  The newy developed approach to model nucleon generalized parton distributions
(GPDs) H and E$ is based on two types of their representation in terms of
double distributions. Within this approach, we re-consider the derivation of
GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of
full GPDs H(x,\xi) and E(x,\xi) in the integrals producing Compton form factors
of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs,
we discuss the relation between the border functions and underlying parton
densities. We find that a substantial contribution to H(x,x) border function
comes from the extra term required by new DD representations and related to
E(x,\xi) GPD.
