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6.2: Enzyme kinetics - Biology

6.2: Enzyme kinetics - Biology


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Enzymes are protein catalysts, they influence the kinetics but not the thermodynamics of a reaction

  • Increase the rate of a chemical reaction
  • Do not alter the equilibrium

Figure 6.2.1: Catalyst activity

  • They increase the rate by stabilizing the transition state (i.e. lowering the energy barrier to forming the transition state (they do not affect the energetics of either the reactant(s) or product(s)

Michaelis-Menten derivation for simple steady-state kinetics

The Michaelis-Menten equation is a mathematical model that is used to analyze simple kinetic data. The model has certain assumptions, and as long as these assumptions are correct, it will accurately model your experimental data. The derivation of the model will highlight these assumptions.

In an enzyme catalyzed reaction the substrate initially forms a reversible complex with the enzyme (i.e. the enzyme and substrate have to interact for the enzyme to be able to perform its catalytic function). The standard expression to show this is the following:

ASSUMPTION #1:

  • There is no product present at the start of the kinetic analysis
  • Therefore, as long as we monitor initial reaction rates we can ignore the reverse reaction of E+P going to ES

ASSUMPTION #2:

  • During the reaction an equilibrium condition is established for the binding and dissociation of the Enzyme and Substrate (Briggs-Haldane assumption)
  • Thus, the rate of formation of the ES complex is equal to the rate of dissociation plus breakdown

ASSUMPTION #3:

  • [E] << [S]
  • The enzyme is a catalyst, it is not destroyed and can be recycled, thus, only small amounts are required
  • The amount of S bound to E at any given moment is small compared to the amount of free S
  • It follows that [ES] << [S] and therefore [S] is constant during the course of the analysis (NOTE: this assumption requires that the reaction is monitored for a short period, so that not much S is consumed and [S] does not effectively change - see next assumption)

ASSUMPTION #4:

  • Only the initial velocity of the reaction is measured
  • [P] = 0 (reverse E + P reaction can be ignored)
  • [S] » [S]initial

ASSUMPTION #5:

  • The enzyme is either present as free enzyme or as the ES complex
  • [E]total = [E] + [ES]

Michaelis-Menten derivation using above assumptions:

Rate of ES formation = k1[E][S] + k-2[E][P]

Assumption #1 says we can ignore the k-2 reaction, therefore:

Rate of ES formation = k1[E][S]

Assumption #5 says [E] = [E]total - [ES], therefore:

Rate of ES formation = k1([E]total - [ES])[S]

The rate of ES breakdown is a combination of the dissociation and the conversion to product:

Rate of ES breakdown = k-1[ES] + k2[ES]

Rate of ES breakdown = (k-1 + k2)[ES]

Assumption #2 says the rate of ES formation equals the rate of breakdown:

k1([E]total - [ES])[S] = (k-1 + k2)[ES]

Rearrange to define in terms of rate constants:

([E]total - [ES])[S] / [ES] = (k-1 + k2) / k1

([E]total [S] / [ES]) - [S] = (k-1 + k2) / k1

Define a new constant, Km = (k-1 + k2) / k1

([E]total [S] / [ES]) - [S] = Km

Solve for the [ES] term (for reasons that will be given in the next step):

[ES] = [E]total [S] / (Km + [S])

The actual reaction velocity measured at any given moment is given by:

V = k2[ES]

Multiple both sides of the above equation by k2:

k2[ES] = k2[E]total [S] / (Km + [S])

thus

V = k2[E]total [S] / (Km + [S])

The maximum possible velocity (Vmax) occurs when all the enzyme molecules are bound with substrate [ES] = [E]total, thus:

Vmax = k2[E]total

Substituting this into the prior expression gives:

V = Vmax [S] / (Km + [S])

This is the mathematical expression that is used to model your experimental kinetic data

It is known as the Michaelis-Menten equation


Experimental approach

The general approach is to add a known concentration of substrate to the enzyme and to determine the initial reaction rate for that concentration of substrate

  • Reaction rates are typically given as moles (or micromole) of product produced per unit of time (sec or min) per mole (or micromole) of enzyme
  • The experiment is repeated for a wide range of substrate concentrations
  • A table of [S] versus V datapoints are collected
  • These datapoints are plotted (V versus S) and should fit a curve that agrees with the Michaelis-Menten equation

The Vmax and Km terms are intrinsic properties of the particular enzyme/substrate combination that you are studying

  • They will be determined from the features of the V versus S plot

Vmax

There are a limited number of enzyme molecules and they can only perform a single reaction at a time. Thus, at high [S] the enzymes can be saturated

  • Under saturating conditions the reaction is going as fast as it can, and additional increases in [S] do not increase the reaction rate.
  • The maximum observable rate is Vmax and the data will asymptote to this value at high [S]
  • At low [S] the reaction rate is generally linearly proportional to the [S] (i.e. at low [S] if you double [S] the V will double)

Km

Km = (k-1 + k2) / k1 = (rate of breakdown of ES)/(rate of formation of ES)

