Love and Hate of Two Circadian Clocks

“

This two-clock story has a long story. The “hate” or negative coupling (as it was initially called) or phase-repulsive coupling (as it was renamed) was first realized when Bmal1-ELuc dataset were processed and represented as phase, phi(t), and they were put into Kuramoto model. I made a very naive mistake of putting two phases in the wrong order in the Kuramoto coupling term, i.e., sin(phase-of-itself - phase-of-partner) instead of sin(phase-of-partner - phase-of-itself). I think it was back in 2008 or 2009. It worked great—but it was rather mysterious that the clocks never completely synchronized, even if there was difference in intrinsic periods. I showed my results to physicists at Kyoto University, at a lab that was once headed by Kuramoto himself, and the assistant professor there volunteered to do the simulation and he failed to reproduce and the simulation was scrapped (hence the 2012 publication stops short at calling it “period coding”). While the first paper was still under review, it was quickly realized that my equation actually used negative coupling and things started to move forward from there. In my mind, there was me and a beautiful lady, on a jogging track, and I would be attracted to her while she would be repulsed by me. The simple consequence of two of us loving and hating one-way, is to run on the track very fast and keep the distance between two of us rather long. I showed this idea at the chronobiology meeting in Hokkaido in 2012 and nobody really had any response. There was a British exchange student from psychology department who I was teaching at the time—and we had fun discussing this. There was my long-time collaborator from Seattle and he and I had fun discussing this. But why the cold response from others (of course, my English accent is not an usual one but...)? It took three more years to show this story in a publication, in 2015. Time was spent on the neurophysiological origin of this repulsion. That part is still not complete, I personally believe, as the electrophysiology of the suprachiasmatic nucleus is quite unique and really different from the ones we learn from the textbook. The mathematical side of the story is quite simple. It really is just two ordinary differential equations. But the simplicity hides many complexities. We describe two sets of two oscillators, one for the summer and the other for the winter, but we do not describe how light transforms one into the other. I am so glad that there was Scott and we could rigorously go through the equations and show the limit of the two equations through quantifying “effective history”. There are much more stories to be told, after a brief stop at this paper.

”