Deviation from the Residue-Based Linear Free Energy Relationship Reveals a Non-Native Structure in Protein Folding

Multiprobe measurements, such as NMR and hydrogen exchange study, can provide the equilibrium constant K and kinetic rate constant k of the structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between residue-specific log K values and residue-specific log k values for the two-state topological isomerization of a 27-residue peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific equilibrium and kinetic constants in various exchange processes, including protein folding, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of log-log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Protein molecules quickly fold into their native structures and change their conformations smoothly. Theoretical studies and molecular simulations advocate that the physicochemical basis is the consistency principle and the minimal frustration principle: Non-native structures/interactions are absent or minimized along the folding pathway. The linearity of the residue-based free energy relationship demonstrates experimentally the absence of non-native structures in transition states. In this context, the hydrogen exchange study of apomyoglobin folding intermediates is particularly interesting. We found that the residues that deviated from the linear relationship corresponded to the non-native structure, which had been identified by other experiments. The rbLFER provides a unique and practical method to probe the dynamic aspects of the transition states of protein molecules.

Applicability Domain of Polyparameter Linear Free Energy Relationship Models for Predicting Equilibrium Partition Coefficients

Polyparameter linear free energy relationships (PP-LFERs) are accurate and robust models to predict equilibrium partition coefficients (K) of organic chemicals. The accuracy of predictions by a PP-LEFR depends on the composition of the respective calibration data set. It is generally expected that extrapolation outside the model calibration domain is less accurate than interpolation. In this study, the applicability domain (AD) of PP-LFERs is systematically evaluated by calculation of the leverage (h), a measure of distance from the calibration set in the descriptor space. Repeated simulations with experimental data show that the root mean squared error of predictions increases with h, and that large prediction errors (>3 SDtraining, the standard deviation of training data) occur more frequently when h exceeds the common threshold of 3 hmean, where hmean is the mean h of all training compounds. Nevetheless, analysis also shows that well-calibrated PP-LFERs with many (e.g., 100), diverse, and accurate training data are highly robust against extrapolation; extreme prediction errors (> 5 SDtraining) are rare. For such PP-LFERs, 3 hmean may be too strict as the cutoff for AD. Evaluation of published PP-LFERs in terms of their AD using 25 chemically diverse, environmentally relevant chemicals as AD probes indicated that many reported PP-LFERs do not cover organosiloxanes, per- and polyfluorinated alkylsubstances, highly polar chemicals, and/or highly hydrophobic chemicals in their AD. It is concluded that calculation of h is useful to identify model extrapolations as well as the strengths and weaknesses of the trained PP-LFERs.

Deuterium Isotope Effects on Acid-Base Equilibrium of Organic Compounds

Deuterium isotope effects on acid–base equilibrium have been investigated using a combined path integral and free-energy perturbation simulation method. To understand the origin of the linear free-energy relationship of ΔpKa=pKaD2O−pKaH2O versus pKaH2O, we examined two theoretical models for computing the deuterium isotope effects. In Model 1, only the intrinsic isotope exchange effect of the acid itself in water was included by replacing the titratable protons with deuterons. Here, the dominant contribution is due to the difference in zero-point energy between the two isotopologues. In Model 2, the medium isotope effects are considered, in which the free energy change as a result of replacing H2O by D2O in solute–solvent hydrogen-bonding complexes is determined. Although the average ΔpKa change from Model 1 was found to be in reasonable agreement with the experimental average result, the pKaH2O dependence of the solvent isotope effects is absent. A linear free-energy relationship is obtained by including the medium effect in Model 2, and the main factor is due to solvent isotope effects in the anion–water complexes. The present study highlights the significant roles of both the intrinsic isotope exchange effect and the medium solvent isotope effect.

Reactivity-Selectivity Principle: Phenyl Group in Indazole Makes It More Lucid

Linear free energy relationship (LFER) plots are constructed for the deprotonation equilibriums (pKaH+) of pyrazolium and indazolium (benzopyrazolium) cations. The reaction constants Taft * and Hammett  are found to be 2.75 and 1.32 for deprotonation (pKaH+) of pyrazolium and indazolium cations respectively. Higher value of Taft * than the Hammett  is explained in terms of extra stability of the indazolium cation due to its greater number of resonance structures. This article is an exercise to undergraduate students for writing different resonance structures of indazolium cation.

