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CN2108: CHEMICAL ENGINEERING LAB PROCESSING I

EXPERIMENT B1

PROTEIN QUANTIFICATION, ACTIVITY AND

SPECIFIC BINDING CONSTANT

CHEN SHAOQIANG U059142U

CHAK TEIK CHUAN U058954A

CHAN LIYI APRILYN U059191M

Group Th2

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Summary

The experiment consisted of 3 parts:

Part 1 involved the determination of the concentration of protein in 2

samples using the FPLC machine. After correlating data with known

concentration curves, the concentration of S25 was found to be 424.217 ppm

and the concentration of S60 was found to be 375.799 ppm.

In part 2, the protein activity of the 2 samples was obtained using a

spectrophotometer to measure the absorbance of the reaction mixture, starch

and protein mixture at 30s intervals until A600 =0.4. The protein activity of S25

and S60 are 6.876U and 4.725U units respectively. The same enzyme incubated

at 60C resulted in a lower protein activity. Hence we concluded that the enzyme

will denature for temperature higher than 250C.

Lastly, in part 3, the specific binding constant of the protein-receptor pair

of -amylase and starch was determined. The protein sample was added to each

of the 5 starch samples of varying concentrations and the absorbance and

concentration readings were recorded with the aid of iodine. Using the Michaelis-

Menten approach, the Lineweaver-Burke plot was used and Km was found to be

501.03 mg/mL.

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Content Page

Summary ............2

I. Introduction .................................................................4

II. Theoretical Background ............................................................5-13

III. Experimental procedure ..........................................................14-19

IV. Results and Analysis ..........................................................20-27

Error Analysis 28-29

V. Discussion ..........................................................30-42

VI. Conclusion ..........................................................43-44

VII Reference 44-45

VII Notation ..45

Appendices ...I - V

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II. Theoretical Background

High Performance Liquid Chromatography (HPLC)

HPLC is a very useful and important technique for isolating and purifying

proteins and peptides. All laboratories have to be equipped with such systems in

order to be complete. In such systems, liquid chromatography of known

concentrations of standard solution is investigated.

The main components of the HPLC system consist of the mobile phase,

the stationary phase, the injection unit, the pressure pump, the in-line detector

and the display.

The mobile phase in HPLC system refers to the solvent from the reservoir

and the stationary phase is the column. The solvent acts as a carrier for the

sample solution, which will be placed in a small container in the injection unit.

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As the sample solution flows through the column under pressure applied

by the pump, differential migration of compounds will occur, according to the

relative interaction forces with the mobile and stationary phases.

Components in the sample which have stronger interactions with the

mobile phase than with the stationary phase will elute from the column faster

leading to a shorter retention time (and vice versa). These will be recorded by a

detector which will send the results to a data processor, which plots a graph. This

graph is based is based on absorbance at 280nm, which is the characteristic

absorbance here for proteins (in particular, the aromatic amino acids).

Each compound would have a characteristic peak under certain

chromatographic conditions, and the area under the peak is indicative of the

concentrations. However, to determine the exact concentration, a calibration

curve needs to be created.

For this experiment, a standard equilibrium curve of -amylase had been

previously prepared with commercial -amylase. The commercial -amylase was

then used as a standard to characterize natural-occurring and unstable -

amylase. Samples of known concentration of -amylase were run through the

machine, and graphs consisting of many peaks will be obtained. Each of these

peak relate to the concentration of the compound added. (See picture 1)

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is directly proportional to concentration of the sample and this gives A = alS,

where a is the absorption coefficient, l is the curette length and S is the

concentration.

Thus, the spectrophotometer is used to measure intensity with respect to

the wavelength of light. It makes use of UV rays (at 600nm) to determine the

absorbance of a sample. A blank samples absorbance is being measured, so

that an unknown samples absorbance can be determined with respect to the

blank sample. This is directly proportional to the amount of starch that remains in

each sample after the reaction with -amylase. Hence, through this approach we

will be able to determine the amount of starch left at certain times, which is

indicative of the reaction rates. This will enable us to calculate protein activity.