  • Km is similar, but not exactly equal to, a dissociation constant (Kd) for the ES complex
  • If k-1 >> k2, then Km » Kd
  • Due to this similarity to the expression for Kd, a low value of Km is often interpreted as a high affinity of the enzyme for the substrate, and a large value for Km is often interpreted as a weak affinity of the enzyme for the substrate
  • Km has units of molar concentration (just like the units for [S])

There is a mathematical treatment that allows for the determination of Km from the experimental V versus [S] data

  • Consider the situation when the [S] being evaluated results in a value of V that is exactly 1/2 of the maximum reaction velocity:

V = Vmax [S] / (Km + [S])

1/2Vmax = Vmax [S] / (Km + [S])

1/2 = [S] / (Km + [S])

Km + [S] = 2[S]

Km = [S]

Thus, Km equals the substrate concentration that results in exactly one half the maximum possible reaction velocity

Figure 6.2.2: Km

Lineweaver-Burke (the "double reciprocal" plot)

  • The Michaelis-Menten equation can be rearranged by taking the reciprocal, to yield:

  • If X = 1/[S] and Y=1/V then this is a linear equation with a slope of Km/Vmax and a Y intercept of 1/Vmax

Figure 6.2.3: 1/S and1/V

  • Since the plot of 1/[S] versus 1/v data should be a straight line, it is easier to fit a linear function to the data in this form, and Vmax and Km can be readily determined from the plot

Reversible Inhibition

There are two major categories of reversible inhibitors: competitive reversible inhibitors, and noncompetitive reversible inhibitors:

Competitive inhibitors

The inhibitor (I) competes with the substrate (S) for the enzyme active site (also known as the S-binding site). Binding of either of these molecules in the active site is a mutually exclusive event

  • The substrate and inhibitor share a high degree of structural similarity. However, the inhibitor cannot proceed through the reaction to produce product.
  • Increasing the concentration of substrate will outcompete the inhibitor for binding to the enzyme active site
  • A competitive reversible inhibitor can be identified by its characteristic effects upon kinetic data

The expression for the Michaelis-Menten expression in the presence of a reversible competitive inhibitor is:

V = Vmax [S] / (Km(1+[I]/Ki) + [S])

Where Ki is the actual EI complex dissociation constant

The effects of the reversible competitive inhibitor on the kinetics are as follows:

  • If no inhibitor is present (i.e. if [I] = 0) then the equations are the same
  • As inhibitor is added, the effect is to modify the apparent value of Km. In particular, the apparent Km will be increased by a value equal to (1 + [I]/KI). If Km is increased, the reaction velocity v will decrease.
  • Note that as [S] gets very large the value of the denominator is essentially equal to [S] and v @ vmax. Thus, the reaction velocity can be driven to vmax with a high enough substrate concentration

The diagnostic criteria for reversible competitive inhibition is that while the apparent Km is affected by addition of the inhibitor, the value of vmax does not change

Figure 6.2.4: Effect of reversible competitive inhibitor

How is the Lineweaver-Burke double reciprocal plot affected by the presence of a reversible competitive inhibitor?

Figure 6.2.5: Double reciprocal plot with reversible competitive inhibitor

Noncompetitive Inhibitors

Noncompetitive inhibitors react with both E and ES (this is because the noncompetitive inhibitor does not bind at the same site in the enzyme as the substrate)

  • Inhibition cannot be overcome by increasing the concentration of S
  • The effect on kinetics is as if the enzyme were less active (vmax is reduced), but that the affinity for substrate is unaffected (Km remains the same) since the substrate binding site is not occupied by the noncompetitive inhibitor.

Figure 6.2.6: Effect of reversible noncompetitive inhibitor

Figure 6.2.7: Double reciprocal plot with noncompetitive inhibitor


Phosphofructokinase 2

Phosphofructokinase-2 (6-phosphofructo-2-kinase, PFK-2) or fructose bisphosphatase-2 (FBPase-2), is an enzyme indirectly responsible for regulating the rates of glycolysis and gluconeogenesis in cells. It catalyzes formation and degradation of a significant allosteric regulator, fructose-2,6-bisphosphate (Fru-2,6-P2) from substrate fructose-6-phosphate. Fru-2,6-P2 contributes to the rate-determining step of glycolysis as it activates enzyme phosphofructokinase 1 in the glycolysis pathway, and inhibits fructose-1,6-bisphosphatase 1 in gluconeogenesis. [1] Since Fru-2,6-P2 differentially regulates glycolysis and gluconeogenesis, it can act as a key signal to switch between the opposing pathways. [1] Because PFK-2 produces Fru-2,6-P2 in response to hormonal signaling, metabolism can be more sensitively and efficiently controlled to align with the organism's glycolytic needs. [2] This enzyme participates in fructose and mannose metabolism. The enzyme is important in the regulation of hepatic carbohydrate metabolism and is found in greatest quantities in the liver, kidney and heart. In mammals, several genes often encode different isoforms, each of which differs in its tissue distribution and enzymatic activity. [3] The family described here bears a resemblance to the ATP-driven phospho-fructokinases, however, they share little sequence similarity, although a few residues seem key to their interaction with fructose 6-phosphate. [4]

