Enzyme kinetics is the study of the rates of
enzyme-catalysed chemical reaction
A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s. In enzyme kinetics, the
reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's
kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in
metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run c ...
, how its activity is controlled, and how a
drug or a modifier (
inhibitor or
activator) might affect the rate.
An enzyme (E) is typically a
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
that promotes a reaction of another molecule, its
substrate (S). This binds to the
active site of the enzyme to produce an enzyme-substrate complex ES, and is transformed into an enzyme-product complex EP and from there to product P, via a
transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
ES*. The series of steps is known as the
mechanism
Mechanism may refer to:
* Mechanism (engineering), rigid bodies connected by joints in order to accomplish a desired force and/or motion transmission
*Mechanism (biology), explaining how a feature is created
*Mechanism (philosophy), a theory that ...
:
: E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P
This example assumes the simplest case of a reaction with one substrate and one product. Such cases exist: for example, a
mutase such as
phosphoglucomutase
Phosphoglucomutase () is an enzyme that transfers a phosphate group on an α-D-glucose monomer from the 1 to the 6 position in the forward direction or the 6 to the 1 position in the reverse direction.
More precisely, it facilitates the interconve ...
catalyses the transfer of a phospho group from one position to another, and
isomerase
Isomerases are a general class of enzymes that convert a molecule from one isomer to another. Isomerases facilitate intramolecular rearrangements in which bonds are broken and formed. The general form of such a reaction is as follows:
A–B ↠...
is a more general term for an enzyme that catalyses any one-substrate one-product reaction, such as
triosephosphate isomerase
Triose-phosphate isomerase (TPI or TIM) is an enzyme () that catalyzes the reversible interconversion of the triose phosphate isomers dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate.
TPI plays an important role in glycolysis and ...
. However, such enzymes are not very common, and are heavily outnumbered by enzymes that catalyse two-substrate two-product reactions: these include, for example, the NAD-dependent
dehydrogenase
A dehydrogenase is an enzyme belonging to the group of oxidoreductases that oxidizes a substrate by reducing an electron acceptor, usually NAD+/NADP+ or a flavin coenzyme such as FAD or FMN. Like all catalysts, they catalyze reverse as well as ...
s such as
alcohol dehydrogenase
Alcohol dehydrogenases (ADH) () are a group of dehydrogenase enzymes that occur in many organisms and facilitate the interconversion between alcohols and aldehydes or ketones with the reduction of nicotinamide adenine dinucleotide (NAD+) to NA ...
, which catalyses the oxidation of ethanol by NAD
+. Reactions with three or four substrates or products are less common, but they exist. There is no necessity for the number of products to be equal to the number of substrates; for example,
glyceraldehyde 3-phosphate dehydrogenase has three substrates and two products.
When enzymes bind multiple substrates, such as
dihydrofolate reductase (shown right), enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. An example of enzymes that bind a single substrate and release multiple products are
protease
A protease (also called a peptidase, proteinase, or proteolytic enzyme) is an enzyme that catalyzes (increases reaction rate or "speeds up") proteolysis, breaking down proteins into smaller polypeptides or single amino acids, and spurring the ...
s, which cleave one protein substrate into two polypeptide products. Others join two substrates together, such as
DNA polymerase
A DNA polymerase is a member of a family of enzymes that catalyze the synthesis of DNA molecules from nucleoside triphosphates, the molecular precursors of DNA. These enzymes are essential for DNA replication and usually work in groups to create ...
linking a
nucleotide
Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecule ...
to
DNA. Although these mechanisms are often a complex series of steps, there is typically one ''rate-determining step'' that determines the overall kinetics. This
rate-determining step
In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step or r/d step) or rate-limiting step. For a given reaction mechanism, the prediction of the ...
may be a chemical reaction or a
conformational change of the enzyme or substrates, such as those involved in the release of product(s) from the enzyme.
Knowledge of the
enzyme's structure is helpful in interpreting kinetic data. For example, the structure can suggest how substrates and products bind during catalysis; what changes occur during the reaction; and even the role of particular
amino acid
Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha a ...
residues in the mechanism. Some enzymes change shape significantly during the mechanism; in such cases, it is helpful to determine the enzyme structure with and without bound substrate analogues that do not undergo the enzymatic reaction.
Not all biological catalysts are protein enzymes:
RNA-based catalysts such as
ribozymes
Ribozymes (ribonucleic acid enzymes) are RNA molecules that have the ability to catalyze specific biochemical reactions, including RNA splicing in gene expression, similar to the action of protein enzymes. The 1982 discovery of ribozymes demons ...
and
ribosomes
Ribosomes ( ) are macromolecular machines, found within all cells, that perform biological protein synthesis (mRNA translation). Ribosomes link amino acids together in the order specified by the codons of messenger RNA (mRNA) molecules to ...
are essential to many cellular functions, such as
RNA splicing and
translation
Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
. The main difference between ribozymes and enzymes is that RNA catalysts are composed of nucleotides, whereas enzymes are composed of amino acids. Ribozymes also perform a more limited set of reactions, although their
reaction mechanisms and kinetics can be analysed and classified by the same methods.
