Effects of Turn Stability and Side-Chain Hydrophobicity on the Folding of β-Structures

Generating High-Precision Force Fields for Molecular Dynamics Simulations to Study Chemical Reaction Mechanisms Using Molecular Configuration Transformer

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that used enhanced sampling in molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limited the use of high-precision potential energy functions for simulations. To address this issue, we presented a scheme for training high-precision force fields for molecular modeling using a previously developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allowed for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We applied this approach to study a Claisen rearrangement reaction and a carbonyl insertion reaction catalyzed by manganese.

Phenolic compounds in walnut pellicle improve walnut (Juglans regia L.) protein solubility under pH-shifting condition

This study focused on the interaction of walnut protein with phenolic extracts of walnut pellicle (PEWP) under alkaline condition, leading to enhancement of protein solubility under neutral condition. First, the change of PEWP under alkaline condition was determined by RP-HPLC and mass spectrometry, and the results showed that most ellagitannins in PEWP could be retained under alkaline condition within 3 h. Interaction between PEWP and walnut protein under pH-shifting condition resulted in the remarkable increase of protein solubility (above 90%) at neutral pH. The results from SDS-PAGE and SEC showed that the improved solubility lied in the formation of large and soluble protein aggregates due to the covalent interaction among walnut protein and polyphenols. A significant change in tertiary structure of protein-phenolic complex was witnessed by fluorescence spectrum and near-UV circular dichroism. Meanwhile, walnut protein-polyphenol interaction led to a slight increase in β-turn while a slight decrease in β-sheet. Combined with amino acid composition, it could be illustrated that the covalent bonding for walnut protein with polyphenol mainly occurred at Lysine residues.

Enhanced sampling in molecular dynamics

Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.

The sensitivity of folding free energy landscapes of trpzips to mutations in the hydrophobic core

The sensitivity of the stability of folded states and free energy landscapes to the differences in the hydrophobic content of the core residues has been studied for the set of 16-residue trpzips, namely, Trpzip4, Trpzip5 and Trpzip6.

Nature of aryl-tyrosine interactions contribute to β-hairpin scaffold stability: NMR evidence for alternate ring geometry

The specific contribution of the acidic-aromatic β-sheet favouring amino acid tyrosine to the stability of short octapeptide β-hairpin structures is presented here. Solution NMR analysis in near-apolar environments suggests the energetically favourable mode of interaction to be T-shaped face-to-edge (FtE) and that a Trp-Tyr interacting pair is the most stabilizing. Alternate aryl geometries also exist in solution, which readily equilibrate between a preferred π···π conformation to an aromatic-amide conformation, without any change in the backbone structure. While the phenolic ring is readily accommodated at the "edge" of FtE aryl interactions, it exhibits an overall lowered contribution to scaffold stability in the "face" orientation. Such differential tyrosine interactions are key to its dual nature in proteins.

Correct folding of an α-helix and a β-hairpin using a polarized 2D torsional potential

A new modification to the AMBER force field that incorporates the coupled two-dimensional main chain torsion energy has been evaluated for the balanced representation of secondary structures. In this modified AMBER force field (AMBER03(2D)), the main chain torsion energy is represented by 2-dimensional Fourier expansions with parameters fitted to the potential energy surface generated by high-level quantum mechanical calculations of small peptides in solution. Molecular dynamics simulations are performed to study the folding of two model peptides adopting either α-helix or β-hairpin structures. Both peptides are successfully folded into their native structures using an AMBER03(2D) force field with the implementation of a polarization scheme (AMBER03(2D)p). For comparison, simulations using a standard AMBER03 force field with and without polarization, as well as AMBER03(2D) without polarization, fail to fold both peptides successfully. The correction to secondary structure propensity in the AMBER03 force field and the polarization effect are critical to folding Trpzip2; without these factors, a helical structure is obtained. This study strongly suggests that this new force field is capable of providing a more balanced preference for helical and extended conformations. The electrostatic polarization effect is shown to be indispensable to the growth of secondary structures.

From thermodynamics to kinetics: enhanced sampling of rare events

Despite great advances in molecular dynamics simulations, there remain large gaps between the simulations and experimental observations in terms of the time and length scales that can be approached. Developing fast and accurate algorithms and methods is of ultimate importance to bridge these gaps. In this Account, we briefly summarize recent efforts in such directions. In particular, we focus on integrated tempering sampling. The efficiency of this sampling method has been demonstrated by applications to a range of chemical and biological problems: protein folding, molecular cluster structure searches, and chemical reactions. The combination of integrated tempering sampling and a trajectory sampling method allows the calculation of rate constants and reaction pathways without predefined collective coordinates.

Important roles of hydrophobic interactions in folding and charge interactions in misfolding of α-helix bundle protein

An enhanced-sampling molecular dynamics simulation is presented to quantitatively demonstrate the important roles of hydrophobic and charge interactions in the folding and misfolding of α-helix bundle protein, respectively.

Theoretical volume profiles as a tool for probing transition states: folding kinetics

The mechanism by which conformational changes, particularly folding and unfolding, occur in proteins and other biopolymers has been widely discussed in the literature. Molecular dynamics (MD) simulations of protein folding present a formidable challenge since these conformational changes occur on a time scale much longer than what can be afforded at the current level of computational technology. Transition state (TS) theory offers a more economic description of kinetic properties of a reaction system by relating them to the properties of the TS, or for flexible systems, the TS ensemble (TSE). The application of TS theory to protein folding is limited by ambiguity in the definition of the TSE for this process. We propose to identify the TSE for conformational changes in flexible systems by comparison of its experimentally determined volumetric property, known as the volume of activation, to the structure-specific volume profile of the process calculated using MD. We illustrate this approach by its successful application to unfolding of a model chain system.