PFK-2 is known as the "bifunctional enzyme" because of its notable structure: though both are located on one protein homodimer, its two domains act as independently functioning enzymes. [5] One terminus serves as a kinase domain (for PFK-2) while the other terminus acts as a phosphatase domain (FBPase-2). [6]

In mammals, genetic mechanisms encode different PFK-2 isoforms to accommodate tissue specific needs. While general function remains the same, isoforms feature slight differences in enzymatic properties and are controlled by different methods of regulation these differences are discussed below. [7]


Papain

Papain may be used to break down tough meat fibers and has been utilized for thousands of years in its native South America. It is sold as a component in powdered meat tenderizer available in most supermarkets. Papain, in the form of a meat tenderizer such as Adolph's, made into a paste with water, is also a home remedy treatment for jellyfish, bee, and wasps stings mosquito bites and possibly stingray wounds, breaking down the protein toxins in the venom. [5]

Gelatin is a protein produced by partial hydrolysis of collagen extracted from the boiled bones, connective tissues, organs and some intestines of animals such as domesticated cattle, pigs, and horses. Gelatin is a solid when cooled, and a liquid when heated. [6]

In this activity you will investigate the action of meat tenderizer, containing the enzyme papain, on gelatin and its ability to "gel." [4]

Materials needed:

Procedure:

The beginning of the procedure is provided below:

  1. Prepare a gelatin solution by heating 1 teaspoon (3.0 g) of gelatin in 100 ml distilled water until dissolved. (Gently mix, do not boil.)
  2. Cool the gelatin solution to room temperature.

Using the prepared gelatin solution and the materials listed above, design an experiment to test the effect of meat tenderizer on the ability of the gelatin to "gel".

Data table

Before beginning design a data table for recording the results.


5.2 Nonlinear least squares regression

With the computational power available today these linearizations are really historical relicts, as we can fit these parameters to our nonlinear model. Nonlinear regression methods essentially sweep through the parameter space, by iteratively changing each parameter and calculating the distance between the model with the current parameter set and the data points. The sum of the squared distance between our model and data is called the residual. The parameter values that minimize the residual are chosen our best fit.

method k_cat ek_cat K_m eK_m
LB 114.836963256884 0.000126942716628018 9.7828737328161 0.15690573532138
EH 113.051061858663 1.09005061012357 9.54408258808163 0.144570335085599
HW 112.685492138659 5.1274104959967e-05 9.48505475242782 0.0008665705020912
NLS 112.186249467533 0.659060143051018 9.40417147589177 0.105901419035103

Bioanalytical Separations

Nektaria Markoglou , Irving W. Wainer , in Handbook of Analytical Separations , 2003

7.2.4 Effect of immobilization on enzyme kinetics

Michaelis–Menten kinetic parameters of immobilized enzymes can be determined using the same general approaches developed for the study of solubilized enzymes. This includes the effect of temperature and pH on enzymatic activity. However some general considerations must be taken into account since immobilization can introduce new difficulties not associated with the free enzyme. Depending upon the method of immobilization and properties of the support, there may be diffusion-related restrictions associated with the immobilized enzyme [ 27 ] and a decrease in enzyme mobility can also affect the mobility of substrates and cofactor.

The mass-transfer of substrates and products influences the reaction system and mass-transfer resistance can arise due to the location of the enzyme in the support or due to the large particle size of the immobilized enzyme. Under these conditions, the immobilized enzyme operates under diffusion-limiting conditions as opposed to reaction-limiting conditions whereby diffusion layers that form around immobilized enzymes govern its catalytic rate [ 28 ]. In this instance, the movement of a substrate from the bulk solution into the unmixed liquid layer surrounding the immobilized enzyme and then through to the active site represents the diffusion layer. A thin diffusion layer in contrast to a thick layer results in limited mass-transfer effects.

These include decreasing the particle size of the support, reduction of the enzyme load, and manipulation of the binding of the enzyme to the support [ 9 ]. However, flow rates appear to be the key parameter. Mass-transfer resistance has been shown to decrease with increased flow-rates and increased stirring [ 29 ]. As such, in the kinetic analysis of immobilized enzymes in flow reactors (IMERs), the investigation of the effect of flow-rate is important in the determination of Km and Vmax of the immobilized enzyme.

The effect of flow-rate on enzymatic activity is illustrated by the changes in the observed enzymatic activity of an immobilized D-glyceraldehyde-3-phosphate dehydrogenase enzyme reactor (GAPDH–IMER) [ 21 ]. GAPDH catalyzes the oxidative phosphorylation of D-glyceraldehyde-3-phosphate (D–GA3P) to produce 1,3-diphosphoglycerate (1,3-DPGA) and the activity of the enzyme can be monitored by following the production of NADH. The effect of flow rate on the production of NADH was determined using flow rates from 0.1 ml/min to 0.8 ml/min, reflecting substrate-enzyme contact times from 8 min. to about 1 min, respectively. The flow rates between 0.1 and 0.4 ml/min produced the greatest amounts of NADH, Fig. 7.3 , which is consistent with a longer reaction time.

Fig. 7.3 . The effect of flow-rate on the observed enzymatic activity of glyceraldehyde-3-phosphate dehydrogenase (GADPH) expressed as the area of the NADH produced during the oxidative phosphorylation of D-glyeraldehyde-3-phosphate.


