We employ a relativistic quark bag picture, the chromo-dielectric soliton model, to discuss the quarks' symmetry structure and momentum distribution in the N-N system. Six-quark clusters are constructed in a constrained mean-field calculation. The corresponding Hamiltonian contains not only an effective interaction between the quarks and a scalar field, which is assumed to parameterize all non-perturbative effects due to the non-linearity of QCD, but also quark-quark interactions mediated through one-gluon-exchange. We also evaluate the quark light-cone distribution functions, characterizing inclusive deep-inelastic lepton scattering, for the nucleon as well as for the six-quark structures. We find a competition between a softening of the q...