Release of plasma coolant.
Next to the matter/antimatter reaction that fuels warp plasma to the engine nacelles, the most important part of Federation warp drives is plasma coolant.
When the matter-antimatter reaction assembly combines deuterium and antideuterium within an energized dilithium crystal, the plasma generated is immensely powerful, and must be cooled by specially designed, yet hazardous, coolant compounds.
Plasma coolant maintains the warp core, cooling any heat safely away from the populated areas of the starship or outpost. It operates in the same manner any coolant is used in an engine. Without it, the engine systems could overheat or fail completely.
The Borg Queen dissolves in the plasma coolant.
Plasma coolant is considered a biohazard and will react violently with organic matter, liquifying it on contact. (Star Trek: First Contact)
A coolant leak has been known to either cause or be the precursor to a warp core breach. (TNG: "Yesterday's Enterprise"; Star Trek Generations)
In 2374, one of USS Voyager's coolant injectors ruptured, causing a plasma coolant leak. (VOY: "Day of Honor")
Background
Coolant dangers aboard a starship have also been depicted in TOS:"Balance of Terror."
The loss of plasma coolant causing adverse effects to the warp core does not seem to apply to the USS Enterprise-E. In Star Trek: First Contact, when Data breached the primary coolant tank in main engineering, it did not appear to have any adverse affect on the engines, even though the warp core was powered. It is possible that Starfleet engineered a solution to this problem. It can also be hypothized that since the warp engines were not active during the "First Contact incident", the ruptering of one of the plasma coolant tanks was not sufficent to cause a thermal overload of the warp core reaction chamber. Or the Plasma could have been diverted to and/or through the other tank in order to maintain the core temperature.