However, a spectrophotometer must be calibrated before it can give

concentration readings. This can be carried out by using samples of known

concentrations to correlate absorbance and concentration by a linear graph. In

this experiment, this was already pre-determined.

Starch iodine complex, Enzyme action

Starch is made up of amylose and amylopectin. Amylopectin consists of

alpha acetal linkage which connects the long chains of glucose units. As a result

of the bond angles in the alpha acetal linkage, amylopectin actually forms a spiral

much like a coiled spring.

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The amylose that is present in starch is the cause of the deep blue color

when starch is added into an iodine solution; iodine molecule enters the amylose

coil. Because the iodine used is in the form of soluble potassium iodide, the ion

form is the tri-iodide ion complex. When this complex enters the amylose coil, it

will for the deep blue color. This is the color that determines the absorbance that

is read by the spectrophotometer. Thus, the absorbance levels recorded can be

related to the concentration of the starch-iodine complex present in the reaction

mixture which is indicative of the protein activity. More starch present would

signify a lesser value of -amylase activity.

The iodine solution, besides providing a colour change that will enhance

readings on the photospectrometer, also has another more important use. It

quenches the reaction, as it will prevent further enzymatic activity by binding

strongly to the substrate (starch). Thus, in addition to facilitating absorption of UV

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waves, the iodine solution also serves as a mean to stop reaction at specific

times.

For a part of this experiment, a sample, S60 have to be incubated in a

water bath at 60o oC. At around 54 C, denaturing of the enzyme occurs; the

hydrogen bonds start to break and the shape of the molecules changed. Thus, at

60oC, the activity of the enzyme decrease will decrease further. It is therefore

expected that the activity for the S25 sample will be much higher than in S60.

Michaelis-Menten approach

Mechanism for a general enzymatic reaction can be represented as the following.

where E is enzyme, S is substrate, P is product, and ES is the enzyme-substrate

complex. Based on this mechanism, Michaelis-Menten kinetics that describes the

rate of enzyme mediated reactions for many enzymes was derived.

SK

Sqq

m

m

+=

Michaelis-Menten equation is given by:

where q is the reaction rate, qmis the maximum reaction rate, S is the substrate

and K is the binding constant, in units consistent with that of S. K is them m

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binding constant, which is the concentration at which the enzyme has an activity

of half its maximum rate. Km has a quantity which indicates the affinity of the

substrate with the receptor. The larger the Km value, the lower the affinity is. qm

is the maximum reaction rate.

The equation can be linearised in a number of ways whereby the experiment

data can be plotted in a graph to obtain the kinetic parameters.

a) Lineweaver-Burke

SqK

qq m

m

m

111 +=

b) Langmuir

Sqq

K

q

S

mm

m 1+=

c) Eadie-Hofstee

S

qKqq mm =

However, each of the above 3 linearisations have their own respective

advantages and disadvantages. (refer to Discussion for more details)

For Lineweaver-Burke equation states, it clearly separates the dependent

and independent variables. However, the most accurate rate values, near qm,

tend to be clustered near the origin, while the rate values least accurately

measured will be found far from the origin and will affect the gradient strongly.

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For Langmuir equation states, the equation tends to spread out the data

points for higher values of q so that the gradient can be determined accurately.

However, the intercept often occurs quite close to the origin so accurate measure

of K is subject to large errors.m

For Eadie-Hofstee equation states, the gradient gives Km while the

intercept gives qm, absolving the need for further computation. However, both

variables contain the measured variable q, which is subject to large errors.

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III. Experimental Procedure

I) Protein Quantification (Determination of concentration of a protein

sample)

In this part of the experiment, the HPLC (shown below) was used to

determine the concentration of the protein samples S25 and S60, using a pre-

determined calibration curve.

Apparatus and Reagents:

1) A HPLC system, which has been properly set up. Solvent (mobile phase)

was 50% acetonitrile, 0.1% trifluroacetile acid in water. Pump flow of the

solvent was set to 1.000 ml/min. Pressure of the pump was set to 40 bar

with a degree of -92kPa. Oven temperature was set at 30C. 280nm

wavelength was used for absorption. (Characteristic wavelength for

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iodine solution to quench the reaction, and the test-tube was shaken to

allow homogeneous mixing. A blue-black colouration was observed.

