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Enzyme kinetics (Part 1)

Clinical Biochemistry Lecture 4a

Lecture outline

1. What can affect the activity of enzymes?a) pH

b) Temperature

a) Enzyme concentration

b) Substrate concentration

c) Inhibitors

1. How are enzymes regulated?

Today

Next week

Enzyme kinetics

In the last lecture, we had looked at how to assay the activity of enzymes, by measuring the rate of products formed / substrates used

Kinetic experiments look at the relationship between the amount of product P formed over a unit of time Ie. the rate of the reaction

[Product]

Time0

Slope = Initial velocity vo

Curve flattens out (rate of reaction slows down)

1. Enzyme kinetics

What can affect the rate of enzyme-catalysed reactions?

a) pH

b) Temperature

c) Enzyme concentration

d) Substrate concentration

e) Inhibitors

a) Effect of pH

pH: measure of [H+ ions] pH vs rate of reaction => bell-

shaped graph Optimum pH: pH at which the

reaction that the enzyme catalyzes proceeds most rapidly

• Most enzymes: pH 7

• Pepsin: pH 2

• Trypsin: pH 9

• Alkaline phosphatase: ??? (refer to practical 2)

Extremes of pH Cause ionic/electrovalent bonds to break, resulting in permanent enzyme

denaturation Cause ionization of amino acids in the enzyme’s active site.

Formation of enzyme-substrate complex depends on the enzyme’s active site and substrate having opposite charges.

If the charges are altered by changes in pH, the enzyme fails to function.

b) Effect of temperature

Temperature vs rate of reaction => bell-shaped curve Every 10oC rise in temperature

results in doubling of the rate of reaction due to kinetic energy.

Optimum temperature ~37oC (rate of reaction is most rapid).

Above 40oC, the rate of reaction begins to decrease because at high temperatures, the enzyme becomes denatured.

c) Effect of enzyme concentration The higher the enzyme concentration, the higher the amount

of substrate is used (in a given period of time)• In tube containing 1x enzyme concentration, 10 substrate

molecules are used (in 30 min) • In tube containing 2x enzyme concentration, 20 substrate

molecules are used (in 30 min)• In tube containing 4x enzyme concentration, 40 substrate

molecules are used (in 30 min)

402010

d) Effect of substrate concentration

Reaction rate vs substrate concentration => hyperbolic curve

A) At low substrate concentrations…a doubling of [S] will double the rate of reaction (Vo)

•reaction rate is proportional to [S]

A

B) At high substrate concentrations…enzymes become fully saturated with substrate and further increase in [S] does not increase rate of reaction (Vo).

•This is because all enzymes are saturated with substrate molecules, and so adding more substrate molecules will not increase the rate of reaction

•reaction rate is independent of [S], and tends towards maximum velocity.

Effect of substrate concentration

B

Vmax and Km

Vmax – The enzyme is converting substrate to product as fast as it can. This is the enzyme’s maximum velocity!

Km Michaelis constant The concentration of substrate required to make the reaction go at half its

maximum velocity

Km

½V

max

V

max

Michaelis constant (Km)

The concentration of substrate required to make the reaction go at half its maximum velocity Km = substrate concentration at ½ Vmax

Measure of affinity that the enzyme has for a substrate A low Michaelis constant means that there is a high

affinity between the enzyme and substrate A high Michaelis constant means that there is a low

affinity between the enzyme and substrate

Independent of [E] and [S]

Measuring Km and Vmax

This can be done by the Michaelis-Menten equation mathematical formula used to study

enzyme kinetics

Vo = Vmax.[S] Km + [S]

Where:Vo = initial velocity or rate of reactionVmax = maximum velocityKm = Michaelis constant[S] = Substrate concentration

Michaelis-Menten equation

How to derive this equation?

Check any biochemistry textbook.

Not important for this module.

Michaelis Menten equation

It describes the kinetics of many but NOT ALL enzymes

It’s derivation assumes that step 2 is the slowest step. If step 1 is slower than step 2, the reaction CANNOT be described by Michaelis Menten kinetics.

Step 1 Step 2 k1 kcat E + S ES E + P k2

Use the Michaelis-Menten equation to calculate Vo, given that Km = 1 mmolL-1 and Vmax = 150 umol L-1min-1

[S](mmol L-1)

Vo(µmol L-1 min-1)

0.5

1.0

2.0

3.0

10.0

Vo = Vmax.[S] Km + [S]

Exercise

Use the Michaelis-Menten equation to calculate Vo, given that Km = 1 mmolL-1 and Vmax = 150 umol L-1min-1

[S](mmol L-1)

Vo(µmol L-1 min-1)

0.5 50

1.0 ?

