Monitoring the folding of Trp-cage peptide by two-dimensional infrared (2DIR) spectroscopy

Unraveling dynamic protein structures by two-dimensional infrared spectra with a pretrained machine learning model

Dynamic protein structures are crucial for deciphering their diverse biological functions. Two-dimensional infrared (2DIR) spectroscopy stands as an ideal tool for tracing rapid conformational evolutions in proteins. However, linking spectral characteristics to dynamic structures poses a formidable challenge. Here, we present a pretrained machine learning model based on 2DIR spectra analysis. This model has learned signal features from approximately 204,300 spectra to establish a "spectrum-structure" correlation, thereby tracing the dynamic conformations of proteins. It excels in accurately predicting the dynamic content changes of various secondary structures and demonstrates universal transferability on real folding trajectories spanning timescales from microseconds to milliseconds. Beyond exceptional predictive performance, the model offers attention-based spectral explanations of dynamic conformational changes. Our 2DIR-based pretrained model is anticipated to provide unique insights into the dynamic structural information of proteins in their native environments.

Artificial Intelligence-based Amide-II Infrared Spectroscopy Simulation for Monitoring Protein Hydrogen Bonding Dynamics

The structurally sensitive amide II infrared (IR) bands of proteins provide valuable information about the hydrogen bonding of protein secondary structures, which is crucial for understanding protein dynamics and associated functions. However, deciphering protein structures from experimental amide II spectra relies on time-consuming quantum chemical calculations on tens of thousands of representative configurations in solvent water. Currently, the accurate simulation of amide II spectra for whole proteins remains a challenge. Here, we present a machine learning (ML)-based protocol designed to efficiently simulate the amide II IR spectra of various proteins with an accuracy comparable to experimental results. This protocol stands out as a cost-effective and efficient alternative for studying protein dynamics, including the identification of secondary structures and monitoring the dynamics of protein hydrogen bonding under different pH conditions and during protein folding process. Our method provides a valuable tool in the field of protein research, focusing on the study of dynamic properties of proteins, especially those related to hydrogen bonding, using amide II IR spectroscopy.

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.

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.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in 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.

A Machine Learning Protocol for Predicting Protein Infrared Spectra

Infrared (IR) absorption provides important chemical fingerprints of biomolecules. Protein secondary structure determination from IR spectra is tedious since its theoretical interpretation requires repeated expensive quantum-mechanical calculations in a fluctuating environment. Herein we present a novel machine learning protocol that uses a few key structural descriptors to rapidly predict amide I IR spectra of various proteins and agrees well with experiment. Its transferability enabled us to distinguish protein secondary structures, probe atomic structure variations with temperature, and monitor protein folding. This approach offers a cost-effective tool to model the relationship between protein spectra and their biological/chemical properties.

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.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

Multiple Decay Mechanisms and 2D-UV Spectroscopic Fingerprints of Singlet Excited Solvated Adenine-Uracil Monophosphate

The decay channels of singlet excited adenine uracil monophosphate (ApU) in water are studied with CASPT2//CASSCF:MM potential energy calculations and simulation of the 2D-UV spectroscopic fingerprints with the aim of elucidating the role of the different electronic states of the stacked conformer in the excited state dynamics. The adenine (1) La state can decay without a barrier to a conical intersection with the ground state. In contrast, the adenine (1) Lb and uracil S(U) states have minima that are separated from the intersections by sizeable barriers. Depending on the backbone conformation, the CT state can undergo inter-base hydrogen transfer and decay to the ground state through a conical intersection, or it can yield a long-lived minimum stabilized by a hydrogen bond between the two ribose rings. This suggests that the (1) Lb , S(U) and CT states of the stacked conformer may all contribute to the experimental lifetimes of 18 and 240 ps. We have also simulated the time evolution of the 2D-UV spectra and provide the specific fingerprint of each species in a recommended probe window between 25 000 and 38 000 cm(-1) in which decongested, clearly distinguishable spectra can be obtained. This is expected to allow the mechanistic scenarios to be discerned in the near future with the help of the corresponding experiments. Our results reveal the complexity of the photophysics of the relatively small ApU system, and the potential of 2D-UV spectroscopy to disentangle the photophysics of multichromophoric systems.

