Volume phase transitions of a DNA gel and a single giant DNA chain caused by spermidine(3+) (SPD(3+)) were investigated. The change in volume for the single DNA (VV(0) approximately 10(-5)) was four orders of magnitude greater than that for the DNA gel ( approximately 10(-1)), while the critical SPD(3+) concentration for the gel (1.8 mM) was one order of magnitude greater than that of the single DNA (0.12-0.25 mM) at the same pH 6.86. We tried to describe mean-field theories with virial expansion, which is valid for the coil-globule transition of a single polymer chain, for the volume phase transitions to explain the reason why such marked differences appeared. Considering the degree of the ordering of Kuhn segments arising from the gel network structure together with the chain length of cross-linked polymer chains, the volume phase transitions were described and then the significant differences were reproduced quantitatively. We concluded that the network structure plays a significant role in the volume phase transition of the gel.