Phosphoglucose isomerase mechanism
tl;dr: The active site catalytic residues (BH+ and B’) are thought to be Lys and a His–Glu dyad, respectively. These facilitate the abstraction of proton from C2 and subsequent protonation on C-1.



Some important points to note:


  "shows histidine protonating c5 oxygen and lysine deprotonating c1
  oxygen to form an open chain aldolase
  ”.



The opening of the ring, is facilitated by Lysine and not by Histidine.



  “Glutamic acid then deprotonates c3 to create an enediol intermediate
  and donates the proton to c1”



It is actually the His–Glu  (B’) dyad (see image below) that abstract this proton from C2. See how this process occurs at the same time as the exchange of H+ (protons) with the solvent or medium. In this step C2 loses a proton while C1 gains a proton (Step 3-4)
Finally a proton is added  from the medium and the ring closes


A proposed reaction mechanism for the Phosphoglucose Isomerase reaction involves general acid–base catalysis by the enzyme:

Step 1


Substrate binding.


Step 2 


An acid, presumably the Lys ε-amino group, catalyzes the opening of the pyranose ring.


Step 3


A base, presumably the imidazole portion of the His–Glu dyad, abstracts the acidic proton from C2 to form a cis-enediolate intermediate (this proton is acidic because it is α to a carbonyl group).


Step 4 


The proton is replaced on C1 in an overall proton transfer. Protons abstracted by bases are labile and exchange rapidly with solvent protons. This step was confirmed by Irwin Rose by demonstrating that $\ce{[2-^3H]G6P}$ is occasionally converted to $\ce{[1-^3H]F6P}$ by intramolecular proton transfer before the $\ce{^3H}$ has had a chance to exchange with the medium.


Step 5 


Ring closure to form the product, which is subsequently released to yield free enzyme, thereby completing the catalytic cycle.




Reaction mechanism of phosphoglucose isomerase