Theoretical analysis on thermodynamic stability of chignolin

Electric field modulated configuration and orientation of aqueous molecule chains

Understanding how external electric fields (EFs) impact the properties of aqueous molecules is crucial for various applications in chemistry, biology, and engineering. In this paper, we present a study utilizing molecular dynamics simulation to explore how direct-current (DC) and alternative-current (AC) EFs affect hydrophobic (n-triacontane) and hydrophilic (PEG-10) oligomer chains. Through a machine learning approach, we extract a 2-dimensional free energy (FE) landscape of these molecules, revealing that electric fields modulate the FE landscape to favor stretched configurations and enhance the alignment of the chain with the electric field. Our observations indicate that DC EFs have a more prominent impact on modulation compared to AC EFs and that EFs have a stronger effect on hydrophobic chains than on hydrophilic oligomers. We analyze the orientation of water dipole moments and hydrogen bonds, finding that EFs align water molecules and induce more directional hydrogen bond networks, forming 1D water structures. This favors the stretched configuration and alignment of the studied oligomers simultaneously, as it minimizes the disruption of 1D structures. This research deepens our understanding of the mechanisms by which electric fields modulate molecular properties and could guide the broader application of EFs to control other aqueous molecules, such as proteins or biomolecules.

Folding Kinetics and Volume Variation of the β-Hairpin Peptide Chignolin upon Ultrafast pH-Jumps

In-depth characterization of fundamental folding steps of small model peptides is crucial for a better understanding of the folding mechanisms of more complex biomacromolecules. We have previously reported on the folding/unfolding kinetics of a model α-helix. Here, we study folding transitions in chignolin (GYDPETGTWG), a short β-hairpin peptide previously used as a model to study conformational changes in β-sheet proteins. Although previously suggested, until now, the role of the Tyr2-Trp9 interaction in the folding mechanism of chignolin was not clear. In the present work, pH-dependent conformational changes of chignolin were characterized by circular dichroism (CD), nuclear magnetic resonance (NMR), ultrafast pH-jump coupled with time-resolved photoacoustic calorimetry (TR-PAC), and molecular dynamics (MD) simulations. Taken together, our results present a comprehensive view of chignolin's folding kinetics upon local pH changes and the role of the Tyr2-Trp9 interaction in the folding process. CD data show that chignolin's β-hairpin formation displays a pH-dependent skew bell-shaped curve, with a maximum close to pH 6, and a large decrease in β-sheet content at alkaline pH. The β-hairpin structure is mainly stabilized by aromatic interactions between Tyr2 and Trp9 and CH-π interactions between Tyr2 and Pro4. Unfolding of chignolin at high pH demonstrates that protonation of Tyr2 is essential for the stability of the β-hairpin. Refolding studies were triggered by laser-induced pH-jumps and detected by TR-PAC. The refolding of chignolin from high pH, mainly due to the protonation of Tyr2, is characterized by a volume expansion (10.4 mL mol-1), independent of peptide concentration, in the microsecond time range (lifetime of 1.15 μs). At high pH, the presence of the deprotonated hydroxyl (tyrosinate) hinders the formation of the aromatic interaction between Tyr2 and Trp9 resulting in a more disorganized and dynamic tridimensional structure of the peptide. This was also confirmed by comparing MD simulations of chignolin under conditions mimicking neutral and high pH.

Molecular Free Energies, Rates, and Mechanisms from Data-Efficient Path Sampling Simulations

Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this limitation by collecting unbiased trajectories and capturing the relevant events. Moreover, the integration of machine learning can boost the sampling while simultaneously learning a quantitative representation of the mechanism. Still, the resulting trajectories are by construction non-Boltzmann-distributed, preventing the calculation of free energies and rates. We developed an algorithm to approximate the equilibrium path ensemble from machine-learning-guided path sampling data. At the same time, our algorithm provides efficient sampling, mechanism, free energy, and rates of rare molecular events at a very moderate computational cost. We tested the method on the folding of the mini-protein chignolin. Our algorithm is straightforward and data-efficient, opening the door to applications in many challenging molecular systems.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

Effects of Externally Applied Electric Fields on the Manipulation of Solvated-Chignolin Folding: Static- versus Alternating-Field Dichotomy at Play

The interaction between a protein and external electric field (EF) can alter its structure and dynamical behavior, which has a potential impact on the biological function of proteins and cause uncertain health consequences. Conversely, the application of EFs of judiciously selected intensity and frequency can help to treat disease, and optimization of this requires a greater understanding of EF-induced effects underpinning basic protein biophysics. In the present study, chignolin─an artificial protein sufficiently small to undergo fast-folding events and transitions─was selected as an ideal prototype to investigate how, and to what extent, externally applied electric fields may manipulate or influence protein-folding phenomena. Nonequilibrium molecular dynamics (NEMD) simulations have been performed of solvated chignolin to determine the distribution of folding states and their underlying transition dynamics, in the absence and presence of externally applied electric fields (both static and alternating); a key focus has been to ascertain how folding pathways are altered in an athermal sense by external fields. Compared to zero-field conditions, a dramatically different─indeed, bifurcated─behavior of chignolin-folding processes emerges between static- and alternating-field scenarios, especially vis-à-vis incipient stages of hydrophobic-core formation: in alternating fields, fold-state populations diversified, with an attendant acceleration of state-hopping folding kinetics, featuring the concomitant emergence of a new, quasi-stable structure compared to the native structure, in field-shifted energy landscapes.

