Using Network Control Principles to Probe the Structure and Function of Neuronal Connectomes

William R. Schafer1, Gang Yan2, 3, Petra E. Vértes4, Emma K. Towlson3, Yee Lian Chew1, Denise S. Walker1, & Albert-László Barabási3 1Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK. 2School of Physics Science and Engineering, Tongji University, Shanghai 200092, China. 3Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. 4Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, UK.

Large-scale efforts are underway to map the neuronal connectomes of many animals, from flies to humans. However, even for small connectomes, such as that of C. elegans, it has been difficult to relate the structure of neuronal wiring patterns to the function of neural circuits. Recent theoretical studies have suggested that control theory might provide a framework to understand structure-function relationships in complex biological networks, including neuronal connectomes. To test this hypothesis experimentally, we have used the complete neuronal connectome of C. elegans to identify neurons predicted to affect the controllability of the body muscles and assess the effect of ablating these neurons on locomotor behavior. We identified 12 neural classes whose removal from the connectome reduced the structural controllability of the body neuromusculature, one of which was the uncharacterized PDB motorneuron. Consistent with the control theory prediction, ablation of PDB had a specific effect on locomotion, altering the dorsoventral polarity of large turns. Control analysis also predicted that three members of the DD motorneuron class (DD4, DD5 and DD6) are individually required for body muscle controllability, while more anterior DDs (DD1, DD2 and DD3) are not. Indeed, we found that ablation of DD4 or DD5, but not DD2 or DD3, led to abnormalities in posterior body movements, again consistent with control theory predictions. We are currently using the control framework to probe other parts of the C. elegans connectome, and are developing more sophisticated approaches behavioral analysis in order to more precisely relate ablation phenotypes to specific muscle groups. We anticipate that the control framework validated by this work may have application in the analysis of larger neuronal connectomes and other complex networks.