Wikiprojekt:Tłumaczenie artykułów/Kinetyka enzymatyczna

Dihydrofolate reductase from E. coli with its two substrates, dihydrofolate (right) and NADPH (left), bound in the active site. The protein is shown as a ribbon diagram, with alpha helices in red, beta sheets in yellow and loops in blue. Generated from 7DFR.

Kinetyka enzymatyczna - dział chemii fizycznej zajmujący się badaniem czasowego przebiegu reakcji chemicznych katalizowanych przez enzymy. Jest to szczegółowy dział kinetyki chemicznej. Także, w bardziej ogólnym ujęciu, kinetyka enzymatyczna to charakterystyka reakcji enzymatycznych ze szczególnym uwzględnieniem ich szybkości, przebiegu i mechanizmów. Badanie kinetyki reakcji z udziałem enzymów pozwala na poznanie sposobu fizjologicznej kontroli enzymów w komórkach, ich roli w metabolizmie czy wpływu inhibitorów i aktywatorów na ich aktywność.

Enzymy to białkowe katalizatory przyspieszające specyficzne reakcje chemiczne wskutek obniżenia energii aktywacji potrzebnej do przebiegu tych reakcji. Enzymy wiążą substraty w swoim centrum aktywnym i przetwarzają na produkty w sekwencji kroków definiowanych przez mechanizmy katalizy enzymatycznej. Mechanizmy te można podzielić na mechanizmy katalizy pojedynczego substratu i katalizy wielu substratów.

Katalizatory niebiałkowe, takie jak rybozymy oparte na RNA, charakteryzują się nieco innymi mechanizmami reakcji i mniejszą różnorodnością katalizowanych reakcji. Jednak ich kinetyka i mechanika działania może być analizowana i klasyfikowana tymi samymi metodami, jakie są używane dla enzymów białkowych.

Kinetic studies on enzymes that only bind one substrate, such as triosephosphate isomerase, aim to measure the affinity with which the enzyme binds this substrate and the turnover rate.

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 proteases, which cleave one protein substrate into two polypeptide products. Others join two substrates together, such as DNA polymerase linking a nucleotide 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 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.

Pomocna w interpretowaniu danych kinetycznych jest znajomość struktury białek. Na postawie struktury można wywnioskować jak i gdzie wiązane są substraty i produkty podczas katalizy, jakim zmianom może podlegać konformacja enzymu i role poszczególnych reszt aminokwasowych w katalizowanej reakcji. W niektórych wypadkach udaje się rozwiązać strukturę przestrzenną enzymu skrystalizowanego razem ze związanym substratem (lub jego analogiem), co dostarcza bezpośrednich wskazówek o tym jak przestrzennie układają się one wobec siebie.

Główne zasady

Prędkość reakcji będzie rosła przy wzroście stężenia substratów, aż do maksymalnego wysycenia miejsc aktywnych

Tak jak wszystkie katalizatory enzymy używają tych samych substratów, czego wynikiem są takie same produkty, jak miało by miejsce w reakcji niekatalizowanej. Enzymy nie zmieniają także stanu równowagi reakcji chemicznej, a jedynie przyspieszają jego ustalenie. Zazwyczaj w obecności enzymu reakcja zachodzi w kierunku takim samym, w jakim by zachodziła spontanicznie, jedynie wzrasta jej szybkość. Enzymy jednak potrafią się wysycić substratami. Oznacza to, że przy stałej ilości enzymu, a rosnącej substratów, prędkość reakcji będzie rosnąć, ponieważ wysycane są kolejne, jeszcze nie zajęte, miejsca aktywne enzymów. Jednak po maksymalnym wysyceniu enzymów substratami, co w praktyce oznacza, że każde miejsce aktywne ma związany substrat lub produkt pośredni reakcji, reakcja osiąga maksymalną prędkość i dalsze dodawanie substratów tego nie zmienia. Dwie najważniejsze cechy enzymu określają jak szybko wysyca się on swoimi substratami (maksymalne stężenie substratu przy stałej ilości enzymu) oraz jak zwiększają szybkość reakcji chemicznej.

Testy aktywności enzymatycznej (ang. Enzyme assays)

Progress curve for an enzyme reaction. The slope in the initial rate period is the initial rate of reaction v. The Michaelis-Menten equation describe how this slope varies with the concentration of substrate.

