BIOCHEMISTRY LAB CHE554

Approach: a chromogenic reaction catalyzed by β-galactosidase is used to visualize the effects of substrate concentration and inhibitors of different types on enzyme-catalyzed reaction velocity.Experiment #7, pages 95-104, 123-130.

Enzyme KineticsMotivation: Enzymes mediate almost all the chemistry in cells, and thus in life. They are the best catalysts known and have applications in every field as tools for synthesis, remediation, chemical recycling and intervention targets.

Killing bacteria by inhibiting their enzymes.

2 http://textbookofbacteriology.net/penicillinWWII.jpg

While human actions or accidents produce injuries, death is very often dealt by bacteria.Up to 90% of the native peoples of America died of European and African diseases even before colonists vied for the land.

http://en.wikipedia.org/wiki/Population_history_of_indigenous_peoples_of_the_Americas

Transpeptidase’s essential role

3

Bacteria resist cell lysis by virtue of their cell walls. The cell wall is constructed of peptidoglycan produced by enzymes. Transpeptidase forms and remodels the peptide crosslinks between layers of peptidoglycan.

http://pharmaxchange.info/press/2011/04/mechanism-of-action-of-penicillin/

Penicillium notatum’s defense

! P. notatum exports a secondary metabolite we call penicillin, which disrupts cell wall synthesis and leads to bacterial death. Penicillin was our first ‘wonder drug’ and has saved many lives.

! However evolution is a live and well, bacteria have evolved.

4http://fullspectrumbiology.blogspot.com/2012/05/penicillin-and-importance-of-medicines.html

Penicillin inhibits one enzyme

5 http://en.wikipedia.org/wiki/Beta-lactamase

but is degraded by another

β lactamases can hydrolyze the reactive lactam ring of penicillin and related antibiotics.

Augmentin:An enzyme inhibitor and an inhibitor of the enzyme that

degrades it.

6

Clavulanic acid inactivates many β

lactamases. It is the additional ingredient in

‘augmentin’.

Amoxicillin inhibits transpeptidase.

http://en.wikipedia.org/wiki/Augmentin

As enzymes gain use in consumer products, remediation strategies, synthesis and more, we need to be able to characterize their activity and factors that interfere with it.

New antibiotics for ‘new’ bacteria

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Targeting virulence: a new paradigm for antimicrobial therapyAnne E Clatworthy, Emily Pierson & Deborah T HungNature Chemical Biology 3, 541 - 548 (2007) Published online: 20 August 2007doi:10.1038/nchembio.2007.24

http://www.nature.com/nchembio/journal/v3/n9/fig_tab/nchembio.2007.24_F1.html

Background (Enzyme Kinetics)

! Enzymes influence the rate at which equilibrium is obtained, but not the equilibrium position of the reaction.

! Kinetics, in this context, is the study of reaction product formation as a function of time. The rate of product formation is a measure of the reaction velocity.

S P→

v = d([P])dt

= −d([S])dt

v = reaction velocity

Biology needs reactions that are not ‘naturally’ fast, because

it needs stable compounds.

9Wolfenden and Snider (2001) Acc. Chem. Res. 34:938-945.

Enzymes accelerate reactions by up to x 1021

10 Wolfenden & Snider (2001) Acc. Chem. Res. 34(12): 938-945

Reaction equilibrium vs. velocity.

! We measure the initial reaction velocity, when [P] ≈ 0 and [S] ≈ [S]0.

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[S]eq[P]eq

[S]0

[P]0

Keq = [S]eq

[P]eq

d[P]/dt = v

v0 = k3[ET] [S]0KM + [S]0

Concentration

time

Rate-limiting step and transition state energy.

! The reaction is accelerated by lowering the free energy of transition state activation.

ΔF° = ΔG° = -RT ln Keq

Keq = e-ΔG°/RT

kvel = e-ΔG /RT‡kBTh

Observed Initial Rate of Reaction

– measure and plot initial velocity (vo) as a function of substrate concentration ([S]0). Initial velocity is used to eliminate effects of product buildup (slowing down reaction).

