Enzyme Lab

Fundamentals of Enzyme Kinetics Department of Biochemistry

History of Enzymes -Enzymes are biological catalysts. -Each enzyme has a genetically determined and unique primary sequences. History of enzyme researches -In 1700s, studies of meat digestion by stomach secretions -In 1800s, studies of conversion of starch into sugar by saliva and plant extract -In 1850s, Louis Pasteur concluded that the fermentation of sugar into alcohol is catalyzed by ‘ferments’. -In 1897s, Buchner discovered that yeast extract could ferment sugar into alcohol and proved that the fermentation can be promoted by molecules that continued to function when it was separated from the cells.

History of Enzymes History of enzyme researches -In 1897s, Kuhne called these molecules that can catalyst the biological reaction as enzymes. -In 1926, Sumner isolated and crystallized urease and found that enzymes are proteins. -Northrop and Kunitz isolated pepsin and found to be also a protein. -Haldane wrote a treatise entitled ‘Enzyme’ and made remarkable suggestion about the interaction between enzyme and substrate. -In the twentieth century, research on enzymes has been intensive in purification of thousand enzymes leading to elucidate the structure and chemical mechanism.

Enzymes -All enzymes are proteins, with exception of some RNA molecules. -Catalytic RNA molecules are called ‘ribozyme’ (self-splicing intron and spliceosome, protein-RNA complex) -Some antibodies can catalyze reaction called ‘abzymes’. Enzymes

Function without additional chemical Components (only proteins)

Function with additional chemical components

Enzymes Additional chemical components for enzyme function

Cofactors One or more metal ions -Fe2+ -Mg2+ -Mn2+ -Zn2+

Coenzymes Complex organic or metalloorganic molecules -NAD+ -PLP -Lipoate -FAD

-Some enzymes require both cofactors and coenzymes. -Some enzymes require either cofactor or coenzyme. -Some enzymes contain many kinds of either cofactors or coenzymes.

Enzymes Holoenzyme = Apoenzyme + Cofactor or Coenzymes Coenzymes or cofactors covalently linked to enzymes arecalled prosthetic groups.

Classification of Enzymes Many enzymes have been named by adding the suffix ‘-ase’.

Enzyme Catalysis of Reactions -Enhancement of the reaction rate is important to living system. -Enzyme can catalyze reaction by providing a specific environment within which a given reaction can occur more rapidly. -An enzyme-catalyzed reaction take places at the defined areas called active site. -The molecules that can bind to the active site are called substrate. -The active site of enzyme is lined with amino acid residues with side chains that can bind the substrate and catalyze its reaction.

Enzyme Catalysis of Reactions -The function of enzymes is a catalyst by affecting on the rate of reaction but they do not affect on chemical equilibrium. -The effect of enzyme catalysis is an decrease in activation energy (∆G#). -Transition state is the highest energy state of compound undergoing to product or returning to substrate.

Enzyme Catalysis of Reactions Principles of enzyme in lowering activation energy -The binding energy (∆GB) between enzyme and substrate is released from weak interactions to lower activation energy (∆G#). -The weak interactions are optimized substrate in transition state: active sites of enzyme are complementary to transition intermediate of substrate facilitating the conversion to product.

∆Gcat = ∆G − ∆GB #

Weak interaction between enzyme and substrate in transition state

Enzyme Kinetics -Enzyme kinetic is the study of enzyme action. -Enzyme action: chemical mechanism of an enzyme catalyze reaction, determining the rate of reaction and responses to changes experimental parameters, substrate concentration, inhibition, temperature and pH. Methods of measuring enzyme activity -Monitoring enzyme activity = Enzyme assay -Selection of a suitable physical and chemical technique for following the appearance of product or disappearance of substrate by widely used techniques, optical properties (light absorption or fluorescence).

Methods of Measuring Enzyme Activity OH O H3C

C H

Lactate Dehydrogenase

C O- + NAD+

H3C

O

C

C O- + NADH+

Pyruvate

Lactate

d [ S ] d [ P] r=− = dt dt

O

A340

Time -[S]: lactate or NAD+ has no absorption in visible range. -[P]: NADH has absorption at 340 nm. -It is possible to monitor the reaction by assay at 340 nm for product formation.