6.2: Enzyme kinetics - Biology

This page describes the book Fundamentals of Enzyme Kinetics (2nd edition) by Athel Cornish-Bowden, published by Portland Press (1995). This page and the pages linked from it are now obsolete as the 3rd edition is now published. There is no intention to update them in the future.

Publication details

The 2nd edition was published by Portland Press, London, 1995

Reprinted 1999 (with corrections), 2001 and 2002. Corrections made in 1999 to the 1995 printing are listed on another page. They are mostly minor.

What the reviewers have thought.

High competence.

This is a rewritten edition of a respected 1979 contribution to enzyme kinetics. Neither the basic outline nor the high competence has been changed, but there have been additions throughout. ( Analytical Biochemistry)

A readable reference text.

This is a readable reference text both for teachers and researchers, and one which confident undergraduates might also dip into. (Clive Bullock in Education in Chemistry)

A renowned expert.

Cornish-Bowden, a renowned expert in the field of enzyme kinetics, focuses on the purely kinetic behavior of enzymes. (K. Cornely in Choice)

Fondamenti per la comprensione.

Il testo fornisce i fondamenti per la comprensione della cinetica enzimatica, qualunque sia il livello di preparazione del lettore. (N.C. in Scienza e Governo)

A truly excellent book.

Cornish-Bowden’s recently revised Fundamentals of Enzyme Kinetics allows me to offer praise while retaining my self respect, for this is a truly excellent book. I have not compared this book with the previous edition, mainly because my copy of that book was borrowed (permanently) by a person unknown. This is probably an indication of the value of the previous edition. I shall be guarding my copy of the present book more carefully. (Ronald Duggleby in Protein Science)

The best presentation available.

A revised edition of a very good text published in 1979. It gives the best presentation available and is an essential complement to modern texts of biochemistry, which tend to minimize their treatment of enzyme kinetics. (Herbert Gutfreund in Molecular Membrane Biology)

A valuable resource.

The book is a valuable resource for those approaching enzyme kinetics for the first time as well as for those wishing to renew their acquaintance with the subject. (Ariane Marolewski in Journal of Medicinal Chemistry)

Outstanding and up to date.

There are several good books on enzyme kinetics but this one is outstanding and up to date. Every biochemical library should have at least two copies, one for reference and one for borrowing, and I advise anyone teaching enzyme kinetics to get their own copy, it will be 㾾/US$29 well invested. (Michael Selwyn in Biochemical Education)

An almost literary book.

My fear is that . those who need to know them would be too intimidated to pick up a whole book on enzyme kinetics. This would be a pity, since Cornish-Bowden has written an almost literary book on what is probably considered by most biochemists to be the dullest and driest of subjects, albeit one with a history as long as classical physical chemistry. (Michael Silverberg in the Quarterly Review of Biology)

I welcome this volume.

The time that has elapsed before the appearance of this new edition has been, in my view, far too long. I welcome this volume not only because of some of the new material that it contains but also because my copies of the earlier versions have long since vanished on permanent loan to unidentifiable students. (Keith Tipton in The Biochemist)

Strongly recommended.

Strongly recommended as an accompaniment to more detailed research literature. (Richard Virden in Experimental Physiology)`

Clear and intelligent intro to enzyme kinetics

This is a superb introduction to enzyme kinetics for advanced undergraduate and graduate students, as well as anyone who has ever taken an introductory biochemistry course. If everyone who is doing enzyme kinetics these days read this book, their experimental design would be far less sloppy, and results much more reliable. It is not nearly as comprehensive as Segel’s book, but its pedagogical value is great. (The only objection I had is that author’s style of exposition sometimes gets a bit too acerbic. But, after all, the author is English :) (A reader from Stockholm, Sweden)

COMPLETE REVIEWS

  • (Anonymous) in Analytical Biochemistry
  • Clive Bullock in Education in Chemistry in Choice in Scienza e Governo (in Italian) in Protein Science in the Journal of Membrane Biology in the Journal of Medicinal Chemistry in Molecular Biotechnology in Biochemical Education in the Quarterly Review of Biology in The Biochemist in Experimental Physiology

