You are being asked to calculate the charge of the side chains of the lonizable

Question

You are being asked to calculate the charge of the side chains of the lonizable amino acids at various pH values. Always round to the nearest 100e place (for instance: if the charge is + 0.005 the answer is Or). Name: Fill out the chart on the next page and turn it in at the start of class February 6. Sample calculation... Calculate the charge of histidine side chain at pH 65. Step 1: In order to solve this I need to know the pKa of the side chain. The Powerpoints has all the pKa values. The side chain of histidine has a pKa of 6. Step 2: Use the Henderson-Hasselbach equation to figure out the percentage of conjugate acid and conjugate base present at the given pH. (we'll go with pH-6). 65 6+ log (A-/HA) A-/HA 3.16 %A,16/4.46 . 100 = 77.6% %HA 1/4.46" 100-22.4 % Step 3: Determine which form is charged- it will be EITHER the conjugate acid OR the conjugate base. In this case the conjugate acid form is positive, and the conjugate base form is neutral Step 4: Use the information from steps 2 and 3 to calculate the overall charge. The conjugate acid form holds a + 1 charge, only 22.4% of the histidine side chains are in the conjugate form. Therefore, the average charge on histidine is 022- *1or 0.22

Explanation / Answer

Amino acids are species which possess both an amine group and a carboxylic acid group thus having in the same molecule a proton acceptor and a proton donor. Numerous amino acid side-chains possess such basic and acidic residues which are capable of proton donation and proton accepting respectively. However, they are only weak acids or bases and so are not completely ionized or protonated unless in very low pH for basic residues and very high pH for acidic residues. Thus it can be inferred that there always exists a certain portion of the uncharged side-chain in equilibrium with the charged side-chain.

For an acid, the deprotonated anion is called the conjugate acid and for a base, the protonated cation is called the conjugate base. For instance chloride ion of HCl is the conjugate acid while imidazolium cation is the conjugate base of imidazole. Amino acid residues being weak acids/bases exists in equilibrium with their conjugates after protonation/deprotonation.

Thus they can be treated as weak acids or bases and their percentage of ionization calculated using the Henderson-Hasselbach equation just the way the pH of a buffer is calculated but only here, the "salt" form is the charged form. That is, for bases, the salt form will be the conjugate base and for acids the conjugate acid. Just as how HCl and NaOH are neutral as solids or in non-polar solvents, amino acid residues will also be neutral when not in their conjugate form.

At a given pH, depending upon the dissociation constant of the residue which gives the extent to which a base will be protonated or the extent to which an acid will ionize, one determines roughly whether the residue will be neutral or ionized. For this rough determination first the nature of the residue is required. Among the given amino acids, Cys, Glu, Asp and Tyr have acidic residues while Lys and Arg have basic residues which enable us to say that the acidic amino acids will be neutral in all pH less than 7 but ionize in all pH above 7. The basic residues similarly will be charged in all pH less than 7 and be neutral in all pH greater than 7. This is determined also by Le Chatlier's principle which translates that in acidic media due to the excess of protons, the weak acids will not ionize completely to maintain the equilibirium concentration of protons and similarly in basic conditions, bases will not ionize completely calling for the precise determination of extent of dissociation which now becomes pH dependant.

Now since we know the pH we want to determine the extent of ionization, we subsitute the pKa of the residue and the pH at which we want to determine and calculate the concentration of charged species to the neutral species where the Henderson-Hasselbach equation helps.

Then from the percentage of charged and uncharged species we determine the final charge in the medium at that pH by the difference between the two multiplied with their charges as given in the final step.

In all these calculations, the concentration of protons in the medium, which gives it its pH is not taken into account as the amino acid residues (actually the whole molecule itself with its acid and amine group) act as a buffer being a sink for protons in case of excess and a source at high pH thus cancelling out that proton or hydroxide concentration and using that to influence its own ionization.

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