Symmetry energy describes how the net nuclear energy changes with changing inequality between neutron and proton numbers. Knowledge of the symmetry energy, and especially its dependence on density in uniform medium, is needed for extrapolating from nuclei to matter in neutron stars. Charge invariance of nuclear interactions can be used to demonstrate that nuclei can be assigned nuclear symmetry coefficients that depend on mass and reflect changes of symmetry energy with density, within nuclear surface. Those coefficients are extracted nucleus-by-nucleus from excitation energies to isobaric analog states. The variation of those coefficients with mass is then used to constrain the density dependence of symmetry energy in uniform matter. As nuclear ground states minimize energy, neutrons and protons displace relative to each other to minimize symmetry energy contribution to the net energy. Universality of the features of neutron and proton distributions in nuclei, in the context of symmetry energy, is discussed.