5) The mixture from each test tube was transferred to a cuvette and

subsequently, was placed in the photospectrometer against the control.

6) The absorbance of the iodine-starch mixture was measured using the UV-

visible spectrophotometer against the control. Concentrations readings

were readily available as the spectrophotometer was pre-calibrated.

Readings were taken twice and the mean was obtained.

7) Measurements were stopped once absorbance dropped below 0.4 as the

reaction was deemed to be completed.

8) Steps 1 to 7 were repeated with S60 instead of S25.

III) Determination of Specific Binding Constants

In this part of the experiment, a linearised form of the Michaelis-Menten

relation was chosen and used to determine the specific binding constant for

starch and -amylase .

Reagents and Apparatus:

1) S25

2) UV-visible spectrophotometer with wavelength set at 600nm

3) 3% Starch solution

4) 0.5mM Iodine solution

5) Micropipettes (1-5ml and 100 to 1000 l)

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solution prepared in step 3. They were then used to zero the

photospectrometer.

7) Each of the mixture in step 5 was then transferred into a cuvette and

placed in the photospectrometer for measurement against the control

prepared in step 6.

8) Since the photospectrometer was pre-calibrated, results for absorbance

and concentrations were generated automatically. 2 readings were taken

for each set and the mean results were recorded and tabulated.

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IV. Results and Analysis

I. Protein Quantification

From the pre-determined calibration curve, the concentration of the protein

sample were calculated automatically by the computer software.

S25 S60

25.0 60.0Temperature (C)

424.217 375.799Concentration (ppm)

424.217 375.799Concentration (mg/l)

Concentration (mg/ml) 0.4242 0.3758

Table 1: Data table for protein quantification of S25 and S60.

(Refer to Appendix I,II for FPLC Chromatogram of S25, S60 respectively)

Since the proteins came from the same source of -amylase, by right, they

should have the same protein concentration, even though the sample S60 would

show some extent of denaturation. However, the two samples S25 and S60,

showed some slight difference in their concentrations.

This could be due to the fact that the denaturation, while not affecting

concentration, would indeed affect the interactions between the protein and the

mobile or stationary phases, due to changing three-dimensional shapes. This

would cause the HPLC, which was supposedly calibrated using -amylase at

25oC, to be inaccurate to a certain extent. Other difficulties encountered in

obtaining accurate results were the small volume of sample provided, which

made withdrawing of samples with the syringe highly difficult and inaccurate.

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II. Protein Activity

Determination of Activity for S25

S25

Absorbance Percentage Concentration

Time(min) 1st

Reading2ndReading

Average1st 2nd

AverageReading Reading

0.5 0.616 0.616 0.616 0.1928 0.1929 0.1929

1.0 0.489 0.489 0.489 0.1518 0.1518 0.1518

1.5 0.377 0.379 0.378 0.1162 0.1168 0.1165

Table 2: Data table for UV Spectrophotometry of S25.

Refer to Appendix III for printouts of UV Spectrophotometry of S25.

Graph of Concentration of Starch(%) against Time (Min)

y = -0.0764x + 0.2301

R2= 0.9981

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time/Min

Conce

ntrationofStarch/%

The graph shows an extremely linear fit, with R2 value of 0.9981. This

indicates that the average reaction rate can be used, and this will be indicative of

the reaction rates at any time. The gradient of the graph will give the reaction

rate, and from there, we can calculate the activity. We used the gradient (ie

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Determination of Activity for S60

S60

Absorbance Percentage ConcentrationTime(min) 1

stReading

2ndReading

Average1st 2nd

AverageReading Reading

0.5 0.752 0.752 0.752 0.2377 0.2374 0.2376

1.0 0.718 0.715 0.717 0.2264 0.2253 0.2258

1.5 0.600 0.601 0.600 0.1875 0.1879 0.1877

2.0 0.535 0.533 0.534 0.1666 0.1660 0.1663

2.5 0.436 0.435 0.435 0.1348 0.1345 0.1347

3.0 0.364 0.369 0.366 0.1121 0.1136 0.1129

Table 3: Data table for UV Spectrophotometry of S60.

