isoelectric points of cysteine and tyrosine

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So, for the non-basic isoelectric point, one must take the average of the pKa1 and pKa2.

However, I noticed that cysteine and tyrosine have side chains with pKas.

(1) Are they subject to deprotonation?

(2) Do their pKa count as pKa2 while calculating isoelectric point?

(3) Cysteine's side chain pKa is about 8 while tyrosine is 10. So I guess tyrosine's amino group would count as pKa2 and side chain as pKa3. Am I right?

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1) Yes.
2) They would be pKa3
3) You consider all three pKa to determine isoelectric pH. X see below
 
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So, for the non-basic isoelectric point, one must take the average of the pKa1 and pKa2.

However, I noticed that cysteine and tyrosine have side chains with pKas.

(1) Are they subject to deprotonation?

(2) Do their pKa count as pKa2 while calculating isoelectric point?

(3) Cysteine's side chain pKa is about 8 while tyrosine is 10. So I guess tyrosine's amino group would count as pKa2 and side chain as pKa3. Am I right?

1) They are subject to deprotonation, although because of cross-linking the thiol proton in cycetine is generally not something asked about in biochemistry. But in terms of titration curves of free cysteine, then that sidechain proton is active.

2) The sequence of the pKas is purely numerical. The lowest value is pKa1, the next lowest is pKa2, and so on.

3) Exactly.

1) Yes.
2) They would be pKa3
3) You consider all three pKa to determine isoelectric pH.

1) You are correct.

2) You are correct and incorrect. In the case of tyrosine, the sidechain is 10.1, making it the weakest proton and pKa3. In the case of cysteine, the sidechain has a pKa of 8.4, which is less than the amino terminal, maiking it pKa2.

3) You are incorrect. The pI is found using TWO pKa values: the pKa that leads to the zwitterion and the pKa that leads from the zwitterion. You can see this on any polyprotic titration curve, where any equivalence point besides the last one is found by averaging the flanking pKa points. The pI is nothing more than the equivalence point where the net charge is zero.
 
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Ah yes, you are correct, though for 2) I merely meant that it was a third pKa value and did not attempt to order them by acidity.
 
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