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.

Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales

This Perspective highlights recent advances in infrared vibrational chemical nano-imaging. In its implementations of scattering scanning near-field optical microscopy (s-SNOM) and photothermal-induced resonance (PTIR), IR nanospectroscopy provides few-nanometer spatial resolution for the investigation of polymer, biomaterial, and related soft-matter surfaces and nanostructures. Broad-band IR s-SNOM with coherent laser and synchrotron sources allows for chemical recognition with small-ensemble sensitivity and the potential for sensitivity reaching the single-molecule limit. Probing selected vibrational marker resonances, it gives access to nanoscale chemical imaging of composition, domain morphologies, order/disorder, molecular orientation, or crystallographic phases. Local intra- and intermolecular coupling can be measured through frequency shifts of a vibrational marker in heterogeneous environments and associated inhomogeneities in vibrational dephasing. In combination with ultrafast spectroscopy, the vibrational coherent evolution of homogeneous sub-ensembles coupled to their environment can be observed. Outstanding challenges are discussed in terms of extensions to coherent and multidimensional spectroscopies, implementation in liquid and in situ environments, general sample limitations, and engineering s-SNOM scanning probes to better control the nano-localized optical excitation and to increase sensitivity.

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.

Achieving Rigorous Accelerated Conformational Sampling in Explicit Solvent

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

Disentangling Peptide Configurations via Two-Dimensional Electronic Spectroscopy: Ab Initio Simulations Beyond the Frenkel Exciton Hamiltonian

Two-dimensional (2D) optical spectroscopy techniques based on ultrashort laser pulses have been recently extended to the optical domain in the ultraviolet (UV) spectral region. UV-active aromatic side chains can thus be used as local highly specific markers for tracking dynamics and structural rearrangements of proteins. Here we demonstrate that 2D electronic spectra of a model proteic system, a tetrapeptide with two aromatic side chains, contain enough structural information to distinguish between two different configurations with distant and vicinal side chains. For accurate simulations of the 2DUV spectra in solution, we combine a quantum mechanics/molecular mechanics approach based on wave function methods, accounting for interchromophores coupling and environmental effects, with nonlinear response theory. The proposed methodology reveals effects, such as charge transfer between vicinal aromatic residues that remain concealed in conventional exciton Hamiltonian approaches. Possible experimental setups are discussed, including multicolor experiments and signal manipulation techniques for limiting undesired background contributions and enhancing 2DUV signatures of specific electronic couplings.

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

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

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

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

Two-dimensional stimulated resonance Raman spectroscopy study of the Trp-cage peptide folding

We report a combined molecular dynamics (MD) and ab initio simulation study of the ultrafast broadband ultraviolet (UV) stimulated resonance Raman (SRR) spectra of the Trp-cage mini protein. Characteristic two dimensional (2D) SRR features of various folding states are identified. Structural fluctuations erode the cross peaks and the correlation between diagonal peaks is a good indicator of the α-helix formation.

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.

Two-Dimensional Infrared (2DIR) Spectroscopy of the Peptide Beta3s Folding

Probing underlying free energy landscape, pathways, and mechanism is the key for understanding protein folding in theory and experiment. Recently time-resolved two-dimensional infrared (2DIR) with femtosecond laser pulses, has emerged as a promising tool for investigating the protein folding dynamics on faster timescales than possible by NMR. We have employed molecular dynamics simulations to compute 2DIR spectra of the folding process of a peptide, Beta3s. Simulated non-chiral and chiral 2DIR signals illustrate the variation of the spectra as the peptide conformation evolves along the free energy landscape. Chiral spectra show stronger changes than the non-chiral signals because cross peaks caused by the formation of the β-sheet are clearly resolved. Chirality-induced 2DIR may be used to detect the folding of β-sheet proteins with high spectral and temporal resolution.