Water-mediated interactions destabilize proteins

Proteins are folded to avoid exposure of the nonpolar groups to water because water-mediated interactions between nonpolar groups are a promising factor in the thermodynamic stabilities of proteins-which is a well-accepted view as one of the unique effects of hydrophobic interactions. This article poses a critical question for this classical view by conducting an accurate solvation free-energy calculation for a thermodynamic cycle of a protein folding using a liquid-state density functional theory. Here, the solvation-free energy for a leucine zipper formation was examined in the coiled-coil protein GCN4-p1, a typical model for hydrophobic interactions, which demonstrated that water-mediated interactions were unfavorable for the association of nonpolar groups in the native state, while the dispersion forces between them were, instead, responsible for the association. Furthermore, the present analysis well predicted the isolated helical state stabilized by pressure, which was previously observed in an experiment. We reviewed the problems in the classical concept and semiempirical presumption that the energetic cost of the hydration of nonpolar groups is a driving force of folding.

Two different regimes in alcohol-induced coil-helix transition: effects of 2,2,2-trifluoroethanol on proteins being either independent of or enhanced by solvent structural fluctuations

Inhomogeneous distribution of constituent molecules in a mixed solvent has been known to give remarkable effects on the solute, e.g., conformational changes of biomolecules in an alcohol-water mixture. We investigated the general effects of 2,2,2-trifluoroethanol (TFE) on proteins/peptides in a mixture of water and TFE using melittin as a model protein. Fluctuations and Kirkwood-Buff integrals (KBIs) in the TFE-H2O mixture, quantitative descriptions of inhomogeneity, were determined by small-angle X-ray scattering investigation and compared with those in the aqueous solutions of other alcohols. The concentration fluctuation for the mixtures ranks as methanol < ethanol ≪ TFE < tert-butanol < 1-propanol, indicating that the inhomogeneity of molecular distribution in the TFE-H2O mixture is unexpectedly comparable to those in the series of mono-ols. On the basis of the concentration dependence of KBIs between the TFE molecules, it was found that a strong attraction between the TFE molecules is not necessarily important to induce helix conformation, which is inconsistent with the previously proposed mechanism. To address this issue, by combining the KBIs and the helix contents reported by the experimental spectroscopic studies, we quantitatively evaluated the change in the preferential binding parameter of TFE to melittin attributed to the coil-helix transition. As a result, we found two different regimes on TFE-induced helix formation. In the dilute concentration region of TFE below ∼2 M, where the TFE molecules are not aggregated among themselves, the excess preferential binding of TFE to the helix occurs due to the direct interaction between them, namely independent of the solvent fluctuation. In the higher concentration region above ∼2 M, in addition to the former effect, the excess preferential binding is significantly enhanced by the solvent fluctuation. This scheme should be held as general cosolvent effects of TFE on proteins/peptides.

Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.

Could Microwave Irradiation Cause Misfolding of Peptides?

Microwaves have been experimentally shown to affect the folding dynamics of peptides and proteins. Using molecular dynamics, we performed all-atom simulations of a model β-peptide in aqueous solution where individual degrees of freedom of solvent molecules were decoupled to allow for investigation at non-equilibrium microwave-irradiated conditions. An elevated rotational temperature of the water medium was found to significantly affect the conformation of the peptide due to the weakened hydrogen-bonding interactions with the surrounding solvent molecules. Cluster analysis revealed that microwave irradiation can indeed act as a promoter in the formation of new misfolded peptide structures of the hairpin type, which are generally associated with the onset of several neurodegenerative disorders such as Alzheimer's, Parkinson's, Huntington's, and Creutzfeldt-Jakob diseases as well as certain cancer types such as amyloidosis.

Structural Dynamics of Neighboring Water Molecules of N-Isopropylacrylamide Pentamer

Poly(N-isopropylacrylamide) (PNIPAM) is a popular polymer widely used in smart hydrogel synthesis due to its thermo-responsive behavior in aqueous medium. Aqueous PNIPAM hydrogels can reversibly swell and collapse below and above their lower critical solution temperature (LCST), respectively. The present work used molecular dynamics simulations to explore the behavior of water molecules surrounding the side chains of a NIPAM pentamer in response to temperature changes (273-353 K range) near its experimental LCST (305 K). Results suggest a strong inverse correlation of temperature with water density and hydrophobic hydration character of the first coordination shell around the isopropyl groups. Integrity of the first and second coordination shells is further characterized by polygon ring analysis. Predominant occurrence of pentagons suggests clathrate-like behavior of both shells at lower temperatures. This predominance is eventually overtaken by 4-membered rings as temperature is increased beyond 303 and 293 K for the first and second coordination shells, respectively, losing their clathrate-like property. It is surmised that this temperature-dependent stability of the coordination shells is one of the important factors that controls the reversible swell-collapse mechanism of PNIPAM hydrogels.