Course adoptions

  • USA
    • University of California at Santa Cruz*: Advanced Biochemistry
    • Clemson University, South Carolina: Enzymes
    • Davidson College, North Carolina: Isocitrate dehydrogenase as a model system for undergraduate research projects
    • University of Georgia at Athens: Enzymology
    • Wesleyan University, Connecticut: Enzyme kinetics
    • Louisiana State University*: Biology
    • Cornell University*: Enzyme structure and mechanism
    • University of Nebraska at Lincoln: Enzymes
    • University of Pennsylvania: Practical Modern Enzymology
    • University of South Florida*: Advances in enzymology
    • University of Texas at Houston*: Enzyme mechanisms and kinetics
    • Fred Hutchinson Cancer Research Center, Seattle: Protein structure, modification and regulation
    • University of Alaska at Fairbanks: Enzymology and bioorganic chemistry
    • University of Washington: Biological mass transport
    • Universitat Autònoma de Barcelona: Enzimologia
    • Universitat de Barcelona: Enzimología
    • University of León*: Enzimología
    • Universidad Complutense de Madrid: Enzimología
    • Universidad de Navarra: Enzimología
    • University of Rioja: Biocatalizadores
    • University of Valencia: Enzimología
    • University of Valencia: Práctica de enzimología
    • Universidad Miguel Hernández: Enzimología
    • Centro Universitario Francisco de Vitoria (Universidad Complutense de Madrid): Enzimología
    • Universidad de Extremadura: Enzimología
    • Universidad de Sevilla: Bioquímica
    • Chalmers University of Technology, Göteborg*: Enzyme kinetics
    • University of Göteborg*: Biokemi
    • University of Uppsala: Biokemisk metodik
    • University of Lund*: Kinetics and thermodynamics in biotechnology
    • Simon Fraser University, British Columbia, Canada: Enzymology
    • Sveucilistite u Zabrebu, Croatia: 3155 Biokemija I, II
    • Åbo Akademi University, Turku, Finland*: Enzymkinetik
    • University of Giessen, Germany: Kinetik
    • Università della Tuscia, Italy: Enzimologia
    • Università degli Studi di Milano, Italy: Biotecnologie speciali
    • Universiti Putra Malaysia: Enzimologi
    • Universidad Nacional Autónoma de México, Mexico: Cinética enzimática
    • University of Canterbury, New Zealand*: Biological chemistry
    • University of Oslo, Norway: Cellulaer biokjemi og reguleringsmekanismer
    • Norwegian University of Science and Technology, Trondheim
    • Universidade de Lisboa, Portugal: Enzymology
    • University of Bath, UK: Biochemistry

    Contents

    1. Basic Principles of Chemical Kinetics

    1.1 Order of a reaction: order and molecularity determination of the order of a reaction

    1.2 Dimensions of rate constants

    1.4 Determination of first-order rate constants

    1.5 The influence of temperature on rate constants: the Arrhenius equation elementary collision theory transition-state theory

    2. Introduction to Enzyme Kinetics

    Warning: Two typographical errors in the original (1995) printing of this chapter are noted elsewhere.

    2.1 Early studies: the idea of an enzyme-substrate complex

    2.2 The Michaelis-Menten equation

    2.3 The steady state of an enzyme-catalysed reaction: the Briggs-Haldane treatment the Michaelis-Menten equation units of enzyme activity the curve defined by the Michaelis-Menten equation ways of writing the Michaelis-Menten equation

    2.4 Validity of the steady-state assumption

    2.5 Graphs of the Michaelis-Menten equation: plotting v against a the double-reciprocal plot the plot of a/v against a the plot of v against v/a the direct linear plot

    2.6 The reversible Michaelis-Menten mechanism: the reversible rate equation the Haldane relationship one-way enzymes

    2.8 Integration of the Michaelis-Menten equation

    3. Practical Aspects of Kinetic Studies

    3.1 Enzyme assays: discontinuous and continuous assays estimating the initial rate increasing the straightness of the progress curve coupled assays

    3.2 Detecting enzyme inactivation

    3.3 Experimental design: choice of substrate concentrations choice of pH, temperature and other conditions use of replicate observations

    3.4 Treatment of ionic equilibria

    4. How to Derive Steady-State Rate Equations

    4.2 The principle of the King-Altman method

    4.3 The method of King and Altman

    4.4 The method of Wong and Hanes

    4.5 Modifications to the King-Altman method

    4.6 Reactions containing steps at equilibrium

    4.7 Analysing mechanisms by inspection: topological reasoning mechanisms with alternative routes dead-end steps

    4.8 Derivation of rate equations by computer

    5. Inhibition and Activation of Enzymes

    5.1 Reversible and irreversible inhibition: catalytic poisons analysis of the rate of inactivation types of reversible inhibition

    5.2 Linear inhibition: competitive inhibition (specific inhibition) mixed inhibition uncompetitive inhibition (catalytic inhibition) summary of linear inhibition types

    5.3 Plotting inhibition results

    5.4 Inhibition by a competing substrate: enzyme specificity testing if two reactions occur at the same site substrate protection experiments

    5.5 Enzyme activation: miscellaneous uses of the term activation specific activation hyperbolic activation and inhibition

    5.6 Design of inhibition experiments

    5.7 Inhibitory effects of substrates: non-productive binding substrate inhibition

    5.8 Chemical modification as a means of identifying essential groups

    6. Reactions of More than One Substrate

    6.2 Classification of mechanisms: ternary-complex mechanisms substituted-enzyme mechanisms comparison between chemical and kinetic classifications

    6.3 Rate equations: compulsory-order ternary-complex mechanism random-order ternary-complex mechanism substituted-enzyme mechanism calculation of rate constants from kinetic parameters

    6.4 Initial-rate measurements in the absence of products: meanings of the parameters apparent Michaelis-Menten parameters primary plots for ternary-complex mechanisms secondary plots for ternary-complex mechanisms plots for the substituted-enzyme mechanism

    6.5 Substrate inhibition: why substrate inhibition occurs compulsory-order ternary-complex mechanism random-order ternary-complex mechanism substituted-enzyme mechanism diagnostic value of substrate inhibition