Refer to Appendix IV for UV Spectrophotometry of S60.

Graph of Concentration of Starch(%) against Time (Min)

y = -0.0525x + 0.2693

R2= 0.9889

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0 0.5 1 1.5 2 2.5 3 3.5

Time/Min

Concentratio

nofStarch/%

2Again, with a R value of 0.9889, the results showed a very good fit with a linear

model. Again, this is indicative that average reaction rates (ie the gradient) can

be used generally and extrapolated to give us the activity of the enzyme. The

slope will give us the reaction rate.

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Specific Binding Constants

Concentration of Starch after8 mins

(%)

absorbanceInitialConcentr

ationof Starch(%)

1stReading

2ndReading

Average1st 2nd

AverageReading Reading

3.0000 0.4720 0.4720 0.4720 1.423 1.423 1.423

1.5000 0.2866 0.2870 0.2866 0.898 0.899 0.899

0.7500 0.1830 0.1856 0.1830 0.586 0.594 0.590

0.3750 0.1091 0.1087 0.1091 0.354 0.353 0.354

0.1875 0.0692 0.0696 0.0692 0.226 0.228 0.227

Table 4: UV Spectrophotometry of Starch (with -amylase).

Please refer to Appendix V for UV Spectrophotometry ofStarch (with -

amylase).

To linearise the model, we have selected the Lineweaver-Burke plot ( to

be discussed in Discussion ), which is derived as below:

+

=

+=

+=

mm

m

m

m

m

m

q

1

S

1

q

K

q

1

SqSK

q1

SK

Sqq

m

m

q

K Plotting

q

1

S

1against will give a straight line with gradient of and a

y-intercept of

mq

1, where q is the maximum reaction rate, and Km m is the

binding constant. The values ofq

1

S

1and can be found from our data as

discussed later.

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q is the reaction rate. It can be approximated by:

min8

volumestarchofconcmean-volumestarchofconcinitialintervaltime

starchofmassfinal-starchofmassinitialq

=

=

Thus, the q we use here will have the units of mg starch/min, and the

volume is 3ml as this is the basis for calibration. It is noted however that this q is

not exact. Reaction rate is a function of concentration; thus, as the reaction

proceeds, reaction rate will change as well. This q is only the average reaction

rate over 8 minutes, and not the exact reaction rate occurring when substrate

concentration is S.

The parametersq

1

S

1and are calculated and tabulated below. Again starch

concentration in % is converted to concentration in mg/ml using a conversion

factor of 10 as mentioned earlier.

InitialConcentration/%

FinalConcentration/%

q/ mgmin-11/S

1/q /mg-1min/mlmg-1

3.0000 0.4720 9.480 0.1055 0.0333

1.5000 0.2866 4.550 0.2198 0.0667

0.7500 0.1830 2.126 0.4703 0.1333

0.3750 0.1091 0.998 1.003 0.2667

0.1875 0.0692 0.444 2.254 0.5333Table 5: Plotting values for Lineweaver-Burke.

With these values, the lineweaver-burke plot can now be plotted and the values

of q and K determined.m m

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Error Analysis

The only error associated with protein quantification is that in the

establishment of the calibration curve, which is unknown in the experiment. How

valid is the calibration, and whether it holds for denatured enzymes or not, we are

not sure.

However, for the determination of protein activity and the determination of

reaction rates, there is huge error associated with the volumes (and hence the

concentration).

Error in pipetting 5ml of iodine = (5.000) + 0.005 ml

Error in pipetting 3ml of starch = (3.000) + 0.005 ml

Error in pipetting 1ml of enzyme = (1.000) + 0.005 ml

Error in 4ml of reaction mixture = (4.000) + 0.010 ml

% Error in concentration = 0.01/4 x 100% = 0.25%

Error in pipetting 0.2ml = (0.2000) + 0.0005ml (smaller pipette used)

Error in volume of 5.2ml = (5.2000) + 0.0055ml

% Error in final concentration = 0.0055 / 5.200 x 100 = 0.1058%

Total Error in concentration = 0.25 + 0.1058 = 0.3558 %

For time, taking in human reaction time into account, the stopwatch is able to

offer accuracy of + 0.1s. We take the smallest time 30s as an example, as error

associated will be the most.

