Tau Response Curves Can Explain Entrainment of Rat Circadian Rhythm to Saw-Tooth Light Intensity Cycles

Abstract

We previously reported that rat circadian rhythms entrained to 24-h light intensity cycles with either of two types of saw-tooth waveforms, ascending (ST-a) and descending (ST-d) cycles. The entrainment could not be explained nonparametrically by a phase response curve for a single ST-d cycle given in constant darkness (DD). In the present study, when the amplitude of the ST-a or ST-d cycles was reduced, the circadian behavioral rhythms still entrained to the cycles in some rats, but not in other rats. The free-running circadian period in DD (t DD) was longer than 24 h in all rats, and was significantly shorter in the entrained rats than in the unentrained rats. The unentrained rats exhibited relative coordination, during which the circadian period (t) varied systematically depending on the phase relationship between the light intensity cycle and the circadian rhythm. We constructed a tau response curve (TRC) by plotting the deviation of t from t DD against the phase of the light intensity cycle (zeitgeber time). Both TRCs for ST-a and ST-d cycles had a very small t-shortening portion at a limited period of zeitgeber times and a large t-lengthening portion. On the other hand, in the entrained rats the onset of the activity period coincided with the zeitgeber time of the t-shortening portion in the TRCs. Taking all together, we interpreted that the rats with shorter t DD could be entrained to the 24-h cycle of ST-a or ST-d by shortening t at a specific zeitgeber time. We concluded that the TRCs represent entraining properties of the saw-tooth light intensity cycles.