From the Metal Gear Wiki

The Genome Soldiers were members of Next Generation Special Forces (aka Space SEALs) and reserve members of FOXHOUND that have undergone virtual reality training and gene therapy experiments, but have little or no actual field experience.

The Next Generation Special Forces were originally a counter-terrorist unit comprised of former members of biochem units, technical escort teams and the Nuclear Emergency Search Team. Their original purpose was to neutralize NBC threats.

After the death of Big Boss and the downfall of Zanzibar Land, members of Big Boss' mercenary dispatching company, (Outer Heaven), were integrated into the unit after the US Government purchased their contracts. The team subsequently merged with Force XXI and were given VR training. Members of the team were also secretly enhanced with Big Boss' "soldier" genes, giving them augmented senses and reflexes.

In 2005, the Genome Soldiers took part in what was scheduled to have been a routine training exercise in Shadow Moses Island. The Genome Soldiers and FOXHOUND (under Liquid Snake's command) staged a revolt on the island, taking over the nuclear facility (where Metal Gear REX was secretly developed) and along with a few hostages. The terrorists (calling themselves the Sons of Big Boss) threatened to launch a nuclear strike if the remains of Big Boss were not delivered to them in less than 24 hours. Almost the entire NGSF unit were subverted to rebellion, with some of the members being brainwashed by Psycho Mantis and others supporting Liquid's cause from their own free will. It was revealed that the Genome Soldiers were suffering from genetic defects as a result of their gene therapy treatments and that Big Boss' remains was the key to their survival.

After the destruction of REX by operative Solid Snake and the death of Liquid, the surviving Genome Soldiers were transferred to the Pease AFB in New Hampshire, where they were imprisoned for treason.