Amino acid pKas

[basophilic]

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Say I make number line for histidine with its 3 pKs: 1.8 (for COOH), 6.0 (for R group), and 9.2 (for NH3)

I'll assign simplified symbols for what the dominant form looks like within those ranges: H3A^2+ (pH < 1.8), H2A^+ (pH 1.8-6.0), HA (zwitterion, for 6-9.2), and A- (pH>9.2)

How would I find ratio of HA to H3A^2+ at pH 4?
Would I take the average of the pK(COOH) and pK(R) and then use Henderson-Hasselbalch equation?

 

[Quinoline]

I think you would have to make 2 HH equations, one for pkaCOOH (H3A^2 vs. H2A^+) and one for pkaR (H2A^+ vs. HA), then take the ratio after solving each. I think the approach you said would be off by a factor of 2.

pH=pk1+log(H2A^+/H3A^2)
pH=pk2+log(HA/H2A^+)

adding equations: 2*pH=(pk1+pk2)+log(HA/H3A^2)
divide both sides by 2: pH=(average pka) + 1/2*log(HA/H3A^2)

 

[basophilic]

Ah that makes sense. Thanks