We analyse the response of osteoblasts on grooved substrates via a model that accounts for the cooperative feedback between intracellular signalling, focal adhesion development and stress fibre contractility. The grooved substrate is modelled as a pattern of alternating strips on which the cell can adhere and strips on which adhesion is inhibited. The coupled modelling scheme is shown to capture some key experimental observations including (i) the observation that osteoblasts orient themselves randomly on substrates with groove pitches less than about 150 nm but they align themselves with the direction of the grooves on substrates with larger pitches and (ii) actin fibres bridge over the grooves on substrates with groove pitches less than about 150 nm but form a network of fibres aligned with the ridges, with nearly no fibres across the grooves, for substrates with groove pitches greater than about 300 nm. Using the model, we demonstrate that the degree of bridging of the stress fibres across the grooves, and consequently the cell orientation, is governed by the diffusion of signalling proteins activated at the focal adhesion sites on the ridges. For large groove pitches, the signalling proteins are dephosphorylated before they can reach the regions of the cell above the grooves and hence stress fibres cannot form in those parts of the cell. On the other hand, the stress fibre activation signal diffuses to a reasonably spatially homogeneous level on substrates with small groove pitches and hence stable stress fibres develop across the grooves in these cases. The model thus rationalizes the responsiveness of osteoblasts to the topography of substrates based on the complex feedback involving focal adhesion formation on the ridges, the triggering of signalling pathways by these adhesions and the activation of stress fibre networks by these signals.