scholarly journals Visual Interpretation of the Meaning of kcat/KM in Enzyme Kinetics

2021 ◽  
Author(s):  
Chiwook Park
Keyword(s):  
Transition State ◽  
Enzyme Kinetics ◽  
Rate Constant ◽  
Reaction Rate ◽  
Reaction Pathway ◽  
Order Rate Constant ◽  
Reaction Energy ◽  
Energy Diagram ◽  
Order Rate ◽  
Main Challenge

kcat and kcat/KM are the two fundamental kinetic parameters in enzyme kinetics. kcat is the first-order rate constant that determines the reaction rate when the enzyme is fully occupied at a saturating concentration of the substrate. kcat/KM is the second-order rate constant that determines the reaction rate when the enzyme is mostly free at a very low concentration of the substrate. Both parameters provide critical information on how the enzyme lowers the energy barriers along the reaction pathway for catalysis. However, it is surprising how often kcat/KM is used inappropriately as a composite parameter derived by dividing kcat with KM to assess both catalytic power and affinity to the substrate of the enzyme. The main challenge in explaining the true meaning of kcat/KM is the difficulty to demonstrate how the reaction energetics of enzyme catalysis determines kcat/KM in a simple way. Here, I report a step-by-step demonstration on how to visualize the meaning of kcat/KM on the reaction energy diagram. By using the reciprocal form of the expression of kcat/KM with the elementary rate constants in kinetic models, I show that kcat/KM is a harmonic sum of several kinetic terms that correspond to the heights of the transition states relative to the free enzyme. Then, I demonstrate that the height of the highest transition state has the dominant influence on kcat/KM, i. e. the step with the highest transition state is the limiting step for kcat/KM. The visualization of the meaning of kcat/KM on the reaction energy diagram offers an intuitive way to understand all the known properties of kcat/KM, including the Haldane relationship.

scholarly journals Determination of the Mechanism of Nucleophilic Reaction of Fenitrothion Using Substituted Phenoxide Nucleophiles in Aqueous Media

2021 ◽  
pp. 40-46
Author(s):  
E. G. Amadi ◽  
C. I. Egwuatu ◽  
C. U. Okoro ◽  
F. O. Obumselu ◽  
M. U. Onuoha
Keyword(s):  
Transition State ◽  
Rate Constant ◽  
Aqueous Media ◽  
Order Rate Constant ◽  
Second Order ◽  
Bond Rupture ◽  
Linear Free Energy Relationship ◽  
Order Rate ◽  
Linear Free Energy ◽  
Nucleophilic Displacement

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.

scholarly journals Kinetic studies of the reduction of neutrophil cytochrome b-558 by dithionite

1986 ◽  
Vol 237 (2) ◽  
pp. 567-572 ◽  
Author(s):  
I Aviram ◽  
M Sharabani
Keyword(s):  
Cytochrome B ◽  
Rate Constant ◽  
Reaction Rate ◽  
Kinetic Studies ◽  
Order Rate Constant ◽  
First Order ◽  
Order Rate ◽  
Ionic Detergent ◽  
Activated Neutrophils ◽  
Membrane Bound

The reduction with dithionite of neutrophil cytochrome b-558, implicated in superoxide generation by activated neutrophils, was investigated by a stopped-flow technique in non-ionic-detergent extracts of the membranes and in crude membrane particles. The dependence of the pseudo-first-order rate constants on the concentration of dithionite was consistent with a mechanism of reduction that involves the dithionite anion monomer SO2.- as the reactive species. The estimated second-order rate constant was 7.8 × 10(6) M-1 × S-1 for Lubrol PX-solubilized cytochrome b-558 and 5.1 × 10(6) M-1 × S-1 for the membrane-bound protein. The similarity of the kinetic constants suggests that solubilization did not introduce gross changes in the reactive site. Imidazole and p-chloromercuribenzoate, known as inhibitors of NADPH oxidase, did not affect significantly cytochrome b-558 reduction rates. The reaction rate of cytochrome b-558 with dithionite exhibited a near-zero activation energy. The first-order rate constant for reduction decreased with increasing ionic strength, indicating a positive effective charge on the reacting protein.

scholarly journals The reactivities and ionization properties of the active-site dithiol groups of mammalian protein disulphide-isomerase