General principles
![KinEnzymo(en)](https://upload.wikimedia.org/wikipedia/commons/0/09/KinEnzymo%28en%29.svg)
The reaction catalysed by an enzyme uses exactly the same reactants and produces exactly the same products as the uncatalysed reaction. Like other
catalysts
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
, enzymes do not alter the position of
equilibrium between substrates and products. However, unlike uncatalysed chemical reactions, enzyme-catalysed reactions display saturation kinetics. For a given enzyme concentration and for relatively low substrate concentrations, the reaction rate increases linearly with substrate concentration; the enzyme molecules are largely free to catalyse the reaction, and increasing substrate concentration means an increasing rate at which the enzyme and substrate molecules encounter one another. However, at relatively high substrate concentrations, the reaction rate
asymptotically approaches the theoretical maximum; the enzyme active sites are almost all occupied by substrates resulting in saturation, and the reaction rate is determined by the intrinsic turnover rate of the enzyme.
[Fromm H.J., Hargrove M.S. (2012) Enzyme Kinetics. In: Essentials of Biochemistry. Springer, Berlin, Heidelberg] The substrate concentration midway between these two limiting cases is denoted by ''K''
M. Thus, ''K''
M is the substrate concentration at which the reaction velocity is half of the maximum velocity.
The two important properties of enzyme kinetics are how easily the enzyme can be saturated with a substrate, and the maximum rate it can achieve. Knowing these properties suggests what an enzyme might do in the cell and can show how the enzyme will respond to changes in these conditions.
Enzyme assays
Enzyme assay
Enzyme assays are laboratory methods for measuring enzymatic activity. They are vital for the study of enzyme kinetics and enzyme inhibition.
Enzyme units
The quantity or concentration of an enzyme can be expressed in molar amounts, as with a ...
s are laboratory procedures that measure the rate of enzyme reactions. Since enzymes are not consumed by the reactions they catalyse, enzyme assays usually follow changes in the concentration of either substrates or products to measure the rate of reaction. There are many methods of measurement.
Spectrophotometric assays observe the change in the
absorbance
Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)". Alternatively, for samples which scatter light, absorbance may be defined as "the negative lo ...
of light between products and reactants; radiometric assays involve the incorporation or release of
radioactivity to measure the amount of product made over time. Spectrophotometric assays are most convenient since they allow the rate of the reaction to be measured continuously. Although radiometric assays require the removal and counting of samples (i.e., they are discontinuous assays) they are usually extremely sensitive and can measure very low levels of enzyme activity. An analogous approach is to use
mass spectrometry to monitor the incorporation or release of
stable isotope
The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific element. Hence, the plural form stable isotopes usually refers to isotopes of the same element. The relative abundanc ...
s as the substrate is converted into product. Occasionally, an assay fails and approaches are essential to resurrect a failed assay.
The most sensitive enzyme assays use
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...
s focused through a
microscope
A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisi ...
to observe changes in single enzyme molecules as they catalyse their reactions. These measurements either use changes in the
fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
of
cofactors during an enzyme's reaction mechanism, or of
fluorescent dyes
A fluorophore (or fluorochrome, similarly to a chromophore) is a fluorescent chemical compound that can re-emit light upon light excitation. Fluorophores typically contain several combined aromatic groups, or planar or cyclic molecules with sev ...
added onto specific sites of the
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
to report movements that occur during catalysis. These studies provide a new view of the kinetics and dynamics of single enzymes, as opposed to traditional enzyme kinetics, which observes the average behaviour of populations of millions of enzyme molecules.
An example progress curve for an enzyme assay is shown above. The enzyme produces product at an initial rate that is approximately linear for a short period after the start of the reaction. As the reaction proceeds and substrate is consumed, the rate continuously slows (so long as the substrate is not still at saturating levels). To measure the initial (and maximal) rate, enzyme assays are typically carried out while the reaction has progressed only a few percent towards total completion. The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. However, equipment for rapidly mixing liquids allows fast kinetic measurements at initial rates of less than one second. These very rapid assays are essential for measuring pre-steady-state kinetics, which are discussed below.
Most enzyme kinetics studies concentrate on this initial, approximately linear part of enzyme reactions. However, it is also possible to measure the complete reaction curve and fit this data to a non-linear
rate equation
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reac ...
. This way of measuring enzyme reactions is called progress-curve analysis. This approach is useful as an alternative to
rapid kinetics when the initial rate is too fast to measure accurately.
Single-substrate reactions
Enzymes with single-substrate mechanisms include
isomerase
Isomerases are a general class of enzymes that convert a molecule from one isomer to another. Isomerases facilitate intramolecular rearrangements in which bonds are broken and formed. The general form of such a reaction is as follows:
A–B ↠...
s such as
triosephosphateisomerase
Triose-phosphate isomerase (TPI or TIM) is an enzyme () that catalyzes the reversible interconversion of the triose phosphate isomers dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate.
TPI plays an important role in glycolysis and ...
or
bisphosphoglycerate mutase, intramolecular
lyases such as
adenylate cyclase
Adenylate cyclase (EC 4.6.1.1, also commonly known as adenyl cyclase and adenylyl cyclase, abbreviated AC) is an enzyme with systematic name ATP diphosphate-lyase (cyclizing; 3′,5′-cyclic-AMP-forming). It catalyzes the following reaction:
:A ...
and the
hammerhead ribozyme
The hammerhead ribozyme is an RNA motif that catalyzes reversible cleavage and ligation reactions at a specific site within an RNA molecule. It is one of several catalytic RNAs (ribozymes) known to occur in nature. It serves as a model system for ...
, an RNA lyase. However, some enzymes that only have a single substrate do not fall into this category of mechanisms.
