DOCSLIB.ORG

Chemical and Enzyme Kinetics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chemical and Enzyme Kinetics Chemical and enzyme kinetics D. Gonze & M. Kaufman November 24, 2016 Master en Bioinformatique et Mod´elisation Contents 1Definitions 4 1.1 Reactionrate .................................. 4 1.2 Examples .................................... 6 1.3 Systemsofchemicalreactions . 10 1.4 Chemical equilibrium . 11 1.5 Effectoftemperature-Arrheniusequation . ... 12 2Enzymekinetics 13 2.1 Enzymes..................................... 13 2.2 Mechanismofenzymereactions . 14 2.3 Equilibrium approximation: Michaelis-Menten equation . .16 2.4 Quasi-steady state assumption: Briggs-Haldane equation . ...... 17 2.5 Reversible Michaelis-Menten kinetics . 19 2.6 Inhibition .................................... 20 2.7 Activation.................................... 23 2.8 Two-substrateenzymekinetics. .24 2.9 Substratecompetition ............................. 27 2.10 Cooperativity: Hill function . 29 2.11Allostericmodel................................. 34 2.12 Zero-order ultrasensitivity . .38 3Generegulation 42 3.1 Transcription, regulation, and transcription factors . ...... 42 3.2 Transcriptional activation . 44 3.3 Transcriptional activation with auto-regulation . .... 47 3.4 Transcriptional activation with multiple binding sites . .49 3.5 Transcriptional activation by a dimeric complex . .52 3.6 Transcriptional inhibition with an inducer . 54 3.7 Combining transcriptional activation and inhibition . .56 4Appendix 58 4.1 Reaction in series - derivation . 58 4.2 Quasi-steadystateapproximation . .60 2 4.3 Validity of the quasi-steady state approximation . ... 63 4.4 Comparison of developed vs compact Michaelis-Menten kinetics . .... 64 4.5 Examples of kinetic values . 65 4.6 Competitive inhibition . 66 4.7 A rapid (but approximative) derivation of the Hill function . ... 68 5References 69 5.1 Textbooks.................................... 69 5.2 Papers...................................... 70 3 1Definitions 1.1 Reaction rate Consider the chemical reaction that transforms the substrates A and B into the products CandD: A+B C+D (1) → The variation in time of the concentration of the substrates (A and B)andtheproducts (C and D), dA dB dC dD , , ,and (2) dt dt dt dt is determined by the rate at which the reaction proceeds. 1 Product 0.8 0.6 0.4 Concentration 0.2 Substrate 0 0 1 2 3 4 5 Time Figure 1: Time evolution of the concentration of the substrate and product. For a chemical reaction to occur, the reacting species must collide, have sufficient energy and be well oriented. The number of collisions is proportional to the concentration of the reacting species. For the reaction (1), the rate law is given by the mass action law: v = kAB (3) Not all collisions are reactive. The rate constant k accounts for the probability that the molecules are well oriented and have sufficient energy to react. The variation in time of the concentration of the substrates and the products is given by dA dB dC dD = = kAB and = = kAB (4) dt dt − dt dt The sign in the right-hand side of these equations stands for the fact that, each time the reaction proceeds, one molecule (mole) of A (and B) disappears while one molecule (mole) of C (and D) appears. More generally, for an (elementary) reaction in which m molecules of A react with p molecules of B and in which the products (C and D) do not affect the reaction rate: mA + pB qC + rD (5) → 4 the rate law is: v = kAmBp (6) Note that the sum m + p is called the order of a reaction. Consider now for example the following reaction: 3A + B A+C (7) → According to Eq. (6), the rate of this reaction is: v = kA3B (8) When we write the evolution of the concentration of A, we must take into consideration the fact that each time this reaction occurs, only two molecules of A are transformed (one is conserved). So, the variation of A is given by: dA = 2v = 2kA3B (9) dt − − The coefficient “2” is the balance for the species A in reaction (7) and the sign “-” stands because, globally, A is consumed. Since v must have the unit [concentration]/[time], the units of k depend on the order of the reaction. In the general case, for a reaction in which for each n molecules (moles) of X transformed p molecules (moles) are recovered at the end: n X + ... p X + ... (10) → the evolution equation for the concentration of X is: dX = η v with η = p n (11) dt X X − ηX is called the stoechiometric coefficient of compound X. This coefficient is positive if, globally, the species is produced (p>n) and negative if the species is consumed (n>p). For example, for the following reaction: A+2B 3A + C (12) → the stoechiometric coefficients of the different species are: η =3 1=2,η =0 2= 2, η =1 0=1. (13) A − B − − C − and the evolution equations are: dA dB dC =2kAB2, = 2kAB2, = kAB2 (14) dt dt − dt 5 1.2 Examples 1st-order kinetics Consider the reaction of 1st-order: A A* (ex: conformational change of a molecule) (15) → or A B + C (dissociation of a molecule into two molecules) (16) → By definition (eq 3), the rate of this reaction is v = kA (17) and the time evolution of the concentration of the substrate A is: dA = kA (18) dt − After integration, we find: −kt A(t)=A0e (19) where A0 is the initial concentration of substrate A (A0 = A(0)). We observe an exponential decrease of the concentration of A with time: 3 A 2.5 0 2 1.5 1 Concentration of A 0.5 0 0 1 2 3 4 5 Time Figure 2: 1st-order kinetics: exponential decrease of the concentration of substrate A. Remark: On the long run, A will converge to 0, i.e. A will be fully degraded. The half-life τ1/2 of A is defined by the time it takes for its concentration A to decrease from its initial value A0 to half of this value, A0/2: A0 − = A e kτ1/2 2 0 ln 2 τ = (20) 1/2 k Note that τ1/2 does not depend on the initial value A0. 6 2nd-order kinetics Let’s take now the reaction: 2A B (2 molecules A fuse together to give one single molecule) (21) → or 2A B+C (2 molecules A react together to give two different molecules) (22) → Its rate is: v = kA2 (23) and the time evolution of the substrate A is dA = 2kA2 (24) dt − After integration, we find: A A(t)= 0 (25) 1+2A0kt where A0 is the initial concentration of substrate A. Here, we observe an hyperbolic decrease of the concentration of A with time: 3 A 2.5 0 2 1.5 1 Concentration of A 0.5 0 0 1 2 3 4 5 Time Figure 3: 2nd-order kinetics: hyperbolic decrease of the concentration of substrate A. 7 Reactions in series Let’s consider the following reactions in series: k k A 1 B 2 C(26) → → Evolution equations for the compounds A, B, and C write: dA = k A (27) dt − 1 dB = k A k B (28) dt 1 − 2 dC = k B (29) dt 2 Assuming that we start with A(0) = A0 and B(0) = C(0) = 0, we find −k1t A(t)=A0e (as before) (30) and, after integration k A B(t)= 1 0 e−k1t e−k2t (31) k k − 2 − 1 1 ! " C(t)=A 1 k e−k1t k e−k2t (32) 0 − k k 2 − 1 # 2 − 1 $ The derivation is detailed in the Appendix. ! " 10 9 C 8 7 A 6 k1=1 k2=0.5 5 A =10 0 B =C =0 4 0 0 Concentration 3 B 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Time Figure 4: Kinetics of reactions in series. 8 Now we can consider the case where A is continuously supplied, so that A remains constant over time: k k k k 0 A 1 B 2 C 3 (33) → → → → The evolution equations for the compound B is, with A(t)=A0 = k0/k1: dB = k A k B (34) dt 1 0 − 2 and the evolution of B is then given by: k A (k A k B )e−k2t B(t)= 1 0 − 1 0 − 2 0 (35) k2 Now, on the long run and regardless of its initial concentration, B reaches a steady state: k A B( )= 1 0 (36) ∞ k2 The derivation of the equation for C(t) is left as an exercise. 22 20 18 B 16 14 12 10 A 8 Concentration 6 k1=1 4 k2=0.5 2 A=10 (const) 0 0 1 2 3 4 5 6 7 8 9 10 Time Figure 5: Kinetics of reactions in series with A = A0 =constant. 9 1.3 Systems of chemical reactions We are usually interested by systems of coupled chemical reactions. n X +n X + ... p X +p X ... 11 1 21 2 → 11 1 21 2 n X +n X + ... p X +p X ... 12 1 22 2 → 12 1 22 2 ... n X +n X + ... p X +p X ... (37) 1R 1 2R 2 → 1R 1 2R 2 The variation of a given compound Xi involved in R reactions is defined by: dX R i = η v = η v + η v + ... + η v (38) dt ir r i1 1 i2 2 iR R r=1 % where vr = rate of reaction r (with r =1, 2, ...R): nir vr = kr Xi i & η = p n = stoechiometric coefficient of compound X in reaction r. ir ir − ir i We illustrate this on the following example: r reaction rate ηXr ηYr 1Ak1 X v = k A η =1 η =0 −→ 1 1 X1 Y 1 2B+Xk2 Y+C v = k BX η = 1 η =1 −→ 2 2 X2 − Y 2 32X+Yk3 3X v = k X2Y η =1 η = 1 −→ 3 3 X3 Y 3 − 4Xk4 D v = k X η = 1 η =0 −→ 4 4 X4 − Y 4 The evolution equations for X and Y are given by (see eq.
