For an enzyme catalyzed oxidation of succinate at pH 7 and 20 degree C, the init

Question

For an enzyme catalyzed oxidation of succinate at pH 7 and 20 degree C, the initial reaction rate, V_0, was measured as a function of the initial substrate concentration, S_0. The following two datasets were generated: (i) Make a plot of V_0 versus V_0/[S] using the data for Dataset I and find the best fit line for this data set using the method of least squares minimization. (ii) Repeat the above data analysis for Dataset II. (iii) Which data set is better? Explain with scientific justification. Use the better data set for the rest of the question. (iv) If the following relationship exists, where K_M and V_max arc constants; V_0 = -K_M (V_0/[S_0]) + V_max What the best value of K_M and V_max/[E_0]. Evaluate k_cat, and its uncertainty? Express the value k_cat, to the correct number of significant digits. Assume: [E_0] = 10.0 plusminus 0.1 mu M, the enzyme concentration.

Explanation / Answer

Ans. Part I and II : The process here in for MS Word 2016 -

1. Enter [S] and V values in excel sheet in separate rows.

2. Generate 1/ [S] and 1/V values in excel sheet.

3. Select 1/[S] and 1/V columns and click on “Insert” tab right to ‘Home’ tab.

4. Select ‘scatter plot’ -displayed as few dots in the graph

5. Select trendline option

6. Add linear trendline and check the option for ‘trendline equation’.

7. It gives a Lineweaver-Burk plot and an equation in from of y = m x + c  

where, y = 1/ V0,       x = 1/ [S],     

Intercept, c = 1/ Vmax           ,

Slope, m = Km/ Vmax   

8. Show R2 value in the graph.

Part III. Data set 2 is better.

A R2 value closer to 1.000 means a better fit for linear regression. R2 (= 0.9548) for data set 2 is closer than that of R2 (= 0.9393) of set 1.

Therefore, data set 2 is better.

Part IV: Calculation Km and Vmax using trendline equation y = 0.6657x + 0.5257 from data set 2.

Including the uncertainties in the equation gives-

            y = (0.6657 ± 0.072453) X + (0.5257± 0.216359)

From, c = (0.5257± 0.216359) = 1 / Vmax

            Or, Vmax = (1/0.5257) ± 0.216359 = 1.90 ± 0.216359

Hence, Vmax = (1.90 ± 0.216359) µM/s             ; where, (± 0.216359 is uncertainty)

From, m = Km / Vmax   

or, Km = m x Vmax = (0.6657 ± 0.072453) x (1.90 ± 0.216359)

= (0.6657 x 1.90) ± (0.072453 + 0.216359)

= 1.26483 ± 0.288812

Hence, Km = (1.26483 ± 0.288812) mM

Part V: Given,

            [Eo] = (10.0 ± 0.1) µM

            Vmax = (1.90 ± 0.216359) µM/s      

Kcat = Vmax / Eo

            = [ (1.90 ± 0.216359) µM/s ] / (10.0 ± 0.1) µM

            = [ (1.90 / 10.0) ± (0.216359 + 0.1) ] s-1

            = (0.19 ± 0.32) s-1

Hence, Kcat = (0.19 ± 0.32) s-1

#1. Calculating uncertainty

1. Enter data in excel sheet. Click on any blank cell.

2. Go to [Formula] tab, click on [fx Insert Function] tab.

3. Select a category “Statistical”

4. Select a function “LINEST”. You get a new window with four rows – Known_ys , known_xs, Const, Stats.

5. Click on symbol (up arrow mark) at right end of known_ys row. A “function argument” window appears. Select the Y-axis column (absorbance). Click on the “down arrow symbol” to proceed to next.

6. Similarly, select X-axis data for known_xs.

7. Write “true” in Const and Stats cells.

8. You get a value “0.2059” in the cell. It is the slope, the same as you get in trendline equation.

9. Drag the cell to another cell to the right. Now, drag the cell to down to get a 2 x 2 table.

10. Go to the functional window (the ‘writing’ space above column marking A, B, C, D ,-- )

11. In windows PC, press [Shift+Ctrl+Enter]. For Mac, press [Command + Enter].

12. You get values in rest of the cells.

13. The cell below slope value gives “0.000264575”= Uncertainty in slope”.

14. The cell right to slope value gives “0.023”= Y-intercept”.

15. The cell below Y-intercept value gives “0.000724569” = Uncertainty in Y-intercept”.

#2. Rule for calculating uncertainty in division:

(A ± DA) unit / (B ± DB) unit = [ (A/ B) ± (DA + DB)] unit

                                                Or,              = (A/ B) unit ± (DA + DB)] unit

The same holds true for multiplication, addition, subtraction except that the sign of division is replaced by their respective sign. Note that uncertainty is added up in the very same way.

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