Simple enzymatic reaction

 

Problem 1 (25 points):
A simple enzymatic reaction:

exhibits a Lineweaver-Burk line that goes through the following coordinates of two points: (0,0.2) and (1,0.8).
Let s0 be the initial concentration of S, c0 be the initial concentration of C and e0 be the initial concentration of the enzyme, E. We also know that k1 = 10k-1, s0 = 100, e0 = 10, c0 =0 and p0 =0.
Find the only correct statement (below) and explain or demonstrate why.
k1 ≈ 1.724
Vmax = 0.2
Km = 3
Km = 5
Develop the dynamical formulas for this reaction and simulate the full enzyme reaction (complex formation phase in one simulation done over a short time horizon, followed by the full product formation simulation done over a longer time horizon).
Finally develop the Michaelis – Menten equation for this reaction and plot this result against the full dynamical formulas on the same plot. Plot the graphics, as before, in the short-time horizon and long-time horizon). Explain the differences you see and why they exist.

Problem 2 (25 points):

You are investigating a new enzyme through Michaelis Menten kinetics, and you have found that it has a maximum velocity of 6.0 μM/s when the [E] is 1.5 x 10-9 M based on the following data:

Initial velocity (V0) [S]0
1.0 μM/s 20 mM
2.0 μM/s 50 mM
3.0 μM/s 100 mM
4.0 μM/s 200 mM
5.0 μM/s 500 mM

Determine Km of this enzymatic reaction (Hint: before going to do a lot of calculations, STOP! THINK! – if it doesn’t come to you, go ahead and do a lot of calculations. I suggest MS Excel for the calculations)
Plot the full Michaelis-Menten reaction using either Matlab or Simulink

 

Problem 3 (25 points): (Multiple Choice Questions requiring Explanations)
Which statements about enzyme catalyzed reactions are NOT true? Explain your answer and explain why the statements that are not true are false (Remember that part of your grade is technical writing skills).
Enzymes form complexes with their substrates
Enzymes lower the energy of activation for chemical reactions
Enzymes change the equilibrium constant (Keq or Kss) for chemical reactions
Many enzymes undergo conformational changes when binding with substrate
For enzymatic reactions to occur at the “active site” of enzymatic proteins, the 3D orientation of substrate molecules is an important feature of the reaction
Enzyme inhibition can always be overcome by adding more substrate
Problem 4 (25 points)
Consider the following set of data and answer the following questions:

a. Plot the data (the velocities are the initial velocities) on a Lineweaver-Burk plot (be sure to label axes)
b. Determine the Km of the reaction without an inhibitor
c. Determine the Vmax of the reaction without an inhibitor
d. The second set of velocities represents the rate of the reaction when
an inhibitor is added. Plot these data on the same graph as above
and determine the new Km and Vmax and the type of inhibitor
(competitive, non-competitive).
e. Can the effects of the inhibitor be over-ridden by adding more
substrate? Why?

 

Sample Solution

Madeleine Beth McCann born 12 May 2003 disappeared on the evening of 3 May 2007 from her bed in a holiday apartment in Portugal, sparking what one newspaper called “the most heavily reported missing-person case in modern history” Still to this day no one knows where she is or what really happened to her. The general public have many theories such as she was abducted”, but the most popular theory is that she was murdered and the parents covered it up.

Was Madeleine abducted?

Madeleine was on holiday from the UK with her parents, Kate and Gerry McCann her twin siblings and a group of family friends and their children. She and the twins had been left asleep at 20:30 in the ground-floor apartment, while the McCanns friends dined in a restaurant 55 metres away.The parents checked on the children throughout the evening, until Madeleine’s mother discovered she was missing at 22:00. Now although this is what the parents have said this statement just doesn’t add up, for example Kate McCann said that when she found out Madeleine was missing she left her other two children in the apartment go and alert her husband at the restaurant, This is where many people think her story is flawed if u had just found out your daughter was abducted why would u leave your other two children home alone to go alert your husband? This is what Gerry McCann said when questioned about not having a baby sitter. “The kids were sound asleep and they were being checked regularly. We didn’t think we needed a babysitter. We are good parents and what we did felt perfectly reasonable at the time.” One of the the family’s neighbours at the time Pamela Isobel Fenn said in her witness statement that she hear “one of the children crying out for approximately one hour and fifteen minutes” There has been many inconsistencies with the parents and other people’s story’s which make it hard to believe that Madeleine was actually abducted.

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