Phenolic preservatives are known to stabilize industrial formulations

of insulin through cooperative binding to six hydrophobic cavities in

the insulin hexamer. Phenol exchange is rapid on hexamer dissolution

timescales, and phenol unbinding upon dilution is likely the first

step in the conversion of (pharmaceutical) hexameric insulin to the

active monomeric form upon injection. However, a clear understanding

of the determinants of the rates of phenol unbinding remains obscure,

chiefly because residues implicated in phenol exchange as determined

by NMR are not all associated with likely unbinding routes suggested

by the best-resolved hexamer structures. In this context, we used

random expulsion molecular dynamics (REMD) to determine potential

(un)binding pathways of phenol from the hexameric insulin-phenol

complex. We observe three different escape pathways for the ligand and

perform detailed free-energy calculations to resolve the potential of

mean forces (PMFs) along these pathways. PMFs are computed with the

help of second order cumulant expansion of Jarzynski's equality and

non-equilibirum work statistics gathered from steered molecular

dynamics (SMD) simulations. Our estimates for (un)binding free energy

(Δ F) of phenolic ligands are within the range of known

experimental and previous simulation magnitudes of this quantity. The

pathway with the lowest free energy barrier involves a leap over the

"gate" formed by IleA10 and HisF5, with simultaneous passage of the ligand

through a narrow channel existing between LeuA13, LeuH17, and the "gate".

PMF profiles also display several weakly-bound intermediate

states during phenol entry and exit from the hexamer.

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