Application of Linear Free Energy Relationships (LFER) to pKaH+ of Benzimidazolium Cations: Chemical Education Perspective

Application of Linear Free Energy Relationships (LFER) to pKaH+ data in water at 25o C of deprotonation of protonated fused ring systems like benzimidazolium cations is carried out in the present work. With a good comparison of the sites of substituents with reference to a functional group in benzene ring and the imidazolium ring, an excellent Hammett correlation is observed for the deprotonation of (pKaH+) of protonated fused ring systems like benzimidazolium cations. For the three substituents OH, MeO and Me at position 4 in the benzimidazole satisfy the correlation with I values. A positive Hammet  values of 1.93 indicates that electron withdrawing substituents facilitate the deprotonation. Under the same conditions a Taft * value of 1.11 is obtained for the deprotonation of 2-substituted-benzimidazolium cations. The available pKaH+ data in 5% aq. ethanol at 30o C of 2-methyl benzimidazolium cations and 2-(hydroxyethyl) benzimidazolium cations also followed Hammett correlation. The lower Hammett  value of 0.89 for 2-(hydroxyethyl) benzimidazolium cation series than that of 1.78 of 2-methyl benzimidazolium cation series is explained in terms of strong intramolecular hydrogen bonding in 2-(hydroxyethyl) benzimidazolium cation which resists the easy deprotonation. Deprotonation of 1-substituted-benzimidazolium cations did not follow Hammett relation.

The Essential Functional Interplay of the Catalytic Groups in Acid Phosphatase

Cooperative interplay between the functional devices of a preorganized active site is fundamental to enzyme catalysis. A deepened understanding of this phenomenon is central to elucidating the remarkable efficiency of natural enzymes, and provides an essential benchmark for enzyme design and engineering. Here, we study the functional interconnectedness of the catalytic nucleophile (His18) in an acid phosphatase by analyzing the consequences of its replacement with aspartate. We present crystallographic, biochemical and computational evidence for a conserved mechanistic pathway via a phospho-enzyme intermediate on Asp18. Linear free-energy relationships for phosphoryl transfer from phosphomonoester substrates to His18/Asp18 provide evidence for cooperative interplay between the nucleophilic and general-acid catalytic groups in the wildtype enzyme, and its substantial loss in the H18D variant. As an isolated factor of phosphatase efficiency, the advantage of a histidine compared to an aspartate nucleophile is around 10^4-fold. Cooperativity with the catalytic acid adds ≥10^2-fold to that advantage. Empirical valence bond simulations of phosphoryl transfer from glucose 1-phosphate to His and Asp in the enzyme explain the loss of activity of the Asp18 enzyme through a combination of impaired substrate positioning in the Michaelis complex, as well as a shift from early to late protonation of the leaving group in the H18D variant. The evidence presented furthermore suggests that the cooperative nature of catalysis distinguishes the enzymatic reaction from the corresponding reaction in solution and is enabled by the electrostatic preorganization of the active site. Our results reveal sophisticated discrimination in multifunctional catalysis of a highly proficient phosphatase active site.

Reconciling Imbalanced Transition State Effects with Nonadiabatic CPET Reactions

Recently there have been several experimental demonstrations of how concerted proton electron transfer (CPET) reaction rates are affected by off-main-diagonal energies, namely the stepwise thermodynamic parameters ΔG°PT and ΔG°ET. Semi-classical structure-activity relationships have been invoked to rationalize these asynchronous linear free energy relation-ships despite the widely acknowledged importance of quantum effects such as nonadiabaticity and tunneling in CPET reactions. Here we report variable temperature kinetic isotope effect data for the asynchronous reactivity of a terminal Co-oxo complex with C–H bonds and find evidence of substantial quantum tunneling which is inconsistent with semi-classical models even when including tunneling corrections. This indicates substantial nonadiabatic tunneling in the CPET reactivity of this Co-oxo complex and further motivates the need for a quantum mechanical justification for the in-fluence of ΔG°PT and ΔG°ET on reactivity. To reconcile this dichotomy, we include ΔG°PT and ΔG°ET in nonadiabatic models of CPET by having them influence the anharmonicity and depth of the proton potential energy surfaces, which we approximate as Morse potentials. With this model we independently reproduce the dominant trend with ΔG°PT + ΔG°ET as well as the subtle effect of ΔG°PT − ΔG°ET (or η) in a nonadiabatic framework. The primary route through which these off-diagonal energies influence rates is through vibronic coupling. Our results reconcile predictions from semiclassical transition state theory with models that treat proton transfer quantum mechanically in CPET reactivity and suggest that similar treatments may be possible for other nonadiabatic processes.