Catalase is an example of this, as the enzyme reacts with a first molecule of
hydrogen peroxide
Hydrogen peroxide is a chemical compound with the formula . In its pure form, it is a very pale blue liquid that is slightly more viscous than water. It is used as an oxidizer, bleaching agent, and antiseptic, usually as a dilute solution (3%â ...
substrate, becomes oxidised and is then reduced by a second molecule of substrate. Although a single substrate is involved, the existence of a modified enzyme intermediate means that the mechanism of catalase is actually a ping–pong mechanism, a type of mechanism that is discussed in the ''Multi-substrate reactions'' section below.
Michaelis–Menten kinetics
As enzyme-catalysed reactions are saturable, their rate of catalysis does not show a linear response to increasing substrate. If the initial rate of the reaction is measured over a range of substrate concentrations (denoted as
, the initial reaction rate (
) increases as
increases, as shown on the right. However, as
gets higher, the enzyme becomes saturated with substrate and the initial rate reaches ''V''
max, the enzyme's maximum rate.
The
Michaelis–Menten kinetic model of a single-substrate reaction is shown on the right. There is an initial
bimolecular reaction between the enzyme E and substrate S to form the enzyme–substrate complex ES. The rate of enzymatic reaction increases with the increase of the substrate concentration up to a certain level called V
max; at V
max, increase in substrate concentration does not cause any increase in reaction rate as there is no more enzyme (E) available for reacting with substrate (S). Here, the rate of reaction becomes dependent on the ES complex and the reaction becomes a
unimolecular reaction with an order of zero. Though the enzymatic mechanism for the
unimolecular reaction ES -> _E + P can be quite complex, there is typically one rate-determining enzymatic step that allows this reaction to be modelled as a single catalytic step with an apparent unimolecular rate constant
''k''cat.
If the reaction path proceeds over one or several intermediates, ''k''
cat will be a function of several elementary rate constants, whereas in the simplest case of a single elementary reaction (e.g. no intermediates) it will be identical to the elementary unimolecular rate constant ''k''
2. The apparent unimolecular rate constant ''k''
cat is also called
turnover number Turnover number has two different meanings:
In enzymology, turnover number (also termed ''k''cat) is defined as the maximum number of chemical conversions of substrate molecules per second that a single active site will execute for a given enzym ...
, and denotes the maximum number of enzymatic reactions catalysed per second.
The
Michaelis–Menten equation describes how the (initial) reaction rate ''v''
0 depends on the position of the substrate-binding
equilibrium and the rate constant ''k''
2.
:
''(Michaelis–Menten equation)''
with the constants
:
This Michaelis–Menten equation is the basis for most single-substrate enzyme kinetics. Two crucial assumptions underlie this equation (apart from the general assumption about the mechanism only involving no intermediate or product inhibition, and there is no
allostericity or
cooperativity). The first assumption is the so-called
quasi-steady-state assumption (or pseudo-steady-state hypothesis), namely that the concentration of the substrate-bound enzyme (and hence also the unbound enzyme) changes much more slowly than those of the product and substrate and thus the change over time of the complex can be set to zero
. The second assumption is that the total enzyme concentration does not change over time, thus
.
A complete derivation can be found
here
Here is an adverb that means "in, on, or at this place". It may also refer to:
Software
* Here Technologies, a mapping company
* Here WeGo (formerly Here Maps), a mobile app and map website by Here Technologies, Here
Television
* Here TV (form ...
.
The Michaelis constant ''K''
M is experimentally defined as the concentration at which the rate of the enzyme reaction is half ''V''
max, which can be verified by substituting
= ''K''
M into the Michaelis–Menten equation and can also be seen graphically. If the rate-determining enzymatic step is slow compared to substrate dissociation (
), the Michaelis constant ''K''
M is roughly the
dissociation constant ''K''
D of the ES complex.
If
/chem> is small compared to then the term and also very little ES complex is formed, thus \approx /chem>. Therefore, the rate of product formation is
:
Thus the product formation rate depends on the enzyme concentration as well as on the substrate concentration, the equation resembles a bimolecular reaction with a corresponding pseudo-second order rate constant . This constant is a measure of catalytic efficiency
In the field of biochemistry, the specificity constant (also called kinetic efficiency or k_/K_), is a measure of how efficiently an enzyme converts substrates into products. A comparison of specificity constants can also be used as a measure of t ...
. The most efficient enzymes reach a in the range of . These enzymes are so efficient they effectively catalyse a reaction each time they encounter a substrate molecule and have thus reached an upper theoretical limit for efficiency ( diffusion limit); and are sometimes referred to as kinetically perfect enzymes. But most enzymes are far from perfect: the average values of and are about and , respectively.
Direct use of the Michaelis–Menten equation for time course kinetic analysis
The observed velocities predicted by the Michaelis–Menten equation can be used to directly model the time course disappearance of substrate and the production of product through incorporation of the Michaelis–Menten equation into the equation for first order chemical kinetics. This can only be achieved however if one recognises the problem associated with the use of Euler's number
The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithms. It is the limit of as approaches infinity, an expressi ...
in the description of first order chemical kinetics. i.e. ''e''−''k'' is a split constant that introduces a systematic error into calculations and can be rewritten as a single constant which represents the remaining substrate after each time period.
