1. Enzyme Kinetics of β-galactosidase Using Varying
Temperatures
By: Alexander Ward
CHM-352 – Dr. Lawrence

2. Abstract: Kineticassaysare performedtodetermine the rate anenzyme turnssubstrate intoproduct.
The concentrationof substrate ismuch greaterthanthe concentrationof enzyme,saturatingthe
enzyme tonegate backwardsreactionsinthe enzyme-substrate complex. The rate the enzyme β-
galactosidase turnsoverortho-nitrophenylgalactopyranoside (ONPG) wasmeasuredatvarying
temperaturesusingthe visiblyactive product,ortho-nitrophenolate,inbasicconditions. The
experimentallydeterminedactivationenergyof β-galactosidaseisequal to36.13 ± 4.9 KJper mol.
Introduction: Anenzyme isa catalystwhichlowersthe activationenergyof areaction. The mechanism
of an enzyme catalyzedreactionis (1) 𝐸 + 𝑆 ⥂ 𝐸𝑆 → 𝐸 + 𝑃,where E is the enzyme (β-galactosidase),S
isthe substrate (ONPG),andPisthe product (galactose andortho-nitrophenol). Because the
concentrationof the substrate will be muchgreaterthanthe concentrationof the enzyme,the enzyme
isconsideredsaturated. Thismeansthe concentrationof the enzymesubstrate complex isequaltothe
initial concentrationof enzyme. The rate constant,k, isthe rate at whichthe enzyme substrate complex
isconvertedinfree enzyme andproduct. Thisrate constant changesbasedonthe function
(2) 𝑘 = 𝐴𝑒−
𝐸 𝐴
𝑅𝑇, where A isa constant, EA is the activationenergy,Risan ideal gasconstant,and T is the
temperature. Usingspectrophotometrytomeasure asample followsBeer’sLaw, (3) A = εbc, where A is
the absorbance, ε isthe extinctioncoefficientforthe visiblyactive species,bisthe pathlength,andc is
the concentrationof the visiblyactive species. Forthisexperiment, εand b are constants,therefore the
absorbance isa functionof the concentrationof ortho-nitrophenolate,(3’)
𝑑𝐴𝑏𝑠
𝑑𝑡
= εb
𝑑[𝑃]
𝑑𝑡
,or the change
inthe concentrationof productovertime. Whenplottingthe change inA420 versestime, we can
experimentallyobtainthe value
𝑑𝐴𝑏𝑠
𝑑𝑡
. The Arrheniusplotisbasedonthe equation,
(4) ln
𝑑𝐴𝑏𝑠
𝑑𝑡
= ln 𝐴εb[ES] ×
𝐸 𝐴
𝑅𝑇
, where A isa constant andthe slope isequal to −
𝐸 𝐴
𝑅
.
Materialsand Methods:Fourseparate waterbaths at differenttemperatures,recordbefore andafter
the temperature of the waterbath. Quenchthe reactionusing1 mL of Na2CO3,whichwill also
deprotonate the ortho-nitrophenolatespecies,makingitvisiblyactive. Startthe reactionby adding0.2
mL of ONPG. The control sample hasnoenzyme present. The samplesA420 were measuredonan
VerniersSpectrophotometer.
Tube Type # of Tubes β-galactosidase Ac. Buffer ONPG
Enzyme (B) 16 0.05 mL 3.0 mL 0
Buffer(C) 4 0 3.0 mL 0
Substrate (D) 1 0 0 10 mL
Table 1: Reagent volumesand compositions.
Time Started(min) Reaction# Time Total (min)
0 1 8
1 2 6
2 3 4
3 4 2
Table 2: Reaction Scheme. Half the total time for the hottestwaterbath. 10 minutes incubationwith
the control sample.

3. Results:
Temperature (K) Tube # Time Incubated(min) A420
291.6 1 8 0.246
2 6 0.201
3 4 0.143
4 2 0.064
Control 10 0.003
299.6 1 8 0.433
2 6 0.327
3 4 0.161
4 2 0.099
Control 10 0.021
308.1 1 8 0.627
2 6 0.501
3 4 0.38
4 2 0.206
Control 10 -0.015
316.0 1 1 0.436
2 2 0.377
3 3 0.276
4 4 0.152
Control 5 0.004
Table 3: MeasuredA420 of each sample.
Each sample hasa nearlylinearchange inabsorbance verseschange intime. Whenplotted,we
can observe aslope equal to
𝑑𝐴𝑏𝑠
𝑑𝑡
=
∆𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 𝑈𝑛𝑖𝑡𝑠 (𝐴𝑈)
∆𝑇𝑖 𝑚 𝑒 (𝑚𝑖𝑛𝑢𝑡𝑒𝑠)
. Because the concentrationof substrate is
much greaterthanthe concentrationof enzyme,the slope shouldbe linearandnotevenoff (
𝑑𝐴𝑏𝑠
𝑑𝑡
≠ 0)
towardsthe endof the time the sample isincubated.

