Single cell organisms such as yeast can survive in very different environments thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure since it is expected to remodel dynamically depending on the stage of growth, division cycle, environmental osmotic pressure and aging. Probing the mechanics of these organisms is therefore of strong interest, however it implies some more difficulties as compared to other mammal cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments of single yeast cells (S. cerevisiae) on poly-L-lysine coated glass plates, in the limit of small deformation with an atomic force microscope (AFM). We compare the mechanical response of single yeast cells grown in different culture media, with different carbon sources to address different energetic metabolisms and at different stages of their proliferation (initial, intermediary and final stationary stages). We develop a multi-scale nonlinear analysis of AFM force-displacement curves that provides evidences for non stationary scaling laws. We propose to model this phenomena based on a multilayered elastic system, each layer following a different scaling law.Read less <