Load more

Recommended publications
  • Single Molecule Enzymology À La Michaelis-Menten
    Single molecule enzymology à la Michaelis-Menten Ramon Grima1, Nils G. Walter2 and Santiago Schnell3* 1 School of Biological Sciences and SynthSys, University of Edinburgh, Edinburgh, UK 2 Department of Chemistry, University of Michigan, Ann Arbor, Michigan, USA 3 Department of Molecular & Integrative Physiology, Department of Computational Medicine & Bioinformatics, and Brehm Center for Diabetes Research, University of Michigan Medical School, Ann Arbor, Michigan, USA * To whom the correspondence should be addressed. E-mail: [email protected] Review article accepted for publication to FEBS Journal special issue on Enzyme Kinetics and Allosteric Regulation 1 Abstract In the past one hundred years, deterministic rate equations have been successfully used to infer enzyme-catalysed reaction mechanisms and to estimate rate constants from reaction kinetics experiments conducted in vitro. In recent years, sophisticated experimental techniques have been developed that allow the measurement of enzyme- catalysed and other biopolymer-mediated reactions inside single cells at the single molecule level. Time course data obtained by these methods are considerably noisy because molecule numbers within cells are typically quite small. As a consequence, the interpretation and analysis of single cell data requires stochastic methods, rather than deterministic rate equations. Here we concisely review both experimental and theoretical techniques which enable single molecule analysis with particular emphasis on the major developments in the field of theoretical stochastic enzyme kinetics, from its inception in the mid-twentieth century to its modern day status. We discuss the differences between stochastic and deterministic rate equation models, how these depend on enzyme molecule numbers and substrate inflow into the reaction compartment and how estimation of rate constants from single cell data is possible using recently developed stochastic approaches.
    [Show full text]
  • Leonor Michaelis and Maud Leonora Menten Celebrating 100 Years of the Michaelis–Menten Equation
    ARTICLE-IN-A-BOX Leonor Michaelis and Maud Leonora Menten Celebrating 100 years of the Michaelis–Menten Equation Leonor Michaelis was an honoured German biochemist and Maud Leonora Menten an honoured Canadian pathologist, during the nineteenth century. Though Michaelis sustained his interest in enzymology and biochemistry, Menten moved to pathology and became a renowned pathologist later in her career. The research collaboration of Michaelis and Menten was phenomenal resulting in the celebrated ‘Michaelis–Menten Equation’. Michaelis and Menten’s classic paper titled ‘Die Kinetik der Invertin wirkung’, published in Biochemische Zeitschrift in 1913 marks its centenary this year. This seminal paper which proved vital for the teaching of enzyme kinetics, was acknowledged with so much appreciation and attention that no textbook in biology for undergraduate and graduate students across the world is complete without a discussion of the Michaelis–Menten Equation. An earlier paper by Victor Henri and Brown lacked one important insight which was reported by Michaelis and Menten: that insight was the analysis of reaction in terms of the initial rate. Michaelis and Menten introduced the concept of measuring the initial activity of the enzyme by mixing it with substrate so that product accumulation would not inhibit the activity. Leonor Michaelis (1875–1949) Leonor Michaelis was born in Berlin, Germany on January 16, 1875. He graduated from the ‘humanistic’ Koellnisches Gymnasium in 1893. This gymnasium was special as unlike the other humanistic gymnasiums, it also included chemistry and physics labs which were not in general use and it was only the keen initiative of two professors that enabled interested students learn the subjects.