4. Figure 1: Kineticsof β-Galactosidase at291.6K. Plotbasedonlinearfit. The slope of the line is0.0302 ±
0.003 AU perminute. AU isequal to absorbance units.
Figure 2: 291.6K Residuals.
.06
.11
.16
.21
.26
.31
2 3 4 5 6 7 8
A420
Time (min)
-2.E-2
-1.5E-2
-1.E-2
-5.E-3
0.E0
5.E-3
1.E-2
1.5E-2
2.E-2
2.5E-2
3.E-2
2 3 4 5 6 7 8
A420Residual
Time (min)

5. Figure 3: Kineticsof β-Galactosidase at299.6K. Plotbasedonlinearfit. The slope of the line is0.0584 ±
0.007 AU perminute.
Figure 4: 299.6K Residuals.
.09
.14
.19
.24
.29
.34
.39
.44
.49
2 3 4 5 6 7 8
A420
Time (min)
-8.E-2
-6.E-2
-4.E-2
-2.E-2
0.E0
2.E-2
4.E-2
6.E-2
8.E-2
2 3 4 5 6 7 8
A420Residual
Time (min)

6. Figure 5: Kineticsof β-Galactosidase at308.1K. Plotbasedonlinearfit. The slope of the line isequal to
0.0692 ± 0.004 AU perminute.
Figure 6: 308.1K Residuals.
.2
.25
.3
.35
.4
.45
.5
.55
.6
.65
.7
2 3 4 5 6 7 8
A420
Time (min)
-4.E-2
-3.E-2
-2.E-2
-1.E-2
0.E0
1.E-2
2.E-2
3.E-2
4.E-2
5.E-2
6.E-2
2 3 4 5 6 7 8
A420Residual
Time (min)

7. Figure 7: Kineticsof β-Galactosidase at316.0K. Potbasedon linearfit. The slope isequal to0.0953 ±
0.01 AU perminute.
Figure 8: 316.0 K Residuals.
.1
.15
.2
.25
.3
.35
.4
.45
.5
1 2 3 4
A420
Time (min)
-4.E-2
-3.E-2
-2.E-2
-1.E-2
0.E0
1.E-2
2.E-2
3.E-2
4.E-2
5.E-2
6.E-2
1 2 3 4
A420Residual
Time (min)

8. Temperature (K) 𝑑𝐴𝑏𝑠
𝑑𝑡
219.6 0.0302 ± 0.003
299.6 0.0584 ± 0.007
308.1 0.0692 ± 0.004
316.0 0.0953 ± 0.01
Table 4: Arrhenius Data. Valuesare derivedfromthe change inA420 vs time at a specifictemperature.
Figure 9: ArrheniusFit Plotconsisting of291.6 K, 299.6 K, and 308.1 K reaction rates. Arrheniusplot
usingthe natural log of slopesatdifferenttemperatures,ina linearfitwithweightedregression. The
sample at316.2 K was omitteddue tonon-linearity,denaturationof the enzymeoccursat high
temperatures. The slope of the line isequal to -4345.9 ± 586 K.
-3.8
-3.6
-3.4
-3.2
-3.
-2.8
-2.6
.0032 .00325 .0033 .00335 .0034 .00345
ln(𝑑Abs/𝑑𝑡)
1/K

9. Figure 10: ArrheniusPlot Residuals.
Usingequation 4, the slope of the Arrheniusplot isequal tothe activationenergydividedbythe
gas constantR, in thiscase -4345.9 ± 586 K. Multiplythe slope byRto findthe activationenergyforβ-
galactosidase,whichisequal 36.13± 4.9 KJ permol.
Conclusion/Discussion:The enzyme unit β-Galactosidaseisnota heatstable protein. The sample inthe
316 K conditionshadareducedreactionrate,due to the hightemperature denaturingthe enzyme. The
Arrheniusplotshows,basedonanatural logscale,a lineardownwardtrend,indicatingincreased
reactionrate basedon increasedtemperature. The activationenergydeterminedbythe experimentis
38.74 ± 4.9 KJ permol. There isnot a literature value due tothe amountof variationinthe enzyme,
such as thermostabilityorwhichspeciesthe enzymewasisolatedfrom.
-2.E-1
-1.E-1
0.E0
1.E-1
2.E-1
3.E-1
4.E-1
5.E-1
.0032457 .0032957 .0033457 .0033957 .0034457
YResidual
X
ArrheniusPlot Residuals