    6.8 Reactions with three or more substrates

    7. Use of Isotopes for Studying Enzyme Mechanisms

    New chapter: not in the original edition

    7.1 Isotope exchange and isotope effects

    7.2 Principles of isotope exchange

    7.3 Isotope exchange at equilibrium

    7.4 Isotope exchange in substituted-enzyme mechanisms

    7.5 Non-equilibrium isotope exchange: chemiflux ratios isomerase kinetics tracer perturbation

    7.6 Theory of kinetic isotope effects: primary isotope effects secondary isotope effects equilibrium isotope effects

    7.7 Primary isotope effects in enzyme kinetics

    8. Environmental Effects on Enzymes

    8.1 pH and enzyme kinetics

    8.2 Acid-base properties of proteins

    8.3 Ionization of a dibasic acid: expression in terms of group dissociation constants molecular dissociation constants bell-shaped curves

    8.5 Ionization of the substrate

    8.6 More complex pH effects

    8.7 Temperature dependence of enzyme-catalysed reactions: temperature denaturation temperature optimum application of the Arrhenius equation to enzymes

    8.8 Solvent isotope effects

    9. Control of Enzyme Activity

    9.1 Function of cooperative and allosteric interactions: futile cycles inadequacy of Michaelis-Menten kinetics for regulation cooperativity allosteric interactions

    9.2 The development of models to explain cooperativity: the Hill equation an alternative index of cooperativity assumption of equilibrium binding in cooperative kinetics the Adair equation mechanistic and operational definitions of cooperativity

    9.3 Analysis of binding experiments: the Scatchard plot

    9.5 Modern models of cooperativity: the symmetry model of Monod, Wyman and Changeux the sequential model of Koshland, Némethy and Filmer association-dissociation models

    10. Kinetics of Multi-Enzyme Systems

    New chapter: not in the original edition

    A hypertext version of this chapter can be consulted on the web.

    Warning: Three typographical errors in the original (1995) printing of this chapter are noted elsewhere.

    10.1 Enzymes in their physiological context

    10.2 Metabolic control analysis

    10.3 Elasticities: definition of elasticity common properties of elasticities enzyme kinetics viewed from control analysis

    10.5 Summation relationships

    10.6 Relationships between elasticities and control coefficients: connectivity properties control coefficients in a three-step pathway expression of summation and connectivity relationships in matrix form connectivity relationship for a metabolite not involved in feedback relationship of flux control coefficients to elasticities and concentration control coefficients

    10.7 Response coefficients: the partitioned response

    10.8 Control and regulation

    10.9 Mechanisms of regulation: metabolite channelling interconvertible enzyme cascades the metabolic role of adenylate kinase

    11. Fast Reactions

    11.1 Limitations of steady-state measurements

    11.2 Product release before completion of the catalytic cycle: burst kinetics active site titration

    11.3 Experimental techniques: classes of method continuous flow stopped flow quenched flow relaxation methods

    11.4 Transient-state kinetics: systems far from equilibrium simplification of complex mechanisms systems close to equilibrium

    12. Estimation of Kinetic Constants

    The topic of this chapter is covered in more detail in a separate book, which includes a PC program Leonora designed for statistical analysis of enzyme kinetic data.

    12.1 The effect of experimental error on kinetic analysis

    12.2 Least-squares fit to the Michaelis-Menten equation: introduction of error in the Michaelis-Menten equation estimation of V and K m corresponding results for a uniform standard deviation in the rates

    12.3 Statistical aspects of the direct linear plot: comparison between classical and distribution-free statistics application to the direct linear plot lack of need for weighting insensitivity to outliers handling of negative parameter estimates

    12.4 Precision of estimated kinetic parameters

    12.5 Residual plots and their uses

    Corrections

    Errors in the first (1995) printing are listed elsewhere. Nearly all of these were corrected in later printings, but a small number survived even to the 3rd edition.

    Page created before 1998
    Last update: 6 February 2012
    Last significant update: 17 November 2004
    Comments to Athel Cornish-Bowden


    Table of Contents

    Part 1: Structure and Function of Enzymes

    1: An Introduction to Enzymes

    • 1.1 WHAT ARE ENZYMES?
    • 1.2 A BRIEF HISTORY OF ENZYMES
    • 1.3 THE NAMING AND CLASSIFICATION OF ENZYMES
    • SUMMARY OF CHAPTER 1
    • PROBLEMS

    2: The Structure of Proteins

    • 2.1 INTRODUCTION
    • 2.2 AMINO ACIDS, THE BUILDING BLOCKS OF PROTEINS
    • 2.3 THE BASIS OF PROTEIN STRUCTURE
    • 2.4 THE DETERMINATION OF PRIMARY STRUCTURE
    • 2.5 THE DETERMINATION OF PROTEIN STRUCTURE BY X-RAY CRYSTALLOGRAPHY
    • 2.6 THE INVESTIGATION OF PROTEIN STRUCTURE IN SOLUTION
    • SUMMARY OF CHAPTER 2
    • PROBLEMS