:
:
:
In 1983 Stuart Beal (and also independently Santiago Schnell
Santiago Schnell FRSC is a Venezuelan theoretical and mathematical biologist. He is the William K. Warren Foundation Dean of the College of Science at the University of Notre Dame, as well as a professor in the Department of Biological Sciences, an ...
and Claudio Mendoza in 1997) derived a closed form solution for the time course kinetics analysis of the Michaelis-Menten mechanism. The solution, known as the Schnell-Mendoza equation, has the form:
:
where W is the Lambert-W function. and where F(t) is
:
This equation is encompassed by the equation below, obtained by Berberan-Santos, which is also valid when the initial substrate concentration is close to that of enzyme,
:
where W is again the Lambert-W function.
Linear plots of the Michaelis–Menten equation
The plot of ''v'' versus above is not linear; although initially linear at low it bends over to saturate at high Before the modern era of nonlinear curve-fitting on computers, this nonlinearity could make it difficult to estimate ''K''M and ''V''max accurately. Therefore, several researchers developed linearisations of the Michaelis–Menten equation, such as the Lineweaver–Burk plot
In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934. The Lineweaver–Burk plot for inhibit ...
, the Eadie–Hofstee diagram
In biochemistry, an Eadie–Hofstee diagram (more usually called an Eadie–Hofstee plot) is a graphical representation of the Michaelis–Menten equation in enzyme kinetics. It has been known by various different names, including Eadie plot, Hof ...
and the Hanes–Woolf plot. All of these linear representations can be useful for visualising data, but none should be used to determine kinetic parameters, as computer software is readily available that allows for more accurate determination by nonlinear regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fi ...
methods.
The Lineweaver–Burk plot
In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934. The Lineweaver–Burk plot for inhibit ...
or double reciprocal plot is a common way of illustrating kinetic data. This is produced by taking the reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of both sides of the Michaelis–Menten equation. As shown on the right, this is a linear form of the Michaelis–Menten equation and produces a straight line with the equation ''y'' = m''x'' + c with a ''y''-intercept equivalent to 1/''V''max and an ''x''-intercept of the graph representing −1/''K''M.
:
Naturally, no experimental values can be taken at negative 1/ the lower limiting value 1/ = 0 (the ''y''-intercept) corresponds to an infinite substrate concentration, where ''1/v=1/Vmax'' as shown at the right; thus, the ''x''-intercept is an extrapolation
In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between know ...
of the experimental data taken at positive concentrations. More generally, the Lineweaver–Burk plot skews the importance of measurements taken at low substrate concentrations and, thus, can yield inaccurate estimates of ''V''max and ''K''M. A more accurate linear plotting method is the Eadie–Hofstee plot. In this case, ''v'' is plotted against ''v''/ In the third common linear representation, the Hanes–Woolf plot, ''v'' is plotted against
In general, data normalisation can help diminish the amount of experimental work and can increase the reliability of the output, and is suitable for both graphical and numerical analysis.
Practical significance of kinetic constants
The study of enzyme kinetics is important for two basic reasons. Firstly, it helps explain how enzymes work, and secondly, it helps predict how enzymes behave in living organisms. The kinetic constants defined above, ''K''M and ''V''max, are critical to attempts to understand how enzymes work together to control metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run c ...
.
Making these predictions is not trivial, even for simple systems. For example, oxaloacetate
Oxaloacetic acid (also known as oxalacetic acid or OAA) is a crystalline organic compound with the chemical formula HO2CC(O)CH2CO2H. Oxaloacetic acid, in the form of its conjugate base oxaloacetate, is a metabolic intermediate in many processes ...
is formed by malate dehydrogenase
Malate dehydrogenase () (MDH) is an enzyme that reversibly catalyzes the oxidation of malate to oxaloacetate using the reduction of NAD+ to NADH. This reaction is part of many metabolic pathways, including the citric acid cycle. Other malate ...
within the mitochondrion. Oxaloacetate can then be consumed by citrate synthase
The enzyme citrate synthase E.C. 2.3.3.1 (previously 4.1.3.7)] exists in nearly all living cells and stands as a pace-making enzyme in the first step of the citric acid cycle (or Krebs cycle). Citrate synthase is localized within eukaryotic cel ...
, phosphoenolpyruvate carboxykinase
Phosphoenolpyruvate carboxykinase (, PEPCK) is an enzyme in the lyase family used in the metabolic pathway of gluconeogenesis. It converts oxaloacetate into phosphoenolpyruvate and carbon dioxide.
It is found in two forms, cytosolic and mitoch ...
or aspartate aminotransferase
Aspartate transaminase (AST) or aspartate aminotransferase, also known as AspAT/ASAT/AAT or (serum) glutamic oxaloacetic transaminase (GOT, SGOT), is a pyridoxal phosphate (PLP)-dependent transaminase enzyme () that was first described by Arthur ...
, feeding into the citric acid cycle
The citric acid cycle (CAC)—also known as the Krebs cycle or the TCA cycle (tricarboxylic acid cycle)—is a series of chemical reactions to release stored energy through the oxidation of acetyl-CoA derived from carbohydrates, fats, and protein ...
, gluconeogenesis or aspartic acid biosynthesis, respectively. Being able to predict how much oxaloacetate goes into which pathway requires knowledge of the concentration of oxaloacetate as well as the concentration and kinetics of each of these enzymes. This aim of predicting the behaviour of metabolic pathways reaches its most complex expression in the synthesis of huge amounts of kinetic and gene expression data into mathematical models of entire organisms. Alternatively, one useful simplification of the metabolic modelling problem is to ignore the underlying enzyme kinetics and only rely on information about the reaction network's stoichiometry, a technique called flux balance analysis
Flux balance analysis (FBA) is a mathematical method for simulating metabolism in genome-scale reconstructions of metabolic networks. In comparison to traditional methods of modeling, FBA is less intensive in terms of the input data required for c ...
