Lecture 13 - Enzyme Kinetics II

8/18/2019 Lecture 13 - Enzyme Kinetics II

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Enzyme Kinetics II

The heavy metal Mercury (Hg)


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Last Lecture

we examined how an enzyme can be characterized kinetically

• conducting reactions with fixed concentrations of substrate

• determining rates of reaction (v) from these

• plotting rate vs [S] to yield Michaelis-Menten curve

This Lecture

• we will examine a linear transformation of the M-M plot

• use these curves to examine the effects of inhibitors on enzyme activity


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time

[ g l u

c o s e

]

y = m x + b

m=d[glucose]/dtThe rate (v) is the increasein glucose liberatedfrom cellulose over time

slope of the line = initial rateor velocity (v) of the reaction

Enzyme + cellulose → Enzyme + glucose


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Determination of reaction rates at varying substrate concentrations

etc.

[S]=4[S]=3

[S]=2

[S]=1

time

[ g l u c o s e ]

multiple progress curves

etc.

[S]=4[S]=3

[S]=2

[S]=1

time

[ g l u c o s e ]

multiple progress curves [S] v

1 0.0012 0.002

3 0.0044 0.0075 0.0106 0.013

Next, plot Rates vs [S]


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Plotting substrate concentration vs rate – The Michaelis-Menten curve

a rectangular hyperbola

[substrate], [S]

rate, v

o

o

oo

o

oo

oo

oo

o o o o

oo Vmax

½ V max

KMProblem: Vmax can only be estimated from the curve

v =Vmax [S]

KM + [S]


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Transformation of the Michaelis-Menten Equation: Lineweaver-Burk Equation

the Lineweaver-Burk transformation involves taking the reciprocal ofthe M-M equation

Notice this is now in the form ofthe equation for a line:y=mx + b

v =Vmax [S]

KM + [S]

KM + [S]

Vmax [S]1v =

[S]

Vmax [S]

KM

Vmax [S]

1

Vmax

+

KM

Vmax [S]+

1v =

1v =

1

Vmax

KM

Vmax [S]+

1v =

1

y = m x + b

the Lineweaver-Burk Equation


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slope =KMVmax

1Vmax

1KM

-

1[S]

1v slope =

KMVmax

1Vmax

1KM

-

1[S]

1v

this transformation is sometimescalled a double-reciprocal plot

1

Vmax

KM

Vmax [S]+

1v =

1

y = m x + b


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[S] v

1 0.0012 0.002

3 0.0044 0.0075 0.0106 0.013

Michaelis-Menten Plot Lineweaver-Burk Plot


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• The Lineweaver-Burk* transformation was originally devised because it isdifficult to ascertain the actual value of Vmax from a Michaelis-Mentenplot

• now however computer programs can be used to fit kinetic data to the equationfor a rectangular hyperbola and thus solve precisely for Vmax and K M

• therefore, Lineweaver-Burk transformations are rarely used for their originalpurpose

• however, they are still qualitatively useful for examining the effect that inhibitorshave on the Vmax and K M characteristics of enzymes

• Now we will consider enzyme inhibitors and use Lineweaver-Burk plots toexamine their effect on enzyme activities

* Eadie-Hofstee and Hanes-Woolf plots are two other common transformations


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Molecules that inhibit enzymes are very important

• they regulate enzyme activity in the body

• but are also found in many other situations

• Poisonse.g. cyanide

• Toxinse.g. from poisonous mushrooms

• Therapeutic Drugs

e.g. Antibioticse.g. Viagarae.g. Ibuprofen (inhibitor of enzyme called Cyclooxygenase (COX))


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There are 3 main types of enzyme inhibition mechanisms

• inhibition is caused by molecules that bind enzymes and altereither the V max or KM of the enzyme


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Competitive Inhibition occurs when a molecule structurally mimics thesubstrate and binds the active site.

blocks (or competes with) the substrate forbinding to the active site

Note the slope of L-B plot is changed

since slope = K M/Vmax , one of these values must havechanged

Note that the y-intercept (1/V max ) has not changedtherefore V max has not been altered

Note that it is the apparent Km that has been altered(the x intercept = -1/K M)

so the apparent K M has been increased (note that thereal affinity of enzyme for substrate has not been altered-just that more substrate needs to be added to competewith inhibitor and saturate the enzyme

adding more substrate will outcompete the inhibitor andthe Vmax can be attained


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Example of a Competitive Inhibitor