    3: The Biosynthesis and Properties of Proteins

    • 3.1 THE BIOSYNTHESIS OF PROTEINS
    • 3.2 THE PROPERTIES OF PROTEINS
    • SUMMARY OF CHAPTER 3
    • PROBLEMS

    4: Specificity of Enzyme Action

    • 4.1 TYPES OF SPECIFICITY
    • 4.2 THE ACTIVE SITE
    • 4.3 THE FISCHER ‘LOCK-AND-KEY’ HYPOTHESIS
    • 4.4 THE KOSHLAND ‘INDUCED-FIT’ HYPOTHESIS
    • 4.5 HYPOTHESES INVOLVING STRAIN OR TRANSITION-STATE STABILIZATION
    • 4.6 FURTHER COMMENTS ON SPECIFICITY
    • SUMMARY OF CHAPTER 4

    5: Monomeric and Oligomeric Enzymes

    Part 2: Kinetic and Chemical Mechanisms of Enzyme-Catalysed Reactions

    6: An Introduction to Bioenergetics, Catalysis and Kinetics

    • 6.1 SOME CONCEPTS OF BIOENERGETICS
    • 6.2 FACTORS AFFECTING THE RATES OF CHEMICAL REACTIONS
    • 6.3 KINETICS OF UNCATALYSED CHEMICAL REACTIONS
    • 6.4 KINETICS OF ENZYME-CATALYSED REACTIONS: AN HISTORICAL INTRODUCTION
    • 6.5 METHODS USED FOR INVESTIGATING THE KINETICS OF ENZYME-CATALYSED REACTIONS
    • 6.6 THE NATURE OF ENZYME CATALYSIS
    • SUMMARY OF CHAPTER 6
    • PROBLEMS

    7: Kinetics of Single-Substrate Enzyme-Catalysed Reactions

    • 7.1 THE RELATIONSHIP BETWEEN INITIAL VELOCITY AND SUBSTRATE CONCENTRATION
    • 7.2 RAPID-REACTION kINETICS
    • 7.3 THE kING AND ALTMAN PROCEDURE
    • SUMMARY OF CHAPTER 7
    • PROBLEMS
    • 8.1 INTRODUCTION
    • 8.2 REVERSIBLE INHIBITION
    • 8.3 IRREVERSIBLE INHIBITION
    • SUMMARY OF CHAPTER 8
    • PROBLEMS

    9: Kinetics of Multi-Substrate Enzyme-Catalysed Reactions

    • 9.1 EXAMPLES OF POSSIBLE MECHANISMS
    • 9.2 STEADY-STATE KINETICS
    • 9.3 INVESTIGATION OF REACTION MECHANISMS USING STEADY-STATE METHODS
    • 9.4 INVESTIGATION OF REACTION MECHANISMS USING NON-STEADY-STATE METHODS
    • SUMMARY OF CHAPTER 9
    • PROBLEMS

    10: The Investigation of Active Site Structure

    • 10.1 THE IDENTIFICATION OF BINDING SITES AND CATALYTIC SITES
    • 10.2 THE INVESTIGATION OF THE THREE-DIMENSIONAL STRUCTURES OF ACTIVE SITES
    • SUMMARY OF CHAPTER 10
    • PROBLEM

    11: The chemical nature of enzyme catalysis

    • 11.1 AN INTRODUCTION TO REACTION MECHANISMS IN ORGANIC CHEMISTRY
    • 11.2 MECHANISMS OF CATALYSIS
    • 11.3 MECHANISMS OF REACTIONS CATALYSED BY ENZYMES WITHOUT COFACTORS
    • 11.4 METAL-ACTIVATED ENZYMES AND METALLOENZYMES
    • 11.5 THE INVOLVEMENT OF COENZYMES IN ENZYME-CATALYSED REACTIONS
    • SUMMARY OF CHAPTER 11

    12: The Binding of Ligands to Proteins

    • 12.1 INTRODUCTION
    • 12.2 THE BINDING OF A LIGAND TO A PROTEIN HAVING A SINGLE LIGAND-BINDING SITE
    • 12.3 COOPERATIVITY
    • 12.4 POSITIVE HOMOTROPIC COOPERATIVITY AND THE HILL EQUATION
    • 12.5 THE ADAIR EQUATION FOR THE BINDING OF A LIGAND TO A PROTEIN HAVING TWO BINDING SITES FOR THAT LIGAND
    • 12.6 THE ADAIR EQUATION FOR THE BINDING OF A LIGAND TO A PROTEIN HAVING THREE BINDING SITES FOR THAT LIGAND
    • 12.7 THE ADAIR EQUATION FOR THE BINDING OF A LIGAND TO A PROTEIN HAVING FOUR BINDING SITES FOR THAT LIGAND
    • 12.8 INVESTIGATION OF COOPERATIVE EFFECTS
    • 12.9 THE BINDING OF OXYGEN TO HAEMOGLOBIN
    • SUMMARY OF CHAPTER 12
    • PROBLEMS