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Error of stopwatch = (30.0) + 0.1 s

Error Associated with time = 0.1/30 x 100 = 0.3333%

Total % Error in rates = 0.3333 + 0.3358 = 0.6891%

Thus, reaction rates value have a error of 0.6891%. This is quite high, however,

in our experiment, we do not take individual readings, but take the gradient from

the line of best fit. The R2 values of all the graphs (protein activity and

lineweaver-burke plot) are all about 0.99, which is quite indicative of a linear

relationship and indicates that random errors are smoothened out.

However, while random errors are minimized through the use of a line of best fit,

we are not sure if the experiment is free of systematic errors. This is because all

calibration were pre-determined and there is no way we could tell if they were

really accurate and applicable for our experiment. Starch concentrations used for

the third part of the experiment ( for binding constant determination ) may also

not be accurate. The fact that serial dilution was used to prepare the starch stock

solutions which were also given to us indicates that there is a high chance that

the exact concentrations of the stock solution (3%, 1.5%, 0.75%, 0.0375%,

0.0187%) may not be exactly what they were labeled with. All these serves to

reduce the accuracy of our results, the protein activity obtained as well as the

binding constant evaluated.

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V. Discussion

1) Briefly describe the experiment that you designed in C1. What are the

protein concentrations in S25 and S60 in mg/mL?

From the results section, the protein concentration in S25 was determined

to be 0.4242 mg/mL and the concentration of S60 was found to be 0.3758

mg/mL.

In the experiment in C1, 2 parts were expected in the design. Firstly, the

calibration curve must be obtained, and next, this calibration curve was to be

used to determine the protein concentration of the unknown samples.

Although the calibration had been done for us, brief steps to obtain the

calibration curve are listed here:

1. Using -amylase stock solution, serial dilution would be carried out to

obtain the solution at different known concentrations.

2. Each of this sample is run through the HPLC machine, set at wavelength

280nm for measuring protein concentration ( absorption due to aromatic

amino acids). Results will be collected and sent to the computer.

3. A characteristic absorption peak will be observed for each sample, and the

area under the peak could be calculated with the aid of computer

software.

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4. A correlation between area of graph and concentration could be

established. (This should be a linear relationship), and the calibration

would be finished.

After calibration was completed, the unknown samples were fed into the

injection unit in the HPLC. Again, these samples would generate a characteristic

peak, and the area under the peak could be evaluated. This area, was correlated

to the concentration by the computer automatically, using the linear relationship

(calibration) obtained earlier, and the concentrations were obtained.

2) Based on the end-points of starch hydrolysis in CII, determine the

protein activity present in S25 and S60. Account for any differences, and

discuss the significance of protein activity vis--vis protein concentration

(answers in Q1) with regards to pharmaceutical drug assay.

From the results above, the protein activities of S25 and S60 are 6.876

and 4.725 units respectively. It is obvious that the activity of the protein S25 is

significantly (about 50%) more than the protein activity of S60. However, as the

protein concentrations of both samples are slightly different, the activity should

be normalized by the protein concentration to have a fair comparison.

Specific Activity of S25 = 6.876U / (0.4242 mg/mL x 1mL) = 16.21 U/mg

Specific Activity of S60 = 4.725U / (0.3758 mg/mL x 1mL) = 12.57 U/mg

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As shown, the specific activity of S25 is still significantly (about 30%) more

than that of S60. Since both enzymes are the same (-amylase), the only

variable which could account for this discrepancy is the temperature they are

stored at. Below shows a sketch of reaction rates against temperature.

This is characteristic of enzyme catalysed reactions. The parabola, or

peak, can be explained in terms of the combined effect of two opposing factors.

First, increasing temperature increases the rate of reaction as molecules have

more kinetic energy and can overcome the activation energy barrier easily was

they collide. In fact, reaction rate approximately doubles for every 10oC increase

in temperature. However, for enzyme-catalysed reactions, there is an opposing

factor, that is, the denaturation of enzyme. At high temperatures, the

intramolecular interactions that give an enzyme its characteristic 3 dimensional

active site structure may be disrupted, causing it to lose its catalytic activity. This

denaturation is often irreversible, even after temperatures have been restored to

lower values. Thus, denaturation is accompanied by a decrease in reaction rate.

