  The resolution of X-ray diffraction microscopy is limited by the maximum dose
that can be delivered prior to sample damage. In the proposed Serial
Crystallography method, the damage problem is addressed by distributing the
total dose over many identical hydrated macromolecules running continuously in
a single-file train across a continuous X-ray beam, and resolution is then
limited only by the available molecular and X-ray fluxes and molecular
alignment. Orientation of the diffracting molecules is achieved by laser
alignment. We evaluate the incident X-ray fluence (energy/area) required to
obtain a given resolution from (1) an analytical model, giving the count rate
at the maximum scattering angle for a model protein, (2) explicit simulation of
diffraction patterns for a GroEL-GroES protein complex, and (3) the frequency
cut off of the transfer function following iterative solution of the phase
problem, and reconstruction of an electron density map in the projection
approximation. These calculations include counting shot noise and multiple
starts of the phasing algorithm. The results indicate counting time and the
number of proteins needed within the beam at any instant for a given resolution
and X-ray flux. We confirm an inverse fourth power dependence of exposure time
on resolution, with important implications for all coherent X-ray imaging. We
find that multiple single-file protein beams will be needed for sub-nanometer
resolution on current third generation synchrotrons, but not on fourth
generation designs, where reconstruction of secondary protein structure at a
resolution of 0.7 nm should be possible with short exposures.