– At some point adding more substrate does not further increase the reaction rate. A plateau is observed corresponding to saturation of the enzyme.

– For single substrate, Vmax occurs when all of substrate is in ES state.

Figure II-8

Background (Michaelis-Menton)

! The Michaelis-Menton equation describes the relationship between initial velocity (vo) and initial substrate concentration ([S]0 ).

– KM (the Michaelis constant) is equal to the substrate concentration that yields vo equal to Vmax/2 .

– This constant is used as a general measure of the stability of the enzyme substrate interaction.

– KM has the form of dissociation constant. The analogy is best when k3 << k2.

– Officially; KM = (k2 + k3) / (k1)– (More generally KM = (k-1 + k2) / (k1) )

– Vmax is the velocity achieved when all enzyme is saturated with substrate.

Lineweaver-Burke! The double-reciprocal plot (Lineweaver-Burke

plot). – Easily calculate KM and Vmax by simply

rearranging Michaelis-Menton equation– plot 1/[S] versus 1/vo

– Still need to measure initial velocity (vo) as a function of substrate concentration (S).

Inhibition

! To combat disease we inhibit enzymes.

! Which kind of inhibition will be most effective (what type of inhibitor would you like to design)?

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• Competitive.• Non-competitive.• Uncompetitive.

vo = Vmax[S]/(KM + [S])

becomes vo = Vmax[S]/(K’M + [S]), K’M = KM(1+[I]/KI)

ES

I

EI

ES E + P

KI

Vmax is not changed. S and I compete for E. Any ES formed reacts at the same rate as in the absence of inhibitor.

Competitive inhibition

From CHE550

Competitive inhibitors.! Competitive inhibitor binds to the free enzyme in

place of the substrate. More substrate is needed to get the same rate, and maximum rate doesn’t change.

! One can see and measure inhibition by plotting 1/[S] versus 1/vo as a function of inhibitor concentration.

ES

I

EI

ES E + PKIe KIsI

ESI

Noncompetitive inhibition

From CHE550

vo = Vmax[S]/(KM + [S])

becomes vo = V’max[S]/(K’M + [S]),

V’max= Vmax/(1+[I]/Kie)

K’M = KM(1+[I]/KIs)/(1+[I]/Kie)

vo = Vmax[S]/(KM + [S])

becomes vo = V’max [S]/(K’M + [S]),

K’M = KM

V’max = Vmax/ (1+[I]/KIs)

Inhibitor binding does not affect the E ↔ ES equilibrium

PURE noncompetitive: KIe = KIs

KIe = KIs

ES

I

EI

ES E + P

KIe KIsI

ESI

From CHE550

Noncompetitive Inhibitors.! Noncompetitive inhibitor binds to free enzyme or

enzyme-substrate complex. Notice how the curves differ from that for a competitive inhibitor.

Figure II-11

Pure non-competitive, Mixed non-competitive

vo = Vmax[S]/(KM + [S])

becomes vo = V’max [S]/(K’M + [S]),

K’M = KM/(1+[I]/K’I)

V’max = Vmax/ (1+[I]/K’I)

ES

I

IES

ES E + P

K’I

I binding affects both the equilibrium among E states and Vmax.

Uncompetitive inhibition

From CHE550

Uncompetitive Inhibitors

! Uncompetitive inhibitor binds only to the enzyme-substrate complex.

β-galactosidase

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Lactose → glucose + galactose.

Homotetramer.Product of the lacZ gene.

The protein can be expressed in two parts. lacZα and lacZΩ.Catalytic activity requires both.

The Experiment (1)! We will employ the enzyme β-galactosidase,

which allows lactose metabolism in the bacterium Escherichia coli.

! We will use o-nitrophenyl-β,D-galactopyranoside (ONPG) instead of lactose because it is hydrolyzed into a color-containing solution (so we can monitor the reaction).

! We will study its kinetics in the absence and presence of inhibitors. This will be done using time-dependent spectroscopy.