The combined effect of this two yield a parabolic curve shown above with an

optimal temperature.

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As such, S60, which has been stored at a higher temperature, showed

higher degree of denaturation. Thus, when the experiment is carried out at a

water bath of 40oC, the denatured enzymes in S60 had already lost much of their

catalytic function, and this accounts for the lower activity. The enzymes in S25,

however, are not denatured, and shows high activity at the optimal temperature

of 40oC (the standard human body temperature, typical optimal point for most

naturally occurring enzymes).

With regards to pharmaceutical assays, the concept of activity is

extremely important. An assay is a procedure where the concentration of a

component part of a mixture is determined. Many drugs act by inhibiting

enzymes, involving the binding of ligands to a target protein, which might induce

certain cell reaction. By studying the structure of a target protein of a particular

disease and knowing about its active or ligand-binding sites, inhibitors or

activators are designed to fit the architectural structure and chemical nature of

that site and manipulate the elicited response.

Thus, in pharmaceutical assays, we are interested in how the activity of

proteins or enzymes (produced by the viral or bacterial microorganisms) have

been modified by the addition of these drugs. The drugs normally do not reduce

protein concentration, (they do not destroy protein), rather, by binding to the

receptor proteins, they render the enzymes inactive and lose their catalytic

functions.

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Thus, by knowing the concentration alone, we will not be able to tell the

effectiveness of these drugs. The effectiveness of a drug is determined by the

change in activity in an enzyme that it can bring. There is no real correlation

between activity and concentration; higher concentration will not necessarily

mean higher activity. Since we are only interested in the effects of drugs in

pharmaceutical assays, and the effect is often a change in enzyme activity rather

than a total destruction of the protein, the activity is a much useful quantity than

the concentration.

3) Explain your choice of the linearised form of the Michaelis-Menten

relation in CIII. Briefly explain the experiment that you designed in

reference to this choice. Determine the binding constant between starch

and -amylase in units of A600.

The 3 forms of linearization that we are provided with are as follows:

a) Lineweaver-Burke

Sq

K

qqm

m

m

111+=

b) Langmuir

Sqq

K

q

S

mm

m 1+=

c) Eadie-Hofstee

S

qKqq mm=

We have chosen the Lineweaver-Burke linearization, even though each of

the 3 forms has its own distinct advantages and disadvantages.

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Firstly, looking at the independent and dependent variables, we have the

following:

a) Lineweaver-Burke:

q

1

S

1against

q

Sagainst Sb) Langmuir:

S

qc) Eadie-Hofstee: againstq

It is now obvious that the Lineweaver-Burke linearization has the obvious

benefit of separating the variables q and S. This is extremely important in our

experiment here, because both q and S has numerous errors associated with it.

This means that for both the Eadie-Hofstee and Langmuir plot, errors associated

will appear on both axis and not isolated on the same axis, which is extremely

bad, as a linear plot may not be obtained at all, after considering the errors. For

the Lineweaver-Burke, errors associated with each variable are isolated in each

axis, so we can ensure a linear plot will be obtained, even if there are systematic

errors associated with each variable (even though the vertical intercept and

gradient, thus K and qm mmay not be accurate). For the Eadie Hofstee, errors in q

will affect the graphs drastically, while for the Langmuir plot, error in S will cause

the plot to be highly inaccurate.

In fact, our fear of the presence of systematic errors in both S and q is

confirmed, as the Langmuir plot and Eadie-Hofstee plots are both non-linear:

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Langmuir plot:

Graph of S/q (minmL-1

) against S (mgmL-1

)

y = -0.0306x + 3.952

R2= 0.6995

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30 35

S (mgmL-1)

S/q(minmL-1)

Eadie-Hofstee plot:

Graph of q (mgmin-1

) against q/S (mLmin-1

)

y = 102.47x - 25.278

R2= 0.7563

-2

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

q/S (mLmin-1)

q(mgmin-1)

With both R2values of only about 0.7, indeed, the graphs are non-linear

and seems to suggest that systematic error in q and S are very significant here.

