lab training – enzyme kinetics &...

2014‐09‐22

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Lab training – Enzyme Kinetics & Photometry

Qing Cheng

[email protected] Division, MBB, KI

Lab lecture

Lab lecture - Enzyme Kinetics and Photometry

Introduction on enzyme and kinetics Order of a reaction, first order kinetics Michaelis-Menten kinetics KM, Vmax and kcat

Lineweaver-Burk plot Enzyme inhibition, competitive and non-competitive inhibition

Spectrophotometer and Beer-Lambert Law

Lab procedure Lab execution Lab report

Safety in the lab

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Introduction – Enzyme

ΔG‡ (with enzyme)

ΔG‡ (without enzyme)

Substrate

Product

Transition state, S‡

Free energy

Reaction progress

ΔG for the reaction

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Enzymes are biological catalysts characterized by Catalytic efficiency Specificity Regulated activity

Enzyme-catalyzed reactions are affected by Enzyme concentration Substrate concentration Temperature pH Inhibitors Activators

SubstrateEnzyme

Product

Lab lecture - Enzyme Kinetics and Photometry 20140922

Kinetics is the study of chemical reaction rate (v, stands for velocity)

Enzyme kinetics is the study of enzyme catalyzed reaction

Determination of kinetics parameter measurement of enzyme activity

First order kinetics v k ∙ S

Zero order kinetics v k ∙ S

Introduction – Kinetics

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Introduction – Order of reactoin

∙

S k P

Reaction rate, v

Substrate concentration [S]

Zero order reaction

First order reaction

k

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Reaction rate is proportional to the substrate’s concentration. This is true when the substrate concentration is low during the reaction, and the substrate is the determine factor for the reaction rate.

Zero order reaction

The reaction rate is independent of the substrate concentration. This is true when the substrate concentration is much higher than the enzyme concentration during the reaction, and the enzyme is the determine factor for the reaction rate.

Michaelis-Menten kinetics

To understand how enzyme functions, we need a kinetic description of their activity.

The reaction rate rises linearly as substrate concentration increases (first order reaction) and then begins to level off and approach a maximum at higher substrate concentration (zero order reaction)

For many enzymes, the reaction rate V0 is defined as the number of moles of product formed per unit time when [P] is low, that is at times close to zero (hence, V0)


Reaction rate, v



Zero order reaction

Reaction rate, v

Time

[S1]

[S2]

[S3]

[S4]V0

V0

V0

V0

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Consider an enzyme that catalyzes the S to P by the following pathway:


⇌ ⇌

⇌ ⇀

V0 = k2[ES]

Rate of ES formation =k1[E][S]

Rate of ES breakdown = (k2+k3)[ES]

V0 is measured when [P] is low, therefore k4 becomes negligible.

Steady state: When [ES] is formed and broken down at the same speed

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Simplify the previous equation by define a new constant, KM, called Michaelis constant

KM has the units of concentration

KM is independent of either [E] or [S]


Solving [ES]

(because at maximum rate, [ES]=[Etot])

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⇌ ⇀

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At very low substrate concentration ( ≪ → ) :

The reaction rate is directly proportional to the substrate concentration

At very high substrate concentration ( ≫ → ):

The reaction rate is maximal, independent of substrate concentration.

When KM is equal to the substrate concentration ( → ):

KM is equal to the substrate concentration at which the reaction rate is halfits maxim value


Reaction rate


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The lower the KM valueThe more efficient the enzyme

Lineweaver-Burk plot

Vmax is difficult to estimate because the initial reaction rate approaching Vmax asymptotically withincreasing substrate concentration. In addition, the high concentration of substrate often inhibitsreaction rate. To solve this problem, Lineweaver and Burk (1934) had inverted the Michaelis-Menten equation, which is referred as Lineweaver-Burk plot (or Double reciprocal plot):


∙

In this equation, 1/V and 1/[S] arevariables, while KM/Vmax and 1/Vmax areconstants. This can be plotted as alinear equation (y = ax + b).Specifically, 1/v is y, 1/[S] is x, KM/Vmax

is a (slope) and 1/Vmax is b (y-intercept). We can accurately calculateKM and Vmax value from a Lineweaver-Burk plot.

y = ax + b

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Nonlinear regression

Indeed, KM and Vmax values can be calculateddirectly from the Michaelis-Menten equationthrough nonlinear regression.


y = ax/(b+x)

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http://www.colby.edu/chemistry/PChem/scripts/lsfitpl.html(in short: http://bit.ly/1re1XU4)

Input the data pairs (V and [S])

Choose fit function: ax/(b+x)

Leave Parameter guesses as it is.

Choose Convergence Mode: Damped or Strongly damped

Click Fit or Fit & Plot (Java needed for plotting)

Nonlinear regression

Indeed, KM and Vmax values can be calculateddirectly from the Michaelis-Menten equationthrough nonlinear regression.


y = ax/(b+x)

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http://www.colby.edu/chemistry/PChem/scripts/lsfitpl.html(in short: http://bit.ly/1re1XU4)

Input the data pairs (V and [S])

Choose fit function: ax/(b+x)

Leave Parameter guesses as it is.

