Nonlinear Free Energy Relationship Research Articles

Leaving Group Ability Observably Affects Transition State Structure in a Single Enzyme Active Site.

A reaction's transition state (TS) structure plays a critical role in determining reactivity and has important implications for the design of catalysts, drugs, and other applications. Here, we explore TS structure in the enzyme alkaline phosphatase using hybrid Quantum Mechanics/Molecular Mechanics simulations. We find that minor perturbations to the substrate have major effects on TS structure and the way the enzyme stabilizes the TS. Substrates with good leaving groups (LGs) have little cleavage of the phosphorus-LG bond at the TS, while substrates with poor LGs have substantial cleavage of that bond. The results predict nonlinear free energy relationships for a single rate-determining step, and substantial differences in kinetic isotope effects for different substrates; both trends were observed in previous experimental studies, although the original interpretations differed from the present model. Moreover, due to different degrees of phosphorus-LG bond cleavage at the TS for different substrates, the LG is stabilized by different interactions at the TS: while a poor LG is directly stabilized by an active site zinc ion, a good LG is mainly stabilized by active site water molecules. Our results demonstrate the considerable plasticity of TS structure and stabilization in enzymes. Furthermore, perturbations to reactivity that probe TS structure experimentally (i.e., substituent effects) may substantially perturb the TS they aim to probe, and thus classical experimental approaches such as free energy relations should be interpreted with care.

Investigation of Solvent Effects on the Reaction of 1-Fluoro-2,4-Dinitrobenzene with Aniline in Molecular-Molecular and Ionic Liquid–Molecular Solvent Mixtures

The solvent effects on the reaction of 1-fluoro-2,4-dinitrobenzene with aniline was studied in various compositions of molecular-molecular solvent mixtures and molecular solvent-2-hydroxyethylammonium formate mixtures as media containing an ionic liquid. A mounting trend with the mole fraction of water in aqueous solution of alcohols up to a maximum at a mole fraction of 0.9 with respect to water was found, but a mild decrease with the mole fraction of ethyl acetate in methanol–ethyl acetate mixtures. A similar increasing trend was observed with increasing methanol, ethanol, 2-propanol and dimethylsulfoxide content in the mixtures containing the ionic liquid. Solvent effect investigations based on linear free energy relationship confirm that polarity has a major effect in molecular-molecular solvent mixtures, whereas polarity and hydrogen–bond acceptor ability were the dominant factors on reaction rate in molecular-ionic solvent mixtures. A nonlinear free energy relationship based on the preferential solvation hypothesis showed differences between the microsphere solvation of the solute and the bulk composition of the solvents. In these mixtures, the intermediate of the reaction was preferentially solvated by the ionic liquid.

Nonlinear Taft Polar Free Energy Relationship: Reactions of N‐Substituted Benzyl Amines with Benzyl Bromide in Methanol

ABSTRACTThe rates of reactions of N‐substituted benzyl amines with benzyl bromide were measured using a conductivity technique in methanol medium. The reaction followed a total second‐order path. The end product of the reaction is identified as dibenzyl alkyl amine (C6H5CH2N(R)CH2C6H5). The rates increased with a decrease in the electron‐donating capacity or with an increase in the Taft σ* value of electron‐donating alkyl substituents (R) such as t‐butyl (σ* = −0.3), i‐propyl (σ* = −0.19), n‐butyl (σ* = −0.13), and ethyl (σ* = −0.1) on nitrogen of the amine until the Taft σ* value becomes zero for the methyl group ( = 0.00), and then the rates decreased with an increase in the electron‐withdrawing capacity or with an increase in the Taft σ* value of electron‐withdrawing substituents (R) such H and C6H5 ( = 0.49 and = 0.6). The locus of the Taft polar free energy relationship has a maximum near the point for N‐methyl benzyl amine, showing that there is a sharp change in the rate‐determining step. A mechanism involving formation of an SN2‐type transition state between the amine nucleophiles and the benzyl bromide and its subsequent decomposition is proposed. Activation parameters were calculated and are discussed.