Chromogenic substrates

Two Experiments

! Day 1: Determine the enzyme concentrations that produce linear kinetics. This concentration will be used for Day 2 experiments

– Steps 1-7, Determine Enzyme Activity– Make the several dilutions of enzyme before

beginning to use the spectrophotometer.– Steps 8-10, data analysis– Calculate the extinction coefficient of ONP.

• Day 2 Kinetic parameters KM, Vmax and KI:– Steps 1-5, Determine KM and Vmax

– Steps 6-9, data analysis– Steps 1-4, Inhibitor Effects on Activity

– Steps 8-10, data analysis (do one inhibitor only)

! The following page lists the people who should use MGP and those who should use MTG.

© A.-F. Miller 2013

Inhibitor to use 27

Name Locker Group InhibitorDanielle Edwards L41C B MTGAn Lien Ho L35C A MGPJoanna Ng L35C B MGPNiranjana Warrier L44C B MTGKaeto Vin-Nnajiofor L34C A MTGMorgan Sizemore L34C B MGPCorey Lee L31C A MGPMatthew Wolfe L31C B MTGDerrick Lewis L28C A MTGTravis Johnson L38C A MGPJessime Kirk L38C B MGPCarl Archemetre L44C A MTGFalak Patel L35C B MTGRobert Reed L41C B MGPDylan Woolum L35C A MGPKalen Wright L41C A MTG

Sec

tion

1S

ectio

n 2

Changes From the Book! We will follow the experimental protocol exactly

for Days 1 and 2 except– Skip steps 11-14 on Day 1 (determination of

enzyme concentration)– use either MGP, or MTG on Day 2 (see prev.

pg. for who should do which).– omit steps 11-13 on Day 2.

! We will not be doing Days 3 and 4.! Technical tweaks

– Do not vortex enzyme-containing solutions. Invert or swish in and out of a pipettor.

– Start a timer as you add enzyme. Record the time at which you make your first absorbance reading if it is not exactly at 30 sec. Do the same for any time point that is not at the target time.

– Work with a buddy who can adjust your pipettor for the next addition while you work with the spectrophotometer.

– For step 10, first plot activity vs. enzyme amount present, and use only points that fall in a linear regime, when calculating your stock solution activity.

Hint for managing the analysis.

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EXPERIMENT 7 Study of the Properties of !-Galactosidase 127

Protocol

Day 1: Determination of the Activity andSpecific Activity of the !-GalactosidaseSolution

1. Set up the following reactions in six 13-by-100-mm glass test tubes. Keep the enzyme solution onice and add it to the tubes below, which are at roomtemperature.

Volume of 0.08 M Sodium Volume of 2.5 mM

Tube Phosphate, pH 7.7 (ml) ONPG (ml)

1 4.0 0.5

2 4.0 0.5

3 4.0 0.5

4 4.0 0.5

5 4.0 0.5

6 4.0 0.5

2. Add 0.5 ml of sodium phosphate buffer, pH 7.7to tube 1 (blank) and mix gently in a Vortexmixer. Blank your spectrophotometer to readzero absorbance at 420 nm against this solu-tion.

3. Add 0.5 ml of undiluted !-galactosidase so-lution to tube 2. Mix gently with a Vortexmixer for 5 sec and place the solution in yourspectrophotometer. Exactly 30 sec after theaddition of the enzyme, record the A420 of the solution in your notebook. Continue torecord the A420 value at 30-sec intervals un-til the A420 value no longer changes (indicatesthat the reaction is complete). This final A420 value will be used later to determine theactivity of !-galactosidase in each reaction(" A420max).

4. Prepare a twofold dilution of the enzyme byadding 250 #l of the !-galactosidase stock so-lution to 250 #l of 0.08 M sodium phosphatebuffer, pH 7.7. Add this entire 0.5-ml solutionto tube 3. Exactly 30 sec after the addition ofthe enzyme, record the A420 of the solution inyour notebook. Continue to record the A420

value at 30-sec intervals. Unlike with tube 2, itis not necessary that this reaction is followed to com-pletion. Rather, you are looking to obtain a set ofA420 values that are linear with respect to time overabout 2 min.