.
Michaelis–Menten kinetics with intermediate
One could also consider the less simple case
:
+ S
<=> _k_]
ES
-> _2 EI
-> _3 + P
where a complex with the enzyme and an intermediate exists and the intermediate is converted into product in a second step. In this case we have a very similar equation
:
but the constants are different
:
We see that for the limiting case , thus when the last step from EI -> E + P is much faster than the previous step, we get again the original equation. Mathematically we have then and .
Multi-substrate reactions
Multi-substrate reactions follow complex rate equations that describe how the substrates bind and in what sequence. The analysis of these reactions is much simpler if the concentration of substrate A is kept constant and substrate B varied. Under these conditions, the enzyme behaves just like a single-substrate enzyme and a plot of ''v'' by gives apparent ''K''M and ''V''max constants for substrate B. If a set of these measurements is performed at different fixed concentrations of A, these data can be used to work out what the mechanism of the reaction is. For an enzyme that takes two substrates A and B and turns them into two products P and Q, there are two types of mechanism: ternary complex and ping–pong.
Ternary-complex mechanisms
In these enzymes, both substrates bind to the enzyme at the same time to produce an EAB ternary complex. The order of binding can either be random (in a random mechanism) or substrates have to bind in a particular sequence (in an ordered mechanism). When a set of ''v'' by curves (fixed A, varying B) from an enzyme with a ternary-complex mechanism are plotted in a Lineweaver–Burk plot
In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934. The Lineweaver–Burk plot for inhibit ...
, the set of lines produced will intersect.
Enzymes with ternary-complex mechanisms include glutathione ''S''-transferase, dihydrofolate reductase and DNA polymerase
A DNA polymerase is a member of a family of enzymes that catalyze the synthesis of DNA molecules from nucleoside triphosphates, the molecular precursors of DNA. These enzymes are essential for DNA replication and usually work in groups to create ...
. The following links show short animations of the ternary-complex mechanisms of the enzymes dihydrofolate reductase and DNA polymerase.
Ping–pong mechanisms
As shown on the right, enzymes with a ping-pong mechanism can exist in two states, E and a chemically modified form of the enzyme E*; this modified enzyme is known as an intermediate. In such mechanisms, substrate A binds, changes the enzyme to E* by, for example, transferring a chemical group to the active site, and is then released. Only after the first substrate is released can substrate B bind and react with the modified enzyme, regenerating the unmodified E form. When a set of ''v'' by curves (fixed A, varying B) from an enzyme with a ping–pong mechanism are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced. This is called a secondary plot.
Enzymes with ping–pong mechanisms include some oxidoreductases
In biochemistry, an oxidoreductase is an enzyme that catalyzes the transfer of electrons from one molecule, the reductant, also called the electron donor, to another, the oxidant, also called the electron acceptor. This group of enzymes usually uti ...
such as thioredoxin peroxidase, transferases
A transferase is any one of a class of enzymes that catalyse the transfer of specific functional groups (e.g. a methyl or glycosyl group) from one molecule (called the donor) to another (called the acceptor). They are involved in hundreds of d ...
such as acylneuraminate cytidylyltransferase and serine protease
Serine proteases (or serine endopeptidases) are enzymes that cleave peptide bonds in proteins. Serine serves as the nucleophilic amino acid at the (enzyme's) active site.
They are found ubiquitously in both eukaryotes and prokaryotes. Seri ...
s such as trypsin
Trypsin is an enzyme in the first section of the small intestine that starts the digestion of protein molecules by cutting these long chains of amino acids into smaller pieces. It is a serine protease from the PA clan superfamily, found in the d ...
and chymotrypsin. Serine proteases are a very common and diverse family of enzymes, including digestive enzymes (trypsin, chymotrypsin, and elastase), several enzymes of the blood clotting cascade and many others. In these serine proteases, the E* intermediate is an acyl-enzyme species formed by the attack of an active site serine residue on a peptide bond in a protein substrate. A short animation showing the mechanism of chymotrypsin is linked here.
Reversible catalysis and the Haldane equation
External factors may limit the ability of an enzyme to catalyse a reaction in both directions (whereas the nature of a catalyst in itself means that it cannot catalyse just one direction, according to the principle of microscopic reversibility The principle of microscopic reversibility in physics and chemistry is twofold:
* First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with resp ...
). We consider the case of an enzyme that catalyses the reaction in both directions:
+
<=> _k_]
ES
<=> _k_]
+
The steady-state, initial rate of the reaction is
is positive if the reaction proceed in the forward direction () and negative otherwise.
:en:Equilibrium constant, Equilibrium requires that , which occurs when . This shows that thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
forces a relation between the values of the 4 rate constants.
The values of the forward and backward ''maximal'' rates, obtained for , , and , , respectively, are and , respectively. Their ratio is not equal to the equilibrium constant, which implies that thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
does not constrain the ratio of the maximal rates. This explains that enzymes can be much "better catalysts" (''in terms of maximal rates'') in one particular direction of the reaction.
On can also derive the two Michaelis constants and . The Haldane equation is the relation .
Therefore, thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
constrains the ratio between the forward and backward values, not the ratio of values.
