CHE 4341 Enzyme Kinematics

Example of an Assay

Hydrolysis of p-nitrophenylacetate by chymotrypsin

Assay tests for activity of enzyme which can be measured by looking at

disappearance of Substrate [S] or appearance of product [P] over time

The amount of p-nitrophenol released / time can be measured using

Beer’s Law (A = cl) w/ Spectrophotometric Analysis!

disappearance of Substrate [S] or appearance of product [P] over time also provides a measure of

RATE of enzymatic reaction

1.0 Unit of E activity is the amount of E causing a defined transformation of

1.0 µmol of substrate per minute at 25ºC under optimal conditions

1 Katal is that catalytic activity which will raise the

rate of reaction by one mole per second in a specified assay system

Activity is proportional to

amount of target protein that is being purified (more activity = more purified protein)

Total Protein

total # of protein present in mixture → can do this spectrophotometrically using Beer’s Law (A=εlc)

All proteins have UV absorbance at

280nm

Indirect Assay

Absorbance shift of dye binding to protein → uses Coomassie Blue → measures protein concentration at absorbance max. of 595

Specific Activity (SA)

measure of enzyme purity and increases during purification (maximal and constant when enzyme is pure)

SA formula

activity / total protein (units/mg)

In example, RATE (kinetics) of chymotrypsin can be measured by

looking at appearance of p- nitrophenol / time

Slanted k is to do with

RATE

k₁

rate for E + S binding to substrate; formation of enzyme-substrate complex

k-₁

reverse rate constant for the dissociation of the enzyme-substrate complex (ES) back into free enzyme (E) and substrate (S)

k₂

the rate-limiting step where the enzyme-substrate complex converts into product and free enzyme

Steady State

d[ES]/dt = 0

Pre-Steady state vs Steady State

steady state should equal 0 because b/c rate of ES formation = rate of ES breakdown

Michaelis-Menten Plot

Michaelis-Menten Kinetics

Michaelis-Menten Equation

Hyperbolic =

non-allosteric enzyme

Michaelis-Menten Kinetics Assumptions

1. Assumes ES complex

2. Assume there is much more [S] than [E]

3. Assume steady state: d [ES] / dt = 0 (rate of ES formation = rate of ES breakdown)

4. Rate (v_o = k₂[ES])

   • Assume k₂ is smallest rate constant!

The maximum rate (V_max) can be reached at

saturating (maximum) substrate concentration → all enzyme is complexed with substrate

Since v_o = k₂[ES], 1^st solve which eqn to find [ES]:

k₁ ([E_t ] - [ES]) [S] = k _-1 [ES] + k₂ [ES]

What is [E_t]?

total enzyme conc

Find [E_t] using

[E] + [ES]

K_M has the same units as

[S]

K_M has

V_max /2

High K_M = large k_-1 or small k₁ =

breakdown of ES favored

Low K_M = large k_-1 or small k₁ =

formation of ES favored

K_M measures

affinity of enzyme for substrate

K_M has an INVERSE proportional relationship with enzyme affinity for substrate

A low K_m means high affinity; a high K_m means a low affinity.

What is the formula for K_m?

K_m = [S] at ½ V_max

The turnover number

V_max = k₂ [E_t]

When the velocity = V_max

k₂ = k_cat = turnover number → k₂ = k_cat = V_max / [E_t]