  We consider a multiband Hubbard model $H_m$ for Cu and O orbitals in
Ba$_{2-x}$Sr$_x$CuO$_{3+\delta}$ similar to the tree-band model for
two-dimensional (2D) cuprates. The hopping parameters are obtained from
maximally localized Wannier functions derived from \textit{ab initio}
calculations. Using the cell perturbation method, we derive both a generalized
$t-J$ model $H_{tJ}$ and a one-band Hubbard model $H_{H}$ to describe the
low-energy physics of the system. $H_{tJ}$ has the advantage of having a
smaller relevant Hilbert space, facilitating numerical calculations, while
additional terms should be included in $H_{H}$ to accurately describe the
multi-band physics of $H_m$. Using $H_{tJ}$ and DMRG, we calculate the
wave-vector resolved photoemission and discuss the relevant features in
comparison with recent experiments. In agreement with previous calculations, we
find that the addition of an attractive nearest-neighbor interaction of the
order of the nearest-neighbor hopping shifts weight from the $3 k_F$ to the
holon-folding branch. Kinetic effects also contribute to this process.