Non-Michaelis–Menten kinetics
Many different enzyme systems follow non Michaelis-Menten behavior. A select few examples include kinetics of self-catalytic enzymes, cooperative and allosteric enzymes, interfacial and intracellular enzymes, processive enzymes and so forth. Some enzymes produce a sigmoid
Sigmoid means resembling the lower-case Greek letter sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς) or the Latin letter S. Specific uses include:
* Sigmoid function, a mathematical function
* Sigmoid colon, part of the l ...
''v'' by plot, which often indicates cooperative binding
Molecular binding is an interaction between molecules that results in a stable physical association between those molecules. Cooperative binding occurs in binding systems containing more than one type, or species, of molecule and in which one of th ...
of substrate to the active site. This means that the binding of one substrate molecule affects the binding of subsequent substrate molecules. This behavior is most common in multimeric
In chemistry and biochemistry, an oligomer () is a molecule that consists of a few repeating units which could be derived, actually or conceptually, from smaller molecules, monomers.Quote: ''Oligomer molecule: A molecule of intermediate relativ ...
enzymes with several interacting active sites. Here, the mechanism of cooperation is similar to that of hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythrocyt ...
, with binding of substrate to one active site altering the affinity of the other active sites for substrate molecules. Positive cooperativity occurs when binding of the first substrate molecule ''increases'' the affinity of the other active sites for substrate. Negative cooperativity occurs when binding of the first substrate ''decreases'' the affinity of the enzyme for other substrate molecules.
Allosteric enzymes include mammalian tyrosyl tRNA-synthetase, which shows negative cooperativity, and bacterial aspartate transcarbamoylase
Aspartate carbamoyltransferase (also known as aspartate transcarbamoylase or ATCase) catalyzes the first step in the pyrimidine biosynthetic pathway ().
In '' E. coli'', the enzyme is a multi- subunit protein complex composed of 12 subunits (3 ...
and phosphofructokinase
Phosphofructokinase (PFK) is a kinase enzyme that phosphorylates fructose 6-phosphate in glycolysis.
Function
The enzyme-catalysed transfer of a phosphoryl group from ATP is an important reaction in a wide variety of biological processes. ...
, which show positive cooperativity.
Cooperativity is surprisingly common and can help regulate the responses of enzymes to changes in the concentrations of their substrates. Positive cooperativity makes enzymes much more sensitive to and their activities can show large changes over a narrow range of substrate concentration. Conversely, negative cooperativity makes enzymes insensitive to small changes in
The Hill equation is often used to describe the degree of cooperativity quantitatively in non-Michaelis–Menten kinetics. The derived Hill coefficient ''n'' measures how much the binding of substrate to one active site affects the binding of substrate to the other active sites. A Hill coefficient of <1 indicates negative cooperativity and a coefficient of >1 indicates positive cooperativity.
Pre-steady-state kinetics
In the first moment after an enzyme is mixed with substrate, no product has been formed and no intermediates exist. The study of the next few milliseconds of the reaction is called pre-steady-state kinetics. Pre-steady-state kinetics is therefore concerned with the formation and consumption of enzyme–substrate intermediates (such as ES or E*) until their steady-state concentrations are reached.
This approach was first applied to the hydrolysis reaction catalysed by chymotrypsin. Often, the detection of an intermediate is a vital piece of evidence in investigations of what mechanism an enzyme follows. For example, in the ping–pong mechanisms that are shown above, rapid kinetic measurements can follow the release of product P and measure the formation of the modified enzyme intermediate E*. In the case of chymotrypsin, this intermediate is formed by an attack on the substrate by the nucleophilic
In chemistry, a nucleophile is a chemical species that forms bonds by donating an electron pair. All molecules and ions with a free pair of electrons or at least one pi bond can act as nucleophiles. Because nucleophiles donate electrons, they are ...
serine in the active site and the formation of the acyl-enzyme intermediate.
In the figure to the right, the enzyme produces E* rapidly in the first few seconds of the reaction. The rate then slows as steady state is reached. This rapid burst phase of the reaction measures a single turnover of the enzyme. Consequently, the amount of product released in this burst, shown as the intercept on the ''y''-axis of the graph, also gives the amount of functional enzyme which is present in the assay.
Chemical mechanism
An important goal of measuring enzyme kinetics is to determine the chemical mechanism of an enzyme reaction, i.e., the sequence of chemical steps that transform substrate into product. The kinetic approaches discussed above will show at what rates intermediates are formed and inter-converted, but they cannot identify exactly what these intermediates are.
Kinetic measurements taken under various solution conditions or on slightly modified enzymes or substrates often shed light on this chemical mechanism, as they reveal the rate-determining step or intermediates in the reaction. For example, the breaking of a covalent bond to a hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
is a common rate-determining step. Which of the possible hydrogen transfers is rate determining can be shown by measuring the kinetic effects of substituting each hydrogen by deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...
, its stable isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...
. The rate will change when the critical hydrogen is replaced, due to a primary kinetic isotope effect
In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for th ...
, which occurs because bonds to deuterium are harder to break than bonds to hydrogen. It is also possible to measure similar effects with other isotope substitutions, such as 13C/12C and 18O/16O, but these effects are more subtle.
