Using scanning tunneling microscopy we have studied the nucleation and growth of unidirectional molecular rows upon adsorption of the amino acid cysteine onto the anisotropic Au(110)-(1x2) surface under ultrahigh vacuum conditions. By modeling a large variety of possible molecular adsorption geometries using density-functional theory calculations, we find that in the optimum, lowest energy configuration, no significant intermolecular interactions exist along the growth direction. Instead the driving force for formation of the unidirectional molecular rows is an adsorbate-induced surface rearrangement, providing favorable adsorption sites for the molecules.