    [Show full text]
  • Explicit Treatment of Non Michaelis-Menten and Atypical Kinetics in Early Drug Discovery
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 October 2020 doi:10.20944/preprints202010.0179.v1 Explicit Treatment of Non Michaelis-Menten and Atypical Kinetics in Early Drug Discovery Bharath Srinivasan#,1 # Mechanistic Biology and Profiling, Discovery Sciences, R&D, AstraZeneca, Cambridge, UK [email protected]; +44 7508382559 Abstract: Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential for sustenance of life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context, to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were tested and implemented for mostly cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more complex systems (for instance, multi-protein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis- Menten (MM) kinetics are rendered inadequate and the development of a new kind of kinetic analysis to study these systems is required. The current review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents
    [Show full text]
  • Enzyme Kinetics at the Molecular Level∗
    GENERAL ARTICLE Enzyme Kinetics at the Molecular Level∗ Arti Dua The celebrated Michaelis–Menten (MM) expression provides a fundamental relation between the rate of enzyme cataly- sis and substrate concentration. The validity of this classical expression is, however, restricted to macroscopic amounts of enzymes and substrates and, thus, to processes with negligi- ble fluctuations. Recent experiments have measured fluctu- ations in the catalytic rate to reveal that the MM equation, though valid for bulk amounts, is not obeyed at the molecu- Arti Dua is an Associate lar level. In this review, we show how new statistical measures Professor in the Indian of fluctuations in the catalytic rate identify a regime in which Institute of Technology Madras. She is a theoretical the MM equation is always violated. This regime, character- chemist, working in the area ized by temporal correlations between enzymatic turnovers, of stochastic reaction is absent for a single enzyme and is unobservably short in the dynamics and statistical classical limit. mechanics of complex fluids. 1. Classical Enzyme Kinetics Enzymes are biological catalysts that accelerate chemical reac- tions manyfold, without getting consumed in the catalytic pro- cess. Several biological processes involving the conversion of substrates to products, thus, rely crucially on the catalytic activity of enzymes. Specific enzymes control and regulate a wide range of life-sustaining processes that vary from digestion, metabolism, absorption, and blood clotting to reproduction. While specificity Keywords depends on the detailed chemical structure of enzyme proteins, Biological catalysts, enzymes, rate kinetics, stochastic enzyme the rate at which the enzymes carry out the catalytic conversion kinetics, Michaelis–Menten depends less on their chemical structure but more on the physical mechanism, enzymatic velocity, parameters, including the amounts of enzymes, substrates, tem- molecular noise.
    [Show full text]
  • Die Kinetik Der Invertinwirkung Von L. Michaelis and Miss Maud L. Menten (Received 4 February 1913.) with 19 Figures in Text
    Die Kinetik der Invertinwirkung Von L. Michaelis and Miss Maud L. Menten (Received 4 February 1913.) With 19 Figures in Text. The Kinetics of Invertase Action translated by Roger S. Goody1 and Kenneth A. Johnson2 The kinetics of enzyme3) action have often been studied using invertase, because the ease of measuring its activity means that this particular enzyme offers especially good prospects of achieving the final aim of kinetic research, namely to obtain knowledge on the nature of the reaction from a study of its progress. The most outstanding work on this subject is from Duclaux4), Sullivan and Thompson5), A.J. Brown6) and in particular V. Henri7). Henri’s investigations are of particular importance since he succeeded, starting from rational assumptions, in arriving at a mathematical description of the progress of enzymatic action that came quite near to experimental observations in many points. We start from Henri’s considerations in the present work. That we have gone to the lengths of reexamination of this work arises from the fact that Henri did not take into account two aspects, which must now be taken so seriously that a new investigation is warranted. The first point to be taken into account is the hydrogen ion concentration, the second the mutarotation of the sugar(s). The influence of the hydrogen ion concentration has been clearly demonstrated by the work of Sörensen8) and of Michaelis and Davidsohn9). It would be a coincidence if Henri in all his experiments, in which he did not consider the hydrogen ion concentration, had worked at the same hydrogen ion concentration.
