  We propose an enhanced approach to the extrapolation of mean potential forces
acting on atoms of solute macromolecules due to their interactions with solvent
atoms in complex biochemical liquids. It improves and extends previous
extrapolation schemes by including additionally new techniques such as an
exponential scaling transformation of coordinate space with weights
complemented by a dynamically adjusted balancing between the least square
minimization of force deviations and the norm of expansion coefficients in the
approximation. The expensive mean potential forces are treated in terms of the
3D-RISM-KH molecular theory of solvation (three-dimensional reference
interaction site model with the Kovalenko-Hirata closure). During the dynamics
they are calculated only after every long enough (outer) time interval, i.e.,
quite rarely to reduce the computational costs. At much shorter (inner) time
steps, these forces are extrapolated on the basis of their outer values. The
equations of motion are then solved using a multiple time step integration
within an optimized isokinetic Nos\'e-Hoover chain thermostat. The new approach
is applied to molecular dynamics simulations of various systems consisting of
solvated organic and biomolecules of different complexity. Namely, we consider
hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y and
protein G in aqueous solution. It is shown that in all these cases, the
enhanced extrapolation provides much better accuracy of the solvation force
approximation than the existing approaches. As a result, it can be used with
much larger outer time steps, leading to a significant speedup of the
simulations.
