Deciphering clock cell network morphology within the biological master clock, suprachiasmatic nucleus: From the perspective of circadian wave dynamics

Abstract

The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of similar to 10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (similar to 25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained 'indegree distribution' as well as a 'physical range distribution of afferent clock cells.' Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced "phase-singularities." The successful, realistic networks have several common features: 1) "indegree" and "outdegree" should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN. Author summary The suprachiasmatic nucleus (SCN) is a tiny nucleus located within a deep brain area, serving the role of the biological master clock for mammals. It is composed of approximately 10,000 clock cells and orchestrates all daily rhythms such as the sleep-wake cycle and heart-beat rate modulation. The SCN is a vitally important part of the brain. Any significant disruptions in the spatiotemporal circadian dynamics inside this small nucleus may potentially lead to circadian arrhythmia akin to cardiac arrhythmia. One of the key elements governing the spatiotemporal circadian dynamics is the SCN clock cell-to-cell network morphology, which is currently largely unknown and very difficult to decipher even with all up-to-date technologies in neuroscience. Therefore, the purpose of this paper is to come up with a mathematical model SCN that has a clock cell network morphology good enough that the model SCN's spatiotemporal phase dynamics during perturbed as well as unperturbed natural states best matches those measured in experiments. We find many interesting features, some of which are 1) the outdegree (number of efferent connections) of each clock cell should have a positive correlation to its indegree (number of afferent connections), 2) the total degree of the cells in the SCN 'core' region is in general much larger than that of the 'shell' region, 3) the number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the number of inter-subdivisional edges should be much less than that of intra-core edges. These features identified via model simulations should be a useful guide for future experimental explorations on the clock cell connectome within the SCN.