Linear and nonlinear free energy relationships in nucleophilic substitution reaction of 2‐bromo‐5‐nitrothiophene with morpholine

AbstractThe reaction of 2‐bromo‐5‐nitrothiophene with morpholine was studied as an aromatic nucleophilic substitution reaction in various compositions of methanol with ethyl acetate and aqueous solution of methanol, ethanol, and propane‐2‐ol at 25°C. The second‐order rate coefficients of the reaction were spectrophotometerically determined. It was shown that a mounting trend with the mole fraction of water in aqueous solution of alcohols and a mild decreasing with the mole fraction of ethyl acetate in methanol–ethyl acetate mixtures. Solvent effect investigations based on linear free energy relationship (LFER) confirm that polarity has a major effect, whereas the hydrogen‐bond donor and acceptor abilities of the media have a minor effect on the reaction rate. A nonlinear free energy relationship based on preferential solvation hypothesis showed differences between the microsphere solvation of the solute and the bulk composition of the solvents, and nonideal behavior was observed in the trend of rate coefficients, which was consistent with LFER results. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 59–67, 2013

Reaction kinetics investigation of 1‐fluoro‐2,4‐dinitrobenzene with substituted anilines in ethyl acetate–methanol mixtures using linear and nonlinear free energy relationships

Aromatic nucleophilic substitution reaction of 1‐fluoro‐2,4‐dinitrobenzene with para‐substituted and meta‐substituted anilines was kinetically investigated in the mixtures of ethyl acetate and methanol at room temperature. The correlation of second‐order rate coefficients with Hammett's substituent constants yields a fairly linear straight line with negative slope in different mole fractions of ethyl acetate–methanol mixtures. The measured rate coefficients of the reaction demonstrated a dramatic variation in ethyl acetate–methanol mixtures with the increasing mole fraction of ethyl acetate. Linear free energy relationship (LFER) investigations confirm that polarity has a major effect on the reaction rate whereas the hydrogen‐bonding ability of the media has a slight effect on it. Nonlinear free energy relationship based on preferential solvation hypothesis showed differences between the microsphere solvation of the solute and the bulk composition of the solvents, and non‐ideal behavior is observed in the trend of the rate coefficients, which cover the LFER results. Copyright © 2011 John Wiley & Sons, Ltd.

Activation of Aldehydic Carbon−Hydrogen Bonds under Aerobic Conditions by Masked Rhodium(III) Porphyrin Cation

RhIII(ttp)CH2CH2OH activated the aldehydic carbon−hydrogen bonds of functionalized aryl and enolizable aldehydes to give high yields of Rh(ttp)COR at 50 °C under both anaerobic and aerobic conditions. The Rh(ttp)(C2H4)OH intermediate was proposed to form via β-hydroxy elimination. The reactions exhibited rate and yield enhancement upon the addition of Ph3P, suggesting ligand-promoted β-elimination. The nonlinear free energy relationship of the Hammett plot suggested a multistepwise reaction with the rate-determining step (binding or activation) dependent on the electronic effect of para substituents of aryl aldehydes.

Establishing the entatic state in folding metallated Pseudomonas aeruginosa azurin

Understanding how the folding of proteins establishes their functional characteristics at the molecular level challenges both theorists and experimentalists. The simplest test beds for confronting this issue are provided by electron transfer proteins. The environment provided by the folded protein to the cofactor tunes the metal's electron transport capabilities as envisioned in the entatic hypothesis. To see how the entatic state is achieved one must study how the folding landscape affects and in turn is affected by the metal. Here, we develop a coarse-grained functional to explicitly model how the coordination of the metal (which results in a so-called entatic or rack-induced state) modifies the folding of the metallated Pseudomonas aeruginosa azurin. Our free-energy functional-based approach directly yields the proper nonlinear extra-thermodynamic free energy relationships for the kinetics of folding the wild type and several point-mutated variants of the metallated protein. The results agree quite well with corresponding laboratory experiments. Moreover, our modified free-energy functional provides a sufficient level of detail to explicitly model how the geometric entatic state of the metal modifies the dynamic folding nucleus of azurin.