1991 ◽  
Vol 275 (2) ◽  
pp. 335-339 ◽  
Author(s):  
H C Hawkins ◽  
R B Freedman
Keyword(s):  
Rate Constant ◽  
Ph Dependence ◽  
Order Rate Constant ◽  
Second Order ◽  
Native Enzyme ◽  
Liver Protein ◽  
Thiol Groups ◽  
Protein Disulphide Isomerase ◽  
Order Rate ◽  
Reactive Groups

1. The number of reactive thiol groups in mammalian liver protein disulphide-isomerase (PDI) in various conditions was investigated by alkylation with iodo[14C]acetate. 2. Both the native enzyme, as isolated, and the urea-denatured enzyme contained negligible reactive thiol groups; the enzyme reduced with dithiothreitol contained two groups reactive towards iodoacetic acid at pH 7.5, and up to five reactive groups were detectable in the reduced denatured enzyme. 3. Modification of the two reactive groups in the reduced native enzyme led to complete inactivation, and the relationship between the loss of activity and the extent of modification was approximately linear. 4. Inactivation of PDI by alkylation of the reduced enzyme followed pseudo-first-order kinetics; a plot of the pH-dependence of the second-order rate constant for inactivation indicated that the essential reactive groups had a pK of 6.7 and a limiting second-order rate constant at high pH of 11 M-1.s-1. 5. Since sequence data on PDI show the presence within the polypeptide of two regions closely similar to thioredoxin, the data strongly indicate that these regions are chemically and functionally equivalent to thioredoxin. 6. The activity of PDI in thiol/disulphide interchange derives from the presence of vicinal dithiol groups in which one thiol group of each pair has an unusually low pK and high nucleophilic reactivity at physiological pH.

The Dephosphorylation of Adenosine 5′ -Triphosphate in a Binary and Ternary Zn2+ Complex

1974 ◽  
Vol 29 (11-12) ◽  
pp. 680-682 ◽  
Author(s):  
Peter Amsler ◽  
David Buisson ◽  
Helmut Sigel
Keyword(s):  
Rate Constant ◽  
Ternary Complex ◽  
Order Rate Constant ◽  
Reactive Species ◽  
Ph Optimum ◽  
First Order ◽  
Order Rate

The dephosphorylation of ATP was characterized by determining the dependence of the first-order rate constant on pH in the absence and presence of Zn2+ and together with Zn2+ and 2,2′-bipyridyl. The Zn2+-accelerated reaction passes through a pH optimum at about 8. The decrease in the rate at higher pH is due to the formation of Zn(ATP) (OH)3-; this species is relatively insensitive towards dephosphorylation. It is concluded that Zn(ATP)2- is the reactive species and that the interaction between N (7) and Zn2+ in this complex is crucial for its reactivity. In the presence of 2,2′-bipyridyl (Bipy) the ternary complex, Zn (Bipy) (ATP)2-, is formed which is rather stable towards dephosphorylation. It is suggested that the described effects of acceleration and inhibition are helpful for understanding the recycled processes in nature.

Kinetics of reconstitution of apotyrosinase by copper

1990 ◽  
Vol 68 (2) ◽  
pp. 476-479
Author(s):  
Donald C. Wigfield ◽  
Douglas M. Goltz
Keyword(s):  
Rate Constant ◽  
Copper Concentration ◽  
Copper Ions ◽  
Copper Ion ◽  
Order Rate Constant ◽  
First Order ◽  
Order Rate ◽  
Pseudo First Order ◽  
Rate Limiting ◽  
Kinetics Of

The kinetics of the reconstitution reaction of apotyrosinase with copper (II) ions are reported. The reaction is pseudo first order with respect to apoenzyme and the values of these pseudo first order rate constants are reported as a function of copper (II) concentration. Two copper ions bind to apoenzyme, and if the second one is rate limiting, the kinetically relevant copper concentration is the copper originally added minus the amount used in binding the first copper ion to enzyme. This modified copper concentration is linearly related to the magnitude of the pseudo first order rate constant, up to a copper concentration of 1.25 × 10−4 M (10-fold excess), giving a second order rate constant of 7.67 × 102 ± 0.93 × 102 M−1∙s−1.Key words: apotyrosinase, copper, tyrosinase.

