Q: 49 in TBR page 147 of Bio Part 2 Molecular Bio book

[sps27]

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Take a look at Q: 49 in TBR page 147 of Bio Part 2 Molecular Bio book. So how the hell did they calculate those numbers based on pka1, pka2, pka3 values for those amino acids.
Histidine + Aspartic Acid (pH = 4.5) ,
Cystein + Tyrosine (pH = 9.2),
Arginine + Lysine (pH = 11.65),
Lysine + Cysteine (9.6)..
There is no explanation given as to how they are getting those values. They just say, take the average of pKa values. Well, for each acid we have 3 values and so for a combination of acids like above, I mean, I don't get it. Any thoughts, insights on this one?

 

[RickP]

Could you please post the question as a reference for the people that don't have access to the question?🙂

 

[sps27]

Ok here is the question, slightly big with tables and values so bear with me.

amino acid , COOH-pKa1 , NH3-pKa2 , SIDE CHAIN-pKa3

Arginine , 1.8 , 9.0 , 12.5
Aspartic Acid 2.0 , 10.0 , 3.9
Cysteine 1.8 , 10.8 , 8.3
Glutamic Acid 2.2 , 9.5 , 4.1
Histidine 1.8 , 9.2 , 6.0
Lysine 2.2 , 9.2 , 10.8
Tyrosine 2.2 , 9.1 , 10.1

The Active sites of different enzymes can contain unique catalytic groups. The properties of these groups are pH sensitive and the initial rates generally show bell shaped curves. Which of the following amino acid pairs best represents the catalytic group for the bell shaped curve. (There is a bell shaped curve which peaks at pH = 9)

a) Histidine and Aspartic Acid
b) Cysteine and Tyrosine
c) Arginine and Lysine
d) Lysine and Cysteine

Ans: The Optimal Activity of the enzyme is where the Initial Velocity is the greatest, which is at Vmax. The pH at Vmax is about 9.0. We want that amino acid whose pKa values border as close as possible to a pH of 9.0. We can get a rough estimate of this by adding the two pKa values of the amino acid pair together and then dividing by 2. For Choice A, we get pH value of 4.95, which is way to the left of the graph and nowhere near the optimal activity of the enzyme. Choice B gives pH value of 9.2, which is extremely close. Choice C gives a pH value of 11.65, which is little further away. Choice D gives pH value of 9.6, which is close to the optimal activity, but not as close as choice B. The correct ans is choice B.

 

[sps27]

Argghhhhhhhh............

As I was typing the question, I finally figured out how they arrived at those values. They added the pKa3 values of the amino acid pair and then averaged it out. Damn!!! The reason I got confused is that pH of an amino acid such as Aspartic Acid since it is acidic will be (2.0+3.9)/2 = 3.0 and Histidine since it is basic it will be (9.2+6.0)/2 = 7.6 ..... so if we average (3.0+7.6)/2 = 5.3 , which is nowhere close to 4.95 as the book claims. And likewise if you do this for other pairs, none of those will be same as the book says. But the passage also say at one point, 'the optimal operating pH of an enzyme therefore depends on the pKa values of the amino acid side chains' . And I totally missed / skipped this line in reading the passage.

Anyways, I understand it now.......