Elastic constants of polymer-grafted lipid membranes

The surface expansion that is induced by the lateral pressure in the brush region of lipid membranes containing grafted polymers is deduced from the s caling and mean-field theories for the polymer brush, together with the equ ation of state for a lipid monolayer at the equivalence pressure with fluid lipid bilayers. Depending on the length and mole fraction of the polymer l ipid, the membrane expansion can be appreciable. Direct experimental eviden ce for this lateral expansion comes from recent spin-label measurements wit h lipid membranes containing poly(ethylene glycol)-grafted lipids. The expa nsion in lipid area modifies the elastic constants of the polymer-grafted m embranes in a way that opposes the direct elastic response of the polymer i tself. Calculations as a function of polymer lipid content indicate that th e net change in isothermal area expansion modulus of the membrane is negati ve but small, in contrast to previous predictions. A similar situation appl ies to the curvature elastic moduli of membranes containing short polymer l ipids. For longer polymer lipids, however, the direct contribution of the p olymer brush to the bending elastic constants dominates, and the increase i n bending moduli with increasing polymer lipid content rapidly exceeds the basal values of the bare lipid membrane. The spontaneous (or intrinsic) cur vature of the component monolayer of polymer lipid-containing membranes is calculated for the first time. The polymer brush contribution to spontaneou s curvature scales quadratically with the polymer length, and at least quad ratically with the mole fraction of polymer lipid.