    [Show full text]
  • One Hundred Years of Michaelis￢ﾀﾓmenten Kinetics
    Perspectives in Science (2015) 4,3–9 Available online at www.sciencedirect.com www.elsevier.com/locate/pisc REVIEW One hundred years of Michaelis–Menten kinetics$ Athel Cornish-Bowdenn Unité de Bioénergétique et Ingénierie des Protéines, Institut de Microbiologie de la Méditerranée, Centre National de la Recherche Scientifique, Aix-Marseille Université, 31 chemin Joseph-Aiguier, 13009 Marseille, France Received 27 January 2014; accepted 3 December 2014 Available online 24 December 2014 KEYWORDS Abstract Michaelis–Menten The year 2013 marked the centenary of the paper of Leonor Michaelis and Maud Menten (Michaelis kinetics; and Menten, 1913), and the 110th anniversary of the doctoral thesis of Victor Henri (Henri, 1903). enzyme-catalysis; These publications have had an enormous influence on the progress of biochemistry, and are more initial-rate equation; often cited in the 21st century than they were in the 20th. Henri laid the groundwork for the steady-state kinetics; understanding of enzyme mechanisms, but his experimental design was open to criticism. He reached Henry–Michaelis–Men- essentially correct conclusions about the action of invertase, but he took no steps to control the ten equation hydrogen-ion concentration, and he took no account of the spontaneous mutarotation of the glucose produced in the reaction. Michaelis and Menten corrected these shortcomings, and in addition they introduced the initial-rate method of analysis, which has proved much simpler to apply than the methodsbasedontimecoursesthatitreplaced.Inthiswaytheydefined the methodology for steady- state experiments that has remained standard for 100 years. & 2015 The Author. Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
    [Show full text]
  • Victor Henri: 111 Years of His Equation
    Biochimie 107 (2014) 161e166 Contents lists available at ScienceDirect Biochimie journal homepage: www.elsevier.com/locate/biochi Review Victor Henri: 111 years of his equation * Athel Cornish-Bowden a, , Jean-Pierre Mazat b, c, Serge Nicolas d a CNRS-BIP, Aix-Marseille Universite, 31 chemin Joseph-Aiguier, B.P. 71, 13402 Marseille Cedex 20, France b CNRS-UMR 5095, 1 Rue Camille Saint Sa€ens, 33077 Bordeaux Cedex, France c University of Bordeaux, 146 rue Leo-Saignat, 33076 Bordeaux Cedex, France d INSERM UMR S894, Institut de Psychologie, Universite Paris Descartes, Laboratoire Memoire et Cognition, 71 avenue Edouard Vaillant, 92774 Boulogne- Billancourt Cedex, France article info abstract Article history: Victor Henri's great contribution to the understanding of enzyme kinetics and mechanism is not always Received 2 July 2014 given the credit that it deserves. In addition, his earlier work in experimental psychology is totally un- Accepted 12 September 2014 known to biochemists, and his later work in spectroscopy and photobiology almost equally so. Applying Available online 20 September 2014 great rigour to his analysis he succeeded in obtaining a model of enzyme action that explained all of the observations available to him, and he showed why the considerable amount of work done in the pre- Keywords: ceding decade had not led to understanding. His view was that only physical chemistry could explain the Victor Henri behaviour of enzymes, and that models should be judged in accordance with their capacity not only to Enzyme kinetics Invertase explain previously known facts but also to predict new observations against which they could be tested.