DFP (Dilsopropylfluorophosphate) Studies on Molecular Mechanisms of Surface-Dependent Activation of Prekallikrein(PK) and Factor XII(Hageman Factor, HF)

1979 ◽  
Author(s):  
J.H. Griffin ◽  
G. Beretta
Keyword(s):  
Enzymatic Activity ◽  
Rate Constant ◽  
Active Sites ◽  
Molecular Mechanisms ◽  
Order Rate Constant ◽  
Factor Xii ◽  
Single Chain ◽  
Hageman Factor ◽  
Order Rate ◽  
Coagulant Activity

Previous 3H-DFP studies showed that HF binding to kaolin does not result in formation of new active sites. New studies show that single chain zymogen HF, in solution or surface bound, reacts slowly with DFP causing loss of coagulant activity and uptake of 1 mol DIP/mol HF with a 2nd order rate constant, k2=0.4 M-1 min-1. High MW kininogen (HMWK) did not affect the rate constant for this reaction. PK reacts with DFP causing loss of coagulant activity with k2=0.6 M-1min-1. These values are ~103lower than for the activated enzymes (160 and 500 M-1 min-1 for HFa and kallikrein respectively) and are similar to values for trypsinogen that exhibits weak enzymatic activity. HF, PK, HMWK, and kaolin were separately preincubated with 40mM DFP for 5 min to inhibit traces of active enzymes. Then, mixing of these reagents in the presence of 40mM DFP caused a burst of cleavage of 131I-HF and 125I-PK, the extent of which depended on the amount of HMWK. To avoid reciprocal proteolysis of HF and PK, “killed” zymogens (DIP-HF or DIP-PK formed by 48 hr incubation with 40mM DFP) were used in place of HF or PK. Controls showed that PK and DIP-PK were similarly cleaved by purified HFa. If DIP-131I-HF or DIP-125I-PK was substituted for HF or PK in mixtures of HF, PK, HMWK, and kaolin, no detectable cleavage occurred. These data allow that inherent activity of single chain forms of HF or PK may trigger-surface dependent reactions, but the vast majority of molecules are activated by reciprocal proteolysis between HF and PK with HMWK as a cofactor.

The mechanisms of hydrolysis of alkyl N-alkylthioncarbamate esters at 100 °C

2005 ◽  
Vol 83 (9) ◽  
pp. 1483-1491 ◽  
Author(s):  
Eduardo Humeres ◽  
Maria de Nazaré M. Sanchez ◽  
Conceição ML Lobato ◽  
Nito A Debacher ◽  
Eduardo P. de Souza
Keyword(s):  
Rate Constant ◽  
Order Rate Constant ◽  
Base Catalysis ◽  
Hydrolysis Rate ◽  
Negative Slope ◽  
General Base ◽  
Order Rate ◽  
Basic Hydrolysis ◽  
Rate Profile ◽  
Hydrolysis Of

The hydrolysis of ethyl N-ethylthioncarbamate (ETE) at 100 °C was studied in the range of 7 mol/L HCl to 4 mol/L NaOH. The pH–rate profile showed that the hydrolysis occurred through specific acid catalysis at pH < 2, spontaneous hydrolysis at pH 2–6.5, and specific basic catalysis at pH > 6.5. The Hammett acidity plot and the excess acidity plot against X were linear. The Bunnett–Olsen plot gave a negative slope indicating that the conjugate acid was less hydrated than the neutral substrate. It was concluded that the acid hydrolysis occurred by an A1 mechanism. The neutral species hydrolyzed with general base catalysis shown by the Brønsted plot with β = 0.48 ± 0.04. Water acted as a general base catalyst with (pseudo-)first-order rate constant, kN = 3.06 × 10–7 s–1. At pH > 6.5 the rate constants increased, reaching a plateau at high basicity. The basic hydrolysis rate constant of ethyl N,N-diethylthioncarbamate, which must react by a BAc2 mechanism, increased linearly at 1–3 mol/L NaOH with a second-order rate constant, k2 = 2.3 × 10–4 (mol/L)–1 s–1, which was 10 times slower than that expected for ETE. Experiments of ETE in 0.6 mol/L NaOH with an excess of ethylamine led to the formation of diethyl thiourea, presenting strong evidence that the basic hydrolysis occurred by the E1cb mechanism. In the rate-determining step, the E1cb mechanism involved the elimination of ethoxide ion from the thioncarbamate anion, producing an isothiocyanate intermediate that decomposed rapidly to form ethylamine, ethanol, and COS.Key words: alkylthioncarbamate esters, ethyl N-ethylthioncarbamate, ethyl N,N-diethylthioncarbamate, hydrolysis, mechanism.

scholarly journals Inactivation of the endogenous argininosuccinate lyase activity of duck δ-crystallin by modification of an essential histidine residue with diethyl pyrocarbonate

