Question

Can help me with these questions please.

30. Sphingosine-1-phosphate (S1P) is important for cell survival. The synthesis of S1P from sphingosine and ATP is catalyzed by the enzyme sphingosine kinase. The velocity of the sphingosine kinase reaction was measured in the presence and absence of threo-sphingosine, a stereoisomer of sphingosine that inhibits the enzyme. The results are shown below.

Sphingosine (uM)	vo (mg /min)	vo (mg /min) with inhibitor
2.5	32.3	8.5
3.5	40	11.5
5.0	50.8	14.6
10	72	25.4
20	87.7	43.9
50	115.4	70.8

Construct a Lineweaver–Burk plot to answer the following questions: (a) What are the apparent KM and Vmax values in the presence and absence of the inhibitor? (b) What kind of an inhibitor is threo-sphingosine? Explain.

11. Calculate KM and Vmax from the following data:

[S] (μM)	vo (mM /s)
0.1	0.34
0.2	0.53
0.4	0.74
0.8	0.91
1.6	1.04

Answer 1

As per the given information,

• Lineweaver–Burk plot is the graphical representation of enzyme kinetics using the inverse of substrate concentration in the X-axis, and inverse of enzyme velocity. In this situation, there are two enzyme velocities, one with and one without the inhibitor.
  Lineweaver-Burke plot 0 0.45 0.05 0.1 0.15 0.2 - 1/Vo(Without inhibitor) 0.25 0.3 0.35 0.4 1/Vo(with threo-sphingosine) -
  
• 
  1/5 1/Vo(Without inhibitor) 1/Vo(with threo- sphingosine) 0.4 0.28 0.2 0.1 0.05 0.02 0.031 0.025 0.0198 0.0138 0.0114 0.0087 0.118 0.0871 0.0681 0.039 0.023 0.014
  plotted this data in that graph,

• a. ) We can easily calculate Km and Vmax both in the absence and presence of inhibitor form the given data.

  In Lineweaver-Burke plot, Km corresponds to the point where the graph intersects with the X-axis and Vmax corresponds to the point where the graph intersects the Y-axis.

  If we extend the graph formed backwards, we get,

• 

  Lineweaver-Burke plot 0.08 0.06 0.04 To 0.05 0.1 0.15 0.2 0.45 0.25 0.3 0.35 0.4 1/Vo(with threo-sphingosine) - 1/Vo[Without inhibitor) -

• We can see, The red and blue lines in the graph intersect at y-axis. At this point, the value of 1/v= 1/Vmax.

  Hence, both in the presence and absence of inhibitor,

  1/Vmax= 0.008(approx form graph)

  Vmax= 1/ 0.008 = 0.99 mg.min-1

  In absence of inhibitor,

  - 1/Km= - 0.075 (approx from the graph)

  Km = 1/ 0.075 = 13.33 μM

  And, in the presence of inhibitor,

  -1/Km = - 0.025 (approx)

  Km = 40 μM

  b.) In the graph we see, both the lines moving together, going to intersect at the Y-axis. This is a property of a competitive inhibitor. Hence, we can conclude that Threo-sphingosine is a competitive inhibitor.

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