Isotopes can also be used to reveal the fate of various parts of the substrate molecules in the final products. For example, it is sometimes difficult to discern the origin of an oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as ...
atom in the final product; since it may have come from water or from part of the substrate. This may be determined by systematically substituting oxygen's stable isotope 18O into the various molecules that participate in the reaction and checking for the isotope in the product. The chemical mechanism can also be elucidated by examining the kinetics and isotope effects under different pH conditions, by altering the metal ions or other bound cofactors, by site-directed mutagenesis
Site-directed mutagenesis is a molecular biology method that is used to make specific and intentional mutating changes to the DNA sequence of a gene and any gene products. Also called site-specific mutagenesis or oligonucleotide-directed mutagenesi ...
of conserved amino acid residues, or by studying the behaviour of the enzyme in the presence of analogues of the substrate(s).
Enzyme inhibition and activation
Enzyme inhibitors are molecules that reduce or abolish enzyme activity, while enzyme activators are molecules that increase the catalytic rate of enzymes. These interactions can be either ''reversible'' (i.e., removal of the inhibitor restores enzyme activity) or ''irreversible'' (i.e., the inhibitor permanently inactivates the enzyme).
Reversible inhibitors
Traditionally reversible enzyme inhibitors have been classified as competitive
Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indivi ...
, uncompetitive, or non-competitive, according to their effects on ''K''M and ''V''max. These different effects result from the inhibitor binding to the enzyme E, to the enzyme–substrate complex ES, or to both, respectively. The division of these classes arises from a problem in their derivation and results in the need to use two different binding constants for one binding event. The binding of an inhibitor and its effect on the enzymatic activity are two distinctly different things, another problem the traditional equations fail to acknowledge. In noncompetitive inhibition the binding of the inhibitor results in 100% inhibition of the enzyme only, and fails to consider the possibility of anything in between. In noncompetitive inhibition, the inhibitor will bind to an enzyme at its allosteric site; therefore, the binding affinity, or inverse of ''K''M, of the substrate with the enzyme will remain the same. On the other hand, the Vmax will decrease relative to an uninhibited enzyme. On a Lineweaver-Burk plot, the presence of a noncompetitive inhibitor is illustrated by a change in the y-intercept, defined as 1/Vmax. The x-intercept, defined as −1/''K''M, will remain the same. In competitive inhibition, the inhibitor will bind to an enzyme at the active site, competing with the substrate. As a result, the ''K''M will increase and the Vmax will remain the same. The common form of the inhibitory term also obscures the relationship between the inhibitor binding to the enzyme and its relationship to any other binding term be it the Michaelis–Menten equation or a dose response curve associated with ligand receptor binding. To demonstrate the relationship the following rearrangement can be made:
:
Adding zero to the bottom (
:
Dividing by Ki
:
This notation demonstrates that similar to the Michaelis–Menten equation, where the rate of reaction depends on the percent of the enzyme population interacting with substrate, the effect of the inhibitor is a result of the percent of the enzyme population interacting with inhibitor. The only problem with this equation in its present form is that it assumes absolute inhibition of the enzyme with inhibitor binding, when in fact there can be a wide range of effects anywhere from 100% inhibition of substrate turn over to just >0%. To account for this the equation can be easily modified to allow for different degrees of inhibition by including a delta ''V''max term.
:
or
:
This term can then define the residual enzymatic activity present when the inhibitor is interacting with individual enzymes in the population. However the inclusion of this term has the added value of allowing for the possibility of activation if the secondary ''V''max term turns out to be higher than the initial term. To account for the possibly of activation as well the notation can then be rewritten replacing the inhibitor "I" with a modifier term denoted here as "X".
:
While this terminology results in a simplified way of dealing with kinetic effects relating to the maximum velocity of the Michaelis–Menten equation, it highlights potential problems with the term used to describe effects relating to the ''K''M. The ''K''M relating to the affinity of the enzyme for the substrate should in most cases relate to potential changes in the binding site of the enzyme which would directly result from enzyme inhibitor interactions. As such a term similar to the one proposed above to modulate ''V''max should be appropriate in most situations:
:
A few examples of reversible inhibition belonging to the competitive and uncompetitive models have been discussed in the following papers.
Irreversible inhibitors
Enzyme inhibitors can also irreversibly inactivate enzymes, usually by covalently modifying active site residues. These reactions, which may be called suicide substrates, follow exponential decay functions and are usually saturable. Below saturation, they follow first order kinetics with respect to inhibitor. Irreversible inhibition could be classified into two distinct types. Affinity labelling is a type of irreversible inhibition where a functional group that is highly reactive modifies a catalytically critical residue on the protein of interest to bring about inhibition. Mechanism-based inhibition, on the other hand, involves binding of the inhibitor followed by enzyme mediated alterations that transform the latter into a reactive group that irreversibly modifies the enzyme.
Philosophical discourse on reversibility and irreversibility of inhibition
Having discussed reversible inhibition and irreversible inhibition in the above two headings, it would have to be pointed out that the concept of reversibility (or irreversibility) is a purely theoretical construct exclusively dependent on the time-frame of the assay, i.e., a reversible assay involving association and dissociation of the inhibitor molecule in the minute timescales would seem irreversible if an assay assess the outcome in the seconds and vice versa. There is a continuum of inhibitor behaviors spanning reversibility and irreversibility at a given non-arbitrary assay time frame. There are inhibitors that show slow-onset behavior and most of these inhibitors, invariably, also show tight-binding to the protein target of interest.
