Date Published: May 16, 2012
Publisher: Public Library of Science
Author(s): Changgui Gu, Zonghua Liu, William J. Schwartz, Premananda Indic, Shin Yamazaki. http://doi.org/10.1371/journal.pone.0036900
The suprachiasmatic nucleus (SCN) is the master circadian clock in mammals and is composed of thousands of neuronal oscillators expressing different intrinsic periods. These oscillators form a coupled network with a free-running period around 24 h in constant darkness and entrainable to the external light-dark cycle (T cycle). Coupling plays an important role in setting the period of the network and its range of entrainment. Experiments in rats have shown that two subgroups of oscillators within the SCN, a ventrolateral (VL) subgroup that receives photic input and a dorsomedial (DM) subgroup that is coupled to VL, can be desynchronized under a short (22-h) T cycle, with VL entrained to the cycle and DM free-running. We use a modified Goodwin model to understand how entrainment of the subgroups to short (22-h) and long (26-h) T cycles is influenced by light intensity, the proportion of neurons that receives photic input, and coupling heterogeneity. We find that the model’s critical value for the proportion of photically-sensitive neurons is in accord with actual experimental estimates, while the model’s inclusion of dispersed coupling can account for the experimental observation that VL and DM desynchronize more readily under the 22-h than under the 26-h T cycle. Heterogeneous intercellular coupling within the SCN is likely central to the generation of complex behavioral patterns.
Circadian (∼24 h) rhythms in physiological and behavioral measures are universal in living things, reflecting the period of the earth’s rotation. In mammals, circadian rhythms are regulated by a master clock in the suprachiasmatic nucleus (SCN) of the hypothalamus, composed of approximately 20,000 neuronal oscillators; SCN neurons are nonidentical, express different intrinsic periods, and are coupled together to form a network with a coherent output . The period of the network’s output signal is adaptable. Under constant darkness, the rhythm has a free-running period close to 24 h; whereas under an external light-dark cycle (T cycle), it is precisely entrained to a period identical to the external cycle.
Here we analyze the photic desynchronization of two subgroups of circadian oscillators in a network model of the suprachiasmatic nucleus. As also demonstrated in experiments with rats exposed to a short T cycle of low light intensity , , a subgroup of oscillators receiving photic input (VL) can entrain to the external cycle while the other, coupled subgroup (DM) expresses an unentrained period greater than 24 h.
We represent each mammalian cell of the network as a Goodwin oscillator. The Goodwin model is a widely used mathematical model to represent the behavior of the gene regulatory network in single cellular circadian oscillators . The model represents the transcription-translation behavior of the single cell by using three variables that include a clock gene mRNA (), a clock protein (), and a transcriptional inhibitor ().