We extracted, from strongly-correlated ab-initio calculations, a complete model for the chain subsystem of the $S\!r_{0.4}C\!a_{13.6}C\!u_{24}O_{41}$ incommensurate compound. A second neighbor $t-J+V$ model has been determined as a function of the fourth crystallographic parameter $\tau$, for both low and room temperature crystallographic structures. The analysis of the obtained model shows the crucial importance of the structural modulations on the electronic structure through the on-site energies and the magnetic interactions. The structural distortions are characterized by their long range effect on the cited parameters that hinder the reliability of analyses such as BVS. One of the most striking results is the existence of antiferromagnetic nearest-neighbor interactions for metal-ligand-metal angles of $90^\circ$. A detailed analysis of the electron localization and spin arrangement is presented as a function of the chain to ladder hole transfer and of the temperature. The obtained spin arrangement is in agreement with antiferromagnetic correlations in the chain direction at low temperature.