Monoamine oxidase, like most protein enzymes, catalyzes reactions largely by positioning the necessary molecules in such a way that they react much faster than they would just by bumping one another randomly. This positioning is accomplished by folding into a structure that binds the components tightly and in the correct orientation. After that it’s just the chemistry that causes an amine to donate hydrogens to a nearby flavin molecule, converting into an imine and then an aldehyde soon after.
Below WT human monoamine oxidase A (PDB: 2Z5X) is shown as a cartoon representation in green. An FAD molecule (red) is covalently attached to Cys-406 (blue). IThe reversible inhibitor harmine (purple) is bound in the active site where a monoamine like dopamine or norepinephrine might bind.
Below residues Tyr-69, Asn-181, Phe-208, Val-210, Gln-215, Cys-323, Ile-325, Ile-335, Leu-337, Phe-352, Tyr-407, and Tyr-444 which form a hydrophobic pocket that fits the monoamine substrate (or in this case the inhibitor) are highlighted in cyan. There are also interactions with the aromatic rings of the inhibitor that help lock it in place (not shown).
Below is a transparent surface representation of MAO-A. You can still make out dopamine in purple (which I mutated into the structure assuming it fits in roughly the same way that the harmine inhibitor did) and FAD in red inside the protein.
If we slice the above image down the middle (below) you can see the internal pocket that FAD (red) fits into as a grayish shadow. You can also see dopamine in purple entering from the left side (marked by an arrow) through a small opening leading into the larger cavity containing the active site. The pore as shown is a bit too small for the substrate, however dynamic fluctuations in the loops near the entrance likely allow it to enter and exit.
The structure of MAO-A positions the substrate in the active site so that it contacts flavin directly. This drives a reaction that oxidizes the substrate’s amine group into an aldehyde group. The mechanism for this reaction is discussed in the section below. MAO-B likely works the same way but the pocket has a slightly different shape and therefore functions better with a different set of substrates.
A post-translational modification of a cysteine residue with FAD near the active site of monoamine oxidase is necessary because FAD takes on an important chemical role as a proton acceptor in the catalysis. FAD is essentially a riboflavin molecule attached to a molecule of ADP as shown below.
Once the protein is chemically modified a monamine, like dopamine or norepinephrine, can use the flavin group as a proton acceptor and form an imine. One of a handful of proposed mechanisms (in other words, this is consistent with the structure but there are no guarantees that it is right) is shown below. In this “polar nucleophilic” mechanism the amine will attack the flavin as shown below. During the reaction the monoamine in red is converted into an imine.
The imine will undergo immediate hydrolysis into an aldehyde in the presence of water as shown below. The incoming imine starts in red and remains in red as it becomes an aldehyde, releasing an ammonium ion in the process.
The positioning of the monoamine directly adjacent to flavin in the protein cavity, as shown in the crystal structures at the beginning, vastly speeds up these reactions. The enzymes work best for primary amines, like amphetamine (below, left), but not for the methyl-subsitituted secondary amines like methamphetamine (below, right) which has a second carbon coming off its amine group.
The issue is not so much the chemistry, which could proceed through the same mechanism shown above, but the biology. I’m not sure exactly what about the methyl group reduces the binding efficiency in this enzyme, but I think it’s safe to say that the presence of that extra carbon atom disrupts the interaction between the amine group and the flavin molecule, either because of its position or its effect on the position of methamphetamine in the binding pocket. Without the precise orientation of the correct chemical groups the enzymatic efficiency of MAO is significantly reduced.
This is similar to the way reversible inhibitors might work. The reversible inhibitor harmine, shown early on in the crystal structure, binds to and obstructs the active site of MAO-A without being oxidized. While it’s there, it prevents access of other monoamines and thus inhibits monoamine oxidation. Since it is bound non-covalently there is nothing preventing it from falling out of the pocket and allowing the enzyme to function normally. This is in contrast to irreversible MAO inhibitors that do bind covalently to the flavin molecule. The mechanisms of these irreversible inhibitors vary, but generally involve some kind of chemical reaction with the flavin molecule that doesn’t end in release of the inhibitor. Rasagiline, for example, will react covalently with the central nitrogen on the flavin group and remain there blocking the active site for the remainder of the protein’s lifetime.
 Son, S.-Y. et al. Structure of human monoamine oxidase A at 2.2-A resolution: the control of opening the entry for substrates/inhibitors. Proceedings of the National Academy of Sciences of the United States of America 105, 5739-44 (2008). http://www.pnas.org/content/105/15/5739.short
 Edmondson, D. E., Mattevi, A., Binda, C., Li, M. and Hubálek, F.. Structure and Mechanism of Monoamine Oxidase. Burger’s Medicinal Chemistry, Drug Discovery and Development (2005). http://onlinelibrary.wiley.com/doi/10.1002/0471266949.bmc111/full
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