Approximation of Reaction Rate -Substrate concentration is not constant at a time during enzyme reaction. The measurement of reaction rate at the initial period can be approximated A0 At = A0 e − kt that the substrate is not changed significantly when it is compared to the At starting concentration. time -At the initial time

At ~ A0

dA r=− = k[ At ] dt = k[ A0 ]

-The velocity of initial period is dependent on initial concentration of substrate called initial velocity. -Initial velocity is useful to measure the rate at defined concentration of substrate.

Concentration Unit

Time Course of Reaction [P]

S

P

[S]

Concentration

Time The time course reaction will be curved; as the concentration of substrates decrease, and products accumulate, the net forward rate decreases reaching to equilibrium. Equilibrium state Slope of the tangent at time zero is initial rate. Time

Initial Rate

Concentration

-Tangents to an experimentally obtained curve are not easy to draw accurately. -The suitable condition is to minimize the curvature by decreasing the concentration of enzyme. Low [E]: more accurate initial velocity Enzyme activity 1 unit = A mount of enzyme which converts one µ mole of substrate per minute. High [E] Time

One-substrate Kinetics The Michaelis-Menten equation (Rapid-equilibrium assumption) I. Concentration of [E]<<[S], therefore the all enzyme molecules are in [ES] complex and [S]~[S0]. II. The initial rate is not affected by reverse reaction from product accumulation because the initial period the product is not significant. III. The binding and dissociation of enzyme to substrate is very fast (rapid-equilibrium assumption), so the rate-limiting step becomes the product-releasing step.

One-substrate Kinetics (Rapid-equilibrium assumption) E+S

k1

k3

ES

k2

k4

E+P

At initial period, the product formation is not significant (k4~0). E+S

k1 k2

k3

ES

E+P e = [ E ] + [ ES ]

Rapid-equilibrium assumption k 2 >> k3

k1[ E ][ S ] = k 2 [ ES ] Because the rate-limiting step is product releasing-step.

v = k3 [ ES ] e = [ E ] + [ ES ]

e = total enzyme concentration

One-substrate Kinetics (Rapid-equilibrium assumption)

k3e[ S ] v= [ S ] + k 2 / k1

Vmax [ S ] v= [S ] + K m

Michaelis-Menten constant Maximum velocity

k2 Km = k1

Vmax = k3 [e]

Km is also referred to dissociation constant (Kd = k2/k1)

One-substrate Kinetics Steady-state assumption -In 1926, Briggs and Haldane showed that the rapid-equilibrium is not restrictive in all enzyme mechanism. -They assume instead a steady state that the concentrations of E and ES remained constant over the period of the rate measurement.

One-substrate Kinetics Steady-state assumption E+S

k1 k2

ES

k3

E+P

The steady-state treatment

d [ ES ] =0 dt

Rate formation of ES Rate decay of ES k 2 [ ES ] + k3 [ ES ]

k1[ E ][ S ] = (k 2 + k3 )[ ES ] (k 2 + k3 ) [ E ] = [ ES ] k1[ S ]

One-substrate Kinetics Steady-state assumption Because the rate-limiting step is product releasing-step.

v = k3 [ ES ] e = [ E ] + [ ES ]

e = total enzyme concentration

k3e[ S ] v= k 2 + k3 [S ] + k1

Vmax [ S ] v= [S ] + K m

Michaelis-Menten constant Maximum velocity

k 2 + k3 Km = k1

Vmax = k3 [e]

Comparison between Rapid-equilibrium and Steady-state Assumption k1

E+S

k2

Rapid-equilibrium assumption Steady-state assumption

ES

k 2 >> k3

Not restrictive

k3

E+P

k2 Km = k1 k 2 + k3 Km = k1

-In case of rapid-equilibrium, k2 >> k3, k2 + k3 ~ k2, so Km ≅ k2/k1. -Michaelis-Menten assumption is only one case of steady-state assumption.

