Residue-based correlation between equilibrium and rate constants is an experimental formulation of the consistency principle for smooth structural changes of proteins
Oct 2023· bioRxiv· Vol 20, pp. n/a· 1 citation· 59 references
BiologyMedicine
TL;DR
It is proposed that the consistency principle is formulated by the quadratic relationship in the double logarithm plot of the residue-specific equilibrium and rate constants of a polypeptide chain.
Abstract
The consistency principle represents a physicochemical condition requisite for ideal protein folding. It assumes that any pair of amino acid residues in partially folded structures has an attractive short-range interaction only if the two residues are in contact within the native structure. The residue-specific equilibrium constant, K, and the residue-specific rate constant, k (forward and backward), can be determined by NMR and hydrogen-deuterium exchange studies. Linear free energy relationships (LFER) in the rate-equilibrium free energy relationship (REFER) plots (i.e., log k vs. log K) are widely seen in protein-related phenomena, but our REFER plot differs from them in that the data points are derived from one polypeptide chain under a single condition. Here, we examined the theoretical basis of the residue-based LFER. First, we derived a basic equation, ρij = ½(ϕi + ϕj), from the consistency principle, where ρij is the slope of the line segment that connects residues i and j in the REFER plot, and ϕi and ϕj are the local fractions of the native state in the transient state ensemble (TSE). Next, we showed that the general solution is the alignment of the (log K, log k) data points on a parabolic curve in the REFER plot. Importantly, unlike LFER, the quadratic free energy relationship (QFER) is compatible with the heterogenous formation of local structures in the TSE. Residue-based LFER/QFER provides a unique insight into the TSE: A foldable polypeptide chain consists of several folding units, which are consistently coupled to undergo smooth structural changes. Significance The physicochemical basis of smooth protein folding has been theoretically explained by the consistency principle. We propose that the consistency principle is formulated by the quadratic relationship in the double logarithm plot of the residue-specific equilibrium and rate constants of a polypeptide chain. The quadratic relationship offers a procedure for the experimental verification of the consistency principle. One application is a ϕ-value analysis, free from the adverse effects of mutations. These results will trigger the development of experimental techniques that enable the determination of accurate residue-specific equilibrium and kinetic parameters for analyzing the transition states of structural changes in proteins.
Hydration plays an essential role in protein–protein interactions. Coarse-grained modeling provides an efficient way to treat hydrated protein complexes without the use of extra-large computational resources. To enhance the capabilities of coarse-grained modeling, we developed an integral equation theory based on the solution of the Ornstein–Zerinke equation to evaluate the hydration structure of peptides and proteins within the framework of coarse-grained modeling. Our current version is based on the SPICA force field, which considers distance-dependent interaction potentials between solvent particles and amino acid segments. Our approach involves two key procedures: an accurate estimation of the structure factor of the uniform fluid and the specific construction of bridge functions obtained from MD simulations. The use of a special hybrid closure allows us to reproduce not only the details of the structure factor, but also the isothermal compressibility obtained from the simulations. The developed bridge functions include two components: an analytical repulsive contribution, which is primarily responsible for the thermodynamic properties, and an attractive contribution obtained from MD simulations. The main assumption in the construction is that the contribution of individual amino acids to the attractive bridge function is additive. By parameterizing the bridge functions, we reproduced details of the hydration structure and accurately calculated the hydration energy for various peptides and proteins. Our method is computationally inexpensive and appears to be suitable for the rapid processing of hydrated proteins of any size.
G. N. Chuev, T. Mamedov, Dmitry O. Morozov· Biomolecules· 0 citations
The data reveal that both the mechanics and kinetics of peptide detachment are sensitive to the identity and sequence position of individual residues, highlighting the power of integrating CG MD and single-molecule force spectroscopy to unravel residue-specific, sequence-dependent factors underlying peptide–lipid interactions.
Ryan S. Smith, Krishna P Sigdel, D. R. Weaver et al.· Langmuir· 0 citations
An improved force field is developed, derived from its parent, Amber ff24EXP-GA, and its evaluation against Amber ff14SB and other contemporary force fields, such as CHARMM36m, in capturing the empirically determined conformational properties of unfolded systems: short peptides that serve as model systems for IDPs, and longer unfolded proteins.
