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Materi Kuliah Biokimia Stmi Ke 11 (Enzyme Kinetics)

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Enzyme Action Each enzyme has a unique three-dimensional shape that binds and recognizes a group of reacting molecules called substrates. The active site of the enzyme is a small pocket to which the substrate directly binds. Some enzymes are specific only to one substrate; others can bind more than one substrate.

Enzyme-Substrate Binding

Models of Enzyme Action Early theory: lock-and-key model. Active site (lock) had the same shape as the substrate (key). Only the right shape key could bind. Current theory: induced fit model. Active site closely resembles but does not exactly bind the substrate. Allows for more flexibility in type of substrate Also explains how the reaction itself occurs. As the substrate flexes to fit the active site, bonds in the substrate are flexed and stressed -- this causes changes/conversion to product.

Molecular RecognitionHow does an enzyme bind a substrate, reduce the activation barrier, and produce a product?

Lock & Key Hypothesis

Induced Fit Hypothesis


C. Factors Affecting Enzyme Activity Enzyme activity is defined as how fast an enzyme catalyzes its reaction. Many factors affect enzyme activity: Temperature: most have an optimum temp around 37oC pH: most cellular enzymes are optimal around physiological pH, but enzymes in the stomach have a lower optimum pH Concentration of enzyme and substrate: have all of the enzyme molecules been used up, even though substrate is still available?

Energy of activation: GG Gcat

Effect of catalysis



Effect of tempGT2 (T1 > T2)


Rate acceleration: mechanisms EXDestabilization of ES: strain, charge, electrostatics

Stabilization of the transition state: covalent bonds, metals, acid-base, and proximity.

E+S ESReduced entropy in ES formation.


Rate acceleration: mechanisms

hydrolysis of a -glycosidic bond yielding a unit of glucose

Major factors: pH, ions, & tempAt pH ~ 7 amino acids exist as zwitterions.

The R group determines pH.

aspartic acid [pKa = 4.0] arginine [pKa = 12.5]

Major factors: pH, ions, & temp pH ionic strength temperature

barley -amylase activity plotted as a function of pH

Major factors: pH, ions, & temp pH ionic strength temperature

Having the correct ions is important. Why?

barley -amylase isozyme 1 [crystallized with Ca2+ (green)]

Major factors: pH, ions, & temp pH ionic strength temperature

barley -amylase with CaCl2 barley -amylase w/o CaCl2

Michaelis-Menten Kineticsk1

E + S ESk-1



Assumptions: [1] Steady-state of the intermediate complex ES [2] Neglect back rxn from product (k-2; not shown) [3] Conservation of mass ([ET] = [E] + [ES])


Vmax [S] Km + [S]

Vmax = k2[ET]where:

Km =

(k-1 + k2) k1

Michaelis-Menten Kinetics

Michaelis-Menten KineticsMany types of inhibition can be included in the MM model as well as multiple substrates and steps:

Inhibition: competitive (rev) noncompetitive (rev) mixed (rev) irreversible

Reaction Schemes: single substrate multiple substrate single displacement double disp (ping-pong)

Reaction Rate vs. Enzyme and Substrate Conc.

Control of Enzyme Activity We dont always need high levels of products of enzymecatalyzed reactions around. What kind of control system is used to regulate amounts of enzyme and products? Two main methods: zymogens, and feedback control.

Zymogens Many enzymes are active as soon as theyre made. However, some are made in an inactive form and stored. This inactive form is called a zymogen or proenzyme. To become active, the body needs only to cleave off a small peptide fragment.

Feedback Control Some enzymes (allosteric enzymes) bind molecules called regulators (different from the substrate) that can affect the enzyme either positively or negatively Positive regulator: speeds up the reaction by changing the shape of the active site -- substrate binds more effectively Negative regulator: slows down reaction by preventing proper substrate binding, again, by changing enzyme shape

Feedback control: the end product acts as a negative regulator. If there is enough of the end product, it will slow down the first enzyme in a pathway.

The kinetics of enzyme catalysis:

Steady state kinetics

A hyperbolic curve between V0 and [S] was revealed by in vitro studies using purified enzymes It was the initial velocity (rate), V0, that was measured, so the change of [S] could be ignored. The catalysis was assumed to occur as:

The enzyme will become saturated at high [S]: the V0 will not be affected by [S] at high [S].

Vmax is extrapolated from the plot: V0 approaches but never quite reaches Vmax.

