The effective interaction between two parallel strands of helical biomolecu
les, such as deoxyribose nucleic acids (DNA), is calculated using computer
simulations of the "primitive" model of electrolytes. In particular we stud
y a simple model for B-DNA incorporating explicitly its charge pattern as a
double-helix structure. The effective force and the effective torque exert
ed onto the molecules depend on the central distance and on the relative or
ientation. The contributions of nonlinear screening by monovalent counterio
ns to these forces and torques are analyzed and calculated for different sa
lt concentrations. As a result, we find that the sign of the force depends
sensitively on the relative orientation. For intermolecular distances small
er than 6 Angstrom it can be both attractive and repulsive. Furthermore, we
report a nonmonotonic behavior of the effective force for increasing salt
concentration. Both features cannot be described within linear screening th
eories. For large distances, on the other hand, the results agree with line
ar screening theories provided the charge of the biomolecules is suitably r
enormalized.