Fibrillar collagens, common tissue scaffolds in live organisms, can also self-assemble in vitro from solution. While previous in vitro studies showed that the pH and the electrolyte concentration in solution largely control the collagen assembly, the physical reasons why such control could be exerted are still elusive. To address this issue and to be able to simulate self-assembly over large spatial and temporal scales, we have developed a microscopic model of collagen with explicit interactions between the units that make up the collagen molecules, as well as between these units and the substrate. We have used this model to investigate assemblies obtained via molecular dynamics deposition of collagen on a substrate at room temperature using an implicit solvent. By comparing the morphologies from our molecular dynamics simulations with those from our atomic-force microscopy experiments, we have found that the assembly is governed by the competition between the collagen-collagen interactions and those between collagen and the substrate. The microscopic model developed here can serve for guiding future experiments that would explore new regions of the parameter space.