1993 ◽  
Vol 293 (2) ◽  
pp. 537-544 ◽  
Author(s):  
H J Lee ◽  
S H Chiou ◽  
G G Chang
Keyword(s):  
Enzyme Activity ◽  
Rate Constant ◽  
Order Rate Constant ◽  
Histidine Residue ◽  
Argininosuccinate Lyase ◽  
First Order ◽  
Diethyl Pyrocarbonate ◽  
Order Rate ◽  
Lyase Activity ◽  
Pseudo First Order

The argininosuccinate lyase activity of duck delta-crystallin was inactivated by diethyl pyrocarbonate at 0 degrees C and pH 7.5. The inactivation followed pseudo-first-order kinetics after appropriate correction for the decomposition of the reagent during the modification period. The plot of the observed pseudo-first-order rate constant versus diethyl pyrocarbonate concentration in the range of 0.17-1.7 mM was linear and went through the origin with a second-order rate constant of 1.45 +/- 0.1 M-1.s-1. The double-logarithmic plot was also linear, with slope of 1.13, which suggested a 1:1 stoichiometry for the reaction between diethyl pyrocarbonate and delta-crystallin. L-Arginine, L-norvaline or L-citrulline protected the argininosuccinate lyase activity of delta-crystallin from diethyl pyrocarbonate inactivation. The dissociation constants for the delta-crystallin-L-arginine and delta-crystallin-L-citrulline binary complexes, determined by the protection experiments, were 4.2 +/- 0.2 and 0.12 +/- 0.04 mM respectively. Fumarate alone had no protective effect. However, fumarate plus L-arginine gave synergistic protection with a ligand binding interacting factor of 0.12 +/- 0.02. The double-protection data conformed to a random Uni Bi kinetic mechanism. Fluorescence-quenching studies indicated that the modified delta-crystallin had minimum, if any, conformational changes as compared with the native delta-crystallin. Inactivation of the enzyme activity was accompanied by an increasing absorbance at 240 nm of the protein. The absorption near 280 nm did not change. Treatment of the modified protein with hydroxylamine regenerated the enzyme activity to the original level. These results strongly indicated the modification of an essential histidine residue. Calculation from the 240 nm absorption changes indicated that only one histidine residue per subunit was modified by the reagent. This super-active histidine residue has a pKa value of approximately 6.8 and acts as a general acid-base catalyst in the enzyme reaction mechanism. Our experimental data are compatible with an E1cB mechanism [Raushel (1984) Arch. Biochem. Biophys. 232, 520-525] for the argininosuccinate lyase with the essential histidine residue close to the arginine-binding domain of delta-crystallin. L-Citrulline, after binding to this domain, might form an extra hydrogen bond with the essential histidine residue.

scholarly journals The interplay of electrostatic fields and binding interactions determining catalytic-site reactivity in actinidin. A possible origin of differences in the behaviour of actinidin and papain

1989 ◽  
Vol 259 (2) ◽  
pp. 443-452 ◽  
Author(s):  
D Kowlessur ◽  
M O'Driscoll ◽  
C M Topham ◽  
W Templeton ◽  
E W Thomas ◽  
...  
Keyword(s):  
Hydrogen Bonding ◽  
Ligand Binding ◽  
Transition State ◽  
Rate Constant ◽  
Ph Dependence ◽  
Order Rate Constant ◽  
Catalytic Site ◽  
Binding Interactions ◽  
Electrostatic Fields ◽  
Transition State Geometry

1. The pH-dependence of the second-order rate constant (k) for the reaction of actinidin (EC 3.4.22.14) with 2-(N'-acetyl-L-phenylalanylamino)ethyl 2'-pyridyl disulphide was determined and the contributions to k of various hydronic states were evaluated. 2. The data were used to assess the consequences for transition-state geometry of providing P2/S2 hydrophobic contacts in addition to hydrogen-bonding opportunities in the S1-S2 intersubsite region. 3. The P2/S2 contacts (a) substantially improve enzyme-ligand binding, (b) greatly enhance the contribution to reactivity of the hydronic state bounded by pKa 3 (the pKa characteristic of the formation of catalytic-site-S-/-ImH+ state) and pKa 5 (a relatively minor contributor in reactions that lack the P2/S2 contacts), such that the major rate optimum occurs at pH 4 instead of at pH 2.8-2.9, and (c) reveal the kinetic influence of a pKa approx. 6.3 not hitherto observed in reactions of actinidin. 4. Possibilities for the interplay of electrostatic effects and binding interactions in both actinidin and papain (EC 3.4.22.2) are discussed.

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