  We embed a theory with Zprime gauge boson (related to extra U(1) gauge group)
into a supersymmetric GUT theory based on SO(10). Two possible sequences of
SO(10) breaking via VEVs of appropriate Higgs fields are considered. Gauge
coupling unification provides constraints on low energy values of two
additional gauge coupling constants related to Zprime interactions with
fermions. Our main purpose is to investigate in detail the freedom in these two
values due to different scales of subsequent SO(10) breaking and unknown
threshold mass corrections in the gauge RGEs. These corrections are mainly
generated by Higgs representations and can be large because of the large
dimensions of these representations. To account for many free mass parameters,
effective threshold mass corrections have been introduced. Analytic results
that show the allowed regions of values of two additional gauge coupling
constants have been derived at 1-loop level. For a few points in
parameter-space that belong to one of these allowed regions 1-loop running of
gauge coupling constants has been compared with more precise running, which is
2-loop for gauge coupling constants and 1-loop for Yukawa coupling constants.
1-loop results have been compared with experimental constraints from
electroweak precision tests and from the most recent LHC data.