    13: Sigmoidal Kinetics and Allosteric Enzymes

    • 13.1 INTRODUCTION
    • 13.2 THE MONOD-WYMAN-CHANGEUX (MWC) MODEL
    • 13.3 THE KOSHLAND-NÉMETHY-FILMER (KNF) MODEL
    • 13.4 DIFFERENTIATION BETWEEN MODELS FOR COOPERATIVE BINDING IN PROTEINS
    • 13.5 SIGMOIDAL KINETICS IN THE ABSENCE OF COOPERATIVE BINDING
    • SUMMARY OF CHAPTER 13
    • PROBLEMS

    14: The Significance of Sigmoidal Behaviour

    • 14.1 THE PHYSIOLOGICAL IMPORTANCE OF COOPERATIVE OXYGEN-BINDING BY HΔEMOGLOBIN
    • 14.2 ALLOSTERIC ENZYMES AND METABOLIC REGULATION
    • SUMMARY OF CHAPTER 14

    Part 3: Application of Enzymology

    15: Investigation of Enzymes in Biological Preparations

    • 15.1 CHOICE OF PREPARATION FOR THE INVESTIGATION OF ENZYME CHARACTERISTICS
    • 15.2 ENZYME ASSAY
    • 15.3 INVESTIGATION OF SUB-CELLULAR COMPARTMENTATION OF ENZYMES
    • SUMMARY OF CHAPTER 15
    • PROBLEM

    16: Extraction and Purification of Enzymes

    • 16.1 EXTRACTION OF ENZYMES
    • 16.2 PURIFICATION OF ENZYMES
    • 16.3 DETERMINATION OF MOLECULAR WEIGHTS OF ENZYMES
    • SUMMARY OF CHAPTER 16
    • PROBLEM

    17: Enzymes as Analytical Reagents

    • 17.1 THE VALUE OF ENZYMES AS ANALYTICAL REAGENTS
    • 17.2 PRINCIPLES OF ENZYMATIC ANALYSIS
    • 17.3 HANDLING ENZYMES AND COENZYMES
    • SUMMARY OF CHAPTER 17
    • PROBLEMS

    18: Instrumental Techniques Available for Use in Enzymatic Analysis

    • 18.1 PRINCIPLES OF THE AVAILABLE DETECTION TECHNIQUES
    • 18.2 AUTOMATION IN ENZYMATIC ANALYSIS
    • 18.3 HIGH-THROUGHPUT ASSAYS (HTA)
    • SUMMARY OF CHAPTER 18

    19: Applications of Enzymatic Analysis in Medicine, Forensic Science and Industry


    Enzyme Kinetics : Principles and Methods , Second Edition

    “Overall, this is an excellent and thorough treatment of a difficult subject. As well as appealing to biochemists, there are also elements of interest to those studying pharmacology and the pharmacokinetic distribution of drugs. The mathematical nature and advanced coverage means that it is most suitable for researchers who already have a strong grounding in the subject. I will certainly be consulting it during my research.” (Biochemist, 29 May 2013)

    “This new, expanded and updated edition of the user–friendly and comprehensive treatise on enzyme kinetics expertly balances theory and practice. This is an indispensable aid for advanced students and professionals working with enzymes, whether biochemists, biotechnologists, chemical biologists, pharmacologists or bioengineers in academia, industry and clinical research.” (Biology Community, 29 November 2012)

    Enzyme kinetics is not a new area in biochemistry. Thirty years ago, enzyme kinetics was one of the most important tools for deconstructing enzymatic mechanisms. With advances in enzyme structure determination and molecular genetics, enzyme kinetics is no longer as prominent. However, enzyme kinetics is still useful to gain insight into enzymes that are too large for NMR studies and that cannot be crystallized. Many enzymes that fit into this category are membrane bound, the kinetics of which are much more complicated. In this new edition (1st ed., 2002), Bisswanger (Univ. of Tübingen, Germany) does a nice job of extending solution enzyme kinetics to membrane-bound enzymes. Setting it apart from other works on the subject, Enzyme Kinetics does not simply deal with substrate binding as a part of the reaction kinetics, but instead devotes about one-third of the text to equilibrium binding between macromolecules and ligands in which no reaction catalysis follows the binding. This binding is then directly connected with enzyme catalyzed reaction kinetics. Enzyme Kinetics was written to serve as a graduate-level course resource and would serve this population well. The inclusion of student problems would be an improvement. Summing Up: Recommended. Graduate students, researchers, and faculty. -- L. J. Liotta, Stonehill College (Choice, February 2009)


    On the Steady-State Method of Enzyme Kinetics

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    Closing remarks

    For the sake of conciseness, this guide has been limited to some of the basic principles of enzymology, together with an overview of the biotechnological applications of enzymes. It is important to understand the relationship between proteins and the nucleic acids (DNA and RNA) that provide the blueprint for the assembly of proteins within the cell. Genetic engineering is thus predominantly concerned with modifying the proteins that a cell contains, and genetic defects (in medicine) generally relate to the abnormalities that occur in the proteins within cells. Much of the molecular age of biochemistry is therefore very much focused on the study of the cell, its enzymes and other proteins, and their functions.


    Watch the video: Enzyme Kinetics (June 2022).


Comments:

  1. Rogan

    Bravo, they are just excellent thinking

  2. Salmoneus

    is understood in two ways like this

  3. Levi

    Nice!



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