Experimental Basis: Michealis-Menten Equation -The relationship between initial rate and substrate concentration is always hyperbolically depenent. At very low substrate

[ S ] << K m ; K m + [ S ] ~ K m v=

Vmax [ S ] K m + [S ]

Vmax [ S ] v= Km At substrate saturation

Vmax = k cat e

The Meaning of Kinetic Parameters I. kcat: catalytic constant (turnover number) -The value of kcat is nearly to the rate-limiting step. E+S

k1 k2

fast

ES

k3 k4

fast

EP

k5

E+P

slow

-The overall rate in enzyme-catalyzed reaction is not faster than step of kcat (k5).

v = k cat [EP ] -At saturated concentration of substrate ([EP] = [E]total).

Vmax = kcat [ E ]total

The Meaning of Kinetic Parameters I. kcat: catalytic constant (turnover number)

-kcat is also referred to the number of cycles that enzyme can catalyze the reaction. -The reciprocal of kcat is referred to the time the enzyme used since it binds to substrate until it releases of product becoming free enzyme.

The Meaning of Kinetic Parameters II. Km: Michaelis-Menten constant -In all case, Km is the substrate concentration at which

Vmax v= 2

-In case of rapid equilibrium that k2 is much more than other steps, the Km can be referred to dissociation constant.

k2 Km = k1

-In case of steady state assumption that k2 is not necessary to be much more than other steps, the Km is a complex of many rate constants. k +k

Km =

2

3

k1

Enzyme inhibition -Inhibitors: some substances alter the activity of an enzyme by combining with it influencing on substrate binding or its turnover number in reducing enzyme activity. -Most inhibitors are structurally resemble substrate but not react or react slowly to enzyme. Types of inhibitor I Reversible inhibitors -Inhibitors can bind and dissociate from enzyme active site II Irreversible inhibitors -Inhibitors that can not be removed from enzyme after binding to enzyme

Competitive inhibition E+S E:S E:P E+P + I -Substances that can compete directly with a normal substrate for an enzymatic binding site. -A competitive inhibitor acts by reducing the concentration of free enzyme available for substrate E:I binding.

Derivations

E+S + I k-2

k2

E:I

k1 k-1

E:S

k3

E+P

Rapid equilibrium for inhibitor binding KI =

[ E ][ I ] [ EI ]

[ E ]T = [ E ] + [ EI ] + [ ES ]

Initial rate (v) v = k3 [ ES ] Maximal velocity (Vmax)

Vmax = k3 [ E ]T

E+S + I k-2

k2

E:I KI =

k1 k-1

Derivations k3 E:S

E+P

Define [E] and [EI] in term of [ES] Steady-state assumption

k1[ E ][ S ] = (k −1 + k3 )[ ES ] Available of [E] in term of [ES] [ E ][ I ] Substitution of [E] into KI [ EI ]

Available of [EI] in term of [ES]

[ E ]T = [ E ] + [ EI ] + [ ES ]

Derivations

E+S + I k-2

k2

k1 k-1

E:S

k3

E+P

Initial rate (v) v = k3 [ ES ]

Vmax = k3 [ E ]T

E:I

k3 [ E ]T [ S ] v= [I ] K m (1 + ) + [S ] KI

Vmax [ S ] v= [I ] K m (1 + ) + [S ] KI

Analysis of the kinetic parameters Primary plot; reciprocal plot of v versus [S]

Vmax [ S ] v= [I ] K m (1 + ) + [S ] KI

1 v

1 Km [I ] 1 1 = (1 + ) + v Vmax K I [ S ] Vmax

1 [S ] Slope varies depending on inhibitor concentration.

Km [I ] (1 + ) Slope = Vmax KI Intercept =

1 Vmax

Analysis of the kinetic parameters Secondary plot; Plot of any term functioning with inhibitor concentration versus inhibitor concentrations

Secondary plot

Km [I ] (1 + ) Slope = Vmax KI

Slope

Km Slope = Vmax K I Km Intercept = Vmax [I]

Uncompetitive inhibition E+S

E:S + I

E:P

E+P

E:S:I

-Uncompetitive inhibitors bind only enzyme-substrate complex and not to free enzyme -Substrate binding could cause an enzyme conformational change suitable for inhibitor binding.

Uncompetitive inhibition 1 K 1 [I ] 1 =( m ) + (1 + ) v Vmax [ S ] K I Vmax

Primary plot

1 v

Km Slope = Vmax

[I ] 1 ) Intercept = (1 + K I Vmax 1 [S ]

Intercept is dependent on inhibitor concentration.

