Under some environmental conditions the halophile Halobacterium halobium synthesizes a membrane protein (MW 26,000) bacteriorhodopsin, which is purple because it contains retinal. Molecules of this protein aggregate into purple patches in the cell membrane. Bacteriorhodopsin acts as a light activated proton pump that provides energy for cell functions. X-ray analysis of this protein reveals that it consists of seven parallel alpha-helical segments, each of which transverses the bacterial cell membrane (thickness 4.5 nm=45Å).
a. Calculate the minimum number of amino acids necessary for one segment of alpha-helix to traverse the membrane completely
b. Estimate the fraction of the bacteriorhodopsin protein that occurs in alpha-helical form.