Hi Lars,
BG-12 and fumaric acid are two different, but related, molecules. BG-12 is dimethyl fumarate. It has the following structure...
It reacts with thiol groups, -SH, such as those found in glutathione and cysteine residues oxidizing them. Cells sense this oxidative stress and activate the transcription of cell protective genes for antioxidant enzymes.
In contrast, fumaric acid is a dicarboxylic acid where the -CH
3 groups are replaced with H.
It doesn't have the same chemical reactivity with thiols and won't activate the cell protectant genes that dimethyl fumarate activates.
One thing to know is that there are many molecules in nature that have similar functional groups as dimethyl fumarate which gives them similar reactivity with thiols. Here's a free review paper which discusses them.
NHE