Development and application of a unique Molecular Dynamics (MD) simulation methodology for studying proton transport ("translocation") in biomolecular systems is of utmost importance. Proton translocation is a process of fundamental importance in biology, which generally occurs via proton shuttling over significant distances (ten or more Angstroms) through intervening water molecules and ionizable amino acid residues. This shuttling process creates an enormous challenge for standard MD simulations because of the dynamically changing bonding topologies occurring over numerous molecular groups.
However, by
virtue of our Multi-state Empirical Valence Bond (MS-EVB) approach,
this challenge has now been met so that explicit proton transport can now
be simulated using the MD Method.
The figure above right shows an example of a description of a protonated water tetramer by the MS-EVB approach
which states: 
, 
, and 
can be derived from 
by assigning each hydrogen of the central hydronium to the corresponding acceptor water molecule. Note that in the different EVB states the atoms coordinates are the same and only the bonding topology changes. With these states, a Hamiltonian matrix 
can be constructed as:
with 
ij = ji and the zeros indicating the assumption of no direct change of states among , and (hence, the corresponding couplings are zeros).
With ij = ji and the zeros indicating the assumption of no direct change of states among , and (hence, the corresponding couplings are zeros).
Assuming the orthogonality of each states, ie.,
,
one can solve the following equation:
,
to obtain 
the eigenvector, whose elements are the EVB coefficients (ci), of the lowest eigenvalue (corresponding to the energy of the most stable state of the reaction). With , the energy and forces can be calculated through the Feyman-Hellman theorem, i.e.,