How quickly can a β-hairpin fold from its transition state?

Understanding the structural nature of the free energy bottleneck(s) encountered in protein folding is essential to elucidating the underlying dynamics and mechanism. For this reason, several techniques, including Φ-value analysis, have previously been developed to infer the structural characteristics of such high free-energy or transition states. Herein we propose that one (or few) appropriately placed backbone and/or side chain cross-linkers, such as disulfides, could be used to populate a thermodynamically accessible conformational state that mimics the folding transition state. Specifically, we test this hypothesis on a model β-hairpin, Trpzip4, as its folding mechanism has been extensively studied and is well understood. Our results show that cross-linking the two β-strands near the turn region increases the folding rate by an order of magnitude, to about (500 ns)⁻¹, whereas cross-linking the termini results in a hyperstable β-hairpin that has essentially the same folding rate as the uncross-linked peptide. Taken together, these findings suggest that cross-linking is not only a useful strategy to manipulate folding free energy barriers, as shown in other studies, but also, in some cases, it can be used to stabilize a folding transition state analogue and allow for direct assessment of the folding process on the downhill side of the free energy barrier. The calculated free energy landscape of the cross-linked Trpzip4 also supports this picture. An empirical analysis further suggests, when folding of β-hairpins does not involve a significant free energy barrier, the folding time (τ) follows a power law dependence on the number of hydrogen bonds to be formed (n_H), namely, τ = τ₀n_H^α, with τ₀ = 20 ns and α = 2.3.

Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip

Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.

Combination of Enveloping Distribution Sampling (EDS) of a Soft-Core Reference-State Hamiltonian with One-Step Perturbation to Predict the Effect of Side Chain Substitution on the Relative Stability of Right- and Left-Helical Folds of β-Peptides

Folding free enthalpies of many not too different polypeptides can be efficiently and accurately predicted with the one-step perturbation (OSP) method using only one or a few molecular dynamics (MD) simulations. In this article, we introduce a combination of enveloping distribution sampling (EDS) and the OSP method (EDS-OSP) and apply it to predict the free enthalpy differences between a right-handed 2.710/12-helix and a left-handed 314-helix for 16 β-peptides with slightly different side-chain substitution patterns. An EDS simulation of a designed soft-core reference-state peptide was carried out in which both helices were sampled. Then, the soft-core atoms were perturbed into physical atoms. Thus, free enthalpy differences between the two helices for the 16 β-peptides can be predicted from only one simulation. The results predicted by EDS-OSP and a previous OSP study are very similar, i.e., the deviations between the results of the 16 peptides are mostly within the order of kBT, and the average absolute deviation is 1.2 kJ mol(-1). Together with the EDS parameter update simulation, about 128 ns of MD simulations needed to be carried out using the EDS-OSP method, while 700 ns of MD simulations were required in the previous OSP study where two separate reference-state simulations and an additional long time MD simulation of one of the 16 β-peptides were carried out. Thus, the computational effort was significantly reduced, i.e., by more than a factor of 5, using the EDS-OSP method. Hence, we consider this method an efficient tool to predict conformational free enthalpy differences from MD simulations.

Molecular dynamics studies of β-hairpin folding with the presence of the sodium ion

Metal ions are ubiquitous in protein systems and play a significant role during their folding processes. Nineteen independent structures were determined for the Na(+)/β-hairpin interacting systems, and their folding pathways are different. (i) For Na(S47), the turn is rapidly shaped with the help of Na(+) and acts as the folding nucleus for the rest regions. Two intermediate states are observed and the resulted structure is the most folded. (ii) For Na(B41), Na(B52), Na(B54), Na(S55) and Na(B56), the inclusive Na(+) ions are anchored by β-strands. The local structures around the Na(+) ions and the turn regions fold simultaneously and serve as two independent folding nuclei. (iii) The other systems have no folding nuclei and correspond to low-folded structures. Long-range electrostatic interactions contribute a lot to the folding, especially from the four negatively charged residues (Glu42, Asp46, Asp47 and Glu56). The initial positions of the Na(+) ions are largely responsible for the different folding behaviors. The interactions with sidechain- rather than backbone-O atoms generally lead to more compact structures. Another factor affecting the folding is whether the O atoms are associated with native H-bonds, and those involved show decreased affinities to metal ions. The addition of water solvent does not induce obvious folding and conformational transitions to the Na(+)/β-hairpin interacting systems.

Infrared study of the stability and folding kinetics of a series of β-hairpin peptides with a common NPDG turn

The thermal stability and folding kinetics of a series of 15-residue β-hairpins with a common Type I [3:5] NPDG turn were studied using Fourier transform infrared spectroscopy (FTIR) and laser-induced temperature jump (T-jump) with infrared detection, respectively. Mutations at positions 3, 5, or 13 in the peptide sequence SEXYXNPDGTWTXTE, where X represents the position of mutation, were performed to study the roles of hydrophobic interactions in determining the thermodynamic and kinetic properties of β-hairpin folding. The thermal stability studies show a broad thermal folding/unfolding transition for all the peptides. T-jump studies indicate that these β-hairpin peptides fold in less than 2 μs. In addition, both folding and unfolding rate constants decrease with increasing strength of hydrophobic interactions. Kinetically, the hydrophobic interactions have more significant influence on the unfolding rate than the folding rate. Φ-value analysis indicates that the hydrophobic interactions between the side chains are mainly formed at the latter part of the transition-state region during the folding process. In summary, the results suggest that the formation of the native structure of these β-hairpins depends on the correct topology of the hydrophobic cluster. Besides the formation of the turn region as a key process for folding as suggested by previous studies, a hydrophobic collapse process may also play a crucial role during β-hairpin folding.