Nanoparticles (NPs) which enter physiological fluids are rapidly coated by proteins, forming a so-called corona which may strongly modify their interaction with tissues and cells relative to the bare NPs. In this work the interactions between a living cell and a nano-object, and in particular the effect on this of the adsorption of serum proteins, are directly examined by measuring the forces arising as an Atomic Force Microscope tip (diameter 20 nm) - simulating a nano-object - approaches and contacts a cell. We find that the presence of a serum protein corona on the tip strongly modifies the interaction as indicated by pronounced increase in the indentation, hysteresis and work of adhesion compared to a bare tip. Classically one expects an AFM tip interacting with a cell surface to be repelled due to cell elastic distortion, offset by tip-cell adhesion, and indeed such a model fits the bare-tip/cell interaction, in agreement with earlier work. However, the force plots obtained with serum-modified tips are very different, indicating that the cell is much more compliant to the approaching tip. The insights obtained in this work may promote better design of NPs for drug delivery and other nano-medical applications.