The eukaryotic cell develops organelles in order to sense and respond to the mechanical properties of its surroundings. These mechanosensing organelles aggregate into symmetry-breaking patterns to mediate cell motion and differentiation on substrate. The spreading of a cell plated onto a substrate is one of the simplest paradigms in which angular symmetry-breaking assemblies of mechanical sensors are seen to develop. We review evidence for the importance of the edge of the cell-extracelullar matrix adhesion area in the aggregation of mechanosensors, and develop a theoretical model of mechanosensors clustering into nascent focal adhesions on this contact ring. To study the spatial patterns arising on this topological feature, we use a 1D lattice model with the nearest-neighbor interaction between individual integrin-mediated mechanosensors.} We find the effective Ginzburg-Landau free energy for this model, and determine the spectrum of spatial modes as the cell spreads and increases its contact area with the substrate. To test our model, we compare its predictions with measured distributions of paxillin in spreading fibroblasts.