Testy aktywności enzymatycznej to wszelkie procedury i doświadczenia mające na celu zmierzenie szybkości i innych cech reakcji enzymatycznych. Ponieważ w reakcjach enzymatycznych enzymy nie zużywają się, nie biorą w nich udziału jako klasyczne substraty czy produkty, w testach ich aktywności monitoruje się zmiany stężenia w czasie substratów bądź produktów. W zależności od ich natury odczyt może być prowadzony na wiele sposobów.

Spectrophotometric assays observe change in the absorbance 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 isotopes as substrate is converted into product.

The most sensitive enzyme assays use lasers focused through a microscope to observe changes in single enzyme molecules as they catalyse their reactions. These measurements either use changes in the fluorescence of cofactors during an enzyme's reaction mechanism, or of fluorescent dyes added onto specific sites of the protein to report movements that occur during catalysis. These studies are providing 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.

On the left is shown a typical progress curve for an enzyme assay. The enzyme produces product at a linear initial rate at the start of the reaction. Later in this progress curve, the rate slows down as substrate is used up or products accumulate. The length of the initial rate period depends on the assay conditions and can range from milliseconds to hours. Enzyme assays are usually set up to produce an initial rate lasting over a minute, to make measurements easier. However, equipment for rapidly mixing liquids allows fast kinetic measurements on 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, 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. 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 isomerases such as triosephosphateisomerase or bisphosphoglycerate mutase, intramolecular lyases such as adenylate cyclase and the hammerhead ribozyme, a 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 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.

Kinetyka Michaelis-Menten

Saturation curve for an enzyme showing the relation between the concentration of substrate and rate

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 [S]), the reaction rate (v) increases as [S] increases, as shown on the right. However, as [S] gets higher, the enzyme becomes saturated with substrate and the 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. Although the enzymatic mechanism for the unimolecular reaction $ES\rightarrow E+P$ reaction can be quite complex, there is typically one rate-determining enzymatic step that allows the mechanism to be modelled as a single catalytic step of rate constant k₂.

${\begin{matrix}v=k_{2}[{\mbox{ES}}]\end{matrix}}$    (Equation 1).

k₂ is also called k_cat or the turnover number, the maximum number of enzymatic reactions catalyzed per second.

At low concentrations of substrate [S], the enzyme exists in an equilibrium between both the free form E and the enzyme–substrate complex ES; increasing [S] likewise increases [ES] at the expense of [E], shifting the binding equilibrium to the right. Since the rate of the reaction depends on the concentration [ES], the rate is sensitive to small changes in [S]. However, at very high [S], the enzyme is entirely saturated with substrate, and exists only in the ES form. Under these conditions, the rate (v≈k₂[E]_tot=V_max) is insensitive to small changes in [S]; here, [E]_tot is the total enzyme concentration

$[{\mbox{E}}]_{\mathrm {tot} }\ {\stackrel {\mathrm {def} }{=}}\ [{\mbox{E}}]+[{\mbox{ES}}]$

which is approximately equal to the concentration [ES] under saturating conditions.

The Michaelis–Menten equation describes how the reaction rate v depends on the position of the substrate-binding equilibrium and the rate constant k₂. Michaelis and Menten showed when k₂ is much less than k_-1 (called the equilibrium assumption) they could derive the following equation:

$v={\frac {V_{\max[}{\mbox{S}}]}{K_{m}+[{\mbox{S}}]}}$    (Equation 2)

This Michaelis-Menten equation is the basis for most single-substrate enzyme kinetics.

The Michaelis constant K_m is defined as the concentration at which the rate of the enzyme reaction is half V_max. This may be verified by substituting [S] = K_m into the Michaelis-Menten equation. If the rate-determining enzymatic step is slow compared to substrate dissociation (k₂ << k_-1), the Michaelis constant K_m is roughly the dissociation constant of the ES complex, although this situation is relatively rare.