2.0 ?

3.0 ?

10.0 ?

Vo = Vmax.[S]

Km + [S]

Vo = 150.[0.5]

1 + [0.5]

Vo = 75

1.5

Vo = 50

Use the Michaelis-Menten equation to calculate Vo, given that Km = 1 mmolL-1 and Vmax = 150 umol L-1min-1

Vo = Vmax.[S]Km + [S]

Vo = 150.[1.0]1 + [1.0]

Vo = 1502

Vo = 75

[S](mmol L-1)

Vo(µmol L-1 min-1)

0.5 50

1.0 75

2.0 ?

3.0 ?

10.0 ?

Problems with determing Km and Vmax from Michaelis-Menten plot Because Vmax is achieved at infinite substrate

concentration, it is difficult to accurately determine Vmax (and Km) from a hyperbolic plot (that is, a graph of initial velocity versus substrate concentration).

Note: Actually, nowadays computer programs can calculate this data accurately from a hyperbolic curve

Lineweaver-Burk plot

Solution: The Michaelis-Menten

equation can be rewritten in order to obtain values for Vmax and Km from a straight line plot.

Lineweaver-Burk equation Called a double-reciprocal

plot

y = mx + c

Derivation of Lineweaver Burk

[ ][ ]SV

SK

vm

o max

1 +=

[ ][ ][ ] mm

M

o VS

S

VS

K

v+=1

[ ] maxmax

111

VSV

K

vM

o

+=

Slope Intercept

[ ][ ]SK

SVv

mo +

= max

Problems with the Lineweaver Burke Transformation

The least accurately measured points (that is low [S] are given the highest weightage)

ov

1

[ ]S1

Least accuratelymeasured points

Alternatives to the Lineweaver Burke Transformation?

Eadie Hofstee Transformation [ ] maxov VS

vK om +−=

[ ]Svo

vo

-Km

Vmax

Helps to :

•Overcome problems with improper weightage by giving equal weightage to all points

•Also reduces need for long extrapolation to find Km in LB plot

Outliers

Aka Woolf-Eadie-Augustinsson-Hofstee plot

Derivation of Eadie Hofstee

[ ] [ ]SVSKv mo max)( =+

[ ] [ ] [ ]SVvS

KvS o

omax)( =+ [ ] maxVv

S

Kvo

o =+

[ ][ ]SK

SVv

mo +

= max

[ ] maxVS

vKmv o

o +−=

SlopeY-intercept

Michaelis-Menten plot

Lineweaver-Burk plot

Eadie-Hofstee plot

[ ] maxVS

vKmv o

o +−=

[ ][ ]SK

SVv

mo +

= max

http://www-biol.paisley.ac.uk/KINETICS/Chapter_2/chapter2_3.html

In summary,

Enzyme kinetics look at the rate of _________ appearing over time (the rate of reaction of the enzyme)

Enzyme activity can be affected by _______, ________, ________ conc, ________ conc and _________.

In summary,

Most enzymes have a _________ pH, ie. The pH at which they catalyse reactions most rapidly Most enzymes are at pH ___

Changes in pH can cause ________ by breaking bonds changing ionization of amino acids in the

active site

In summary,

Enzymes also have an optimum temperature, usually about _____. As temperature rises, rate of reaction

increases due to _______________ Beyond certain temp, rate of reaction

decreases due to _______________ Bell-shaped curve

In summary,

The higher the enzyme concentration, the _______ the rate of reaction

At low substrate concentration, ↑ [S] will __________ Vo [S] is ___________ ____ Vo

At high substrate concentration, ↑ [S] will _____________ Vo [S] is ___________ ____ Vo

In summary,

Vmax is the enzyme’s ________ _______ Km is the ________ at ________

It is known as the _________ constant Low Km means _____ affinity of substrate for

enzyme

Michaelis Menten equation describes kinetics of most enzymes Write the equation here:

In summary

The problem with determining Vmax and Km from a M&M plot is:

We can also find Vmax and Km by the Lineweaver Burk plot

• Equation :

• Problem:

Eadie Hofstee plot• Equation: