  We extend the Saffman theory of membrane hydrodynamics to account for the
correlated motion of membrane proteins, along with the effect of protein
concentration on that correlation and on the response of the membrane to
stresses. Expressions for the coupling diffusion coefficients of protein pairs
and their concentration dependence are derived in the limit of small protein
size relative to the inter-protein separation. The additional role of membrane
viscosity as determining the characteristic length scale for membrane response
leads to unusual concentration effects at large separation -- the transverse
coupling increases with protein concentration, whereas the longitudinal one
becomes concentration-independent.