The more normal situation where k₂ > k_-1 is sometimes called Briggs-Haldane kinetics. The Michaelis–Menten equation still holds under these more general conditions, as may be derived from the steady-state approximation. During the initial-rate period, the reaction rate v is roughly constant, indicating that [ES] is similarly constant (cf. equation 1):

${\frac {d}{dt}}[{\mbox{ES}}]=k_{1}[{\mbox{E}}][{\mbox{S}}]-k_{2}[{\mbox{ES}}]-k_{-1}[{\mbox{ES}}]\approx 0$

Therefore, the concentration [ES] is given by the formula

$[{\mbox{ES}}]\approx {\frac {[{\mbox{E}}]_{\mathrm {tot} }[{\mbox{S}}]}{[{\mbox{S}}]+K_{m}}}$

where the Michaelis constant K_m is defined

$K_{m}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {k_{2}+k_{-1}}{k_{1}}}\approx {\frac {[{\mbox{E}}][{\mbox{S}}]}{[{\mbox{ES}}]}}$

([E] is the concentration of free enzyme). Taken together, the general formula for the reaction rate v is again the Michaelis-Menten equation:

$v=k_{2}[\mathrm {ES} ]={\frac {k_{2}[{\mbox{E}}]_{\mathrm {tot} }[{\mbox{S}}]}{[{\mbox{S}}]+K_{m}}}={\frac {V_{\max[}{\mbox{S}}]}{[{\mbox{S}}]+K_{m}}}$

The specificity constant $k_{cat}/K_{m}$ is a measure of how efficiently an enzyme converts a substrate into product. Using the definition of the Michaelis constant $K_{m}$, the Michaelis-Menten equation may be written in the form

$v=k_{2}[\mathrm {ES} ]={\frac {k_{2}}{K_{m}}}[{\mbox{E}}][{\mbox{S}}]$

where [E] is the concentration of free enzyme. Thus, the specificity constant is an effective second-order rate constant for free enzyme to react with free substrate to form product. The specificity constant is limited by the frequency with which the substrate and enzyme encounter each other in solution, as high as 10¹⁰ M⁻¹ s⁻¹. Remarkably, this maximum rate is largely unaffected by the size of either the substrate or the enzyme. The ratio of the specificity constants for two substrates is a quantitative comparison of how efficient the enzyme is in converting those substrates. The slope of the Michaelis-Menten graph at low substrate concentration [S] (when [S] << K_m) also yields the specificity constant.

Linear plots of the Michaelis-Menten equation

Lineweaver–Burk or double-reciprocal plot of kinetic data, showing the significance of the axis intercepts and gradient

Using an interactive Michaelis–Menten kinetics tutorial at the University of Virginia, the effects on the behaviour of an enzyme of varying kinetic constants can be explored.

The plot of v versus [S] above is not linear; although initially linear at low [S], it bends over to saturate at high [S]. 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 linearizations of the Michaelis-Menten equation, such as the Lineweaver-Burk plot, the Eadie-Hofstee diagram and the Hanes-Woolf plot. All of these linear representations can be useful for visualizing 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 methods.

The Lineweaver-Burk plot or double reciprocal plot is common way of illustrating kinetic data. This is produced by taking the reciprocal 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 = mx + c with a y-intercept equivalent to 1/V_max and an x-intercept of the graph representing -1/K_m.

${\frac {1}{v}}={\frac {K_{m}}{V_{\max[}{\mbox{S}}]}}+{\frac {1}{V_{\max }}}$

Naturally, no experimental values can be taken at negative 1/[S]; the lower limiting value 1/[S] = 0 (the y-intercept) corresponds to an infinite substrate concentration, where 1/v=1/V_max as shown at the right; thus, the x-intercept is an extrapolation 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/[S]. In the third common linear representation, the Hanes-Woolf plot, [S]/v is plotted against [S]. 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.

Znaczenie praktyczne stałych kinetycznych

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.

Making these predictions is not trivial, even for simple systems. For example, oxaloacetate is formed by malate dehydrogenase within the mitochondrion. Oxaloacetate can then be consumed by citrate synthase, phosphoenolpyruvate carboxykinase or aspartate aminotransferase, feeding into the citric acid cycle, 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. Although this goal is far in the future for any eukaryote, attempts are now being made to achieve this in bacteria, with models of Escherichia coli metabolism now being produced and tested.

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 [S] 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 [S] curves (fixed A, varying B) from an enzyme with a ternary-complex mechanism are plotted in a Lineweaver–Burk plot, the set of lines produced will intersect.

Enzymes with ternary-complex mechanisms include glutathione S-transferase, dihydrofolate reductase and DNA polymerase. The following links show short animations of the ternary-complex mechanisms of the enzymes dihydrofolate reductase and DNA polymerase.

