas required increase with system size. Achieving convergence of systems with slow transition kinetics is often difficult. Several methods have been proposed to overcome the size and convergence speed issues of standard T-REM. One of these is the Reservoir Replica Exchange Method (R-REM), in which the conformational search and temperature equilibration are separated by exchanging with a pre-existing reservoir of structures. This approach allows the integration of computationally efficient search algorithms with replica exchange. The Conformational Space Annealing (CSA) method has been shown to be able to determine the global energy minimum of proteins efficiently and has been used in structure prediction successfully. CSA uses a genetic algorithm to generate a diverse set of conformations to determine the minimum energy structure. We combine these methods by using conformations generated by the CSA method to build a reservoir. R-REM is then used to seed the top replica with the structures from the reservoir; fast convergence at every temperature is observed. The efficiency of this method is then demonstrated with model peptides and small proteins, and significant improvement of efficiency is observed while maintaining the overall shape of the free energy landscape.