Liposomes are promising molecules in gene transfer technology because of their similarity to cell membranes and their charge interactions with negatively charged DNA. Estimate the charge on the outside surface of a liposome of diameter 1 um. Suppose a typical phospholipid head has a diameter of 1 nm and carries a charge of one proton (1.6021 x 10^-19 C). Assume that the surface of the spherical liposome is comprised of phospholipid heads packed together as tightly as possible in a configuration known as hexagonal packing, which minimizes the inevitable vacant space that occurs when circles pack against one another.