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The R2value is extremely close to 1, indicating a first order reaction. This

brings about another problem in the range of data points which will be discussed

later in detail.

This graph shows that the q determined is highly inaccurate as q is indeed

a very strong function of substrate concentration S. Another main inaccuracy in q

lies in the calibration of the photospectrometer. As discussed previously in results

and analysis for part II of the experiment, the fact that the vertical intercepts of

the graphs for protein activity are not 0.4 seems to suggest a systematic error

with the calibration. The q against S plot should also pass through the origin,

which was not observed here.

The numerous (extremely significant) errors with q and S means thatonly

the Lineweaver-Burke plot, with the variables separated, is able to give a linear

plot. (Hence our choice) However, the accuracy of the binding constant will be

severely compromised too.

The Lineweaver-Burke plot has its own drawbacks as well. As both its axis

are the reciprocals of variables, this means that unequal weights are given to

data points, distorting the error structure. Very small values of q and S will have

extremely high weightage in the graph. This is not optimal as small values have

higher associated errors. The Eadie-Holfstee plot will offer an even weightage of

points; however, due to the numerous errors in q and S, it becomes necessary to

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separate the variables on the axis, leaving the Lineweaver-Burke plot as the only

valid choice.

In the experiment we designed, we are supposed to obtain a value for the

binding constant, Km. The calibration had already been done for us, but it could

be done by running the experiment with different known concentrations of starch,

finding the absorbance for each value, and obtaining a correlation of

concentration with absorbance using the Beer-Lamberts law (previously

discussed).

Following the experimental procedures detailed earlier in Experimental

Procedures, we are able to obtain values of S and corresponding q (which is

taken to be average rate for 8 minutes instead of instantaneous rate), converted

to relevant units, by using appropriate formula, conversions and assumptions

mentioned earlier.

A special thing to note here is that since the Lineweaver-Burke plot uses

the reciprocals of S and q, in selecting the concentrations for starch, we should

not distribute them linearly, but rather geometrically. This means that the

concentrations that we choose are obtained by multiplying with a factor of half

(dilution factor of 2, from 3% to 0.1875%), so that the data points would be better

spread out in contrast with a linear distribution.

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With calculated values of the reciprocal of S and q, we then plotted the

Lineweaver-Burke plot (See Results and Analysis). The gradient and the vertical

intercept resulting linear plot was found and q and Km m found, from the relations

listed below.

q

1

S

1

Gradient =

m

m

q

K

y-intercept =

mq

1

+

=

mm

m

q

1

S

1

q

K

q

1

x-intercept = -

mK

1

From the results section, we have:

q = 123.09mg/minm

K = 501.03 mg/mLm

However, there are numerous inaccuracies associated with these values.

Firstly, is the selection of the data points. As shown previously, the plot of q

against S shows an extremely linear plot. This indicates that the values of S

chosen are too small, and the reaction resembles a first order reaction rather

than the Michaelis-Menten kinetics model.

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This means that qmwill be extremely large, as a first order reaction shows

no saturation kinetics (unlike the Michaelis Menten, which approach zero order at

high S). This explains the ridiculously large qmobtained; by doing an experiment

in the linear, first order ( low S ) portion of the Michaelis-Menten kinetics, we are

unable to get a holistic view of the whole mechanics. Thus, qm cannot be

determined and is likely to be full of errors.

Thus, this q is likely to be too high. This qm malso carries with it a very high

degree of error as the vertical intercept (reciprocal of qm) is very small, and any

small changes in the vertical intercept will bring about a huge change in qm. With

an inaccurate q , the accuracy of Km m will be affected as well, although the

gradient of the graph (or the ratio K / qm m should be pretty accurate if the

photospectrometers calibration was free of systematic error and the starch

concentrations were accurate.

According to the Beer Lamberts Law, absorbance is directly proportional

to concentration. Thus, to find Km in units of absorbance, we just multiply the

value of Km in in concentration units by a relevant conversion factor. To obtain

the correlation of Beer-Lamberts Law, we plot a graph of absorbance against

substrate concentration, S.