Adenosine regulates sleep:upon prolonged wakefulness, adenosine levels rise and promotesleepiness by interacting with neuron receptors

Caffeine, which is a structural mimic (analogue) of adenosine, blocks adenosinefunction by binding to the same neuronal receptors (enzymes).

adenos ine

http://localhost/var/www/apps/conversion/tmp/scratch_1//upload.wikimedia.org/wikipedia/commons/e/e8/Adenosin.svghttp://localhost/var/www/apps/conversion/tmp/scratch_1//upload.wikimedia.org/wikipedia/commons/e/e8/Adenosin.svghttp://localhost/var/www/apps/conversion/tmp/scratch_1//upload.wikimedia.org/wikipedia/commons/1/1f/Purines.svg


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Uncompetitive Inhibition

the inhibitor does not bind the active site, but insteadbinds the ES, the enzyme-substrate complex, and preventsthe conversion of substrate to product

Note the slope of L-B plot remains the same, thereforeeither there is no effect on either Km or Vmax (whichwould mean that there is no inhibition) OR both havebeen changed.

Note that the y intercept is increased, therefore Vmaxhas been decreased AND the x-intercept has increasedtherefore Km has decreased

so this inhibition primarily results from the fact that the

maximal velocity of the enzyme is severely decreased -unlike competitive inhibition, this cannot be rescued byadding more substrate

the decrease in Km (which should mean the enzyme nowhas a greater affinity for substrate) results from fact that

the equilibrium shifts towards formation of more ES complexas more inhibitor binds.


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E + S ES E + Pk

-1

k 1

k 2

E + S ES E + Pk

-1

k 1

k 2

E + S ES E + Pk

-1

k 1

k 2

E + S ES E + Pk

-1

k 1

k 2

Effects of Uncompetitive Inhibitors on K M and Vmax

KM is actually a combined rate constant that describes the formation and breakdownof the ES complex

in most reactions, k 2 is usually much lower than k 1therefore K M approximately reduces to:

(k-1 + k 2)

k1 KM =

(k-1 + k 2)

k1 KM =

k1

(k-1 + k 2)= 1

KM

k1

(k-1 + k 2)= 1

KM

k -1

k1KM =

since all enzyme is progressively trapped in the ES form, this mimicsan increase in k 1 rate constant thus decrease in K M

when enzyme is saturated with substrate then the enzyme is operating as fastas it can and V max = k2[ET] and …

since the ES complex is trapped by the inhibitor, k 2/ kcat becomes very low and

Vmax is depressed and cannot be rescued by more substrate.

Vmax

[ET]k 2 = = kcat


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Noncompetitive Inhibition

here the inhibitor neither binds to the active site

nor binds the Enzyme-Substrate complex but ratherbinds to a different site on enzyme.

this is the opposite of competitive inhibition in thatit is the Vmax that is altered (decreased) where as the Kmremains unchanged.

this means that the enzyme still has the same affinityfor the substrate, but the inhibitor negatively affectsthe conversion of substrate to product

whenever the Vmax is affected, the kcat parameter will also

be affected since kcat = Vmax/E T

non-competitive inhibition also cannot be rescued byincreases in [S]

E + S ES E + Pk

-1

k 1

k 2

fast slow

E + S ES E + Pk

-1

k 1

k 2

fast slow


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Examples of Non-competitive Inhibitors

Heavy Metals like Lead (Pb), Mercury (Hg), Silver (Ag), Chromium (Cr)

Two effects

1) Interference with co-factor and co-enzyme function

Ferrochelatase (an enzyme) catalyzes joining of protoporphyrin and Fe 2+ toform heme. Pb inhibits ferrochelatase.

http://www.google.ca/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http://omlc.org/spectra/hemoglobin/hemestruct/&ei=e_8-VKT1BZGoyATJ34HwDg&bvm=bv.77648437,d.aWw&psig=AFQjCNEXsEQsmqEK9v9ftskJ0x7D-2WDjg&ust=1413501149611094


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Inhibitor Type Effect

Competitive Increased K MVmax unchanged

Uncompetitive Decreased V maxDecreased K MRatio of K M/Vmax unchangedkcat decreased

Noncompetitive Decreased V maxKM unchangedkcat decreased


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Example of common Enzyme Inhibitors

permethrin

Voltage-gated Na channels regulate Na + ion passage acrossaxon membranes. Ingredients in insecticides (e.g. pyrethroidslike permethrin) trap the channel in an open conformation,preventing repolarization of the membrane.

