Casimir and mean-field interactions between membrane inclusions subject toexternal torques

Inclusions embedded in fluctuating fluid membranes have been shown to exper ience membrane mediated forces decaying as 1/R-4. Modeling the inclusions a s local constraints on the membrane curvature tensor, we show that the pres ence of external torques (mechanical or field-induced) strongly enhances an d increases the range of the interactions. Repulsive mean-field contributio ns and attractive fluctuation (Casimir) contributions of range 1/R-2 or lon ger are found, which may combine to yield equilibrium distances.