Multiple Substitution Effects and Three-Dimensional Nonlinear Free-Energy Relationships in the Electrochemical Reduction of the N,N‘-Dibenzyl Viologen and the 4-Benzoyl-N-benzylpyridinium Cation

The simultaneous effect of two substituents on the redox potentials, E1/2's, of N,N‘-di(p-substituted benzyl)viologens (1-X,Y) and of 4-(p-substituted benzoyl)-N-(p-substituted benzyl) pyridinium cations (2-X,Y), was investigated in terms of the substituent constants, σp-Xand σp-Y. Systems 1-X,Y and 2-X,Y were chosen because they both undergo successive outer sphere one electron (1-e) reductions, and therefore there is no ambiguity regarding the mechanism or the rate-determining step. Substituents (X and Y) were chosen among the −NO2, −Br, and −OCH3 groups in six different combinations for 1-X,Y's and nine different ones for 2-X,Y's. Response surfaces are essentially three-dimensional Hammett plots. Statistical analysis according to a quadratic model derived from the Taylor series expansion of the general extrathermodynamic relationship E1/2 = F(σp-X,σp-Y) that describes the dependence of E1/2's on the substituent constants shows that the substitution effect is not additive. Quite strong nonlinear terms a...

A quantitative model of ultraviolet matrix-assisted laser desorption/ionization including analyte ion generation.

A quantitative model of ionization in ultraviolet matrix-assisted laser desorption/ionization (Knochenmuss, R. J. Mass Spectrom. 2002, 37, 867) is extended to include secondary ion-molecule reactions. Matrix-to-analyte charge-transfer reaction kinetics are described by a hard-sphere Arrhenius expression. The activation energy is derived from the reaction exoergicity using a nonlinear free energy relationship. The approach is applied to the specific case of proton-transfer reactions. With no adjustable parameters, the model correctly predicts the existence and characteristics of the matrix and analyte suppression effects, the shapes of the two-pulse time-delayed yield curves, and the dependence of analyte yields on laser fluence, molecular weight, relative concentrations, and reaction exoergicity.

Evidence for Sequential Barriers and Obligatory Intermediates in Apparent Two-state Protein Folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.

Non-linear rate-equilibrium free energy relationships and Hammond behavior in protein folding

Non-linear rate-equilibrium relationships upon mutation or changes in solvent conditions are frequently observed in protein folding reactions and are usually interpreted in terms of Hammond behavior. Here we first give a general overview over the concept of transition state movements in chemical reactions and discuss its application to protein folding. We then show examples for genuine Hammond behavior and for apparent transition state movements caused by other effects like changes in the rate-limiting step of the folding reaction or ground state effects, i.e. structural changes in either the native state or the unfolded state. These examples show that apparent transition state movements can easily be mistaken for Hammond behavior. We describe experimental tests using self- and cross-interaction parameters to distinguish between structural changes in a single transition state following Hammond behavior and apparent transition state movements caused by other effects.

Nonlinear free energy relationship in the general-acid-catalyzed acylation of rat kidney gamma-glutamyl transpeptidase by a series of gamma-glutamyl anilide substrate analogues.

The gamma-glutamyl transpeptidase (GGT) purified from rat kidney reacts with a series of eight parasubstituted L-glutamyl gamma-anilides, in the presence of Gly-Gly, catalyzing the formation of gamma-Glu-Gly-Gly (pH 8.0, 37 degrees C). The transpeptidation reaction was followed through the discontinuous colorimetric determination of the concentration of released parasubstituted aniline. Steady-state kinetic studies were performed to measure k(cat) and K(M) values for each anilide substrate. A Hammett plot constructed by the correlation of log(k(cat)) and the sigma(-) parameter for each anilide substrate displays statistically significant upward curvature, consistent with a general-acid-catalyzed acylation mechanism in which the geometry of the transition state changes with the nature of the para substituent. Kinetic isotope effects were measured and are consistent with a reaction involving a proton in flight at the rate-limiting transition state. The pH-rate profiles measured over pH 7.0-9.5 are bell-shaped with kinetic pK(a) values that may be attributed to the active site nucleophile (or its general-base catalytic partner) and the active-site general acid. The variation of the latter pK(a) value as a function of temperature is consistent with an enthalpy of ionization expected for an ammonium ion acting as a general acid. Examination of the variation of k(cat) as a function of temperature gave values for the enthalpy and entropy of activation that are similar to those determined for the general-acid-catalyzed breakdown of the tetrahedral intermediate formed during acylation of chymotrypsin by similar amide substrates.

