Understanding the molecular mechanisms which nature uses to control biomineral growth is a fundamental science goal with profound medical implication. In the case of calcium oxalate, a microscopic understanding of the interactions which regulate the growth and stabilization of metastable phases would permit to inhibit the growth of the crystals which are the main components of kidney stones. Here we use a combination of ab initio and force-field -based molecular dynamics simulations to unravel how specific molecular interactions occurring on calcium oxalate dihydrate surface can promote an anisotropic crystal growth. We find that the calcium oxalate dihydrate (100) and (101) surfaces are both hydrophilic and solvated by a strongly bound layer of water; however, they exhibit important differences in their ability to bind water and peptides, such poly Glu. In particular, on the (100) surface, the more exposed Ca2+ ions can more strongly bind to negatively charged groups, exerting a protecting action on the surface and preventing its further growth. This mechanism in turn would favor an anisotropic growth of the calcium oxalate dihydrate crystals in the  direction, as observed in experiments.