What structures in the brain are called upon to strengthen coupling between bilateral movements? It is very difficult for the normally-coordinated person to be able to pat his/her head and rub his/her stomach at the same time (or pick a similar activity).  It seems to be possible to maintain the separate hand motions over the short term, but keeping the movements separate is almost impossible to keep up.  One ends up either rubbing the head while rubbing the stomach or patting the head while patting the stomach before long.  Effectively, there seems to be a "locking" between the motor cortices across the hemispheres during bilateral movements of the arms.

Given all of this complex coordination that is possible between the two arms/hands, what are the structures within the brain that are called upon to strengthen the coupling between the two arms during bilateral movements?  Why do the hemispheres try to lock their activity rather than letting both arms act independently?
It's not so much a "locking" between the two hemispheres as it is a combination of an asymmetrical representation of the ipsilateral (same side) limb in cortex, and phase transitions, which bring the limbs into a more energetically favorable state.

Kelso (1984) compares the phase transition to that of a racehorse, which is able to adjust its gait for the optimal use of oxygen in its blood.  In his study, regardless of whether a subject's limb was loaded or unloaded during a trial, there was a phase resetting after the subject reached a certain frequency (constant within subjects).  You can see in the diagram below that the dotted line of one arm's trajectory is 180&deg; out of phase with the other, the solid line, and at a certain point, they fall into lockstep.



Ziemann (2001) study points to another possible reason for the synchronization.  In right handed subjects, there tends to be a dominance of the left motor cortex in the activation of the ipsilateral hand.  Trying to do different motions with both hands may "pull" the activity towards what the left hand is doing.  Presumably, there might be a similar behavior in left-handed subjects, but as in hearing and language, there is not a perfect symmetry of cortical features for left-handers.    

In terms of structures that do govern bilateral coordination, Sadato et al (1997) used PET scanning to establish that, at least in right handed subjects, the right dorsal premotor area along with the right posterior supplementary motor area, were significantly more active while making parallel movements.  I found no further evidence of it, but this could be a channel through which some of the phase shifting is taking place.

References


Kelso, J.A.S. (1984).  Phase transitions and critical behavior in human bimanual coordination.  American Journal of Physiology, 246 (Regulatory Integrative Comp. Physiol 15):R1000-1004.
Sadato, N., Yonekura, Y., et al (1997).  Role of the supplementary motor area and the right premotor cortex in the coordination of bimanual finger movements.  Journal of Neuroscience, 17(24): 9667-9674. PDF
Sakurada, T., Gomi, H., Ito, K. (2009). Multiple interactions between hemispheres of the brain modulating coupling of bilateral movements. The 31st Annual International Conference of the IEEE EMBS Minneapolis, Minnesota, USA, September 2-6, 2009: 5922-5925.
Ziemann, U., Hallett, M. (2001).  Hemispheric asymmetry of ipsilateral motor cortex activation during unimanual motor tasks: further evidence for motor dominance.  Clinical Neurophysiology, 112: 107-113.