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All atom molecular dynamics simulations with explicit water were done to study the interaction between two parallel double-stranded DNA molecules in the presence of the multivalent counterions putrescine (2+), spermidine (3+), spermine (4+) and cobalt hexamine (3+). The inter-DNA interaction potential is obtained with the umbrella sampling technique. The attractive force is rationalized in terms of the formation of ion bridges, ie, multivalent ions which are simultaneously bound to the two opposing DNA molecules. The lifetime of the ion bridges is short on the order of a few nanoseconds.