Mechanizm Ping–pong

Jak pokazano po prawej, enzymy, których mechanizm reakcji jest mechanizmem ping-pong (w j.polskim częściej nazywany mechanizmem podwójnego przeniesienia)mogą istnieć w dwóch stanach, w stanie E oraz chemicznie zmodyfikowanej formie enzymu - E*; ta modyfikacja enzymu jest znana jako reakcja zaawansowana. W takim mechanizmie, substrat A wiąże się, zmienia enzym E do postaci E* przez (np. transferowanie grupy chemicznej do stanu aktywnego), a potem jest uwalniany. Tylko po tym pierwszy substrat może być uwolniony, a następny (B)może się przyłączyć i reagować ze zmodyfikowanym enzymem, regenerując niezmodyfikowaną (początkową) formę enzymu E. Kiedy zestawimy krzywą "v" od "S", przy czym A będzie stałą, a B zmienną, z enzymem o mechanizmie ping-pong, otrzymamy na wykresie Lineweaver–Burk zestaw linii równoległych.

Enzymy o mechanizmie ping - pong zawierają w swojej podgrupie pewne oksyreduktazy, takie jak peroksydazy, transferazy, takich jak "acylneuraminate cytydilyltransferase" (EC 2.7.7.43) oraz proteaz serynowych takich jak trypsyna i chymotrypsyna. Proteazy serynowe są bardzo częstymi i różnorodnymi klasami enzymów, zawierającymi enzymy trawienne (trypsyna, chymotrypsyna), kilka enzymów ze szlaku krwi oraz wiele innych. W tych proteazach serynowych, stan aktywny E* jest acyloenzymem, grupą wyspecjalizowaną do atakowania stanu aktywnego seryny w miejscu wiązania peptydowego w substracie proteinowym.

Mechanizm ping - pong wykorzystywany jest przy oznaczaniu aktywności aminotransferazy alaninowej. Grupa α-aminowa wielu aminokwasów może być przenoszona na α-ketoglutaran w reakcji, której mechanizm nazywamy mechanizmem podwójnego przeniesienia (reakcja ping-pong, lub jeśli jest dwusubstratowa i dwuproduktowa - Bi bi Ping pong). Cechą charakterystyczną dla tego mechanizmu katalizy jest występowanie enzymu z podstawioną grupą(E*), a więc pośredniej formy enzymu, który uległ czasowej modyfikacji. Zatem aminotransferaza alaninowa jest katalizatorem, który przeniesie grupę aminową z alaniny na α-ketoglutaran, a produktami tejże reakcji są pirogronian i glutaminian. Po przywiązaniu alaniny do enzymu(E) odczepia się grupa aminową,która następnie zostaje przeniesiona na fosforan pirydoksalu (PLP)(koenzym aminotransferaz i liaz), a z aminotransferazy uwalnia się pirogronian. Drugi substrat, α-ketoglutaran, wiąże się do zmodyfikowanego chemicznie enzymu(E*) i dostaje od niego grupę aminową. Końcowo zostaje uwolniony jako produkt reakcji - glutaminian.

Non-Michaelis–Menten kinetics

Saturation curve for an enzyme reaction showing sigmoid kinetics

Some enzymes produce a sigmoid v by [S] plot, which often indicates cooperative binding of substrate to the active site. This means that the binding of one substrate molecule affects the binding of subsequent substrate molecules. This behaviour is most common in multimeric enzymes with several interacting active sites. Here, the mechanism of cooperation is similar to that of haemoglobin, 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 and phosphofructokinase, 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 [S] and their activities can show large changes over a narrow range of substrate concentration. Conversely, negative cooperativity makes enzymes insensitive to small changes in [S].

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 the attack of the substrate by the nucleophilic 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.

Mechanizm chemiczny

Ważnym celem pomiaru kinetyki enzymatycznej jest określenie chemicznych mechanizmów reakcji enzymatycznje, tj. kolejność chemicznych etapów które zamieniają substrat w produkt. 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 atom 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, its stable isotope. The rate will change when the critical hydrogen is replaced, due to a primary kinetic isotope effect, which occurs because bonds to deuterium are harder to break then 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 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 of conserved amino acid residues, or by studying the behaviour of the enzyme in the presence of analogues of the substrate(s).

