Carpentry and Woodworking - Mold removal from antique wood

I have an antique dark oak bookcase that sustained serious water damage in a move.

It has thick, white buildup where the mold took root.

What is the best way to remove the mold without further damaging the wood and, if possible, without damaging the original patina of the piece?

The simplest method for killing mildew on wood is to use bleach. I would start with a solution 10% bleach in water. Spray it on, let it sit for 5 minutes, the wipe the surface clean, then wipe with a cloth dampened with water to remove the remaining bleach. It may be necessary to repeat this, if it appears to work somewhat. If it has no apparent effect, try bleach 25% in water. This is a strong mixture, so wear protective clothing and work in an environment where the bleach spilling or running off won't damage anything. Work quickly to avoid damaging the wood further.

If the mildew took hold and laid down a base of the white string root-like structure, it may well have gotten through the finish into the wood. If this is the case, removing the mildew and stain will likely expose a damaged area on the piece. There is every likelihood that the damaged area will not be repairable without refinishing the piece.