On the relationship between drug’s size, cell membrane mechanical properties and high levels of multi drug resistance: a comparison to published data

Abstract

Multi drug resistance (MDR) or cross resistance to drugs was initially explained on the basis that MDR cells express drug transporters that expel membrane-embedded drugs. However, it is now clear that transporters are a single piece from a complex puzzle. An issue that has been solved recently is, given that these transporters have to handle drugs, why should a membrane-embedded drug and a transporter meet? To solve this problem, a theory has been suggested considering the interaction between the cell membrane mechanical properties and the size of drugs. In simple terms, this theory proposes that an excess in the packing of lipid in the inner leaflet of the membrane of MDR cells is responsible for blocking drugs mechanically as a function of their sizes at the membrane level, thus impairing their flux into the cytosol. In turn it is expected that this would allow any membrane embedded drug to diffuse toward transporters. The study concluded that the size of drugs is necessarily important regarding the mechanical interaction between the drug and the membrane, and likely to be central to MDR. Remarkably, an experimental study based on MDR and published years ago concluded that the molecular weight (MW) of drugs was central to MDR (Biedler and Riehm in Cancer Res 30:1174–1184, 1970). Given that size and MW are linked together, I have compared the former theory to the latter experimental data and demonstrate that, indeed, basic membrane mechanics is involved in high levels of cross resistance to drugs in Pgp expressing cells.

Appendix

Assuming a flat membrane composed of two leaflets and containing, N _in lipids in the inner leaflet and, N _out lipids in the outer leaflet (N _in > N _out). The relative lipid number asymmetry: ΔN/N ₀, with ΔN = (N _in − N _out) and N ₀ = (N _in + N _out)/2, generates a differential packing across the membrane of thickness, h. In turn this generates a momentum (i.e. a bending force): ∼ h K ΔN/N ₀, that is proportional to the elastic modulus of leaflets, K, and that tends to bend the membrane inwardly (Fig. 1c).

However, the bending stiffness of the membrane, i.e. the membrane bending modulus k _c, balances the inward bending by an outward bending force that is proportional to k _c and inversely proportional to the radius, R, of the vesicle to be created: ∼ k _c/R. As such the bending stiffness of the membrane imposes a limit to the creation of too small vesicles.³ Finally, given this mechanical model of membrane budding, the optimal size of vesicles is dictated by the equilibrium between the inward and outward bending forces, namely: h KΔN/N ₀ ∼ k _c /R ⇒ R ∼ k _c /(hKΔN/N ₀). A detailed analysis gives R = 8k _c/hK(ΔN/N ₀)(Rauch and Farge 2000).