Ab initio molecular orbital theory is used to investigate the coenzyme- B12-dependent rearrangement of 2-methyleneglutarate to (R)-3- methylitaconate catalyzed by 2-methyleneglutarate mutase. We use a 'model system' approach whereby substituents such as carboxylate groups are replaced by computationally less expensive hydrogen atoms. The validity of this approach is tested and supported by investigations which compare the results obtained with and without this simplification. In both rearranging systems, we find a recently suggested mechanism, involving a transient fragmentation of the substrate followed by recombination of the fragments, to be associated with a high activation energy. A cyclization/ring-opening (addition/elimination) mechanism is found to require substantially less energy than the fragmentation/recombination mechanism. Even lower in energy requirements are mechanisms involving protonation/deprotonation of the substrates.