A technique is described to determine umbrella biasing potentials that can be used to enhance sampling of rotational isomeric states in molecular simulations of polypeptides in water. The analytical biasing potential function are obtained through fitting of potentials of mean force obtained by thermodynamic integration simulations to a small number of functions used to describe dihedral torsion. The resulting dramatic increase in efficiency of sampling is illustrated by comparison of molecular simulations of the alanine-dipeptide molecule in aqueous solution, with and without the use of the biasing potentials. The same biasing potentials were used in simulations of the alanine-tripeptide and the alanine-heptapeptide in aqueous solution. Similar dramatic increases in sampling efficiency were observed for these simulations, when the biasing potentials were applied, which suggests that these biasing potentials, although determined for the dipeptide, may be transferable to larger peptide chains. It is illustrated how the biasing potentials can be used in biasing potential annealing simulations, leading to rapid folding of peptide chains into aqueous solutions structures with low energy.