    [Show full text]
  • General Laws for the Action of Diastases
    General Laws for the Action of Diastases Victor Henri Doctor of Philosophy (University of Göttingen), Doctor of Science and Préparateur at the Sorbonne, To my dear Master, Monsieur Dastre Professor at the Sorbonne Homage of recognition and devotion published in 1903 by Librairie Scientifique A. Hermann, Paris, as Lois générales de l’action des diastases Translated by Athel Cornish-Bowden with corrections by Jean-Pierre Mazat. 1 2 Contents 3 Contents Introduction to the translation 5 Preface 9 Introduction: current state of knowledge of catalysis 11 §1. Definition of catalytic activity according to Berzelius 11 §2. The difficulty of giving a simple definition of catalytic activity 11 §3. Disproportion between the quantity of catalyst and the mass of reactants transformed 12 §4. When the reaction that occurs in the presence of the catalyst reaches an equilibrium, the presence of the catalyst does not change the position of this equilibrium 13 §5. Effect of catalysts on the rate law of a reaction. Classification of catalytic activities 15 §6. Summary of the study of catalytic activities 20 §7. Main points in the study of the rates of chemical reactions 21 Chapter I: History of research on the laws of action of diastases 24 §8. O’Sullivan and Tompson’s research 24 §9. Tammann’s research 25 §10. Duclaux’s research 27 §11. A. J. Brown’s research 29 §12. H. Brown and Glendinning’s research 30 §13. Herzog’s experiments 31 §14. Summary of the history 32 Chapter II: Experiments on invertin 33 §15. Method 33 §16. Study of the rate of inversion 34 §17.
    [Show full text]
  • Commemorating the 1913 Michaelismenten
    REVIEW ARTICLE Commemorating the 1913 Michaelis–Menten paper Die Kinetik der Invertinwirkung: three perspectives Ute Deichmann1, Stefan Schuster2, Jean-Pierre Mazat3,4 and Athel Cornish-Bowden5 1 Jacques Loeb Centre for the History and Philosophy of the Life Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel 2 Department of Bioinformatics, Friedrich Schiller University of Jena, Germany 3 CNRS-UMR 5095, Bordeaux, France 4 University of Bordeaux, France 5 Unite de Bioenerg etique et Ingenierie des Proteines, Institut de Microbiologie de la Mediterran ee, Centre National de la Recherche Scientifique and Aix-Marseille Universite, France Keywords Methods and equations for analysing the kinetics of enzyme-catalysed reac- enzyme kinetics; Henri; history and tions were developed at the beginning of the 20th century in two centres in philosophy; initial rate; Menten; Michaelis; particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis steady state and Maud Menten. Henri made a detailed analysis of the work in this area Correspondence that had preceded him, and arrived at a correct equation for the initial rate A. Cornish-Bowden, Unitede of reaction. However, his approach was open to the important objection Bioenerg etique et Ingenierie des Proteines, that he took no account of the hydrogen-ion concentration (a subject lar- Institut de Microbiologie, de la gely undeveloped in his time). In addition, although he wrote down an Mediterran ee, Centre National de la expression for the initial rate of reaction and described the hyperbolic form Recherche Scientifique, Aix-Marseille of its dependence on the substrate concentration, he did not appreciate the Universite, 31 chemin Joseph-Aiguier, great advantages that would come from analysis in terms of initial rates 13402 Marseille Cedex 20, France Fax: +33 491 16 40 97 rather than time courses.
    [Show full text]
  • One Hundred Years of Michaelis–Menten Kinetics$
    Perspectives in Science (]]]]) ], ]]]–]]] Available online at www.sciencedirect.com www.elsevier.com/locate/pisc REVIEW One hundred years of Michaelis–Menten kinetics$ Athel Cornish-Bowdenn Unité de Bioénergétique et Ingénierie des Protéines, Institut de Microbiologie de la Méditerranée, Centre National de la Recherche Scientifique, Aix-Marseille Université, 31 chemin Joseph-Aiguier, 13009 Marseille, France Received 27 January 2014; accepted 3 December 2014 KEYWORDS Abstract Michaelis–Menten The year 2013 marked the centenary of the paper of Leonor Michaelis and Maud Menten (Michaelis kinetics; and Menten, 1913), and the 110th anniversary of the doctoral thesis of Victor Henri (Henri, 1903). enzyme-catalysis; These publications have had an enormous influence on the progress of biochemistry, and are more initial-rate equation; often cited in the 21st century than they were in the 20th. Henri laid the groundwork for the steady-state kinetics; understanding of enzyme mechanisms, but his experimental design was open to criticism. He reached Henry–Michaelis–Men- essentially correct conclusions about the action of invertase, but he took no steps to control the ten equation hydrogen-ion concentration, and he took no account of the spontaneous mutarotation of the glucose produced in the reaction. Michaelis and Menten corrected these shortcomings, and in addition they introduced the initial-rate method of analysis, which has proved much simpler to apply than the methodsbasedontimecoursesthatitreplaced.Inthiswaytheydefined the methodology for steady- state experiments that has remained standard for 100 years. & 2015 The Author. Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
    [Show full text]
  • One Hundred Years of Michaelis–Menten Kinetics$
    Perspectives in Science (2015) 4,3–9 Available online at www.sciencedirect.com www.elsevier.com/locate/pisc REVIEW One hundred years of Michaelis–Menten kinetics$ Athel Cornish-Bowdenn Unité de Bioénergétique et Ingénierie des Protéines, Institut de Microbiologie de la Méditerranée, Centre National de la Recherche Scientifique, Aix-Marseille Université, 31 chemin Joseph-Aiguier, 13009 Marseille, France Received 27 January 2014; accepted 3 December 2014 Available online 24 December 2014 KEYWORDS Abstract Michaelis–Menten The year 2013 marked the centenary of the paper of Leonor Michaelis and Maud Menten (Michaelis kinetics; and Menten, 1913), and the 110th anniversary of the doctoral thesis of Victor Henri (Henri, 1903). enzyme-catalysis; These publications have had an enormous influence on the progress of biochemistry, and are more initial-rate equation; often cited in the 21st century than they were in the 20th. Henri laid the groundwork for the steady-state kinetics; understanding of enzyme mechanisms, but his experimental design was open to criticism. He reached Henry–Michaelis–Men- essentially correct conclusions about the action of invertase, but he took no steps to control the ten equation hydrogen-ion concentration, and he took no account of the spontaneous mutarotation of the glucose produced in the reaction. Michaelis and Menten corrected these shortcomings, and in addition they introduced the initial-rate method of analysis, which has proved much simpler to apply than the methodsbasedontimecoursesthatitreplaced.Inthiswaytheydefined the methodology for steady- state experiments that has remained standard for 100 years. & 2015 The Author. Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
    [Show full text]
  • Rates of Enzymatic Reactions CHAPTER 14
    JWCL281_c14_482-505.qxd 2/19/10 2:21 PM Page 482 Rates of Enzymatic Reactions CHAPTER 14 1 Chemical Kinetics 1. It is through kinetic studies that the binding affinities A. Elementary Reactions of substrates and inhibitors to an enzyme can be deter- B. Rates of Reactions mined and that the maximum catalytic rate of an enzyme C. Transition State Theory can be established. 2 Enzyme Kinetics 2. By observing how the rate of an enzymatic reaction A. The Michaelis–Menten Equation varies with the reaction conditions and combining this in- B. Analysis of Kinetic Data formation with that obtained from chemical and structural C. Reversible Reactions studies of the enzyme, the enzyme’s catalytic mechanism 3 Inhibition may be elucidated. A. Competitive Inhibition B. Uncompetitive Inhibition 3. Most enzymes, as we shall see in later chapters, func- C. Mixed Inhibition tion as members of metabolic pathways. The study of the 4 Effects of pH kinetics of an enzymatic reaction leads to an understanding of that enzyme’s role in an overall metabolic process. 5 Bisubstrate Reactions A. Terminology 4. Under the proper conditions, the rate of an enzymat- B. Rate Equations ically catalyzed reaction is proportional to the amount of C. Differentiating Bisubstrate Mechanisms the enzyme present, and therefore most enzyme assays D. Isotope Exchange (measurements of the amount of enzyme present) are Appendix: Derivations of Michaelis–Menten based on kinetic studies of the enzyme. Measurements of Equation Variants enzymatically catalyzed reaction rates are therefore among A. The Michaelis–Menten Equation for Reversible Reactions— the most commonly employed procedures in biochemical Equation [14.30] and clinical analyses.
    [Show full text]