Concentration/mgmL-1 4.72 2.87 1.83 1.09 0.069

Absorbance/A 1.423 0.899 0.590 0.354 0.227600

Table 6: Plotting values for Calibration Curve.

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Graph of Absorbance (A600) against S (mgmL-1

)

y = 0.2966x + 0.0343R2= 0.9993

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

S (mgmL-1)

Absorbance(A600)

Indeed, this shows a very good linear relationship (R2 > 0.99), indicating

that the Beer Lamberts law is valid. The fact that the graph does not pass

through the origin is probably due to some systematic or rounding off error.

From the graph, absorbance = 0.2966 x S + 0.0343

K = 0.2966 x 501.03 + 0.0343m

= 148.6 A600

This is of course, with the assumption that Beer Lamberts law is valid and

can be extrapolated. Again, this value of Kmis not likely to be very accurate due

to the various forms of significant errors as mentioned previously.

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VI. Conclusion

In the first part of the experiment, we determined the enzyme

concentration of two unknown samples, S25 and S60 to be 424.217 ppm and

375.799 ppm respectively. This was done using the HPLC equipment with

absorbance being measured at 280nm, the characteristic wavelength for proteins

which contains aromatic amino acids.

In the second part of the experiment, we determined the activity of the 2

samples, making use of the UV spectrophotometer and the starch iodine

complex to measure the concentration at regular time intervals. From here, the

mean rate of reaction (gradient of graph) was found and the activity determined.

The activity for S25 and S60 were 6.876U and 4.725U respectively. The lower

activity for S60 was probably due to the denaturation and loss of catalytic activity

of enzymes stored at high temperatures.

In the last part of the experiment, Km, the binding constant for the enzyme

S25 was determined to be 501.05mg/mL. This was done by making use of the

Lineweaver-Burke plot to linearise the Michaelis-Menten kinetics, plotting a

double reciprocal plot of q and S. S was varied and the corresponding q was

taken to be the average rate over 8 minutes.

However, 4 significant factors cause this value of Km to have high

associated errors. Firstly, the usage of average rate is not justified, as reaction

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rate is a strong function of concentration and thus time; secondly, the range of

data points limit it to the linear, low concentration, first order portion of the

Michaelis-Menten Kinetics, making determination of qm impossible; thirdly, there

is suspect of systematic errors in the concentration of the starch stock solution

and in the calibration of the photospectrometer, as indicated by our graphs; lastly

the choice of the Lineweaver-Burke plot (which is inevitable as the errors cause

the other 2 plots to be non-linear, see Discussion above) means error distortion

and magnification of measurements and other errors the small value of vertical

intercept (reciprocal of qm) means a small change in the value will cause a great

change in q and subsequently K .m m

VII. References

Bruce Alberts, Dennis Bray, Karen Hopkin, Alexander Johnson, Julian Lewis,

Martin Raff, Keith Roberts, Peter Walter 2004. Essential Cell Biology (Second

Edition) Garland Science Publishing Company. New York.

Campbell, Neil.A, 1992.Biology(Third Edition), The Benjamin/Cummings

Publishing company. Redwood City, California.

Enzymes: Function and Structure

http://www.chemsoc.org/networks/learnnet/cfb/enzymes.htm

Retrieved from the Internet 20 Feb 2007

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High Performance Liquid Chromatography : A Users Guide

http://kerouac.pharm.uky.edu/ASRG/HPLC/hplcmytry.html

Retrieved from the Internet 20 Feb 2007

Organic Chemistry by John McMurry, 6thEdition.

The Spectrophotometer

http://www.biology.lsu.edu/introbio/tutorial/Spec/spectrophotometry.html

Retrieved from the Internet 20 Feb 2007

Vogels Textbook of Practical Chemistry, 5thedition.

VIII. Notation

A = Absorbance at wavelength 600600

HPLC = High Performance Liquid Chromatography

= Binding ConstantKm

q = Reaction rate

q = Maximum Reaction Ratem

S = Substrate Concentration (Starch)

t = Time

UV = Ultraviolet