5. Prepare a fivefold dilution of the enzyme byadding 100 #l of the !-galactosidase stock solu-tion to 400 #l of 0.08 M sodium phosphatebuffer, pH 7.7. Add this entire 0.5-ml solutionto tube 4. Exactly 30 sec after the addition of theenzyme, record the A420 of the solution in yournotebook. Continue to record the A420 value at30-sec intervals. Unlike with tube 2, it is not nec-essary that this reaction is followed to completion.Rather, you are looking to obtain a set of A420 valuesthat are linear with respect to time over about 5 min.

6. Prepare a 10-fold dilution of the enzyme byadding 50 #l of the !-galactosidase stock solu-tion to 450 #l of 0.08 M sodium phosphatebuffer, pH 7.7. Add this entire 0.5-ml solutionto tube 5. Exactly 30-sec after the addition of theenzyme, record the A420 of the solution in yournotebook. Continue to record the A420 value at30-sec intervals. Unlike with tube 2, it is not nec-essary that this reaction is followed to completion.Rather, you are looking to obtain a set of A420 valuesthat are linear with respect to time over about 5 min.

7. Prepare a 20-fold dilution of the enzyme byadding 25 #l of the !-galactosidase stock solu-tion to 475 #l of 0.08 M sodium phosphatebuffer, pH 7.7. Add this entire 0.5-ml solutionto tube 6. Exactly 30 sec after the addition of theenzyme, record the A420 of the solution in yournotebook. Continue to record the A420 value at30-sec intervals. Unlike with tube 2, it is not nec-essary that this reaction is followed to completion.Rather, you are looking to obtain a set of A420 valuesthat are linear with respect to time over about 5 min.

8. Prepare a plot of A420 versus time for the dataobtained from the reactions in tubes 2 to 6. Plotthe data from all five reactions on a single graphfor comparison.

9. Draw a “best-fit” curve through each set of datapoints. For each curve, determine over whattime frame the reaction kinetics appear linear(where "A420/"time yields a straight line). Cal-culate the slope of the linear portion of eachcurve.

10. Use the following equation to determine the !-galactosidase activity (micromoles of ONPGhydrolyzed per minute/per milliliter of en-zyme) in each reaction:

Activity $("A420/"time)(1.25/"A420max)%%%%

Vp

For step 10 you will see:

The purpose of this equation is to convert ΔA420 to ‘concentration of product formed’.i.e. we need an extinction coefficient!

We will use the imperfect solution of assuming that the timecourse you allowed to go to completion converted ALL substrate to product. Therefore the final (max) [P] = initial [S] = 0.25 mM (show how I got this).

ε = ΔA420, max / 0.25 mM. C(t) = ΔA420(t)/(ΔA420 / 0.25 mM)You made 5 ml of solution. Thus the number of moles of P you formed is5x10-3 L x ΔA420(t)* 0.25 x 10-3 mole L-1 /ΔA420,max P = 1.25 x10-6 moles x ΔA420(t) /ΔA420,max

Data Analysis

Run your long time course with a buddy, each of you can put a tube in the same spectrophotometer and you can each take turns reading absorbances

Data Analysis

Prepare a table in advance so that during the experiment you will be filling in boxes with absorbances (also allow a column for time of observation). Write your results down in real time.

Example Data from Day 1

Enzyme Activity at One Concentration

Look for linearity over 2-4 minutes

A420

A420

Linear regime for enzyme activity

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! For point 10, instead of averaging, use the slope of the linear range to calculate activity on a per-volume basis (volume of stock solution).

related to 1/dilution

related to slope of

A420 vs. time

Experimental Considerations

! Pay careful attention to which steps have experiments and which have data analysis. You can do the data analysis later.

! Make sure your data is saved, for example to the hard drive of one of the computers, in case your memory stick goes bad.

! Delete all old files from the spec. to free up more ‘experiments’ for use.

! It will be easy to confuse substances, so please be careful.

Safety Considerations

! Observe all normal laboratory safety practices.