Enzyme inhibition

Kinetic scheme for reversible enzyme inhibitors

Enzyme inhibitors are molecules that reduce or abolish enzyme activity. These are either reversible (i.e., removal of the inhibitor restores enzyme activity) or irreversible (i.e., the inhibitor permanently inactivates the enzyme).

Reversible inhibitors

Reversible enzyme inhibitors can be classified as competitive, uncompetitive, non-competitive or mixed, 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, as shown in the figure to the right and the table below. The particular type of an inhibitor can be discerned by studying the enzyme kinetics as a function of the inhibitor concentration. The four types of inhibition produce Lineweaver–Burke and Eadie–Hofstee plots that vary in distinctive ways with inhibitor concentration. For brevity, two symbols are used:

$\alpha =1+{\frac {[{\mbox{I}}]}{K_{i}}}$      and      $\alpha ^{\prime }=1+{\frac {[{\mbox{I}}]}{K_{i}^{\prime }}}$

where K_i and K'_i are the dissociation constants for binding to the enzyme and to the enzyme–substrate complex, respectively. In the presence of the reversible inhibitor, the enzyme's apparent K_m and V_max become (α/α')K_m and (1/α')V_max, respectively, as shown below for common cases.

		Type of inhibition	Km apparent	Vmax apparent
Ki only	($\alpha ^{\prime }=1$)	competitive	$K_{m}\alpha ~$	$~V_{\max }~$
Ki' only	($\alpha =1~$)	uncompetitive	${\frac {K_{m}}{\alpha ^{\prime }}}$	${\frac {V_{\max }}{\alpha ^{\prime }}}$
Ki = Ki'	($\alpha =\alpha ^{\prime }$)	non-competitive	$~K_{m}~$	${\frac {V_{\max }}{\alpha ^{\prime }}}$
Ki ≠ Ki'	($\alpha \neq \alpha ^{\prime }$)	mixed	${\frac {K_{m}\alpha }{\alpha ^{\prime }}}$	${\frac {V_{\max }}{\alpha ^{\prime }}}$

Non-linear regression fits of the enzyme kinetics data to the rate equations above can yield accurate estimates of the dissociation constants K_i and K'_i.

Irreversible inhibitors

Enzyme inhibitors can also irreversibly inactivate enzymes, usually by covalently modifying active site residues. These reactions follow exponential decay functions and are usually saturable. Below saturation, they follow first order kinetics with respect to inhibitor.

Mechanisms of catalysis

The energy variation as a function of reaction coordinate shows the stabilisation of the transition state by an enzyme.

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. After binding takes place, one or more mechanisms of catalysis lower the energy of the reaction's transition state 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 state for catalysis to occur.

Further reading

• Athel Cornish-Bowden, Fundamentals of Enzyme Kinetics. (3rd edition), Portland Press 2004, ISBN 1-85578-158-1.
• Irwin H. Segel, Enzyme Kinetics : Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. Wiley-Interscience; New Ed edition 1993, ISBN 0-471-30309-7.
• Alan Fersht, Structure and Mechanism in Protein Science : A Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman, 1998. ISBN 0-7167-3268-8
• Santiago Schnell, Philip K. Maini, A century of enzyme kinetics: Reliability of the K_M and v_max estimates, Comments on Theoretical Biology 8, 169–187, 2004 DOI: 10.1080/08948550390206768
• Chris Walsh, Enzymatic Reaction Mechanisms. W. H. Freeman and Company. 1979. ISBN 0-7167-0070-0
• Nicholas Price, Lewis Stevens, Fundamentals of Enzymology, Oxford University Press, 1999. ISBN 0-19-850229-X
• Tim Bugg, An Introduction to Enzyme and Coenzyme Chemistry Blackwell Publishing, 2004 ISBN 1-4051-1452-5

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
• ExCatDB — A database of enzyme catalytic mechanisms
• BRENDA — Comprehensive enzyme database, giving substrates, inhibitors and reaction diagrams
• SABIO-RK — A database of reaction kinetics
• Joseph Kraut's Research Group, University of California San Diego — Animations of several enzyme reaction mechanisms
• Symbolism and Terminology in Enzyme Kinetics — A comprehensive explanation of concepts and terminology in enzyme kinetics
• An introduction to enzyme kinetics — An accessible set of on-line tutorials on enzyme kinetics
• Enzyme kinetics animated tutorial — An animated tutorial with audio