linear free energy relationship
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2022 ◽  
Author(s):  
Daisuke Fujinami ◽  
Seiichiro Hayashi ◽  
Daisuke Kohda

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.


2022 ◽  
Author(s):  
Satoshi Endo

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.


Molecules ◽  
2021 ◽  
Vol 26 (24) ◽  
pp. 7687
Author(s):  
Meiyi Liu ◽  
Jiali Gao

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.


2021 ◽  
Author(s):  
Sanjeev Rachuru ◽  
Jagannadham Vandanapu

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.


2021 ◽  
Vol 9 ◽  
Author(s):  
Deliang Chen ◽  
Xiaoqing Huang ◽  
Yulan Fan

Developing models for predicting molecular properties of organic compounds is imperative for drug development and environmental safety; however, development of such models that have high predictive power and are independent of the compounds used is challenging. To overcome the challenges, we used a thermodynamics-based theoretical derivation to construct models for accurately predicting molecular properties. The free energy change that determines a property equals the sum of the free energy changes (ΔGFs) caused by the factors affecting the property. By developing or selecting molecular descriptors that are directly proportional to ΔGFs, we built a general linear free energy relationship (LFER) for predicting the property with the molecular descriptors as predictive variables. The LFER can be used to construct models for predicting various specific properties from partition coefficients. Validations show that the models constructed according to the LFER have high predictive power and their performance is independent of the compounds used, including the models for the properties having little correlation with partition coefficients. The findings in this study are highly useful for applications in drug development and environmental safety.


Author(s):  
E. G. Amadi ◽  
C. I. Egwuatu ◽  
C. U. Okoro ◽  
F. O. Obumselu ◽  
M. U. Onuoha

The mechanism of the nucleophilic displacement reaction at the phosphorus centre of organophosphates was determined. Phenoxide nucleophiles were reacted with fenitrothion (O,O-dimethyl O-(3-methyl-4-nitrophenyl) phosphorothioate) in water at 25oC and pseudo-first order rate constant measurements taken. Second-order rate constant (kNuc) was determined for the different concentrations of nucleophiles while the second-order rate constant (klg) for the investigation of 2,4-dichlorophenoxide ion with and series of aryl phosphorothioate esters was also determined. Linear free energy relationship was further determined using the Brϕnsted-type plot. The plots are linear over a range of pKaNuc of 7.15-11.10 that straddles the pKa of the leaving 3-methyl-4-nitrophenoxide ion (pKa = 7.20) with statistically acceptable linear correlations (R2 = 0.987) and (R2 = 0.980). The linearity in the traditional Brϕnsted-type plots shows the sensitivity of the nucleophilic displacement to the basicity of the nucleophiles and hence is consistent with a single transition-state mechanism whose barrier to decomposition is low hence concerted. Analysis of the values of βNuc, βLg and βeq (0.734) with the effective charge distribution in the transition state shows that it has no positive character. The Leffler index presents bond formation being slightly ahead of bond rupture.


2021 ◽  
Vol 8 ◽  
Author(s):  
Alyssa Dubrow ◽  
Iktae Kim ◽  
Elias Topo ◽  
Jae-Hyun Cho

Biomolecular recognition often involves conformational changes as a prerequisite for binding (i.e., conformational selection) or concurrently with binding (i.e., induced-fit). Recent advances in structural and kinetic approaches have enabled the detailed characterization of protein motions at atomic resolution. However, to fully understand the role of the conformational dynamics in molecular recognition, studies on the binding transition state are needed. Here, we investigate the binding transition state between nonstructural protein 1 (NS1) of the pandemic 1918 influenza A virus and the human p85β subunit of PI3K. 1918 NS1 binds to p85β via conformational selection. We present the free-energy mapping of the transition and bound states of the 1918 NS1:p85β interaction using linear free energy relationship and ϕ-value analyses. We find that the binding transition state of 1918 NS1 and p85β is structurally similar to the bound state with well-defined binding orientation and hydrophobic interactions. Our finding provides a detailed view of how protein motion contributes to the development of intermolecular interactions along the binding reaction coordinate.


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