Question

1. Calculate the average of the first 10 second values (initial velocity)  for all concentrations and draw the curve.

2. Calculate the inverse of initial velocities vs inverse of concentrations. Draw the Lineweaver- Burk line.

3. Answer: a.) Vmax; b.) Km.

	Table 2
	Time (s)	30 µg/µL	50 µg/µL	100 µg/µL	150 µg/µL	500 µg/µL
	0	0	0	0	0	0
	10	0.021	0.024	0.023	0.039	0.063
	20	0.024	0.035	0.024	0.041	0.066
	30	0.027	0.034	0.019	0.041	0.074
	40	0.026	0.039	0.007	0.044	0.073
	50	0.03	0.044	0.011	0.047	0.075
	60	0.028	0.039	0.008	0.049	0.071
	70	0.029	0.045	0.009	0.051	0.07
	80	0.035	0.048	0.024	0.055	0.076
	90	0.037	0.048	0.021	0.052	0.072
	100	0.047	0.043	0.017	0.055	0.073
	110	0.044	0.042	0.017	0.054	0.075
	120	0.038	0.044	0.015	0.057	0.079

Answer 1

PART 1.

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Mean or average velocity for first 10 seconds = average of velocity at 0s and 10s =  0.010500 , 0.012000 , 0.011500 , 0.019500 , 0.031500

This average velocity also becomes the initial velocity as per the question.

The plot of the mean/initial velocity v/s concentration is show below.

PART 2.

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The Lineweaver Burk plot is the plot if inverse velocity v/s inverseconcentration.

The plot is shown below. However, its curved and not a straight line.

Now, because it is not a straight line, we need to find the approximate linear fit. There are multiple ways of doing it. For example, a) find the best fit line, or b) try to get the trend by using the initial and final values or c) use the first two values, since at larger values, there can be deviation from the Lineweaver-burk phenomenon.

In this, I will use the initial and final values to get the trend.

The first and the last value of initial velocity are  0.010500 , 0.031500 for concentrations 30 and 500 ug/uL. The corresponding inverse velocity values are  95.238 31.746, while the corresponding  inverse concentration values are   0.0333333 0.0020000.

The plot of the inverse values gives:

Obviously, this is a straight line.

PART 3.

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The slope of this line = slope = (95.238 - 31.746)/(0.0333333 0.0020000) = 2026.3

One now needs to find the equation of the Lineweaver burk line. Let it be y = mx + c, where m = slope and c = y-intercept.

We already found the slope = 2026.3 = m.

Now substitute the values of inverse velocity values = 95.238 and inv concentration = 0.0333333 and m = 2026.3, into y = mx+c. This gives c = 27.693.

Thus the equation of the Lineweaver Burk line is  

In the above equation, we have taken y = 1/v, where v = velocity and x = 1/S, where S = concentration in ug/uL

The equation corresponding to the lineweaver burk line is:

where, = velocity, = a constant, = concentration and is the max velocity.

We now just need to compare Equations (1) and (2), to get the values of Km and

Comparing the y-intercept between equations (1) and (2), we get

. Or, this means, .

Note: This is higher than the initial velocity of 0.0315 at concentration = 500ug/uL. (See part 1, for the value 0.0315).

Comparing the slopes,

Substituting from Equation (3), we get