  A new statistical mechanics formulation of characterizing the structural
fluctuation of protein correlated with that of water is presented based on the
generalized Langevin equation and the 3D-RISM/RISM theory of molecular liquids.
The displacement vector of atom positions and their conjugated momentum, are
chosen for the dynamic variables for protein, while the density fields of atoms
and their momentum fields are chosen for water. Projection of other degrees of
freedom onto those dynamic variables using the standard projection operator
method produces essentially two equations which describe the time evolution of
fluctuation concerning the density field of solvent and the conformation of
protein around an equilibrium state, which are coupled with each other. The
equation concerning the protein dynamics is formally akin to that of the
coupled Langevin oscillators, and is a generalization of the latter, to atomic
level. The most intriguing feature of the new equation is that it contains the
variance-covariance matrix as the "Hessian" term describing the "force"
restoring an equilibrium conformation, which is the second moment of the
fluctuation of atom positions. The "Hessian" matrix is naturally identified as
the second derivative of the free energy surface around the equilibrium. A
method to evaluate the Hessian matrix based on the 3D-RISM/RISM theory is
proposed. Proposed also is an application of the present formulation to the
molecular recognition, in which the conformational fluctuation of protein
around its native state becomes an important factor as exemplified by so called
"induced fitting".
