  Theoretical studies of protein folding on lattice models relie on the
assumption that water close to amino-acids is always in thermal equilibrium all
along the folding pathway. Within this framework, it has always been considered
that out-of-equilibrium properties, such as folding time, could be evaluated
equivalently from an averaging over a collection of trajectories of the protein
with water described eitherexplicitly or through a mean-field approach. To
critically assess this hypothesis, we built a two-dimensional lattice model of
a protein in interaction with water molecules that can adopt a wide range of
conformations. This microscopic description of the solvent has been used
further to derive an effective model by averaging over all the degrees of
freedom of the solvent. At thermal equilbrium, the two descriptions are
rigourously equivalent, predicting the same folded conformation of the protein.
The model allows exact calculations of some relaxation properties using the
master equations associated to both solvent descriptions. The kinetic patterns
associated to the folding pathways are remarkably different. In this work we
demonstrate, that an effective description of the solvent can not described
properly the folding pathway of a protein. The microscopic solvent model, that
describes correctly the microscopic routes, appears to be the only candidate to
study folding kinetics.
