Osmium tetroxide reaction with cell membrane
According to the paper The chemical nature of osmium tetroxide fixation and staining of membranes by x-ray photoelectron spectroscopy[1] by White et al. (1976), 


  The results support a scheme for the reaction of osmium tetroxide with tissues in which the initial reaction site is the double bonds of unsaturated lipids to form $\ce{Os(VI)}$ derivatives. Subsequent hydrolysis and further reduction yield complexes of $\ce{Os(IV)}$ and $\ce{Os(III)}$. A mixture of these three states is present in membrane specimens during microscopic observation. $\ce{Os(VI)}$ and $\ce{Os(IV)}$ could be present as osmate esters and osmium dioxide, respectively; $\ce{Os(III)}$ could be present as an oxo- or amino complex(es).


However, since $\ce{OsO4}$ reacts with biological material, the above list is probably incomplete.

Riemersma[2] suggests that negatively charged colloidally dispersed osmium dioxide hydrate is deposited at the polar ends of lipids that contain a positively charged (phosphoryl)choline moiety (lecithin, phosphatidylcholines, etc). In this case we would have a pure Coulomb interaction.



References


White DL, Andrews SB, Faller JW, Barrnett RJ, Biochim Biophys Acta, 436(3):577-92 (1976).
Jelle C. Riemersma, J. Histochem. Cytochem, 11, 436-442 (1963)