Gibbs free energy values obtained from quantum-chemical calculations were used to determine the formation constants of homo- and heteroligand copper(II) complexes with various ligands (amino acids, diimines, and phosphorylated dithiocarbamates) in an aqueous medium. A computationally robust, yet moderately expensive, level of theory—B3LYP/def2-TZVPPD—was employed. Solvent effects were accounted for using two models: C-PCM and SMD. A key prerequisite for obtaining reliable results is the use of a reference complex with a known formation constant that is structurally and solvation-wise similar to the compound under study. In this context, “similarity” implies identical stoichiometry, the same coordination number, the same number of water molecules in the inner coordination sphere; matching charges, however, is considerably less critical. The importance of considering conformers and isomers to obtain the most accurate values is demonstrated. The more rigid the structure and the greater the degree of similarity between the studied and reference compounds, the better the agreement between calculated and experimental data; the discrepancy can be as low as 0.1–0.2 logarithmic units. When an appropriate reference is selected, the average deviation of the calculated stability constants is less than 1 logarithmic unit.
N. S. Aksenin, Mikhail S. Bukharov, V. Shtyrlin et al.· Inorganics· 0 citations
Amino acid behavior in water-mediated processes is not well captured by hydrophobicity or side-chain class alone, because residues with similar hydropathy can differ in charge localization, geometry, surface exposure, and hydration response. The objective of this study is to determine whether integrating complementary molecular representations can reveal a chemically interpretable molecular coordinate that organizes amino acid behavior across distinct water-mediated processes. We fused electronic-, structural-, and solvation-level representations into a similarity network and embedded it spectrally to obtain a one-dimensional coordinate, Z F, which captures coupled variation in electrostatics-, geometry-, and hydration-related features. Across gas hydrate formation, ice recrystallization inhibition, and CaCO3 crystallization, Z F provides a consistent residue-level coordinate and captures interaction trends that differ in direction from those described by the Kyte–Doolittle hydropathy scale in the latter two systems.
Yusung Ok, Y. Park· Journal of Chemical Informat...· 0 citations
We present a coarse-grained model that describes the unfolding process and thermodynamics of ribonucleic acid (RNA) molecules. We obtained and analyzed a set of 1944 three-dimensional RNA structures of various molecular weights and under diverse conditions from the Protein Data Bank. We reduced the description of these molecules from an all-atom representation to a single interacting point per nucleotide, located at its center of mass. From this information, we calculated characteristic properties of the RNA chains, such as the bond distribution function and the contour length, which allowed us to estimate the most probable distance between two nucleotides linked by a phosphodiester bond as a = 5.5 ± 0.4 Å. We also calculated the radius of gyration of these chains, through which we obtained an estimate of the Flory exponent, ν = 0.33 ± 0.01, and a fractal dimension, d F = 3.03 ± 0.09. Furthermore, we determined the persistence length to be l p = 9.5 ± 4.1 Å. On the other hand, the different molecular configurations were used to improve the statistics of the pair distribution functions for various degrees of freedom. These were employed to obtain effective interaction potentials in a previous model [Villada-Balbuena, M.; Carbajal-Tinoco, M. D. J. Chem. Phys. 2024, 161, 165104.], which underwent a series of improvements, reducing the number of fitting parameters and enhancing the description of the radial-angular interaction. The fitting parameters of these potentials were optimized through Brownian dynamics (BD) simulations using the iterative Boltzmann inversion algorithm. The optimized potentials were used in steered BD simulations to model the mechanical unfolding at a constant velocity of a series of hairpins and pseudoknots. The results of these simulations are contrasted with experimental data, achieving excellent agreement. During the unfolding process, we monitored the configurational temperature (CT) of the model’s different degrees of freedom as well as the total CT. We used Jarzynski’s equality to calculate the Helmholtz free energy change, ΔA. Through ΔA and the integral of the force–extension curve, we obtained the Gibbs free energy change ΔG, which was successfully compared with the experimental results of RNA molecules unfolding using optical tweezers. Finally, based on the internal energy change values from the simulations, we estimated the entropy change ΔS. These values were compared with entropy changes from theoretical models. Finally, we utilized our model to calculate the changes in the aforementioned thermodynamic functions for molecules associated with viral protein expression.
Mario Villada-Balbuena, M. D. Carbajal-Tinoco· Journal of Chemical Theory a...· 0 citations