The effect on V0 of varying [S] is measured when the enzyme concentration is held constant. Hyperbolic relationship between V0 and [S]

A mathematical relationship between V0 and [S] was established (Michaelis and Menten, 1913; Briggs and Haldane, 1925)k1 k2

) E+S ES E+P ( Formation of ES is fast and reversible. The reverse reaction from PS (k-2 step) was assumed to be negligible. The breakdown of ES to product and free enzyme is the rate limiting step for the overall reaction. ES was assumed to be at a steady state: its concentration remains constant over time. Thus V0 = k2[ES]





Steady-state assumption: Rate of ES formation=rate of ES breakdown

k1([Et]-[ES])[S]=k-1[ES] + k2[ES] ([Et] is the total enzyme concentration.) Km is called the Solve the equation for [ES]:Michaelis constant.

V0 = k2[ES]

The maximum velocity is achieved when all the enzyme is saturated by substrate, i.e., when [ES] =[Et]. Thus Vmax =k2[Et]The Michaelis-Menten Equation

When [S] > Km

The Michaelis-Menten Equation nicely describes the experimental observations.The substrate concentration at which V0 is half maximal is Km

The Vmax and Km values of a certain enzyme can be measured by the double reciprocal plot (i.e., the Lineweaver-Burk plot).

The double reciprocal plot: 1/V0 vs 1/[S]

The Michaelis-Menten equation, but not their approximated mechanism applies to a great many enzymes Most enzymes (except the regulatory enzymes) have been found to follow the Michaelis-Menten kinetics, but their actual mechanisms are usually more complicated (by having more intermediate steps) than the one assumed by Michaelis and Menten. The values of Vmax and Km alone provide little information about the number, rates, or chemical nature of discrete steps in the reaction.

The actual meaning of Km depends on the reaction mechanismk1 k -1

For If k2 is rate-limiting, k2> [E] dinyatakan sebagai:E+S


k2ES E+P


Laju penambahan [ES] pada waktu t (pada periode awal dimana pembentukan [P] diabaikan dinyatakan sebagai: d[S]/dt =k1 [E][S] - k-1 [ES] - k2 [ES] d[S]/dt = k1 ([Eo] - [ES])([So] [ES] [P]) - k-1 [ES] - k2 [ES] karena : [So]>>[Eo], maka ([So]-[ES]-[P] ~ [So] Jadi : d[S]/dt = k1 ([Eo] - [ES])([So] ) - k-1 [ES] - k2 [ES]

Integrasi persamaan tersebut akan menunjukkan perubahan ES terhadap waktu






dimana [So] >> [Eo]




Induction period Transient or pre steady state phase

Steady state phase


Bagian linier dari grafik [P] vs t menunjukkan fase steady state dari reaksi dengan slope = k2[E][So]/([So]/Km) yang didapat dari mensubstitusi (k-1 + k2)/k1 dengan Km dari persamaan integrasinya Jika bagian grafik steady state linier, ekstrapolasinya akan memotong sumbu t pada t = 1/(k1[So]+Km) dan disebut sebagai periode induksi. Kurva perubahan konsentrasi akan lebih rumit bila reaksinya seperti; E+S ES EP E+P

Dengan tahap laju yang menentukan (rate-limiting-step) adalah EP menjadi E dan P.





dimana EP menjadi E dan P sebagai penentu

Konstr.EP E P ES


Vmax is determined by kcat, the rate constant of the rate-limiting step Vmax = kcat[Et] kcat equals to k2 or k3 or a complex function of both, depending on which is the rate-limiting step. kcat is also called the turnover number: the number of substrate molecules converted to product in a given unit of time per enzyme molecule when the enzyme is saturated with substrate.

40,000,000 molecules of H2O2 are converted to H2O and O2 by one catalase molecule within one second!

The kinetic parameters kcat and Km are often studied and compared for different enzymes Km often reflects the normal substrate concentration present in vivo for a certain enzyme. The catalytic efficiency of different enzymes is often compared by comparing their kcat/Km ratios (the specificity constant). kcat/Km is an apparent second-order rate constant (with units of M-1S-1), relating the reaction rate to the concentrations of free enzyme and substrate.

The value of kcat/Km has an upper limit (for the perfected enzymes) It can be no greater than k1. The decomposition of ES to E + P can occur no more frequently that E and S come together to form ES. The most efficient enzymes have kcat/Km values near the diffusioncontrolled limit of 108 to 109 M-1S-1.

Catalytic perfection (rate of reaction being diffusion-controlled) can be achieved by a combination of different values of kcat and Km.

Rate enhancement is often used to describe the efficiency of an enzyme




kcatRate enhancement: ratio of the rates

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