Uncompetitive inhibition [I ] 1 ) Intercept = (1 + K I Vmax

Secondary plot

1 Slope = K IVmax

Intercept

Intercept = [I]

1 Vmax

Non-competitive inhibition E+S + I

E:S + I

E:P

E+P

KI for E ≅ KI for ES E:I

E:S:I

-Non-competitive inhibitor can combine with both enzyme Form, ES or E molecule to produce dead-end complex. -KI for E ≠ KI for ES, mixed inhibition

Non-competitive inhibition 1 Km [I ] 1 [I ] 1 = (1 + ) + (1 + ) v Vmax K I [S ] K I Vmax

Primary plot

1 v

Km [I ] (1 + ) Slope = Vmax KI

[ I ] 1 Intercept = (1 + ) K I Vmax 1 [S ] Both slope and intercept vary depending on inhibitor concentration.

Non-competitive inhibition Secondary plot

Slope

Km Vmax K I

Km Vmax [I]

Km [I ] (1 + ) Slope = Vmax KI

Intercept

1 K IVmax

1 Vmax [I]

Intercept = (1 +

[I ] 1 ) K I Vmax

Effect of inhibitor on kinetic parameters Vmax [ S ] v= [I ] K m (1 + ) KI

Competitive inhibitor

Vmax [S ] [I ] (1 + ) KI v= Km + [S ] [I ] (1 + ) KI

Uncompetitive inhibitor

Noncompetitive inhibitor

Vmax [S ] [I ] (1 + ) KI v= K m + [S ]

Two-substrate Kinetics A+B

Enz

P+Q

-For one substrate reaction, there is no argument about the order of addition of reactants. -For more than one substrate, there are possibilities of order of substrate in a reaction. I. Ternary complex (Sequential mechanism) -Reaction can not be occurred until both substrates are bound at enzyme active site. A+B+E

EAB

P+Q

Two-substrate Kinetics I. Ternary complex (Sequential mechanism) Compulsory-order mechanism EA

E

EAB

EPQ

EP

E

- Substrate B can not bind to free enzyme, but only to binary complex of EA. Random-order mechanism EP

EA E

EAB EB

E

EPQ EQ

-An either pathway in binding substrate A and B to enzyme forming a central complex (EAB).

Two-substrate Kinetics II. Ping-Pong mechanism -Substrate A and B do not meet at the enzyme active site, no EAB complex. -One substrate must leave something on the enzyme to be passed on to the other substrate. A E

B

P EA

E'

Q E'B

E

-E′ can be referred to reducing equivalent, chemical group such as phosphate group, acyl group and amino group. (enzyme substitution mechanism or double displacement mechanism)

Two-substrate Kinetics I. Ternary complex (Sequential mechanism) Reaction of enzyme alcohol dehydrogenase requires ternary complex. Alcohol:NAD+:Enz

Acetalehyde:NADH:Enz

II. Ping-Pong mechanism Reaction of enzyme glucose oxidase. Enzyme is in either reduced and oxidized form during catalysis. Glucose + E-FAD E-FADH2 + O2

1-ketoglucose + E-FADH2 E-FAD + H2O2

Two-substrate Kinetics General equation of two-substrate kinetics (Dalziel′s equation) I. Ternary complex (Sequential mechanism)

e φ A φB φ AB = φ0 + + + v [ A] [ B ] [ A][ B ] II. Ping-Pong mechanism

e φ A φB = φ0 + + v [ A] [ B] At high concentration of A and B

kcat = φ0

−1

e Vmax

= φ0

Vmax = kcat e

Kinetic study of Two-substrate Reaction -Determining of initial velocity (v) by fixing one concentration of substrate [B] with varied concentrations of [A] -Determining the reaction mechanism by primary plot, e/v versus reciprocal values of substrate concentrations -Determining of all Dalziel′s parameters from primary and secondary plot e/v

[B]

e/v

[B] [B]

[B] [B] [B] [B]

[B] 1/[A] Ternary complex (Sequential mechanism)

1/[A] Ping-Pong mechanism