Mechanisms of catalysis
The favoured model for the enzyme–substrate interaction is the induced fit model. This model proposes that the initial interaction between enzyme and substrate is relatively weak, but that these weak interactions rapidly induce conformational changes in the enzyme that strengthen binding. These conformational changes also bring catalytic residues in the active site close to the chemical bonds in the substrate that will be altered in the reaction. Conformational changes can be measured using circular dichroism or dual polarisation interferometry
Dual-polarization interferometry (DPI) is an analytical technique that probes molecular layers adsorbed to the surface of a waveguide using the evanescent wave of a laser beam. It is used to measure the conformational change in proteins, or othe ...
. After binding takes place, one or more mechanisms of catalysis lower the energy of the reaction's transition state
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked ...
by providing an alternative chemical pathway for the reaction. Mechanisms of catalysis include catalysis by bond strain; by proximity and orientation; by active-site proton donors or acceptors; covalent catalysis and quantum tunnelling.[
Enzyme kinetics cannot prove which modes of catalysis are used by an enzyme. However, some kinetic data can suggest possibilities to be examined by other techniques. For example, a ping–pong mechanism with burst-phase pre-steady-state kinetics would suggest covalent catalysis might be important in this enzyme's mechanism. Alternatively, the observation of a strong pH effect on ''V''max but not ''K''M might indicate that a residue in the active site needs to be in a particular ]ionisation
Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecu ...
state for catalysis to occur.
History
In 1902 Victor Henri
Victor Henri (6 June 1872 – 21 June 1940) was a French-Russian physical chemist and physiologist. He was born in Marseilles as a son of Russian parents. He is known mainly as an early pioneer in enzyme kinetics. He published more than 500 pape ...
proposed a quantitative theory of enzyme kinetics, but at the time the experimental significance of the hydrogen ion concentration was not yet recognized. After Peter Lauritz Sørensen had defined the logarithmic pH-scale and introduced the concept of buffering in 1909 the German chemist Leonor Michaelis
Leonor Michaelis (16 January 1875 – 8 October 1949) was a German biochemist, physical chemist, and physician, known for his work with Maud Menten on enzyme kinetics in 1913, as well as for work on enzyme inhibition, pH and quinones.
E ...
and Dr. Maud Leonora Menten
Maud Leonora Menten (March 20, 1879 – July 17, 1960) was a Canadian physician and chemist. As a bio-medical and medical researcher, she made significant contributions to enzyme kinetics and histochemistry and invented a procedure that rema ...
(a postdoctoral researcher in Michaelis's lab at the time) repeated Henri's experiments and confirmed his equation, which is now generally referred to as Michaelis-Menten kinetics (sometimes also ''Henri-Michaelis-Menten kinetics''). Their work was further developed by G. E. Briggs and J. B. S. Haldane
John Burdon Sanderson Haldane (; 5 November 18921 December 1964), nicknamed "Jack" or "JBS", was a British-Indian scientist who worked in physiology, genetics, evolutionary biology, and mathematics. With innovative use of statistics in biolog ...
, who derived kinetic equations that are still widely considered today a starting point in modeling enzymatic activity.
The major contribution of the Henri-Michaelis-Menten approach was to think of enzyme reactions in two stages. In the first, the substrate binds reversibly to the enzyme, forming the enzyme-substrate complex. This is sometimes called the Michaelis complex. The enzyme then catalyzes the chemical step in the reaction and releases the product. The kinetics of many enzymes is adequately described by the simple Michaelis-Menten model, but all enzymes have internal motions that are not accounted for in the model and can have significant contributions to the overall reaction kinetics. This can be modeled by introducing several Michaelis-Menten pathways that are connected with fluctuating rates, which is a mathematical extension of the basic Michaelis Menten mechanism.
Software
ENZO (Enzyme Kinetics) is a graphical interface tool for building kinetic models of enzyme catalyzed reactions. ENZO automatically generates the corresponding differential equations from a stipulated enzyme reaction scheme. These differential equations are processed by a numerical solver and a regression algorithm which fits the coefficients of differential equations to experimentally observed time course curves. ENZO allows rapid evaluation of rival reaction schemes and can be used for routine tests in enzyme kinetics.
ENZO server
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See also
*Protein dynamics Proteins are generally thought to adopt unique structures determined by their amino acid sequences. However, proteins are not strictly static objects, but rather populate ensembles of (sometimes similar) conformations. Transitions between these stat ...
*Diffusion limited enzyme
A diffusion-limited enzyme catalyses a reaction so efficiently that the rate limiting step is that of substrate diffusion into the active site, or product diffusion out. This is also known as kinetic perfection or catalytic perfection. Since ...
*Langmuir adsorption model
The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressu ...
Footnotes
:α.''
Link: Interactive Michaelis–Menten kinetics tutorial (Java required)
:β.''
:γ.''
:δ.''
References
Further reading
Introductory
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Advanced
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External links
Animation of an enzyme assay
— Shows effects of manipulating assay conditions
MACiE
— A database of enzyme reaction mechanisms
ENZYME
— Expasy enzyme nomenclature database
ENZO
— Web application for easy construction and quick testing of kinetic models of enzyme catalyzed reactions.
ExCatDB
— A database of enzyme catalytic mechanisms
BRENDA
— Comprehensive enzyme database, giving substrates, inhibitors and reaction diagrams
SABIO-RK
— A database of reaction kinetics
— Animations of several enzyme reaction mechanisms
Symbolism and Terminology in Enzyme Kinetics
— A comprehensive explanation of concepts and terminology in enzyme kinetics
— An accessible set of on-line tutorials on enzyme kinetics
— An animated tutorial with audio
{{DEFAULTSORT:Enzyme Kinetics
Catalysis