https://en.wikipedia.org/wiki/File:Permethrin-2D-skeletal.pnghttps://en.wikipedia.org/wiki/File:Permethrin-2D-skeletal.pnghttp://www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCNXEpMyh0cgCFcZ2PgodlvQIKQ&url=http%3A%2F%2Fwww.bio.miami.edu%2Ftom%2Fcourses%2Fbil255%2Fbil255goods%2F15_mempot.html&psig=AFQjCNGdAbq1XD_vKX7vI-4-gGy1x5ldZQ&ust=1445437771323545http://www.google.ca/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=ZJDBvq0uvs63zM&tbnid=i2EKix4j4QJ_yM:&ved=0CAUQjRw&url=http://www.automation-drive.com/insecticide-raid&ei=AO5NUvSZD4PRqAGikYDAAg&bvm=bv.53537100,d.aWM&psig=AFQjCNHVCJRskHTTl3x7zZBTqQBAmFOrWg&ust=1380925305976747


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the most common herbicide in the world

RoundUp – Glyphosphate

analog of phosphoenolpyruvate, binds to EPSP synthase.

precursor fortyrosinephenylalaninetryptophan

synthesis

https://en.wikipedia.org/wiki/File:Glyphosate.svghttps://en.wikipedia.org/wiki/File:EPSPreactionII.tifhttp://www.google.ca/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=uwh81NR2fb1vFM&tbnid=2QYgKMop4LjSvM:&ved=0CAUQjRw&url=http://www.rightinginjustice.com/news/2011/06/20/report-links-herbicide-roundup-to-birth-defects/&ei=2O1NUoOAC8rmrAGIvIHQBA&bvm=bv.53537100,d.aWM&psig=AFQjCNHH23wpCIZQao2ZTDQh1VU8mp-XRg&ust=1380925260382957


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cyanide and carbon monoxide both bind heme co-factors and inhibit theenzyme complex Cytochrome c oxidase

structure of cyanide anion

http://www.google.ca/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http://commons.wikimedia.org/wiki/File:Cyanid-Ion.svg?uselang=zh-sg&ei=IMdFVPvtENGGyASe5YLYAQ&bvm=bv.77880786,d.aWw&psig=AFQjCNGyJVrJTCJjsPC-VpICtaExOalj1A&ust=1413945481269763http://localhost/var/www/apps/conversion/tmp/scratch_1//upload.wikimedia.org/wikipedia/commons/3/39/Cmplx4.PNG


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November 18, 1978: 909 people die from consuming cyanide in JonestownGuyana at the behest of a charismatic religious leader, Jim Jones.

https://www.google.ca/imgres?imgurl&imgrefurl=http://www.danielbuckleyarts.com/home/bios/daniel-buckley-composer/the-jonestown-project/&h=0&w=0&sz=1&tbnid=uVR-RER_hdAHvM&tbnh=263&tbnw=191&zoom=1&docid=H0CetkurKMjjlM&ei=QrhMUtz_PJL09gT2loCQAw&ved=0CAEQsCUhttp://www.google.ca/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=MSXv5kJ8DOqRVM&tbnid=MTNiVfYn0tN2kM:&ved=0CAUQjRw&url=http://cluesforum.info/viewtopic.php?p=2386876&sid=e4e259a6a918ceff0b576d845c08dfef&ei=wbdMUp8MiejyBLqegMAD&bvm=bv.53371865,d.aWc&psig=AFQjCNGJiL4cJmiiUkFFxxY7bU0qljlLBw&ust=1380845760396651


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Amanitin

• a cyclic 8 amino acid peptide produced byseveral genera of mushrooms

• binds and inhibits RNA polymerase

• reduces mRNA synthesis from a rate of3000 nt/min to about 30 nt/min.


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Aspirinacetylsalicylic acid

Ibuprofen

Inhibit the COX (cyclooxygenase) enzymes thatcontrol release of chemicals that mediate se nsationof pain

Structure of COX-1

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Viagara (Sildenafil citrate)

inhibits an enzyme called cGMP-specific phosphodiesterase which regulatesblood vessel dilation and blood flow in tissue.

Originally tested as a treatment for reduced blood flow in heart muscle which

can lead to angina. It didn’t work well but volunteers reported unusual side effects during the clinical trials. The pharmaceutical company (Pfizer) took note.
http://localhost/var/www/apps/conversion/tmp/scratch_1//upload.wikimedia.org/wikipedia/commons/4/48/Sildenafil.svg

Lecture 13 - Enzyme Kinetics II

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