Novel Prediction for the Driving Force and Guest Orientation in the Complexation of α- and β-Cyclodextrin with Benzene Derivatives

Taking the possibility of different inclusion orientations into consideration, a nonlinear free energy relationship model has been established by means of a genetic algorithm for the molecular recognition of α- and β-CD with mono- and 1,4-disubstituted benzenes. The association constants (Ka) for the inclusion complexation of α- and β-cyclodextrin with a number of benzene derivatives were evaluated by the model from the substituent molar refraction Rm, hydrophobic constant π, and Hammett constant σ, which respectively reflect the volume, hydrophobicity, and electronic property of the substituents in the guest compounds. The Ka values calculated by the model are quite close to those determined experimentally. It suggested that the van der Waals force, hydrophobic interactions, and electronic effects comprise the main driving forces for CD molecular recognition. Furthermore, van der Waals force plays a dominant role in α-CD complexation; on the other hand, van der Waals force and hydrophobic interactions play the major roles in β-CD complexation. The model is capable of quantitatively estimating the orientation of guest compounds in CD cavities. The predictions in both driving force and the orientation are in good agreement with the experimental studies.

Nonlinear free energy relationships in Arc repressor unfolding imply the existence of unstable, native-like folding intermediates.

Under strongly denaturing conditions, the logarithm of the rate constant for dissociation/unfolding of the wild-type Arc dimer varies in a nonlinear fashion with denaturant concentration. To assess the unfolding/dissociation behavior under conditions favoring the native structure, we mixed Arc variants labeled with fluorescence acceptor or donor groups and used energy transfer to monitor the increase in heterodimer with time. Under the conditions of this experiment, the rate at which the heterodimer concentration approaches its equilibrium value is determined by rate of dissociation and unfolding of the protein. Using this method and traditional denaturant-jump experiments, rate constants for unfolding/dissociation were determined over a wide range of stabilizing and destabilizing conditions. In each case examined, plots of log(ku) versus denaturant showed significant curvature under strongly denaturing conditions, even though other kinetic experiments indicates that the unfolding/dissociation reactions remain largely two-state. This curvature can be explained most readily by a series of unstable intermediates in the unfolding pathway, with denaturant-induced changes in the kinetic step that is rate-limiting. Alternatively, curvature might result from Hammond behavior in which the structure of the transition state becomes more native-like as the stability of native Arc decreases with increasing denaturant.

Thermodynamic relationships of complex formation: Part I. Non-linear free energy relationships (NLFER) in Ag(I) complex formation in aqueous solutions

The free energy changes for Ag(I) single and mixed ligand complex formation in water solution at T = 25 ° C and ionic strength μ = 1 for KNO 3 has been examined. Ionic charges of both the substratum and ligand in the reaction Sub + L = Sub-L do not play the most prominent role in driving the formation of these complexes in the investigated medium. The mutual substratum-to-ligand chemical affinity depends of course on the nature of the central ion and the ligand but also on the nature of their chemical environment. The already coordinated ligand (ligands) modify the ability of the central ion to form further coordinative bonds in inverse ratio to the overall thermodynamic stability of the substratum. On these bases, the occurrence of Non-Linear Free Energy Relationships are postulated.

Physical properties of oligonucleotides containing phosphoramidate-modified internucleoside linkages

