For a 0.1 M aqueous solution of lysine, the pH at which it carries no net charge is ..........
(pKa values for: α-carboxylic group = 3.1, α-amino group = 8.0, ε-amino group = 10.8)
The pH at which lysine carries no net charge is known as its isoelectric point, or pI. To find the pI of lysine, we need to consider the pKa values of its ionizable groups: the α-carboxylic group (pKa=3.1), the α-amino group (pKa=8.0), and the ε-amino group (pKa=10.8).
Lysine, an amino acid, can exist in different ionic forms depending on the pH. The point at which the net charge is zero is where the positive and negative charges balance. At the isoelectric point, lysine is primarily in the zwitterionic form, with its α-amino and ε-amino groups protonated and its α-carboxylic group dissociated.
To calculate the pI, we average the pKa values of the acidic and basic groups that are responsible for the species in the zwitterionic state. For lysine, this involves the pKa of the α-amino group (8.0) and the ε-amino group (10.8):
pI = (pKaα-amino + pKaε-amino) / 2
Plugging in the values:
pI = (8.0 + 10.8) / 2 = 9.4
The calculated isoelectric point (pI) is 9.4
A dipeptide, “x”, on complete hydrolysis gives “y” and “z”; “y” on treatment with aqueous HNO$_2$, produces lactic acid. On the other hand, “z” on heating gives the following cyclic molecule. 
Based on the information given, the dipeptide X is:
Identify the taxa that constitute a paraphyletic group in the given phylogenetic tree.
The vector, shown in the figure, has promoter and RBS sequences in the 300 bp region between the restriction sites for enzymes X and Y. There are no other sites for X and Y in the vector. The promoter is directed towards the Y site. The insert containing only an ORF provides 3 fragments after digestion with both enzymes X and Y. The ORF is cloned in the correct orientation in the vector using the single restriction enzyme Y. The size of the largest fragment of the recombinant plasmid expressing the ORF upon digestion with enzyme X is ........... bp. (answer in integer) 