  We present a study of the correlations between spectral, timing properties
and mass accretion rate observed in X-rays from the Galactic Black Hole (BH)
binary GRS 1915+105 during the transition between hard and soft states. We
analyze all transition episodes from this source observed with RXTE,
coordinated with Ryle Radio Telescope (RT) observations. We show that
broad-band energy spectra of GRS 1915+105 during all these spectral states can
be adequately presented by two Bulk Motion Comptonization (BMC) components: a
hard component (BMC1, photon index Gamma_1=1.7-3.0) with turnover at high
energies and soft thermal component (BMC2, Gamma_2=2.7-4.2) with characteristic
color temperature <1 keV, and the redskewed iron line (LAOR) component. We also
present observable correlations between the index and the normalization of the
disk "seed" component. The use of "seed" disk normalization, which is
presumably proportional to mass accretion rate in the disk, is crucial to
establish the index saturation effect during the transition to the soft state.
We discovered the photon index saturation of the soft and hard spectral
components at values of 4.2 and 3 respectively. We present a physical model
which explains the index-seed photon normalization correlations. We argue that
the index saturation effect of the hard component (BMC1) is due to the soft
photon Comptonization in the converging inflow close to BH and that of soft
component is due to matter accumulation in the transition layer when mass
accretion rate increases. In addition to our spectral model components we also
find a strong feature of "blackbody-like" bump which color temperature is about
4.5 keV in eight observations of the intermediate and soft states. We discuss a
possible origin of this "blackbody-like" emission.