Because of their nuclease resistance and ability to form substrates for RNase H, antisense oligodeoxynucleotides (ODNs) possessing several methoxyethylphosphoramidate linkages at both termini have proven effective at targeting the degradation of specific mRNAs in Xenopus embryos. The efficacy of these compounds subsequently observed in tissue culture focused our attention on the issue of cellular uptake. To investigate the extent to which phosphate backbone modifications may increase the lipophilicity of ODNs, and thereby increase passive uptake by cells, the partitioning of a series of phosphoramidate-modified compounds between aqueous and organic phases was examined. The octanol:water partition coefficient of an unmodified, mixed-sequence 16-mer was 1.75 x 10(-5). The log of the partition coefficient increased in a sigmoidal manner with the number of methoxyethylphosphoramidate internucleoside linkages, indicating a nonlinear free energy relationship. The highest level of partitioning demonstrated was approximately 4 x 10(-3) (a 230-fold increase), attained when 11 of the 15 phosphodiesters were modified. An increase in hydrophobicity was also attained with C8 and C10 alkylamines acting as phase-transfer agents. The melting temperatures of heteroduplexes formed between a phosphoramidate-modified ODN and a complementary unmodified DNA strand decreased by approximately 1.5 degrees C for every phosphate group modification. ODNs can thus be extensively derivatized without substantially compromising duplex formation under physiological conditions.

Linear free energy ortho-correlations in the thiophen series. Part 7. Kinetics of the reaction of some 3-substituted 2-thenoyl chlorides with aniline in benzene

The rate constants for the reactions of some 3-substituted 2-thenoyl chlorides (I; X = OMe, Me, SMe, H, I, Br, SOMe, and SO2Me) with aniline in benzene have been measured. A plot of the logarithm of the rate constants versus the –ΔpKa values of the corresponding acids furnishes an example of a non-linear free energy relationship, indicating the occurrence of different reaction mechanisms for 2-thenoyl chlorides with, respectively, electron-attracting and -repelling substituents at C-3.

ChemInform Abstract: SUBSTITUENT EFFECTS IN CONCERTED REACTIONS. A NONLINEAR FREE‐ENERGY RELATIONSHIP FOR THE 3,3‐SHIFT AND THE DIELS‐ADLER REACTION

Chemischer InformationsdienstVolume 10, Issue 44 Preparative Organic Chemistry ChemInform Abstract: SUBSTITUENT EFFECTS IN CONCERTED REACTIONS. A NONLINEAR FREE-ENERGY RELATIONSHIP FOR THE 3,3-SHIFT AND THE DIELS-ADLER REACTION J. J. GAJEWSKI, J. J. GAJEWSKISearch for more papers by this author J. J. GAJEWSKI, J. J. GAJEWSKISearch for more papers by this author First published: October 30, 1979 https://doi.org/10.1002/chin.197944113AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume10, Issue44October 30, 1979 RelatedInformation

Substituent effects in concerted reactions. A nonlinear free-energy relationship for the 3,3-shift and the Diels-Alder reaction

Substituent effects in concerted reactions. A nonlinear free-energy relationship for the 3,3-shift and the Diels-Alder reaction

The competing mechanisms of substitution, hydrolysis, and cyclization of 1-chloro- and 1,4-dichloro-2,3-diazabuta-1,3-dienes

In aqueous dioxan 1-chloro- and 1,4-dichloro-1,4-diaryl-2,3-diazabuta-1,3-dienes (2) and (3) are smoothly converted to arylidenearenecarbohydrazides (5) and 2,5-diaryl-1,3,4-oxadiazoles (6) respectively. Substituent effects in Ar1(ρ=–2·3) and Ar2(ρ=–1·2) on the rates of hydrolysis have been measured for both series of compounds and indicate a similar slow step in both reactions, viz. unimolecular C–Cl bond cleavage to form a stabilized azocarbonium ion in which there is efficient delocalization of charge towards the remote aryl ring. This is in agreement with the observed variation of rate with solvent (m= 0·97) and the large common ion effect. In acidic solution azomethine bond hydrolysis (with formation of arenecarbaldehyde and substituted benzohydrazide) competes with C–Cl bond cleavage for the monochlorides (2). The dichlorides (3) do not undergo CN bond cleavage under these conditions but an intermediate in the cyclization of (3) to (6)(N-benzoylbenzohydrazonyl chloride) is sufficiently long lived to permit its spectrophotometric detection in acid. In basic solution both series of compounds (2) and (3) undergo SN2 attack by HO– but only if electron-withdrawing substituents are present; otherwise the rate is depressed at high [HO–]. This change-over in mechanism results in markedly non-linear free energy relationships for hydrolysis in this region.