Choose Convergence Mode: Damped or Strongly damped

Click Fit or Fit & Plot (Java needed for plotting)

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Inhibition of enzyme activity

Competitive inhibition

Noncompetitive inhibition


Enzyme Enzyme

Competitive inhibitor

Enzyme

Noncompetitive inhibitor

Substrate

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Competitive inhibition


Enzyme


No inhibitor

Competitive inhibitorNo inhibitor

+ Competitive inhibitor

Vmax is not affected KM is increased

+I

EI

E + S ES E + P

ki S

I

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Noncompetitive inhibition


No inhibitor


S IE + I ES E + P

kiS

EI EIS ×

No inhibitor

+ Noncompetitive inhibitor

Enzyme


Vmax is decreasedKM is not affected

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No inhibitor

Mix inhibition

Vmax is decreasedKM is not affected

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No inhibitor


No inhibitor


Vmax is not affected KM is increased

Vmax is decreasedKM is increased

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Photometry - Spectrophotometer

How to measure the chemical reactions rate

Different molecules have different absorption

Some molecules (e.g. proteins) have several absorbance peaks during the wave scan

Spectrophotometer

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Light source Filter Sample Detector Readout


Photometry - Beer-Lambert law

Beer-Lambert law is a mathematical means of expressing how light is absorbed bymatter. The law states that the amount of light emerging from a sample isdiminished by three physical phenomena:

The concentration of absorbing sample in its pathway (C, in unit of molarity, M)

The distance the light travels through the sample (ℓ, in units of centimeters, cm)

The probability that the light of that particular wavelength will be absorbed bythe material, also known as molar absorption (or extinction) coefficient (ε), inunits that are reciprocals of molarity and distance in centimeters, M-1cm-1)

T: 0 - 1

A: ∞ - 0

Due to technical limitation, the best readingrange of spectrophotometer is normallyfrom 0.1 – 1, thus:

o If A is too high, dilute the sampleo If A is too low, concentrate the sample

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Lab training

Enzyme: Alkaline Phosphatase (ALP)

Remove phosphate groups from many types of molecules.

Function as a dimer, and take effect under alkaline conditions

Made in liver, bone, and other tissues.

It can be measured in a routine blood test. Abnormally high serumlevels of ALP may indicate bone, liver disease, etc.

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Lab training – Outline

Determine the following parameters of alkaline phosphataseusing p-nitro-phenyl-phosphate (NPP) as substrate

Optimal pH

KM

Vmax

Inhibition

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p-Nitro-Phenyl-Phosphate (NPP)

p-Nitrophenol

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Determine the maximal absorbance (λmax) for p-nitrophenol

Set wavelength scan in the range of 350 – 500 nm

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Calculating molar absorption coefficient (ε) using Beer-Lambert law

∙ ∙ ∙

Lab training – Maximal absorbance


Lab training – Incubation time

The effect of incubation time on the amount of product formed

Incubation at 40⁰C water bath

Incubation time (9 different time from 0.5-20 min)

Measure absorbance within 15 min at the end of the reaction

Plot: amount of product formed (y-axis) against time (x-axis)

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dH2ONFF

Buffer with pH 9.5

Testing tubes (× 9)Add enzyme

Blank tubes (× 9)Add dH2O

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Lab training – Optimal pH

The effect of pH on the reaction rate (v)


Incubation time: 10 min


Plot: amount of product formed (y-axis) against time (x-axis)

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dH2ONFF

Buffer with differnt pH

Testing tubes (× 9)Add enzyme

Blank tubes (× 9)Add dH2O


Lab training – KM, Vmax, Inhibition

Determine the KM and Vmax value for alkaline phosphatase, and the inhibition type of the inhibitor provided


Incubation time: 10 min


Michaelis-Menten plot: Reaction rate (y-axis) against [S] (a-axis)

Lineweaver-Burk plot: 1/V (y-axis) against 1/[S] (a-axis)

Determine KM, Vmax, and inhibition type

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Each series contains 6 tubes with different substrate concentration [S]

a. With enzyme onlyb. With enzyme and 1st inhibitor (0.5 mM phosphate solution)c. With enzyme and 2nd inhibitor (1 mM phosphate solution)d. Blank (with neither enzyme nor the inhibitor)

a b c d

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Lab training – Case study (ADH)

KM determination for alcohol dehydrogenase

Determine KM, Vmax, of alcohol dehydrogenase using eithermethanol or ethanol as substrate from the values in the labcompendium.

Determine inhibition type of ethanol on ADH when usingmethanol as substrate.

Calculate the blood alcohol content (BAC) in the patientundergone ethanol treatment.

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Lab note and reports

Write lab notes carefully, which should be approved and countersigned by your teaching assistant.

A written lab report is needed

Brief introduction and aim

Brief description of the execution of the lab work

Results including all the raw data, calculations including the equation, and all the plots.

Don’t forget to specify units in calculations and plots

Brief conclusions and discussion

Answer all the questions in the compendium.

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Lab safty

Lab coat, goggles, gloves

No eating or drinking in the lab

Mouth pipetting is prohibited

Prevent accidents

Be well prepared

Work calmly

When you leave the lab

Wash hands

Remove lab coat

Use your judgment

Ask teaching assistant

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Question?

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lab training – enzyme kinetics &...

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