Scattering from phase-separated vesicles. I. An analytical form factor for multiple static domains

This is the first in a series of papers considering elastic scattering from laterally heterogeneous lipid vesicles containing multiple domains. Unique among biophysical tools, small-angle neutron scattering can in principle give detailed information about the size, shape and spatial arrangement of domains. A general theory for scattering from laterally heterogeneous vesicles is presented, and the analytical form factor for static domains with arbitrary spatial configuration is derived, including a simplification for uniformly sized round domains. The validity of the model, including series truncation effects, is assessed by comparison with simulated data obtained from a Monte Carlo method. Several aspects of the analytical solution for scattering intensity are discussed in the context of small-angle neutron scattering data, including the effect of varying domain size and number, as well as solvent contrast. The analysis indicates that effects of domain formation are most pronounced when the vesicle's average scattering length density matches that of the surrounding solvent.