We introduce
a two-dimensional version of the method called on-the-fly free energy
parametrization (OTFP) to reconstruct free-energy surfaces using Molecular
Dynamics simulations, which we name OTFP-2D. We first test the new
method by reconstructing the well-known dihedral angles free energy
surface of solvated alanine dipeptide. Then, we use it to investigate
the process of K<sup>+</sup> ions translocation inside the Kv1.2 channel.
By comparing a series of two-dimensional free energy surfaces for
ion movement calculated with different conditions on the intercalated
water molecules, we first recapitulate the widely accepted <i>knock-on</i> mechanism for ion translocation and then confirm
that permeation occurs with water molecules alternated among the ions,
in accordance with the latest experimental findings. From a methodological
standpoint, our new OTFP-2D algorithm demonstrates the excellent sampling
acceleration of temperature-accelerated molecular dynamics and the
ability to efficiently compute 2D free-energy surfaces. It will therefore
be useful in large variety complex biomacromolecular simulations
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