Characterization and Modeling of Intermittent Locomotor Dynamics in Clock Gene-Deficient Mice

The scale-invariant and intermittent dynamics of animal behavior are attracting scientific interest. Recent findings concerning the statistical laws of behavioral organization shared between healthy humans and wild-type mice (WT) and their alterations in human depression patients and circadian clock gene (Period 2; Per2) mutant mice indicate that clock genes play functional roles in intermittent, ultradian locomotor dynamics. They also claim the clinical and biological importance of the laws as objective biobehavioral measures or endophenotypes for psychiatric disorders. In this study, to elucidate the roles of breakdown of the broader circadian regulatory circuit in intermittent behavioral dynamics, we studied the statistical properties and rhythmicity of locomotor activity in Per2 mutants and mice deficient in other clock genes (Bmal1, Clock). We performed wavelet analysis to examine circadian and ultradian rhythms and estimated the cumulative distributions of resting period durations during which locomotor activity levels are continuously lower than a predefined threshold value. The wavelet analysis revealed significant amplification of ultradian rhythms in the BMAL1-deficient mice, and instability in the Per2 mutants. The resting period distributions followed a power-law form in all mice. While the distributions for the BMAL1-deficient and Clock mutant mice were almost identical to those for the WT mice, with no significant differences in their parameter (power-law scaling exponent), only the Per2 mutant mice showed consistently and significantly lower values of the scaling exponent, indicating the increased intermittency in ultradian locomotor dynamics. Furthermore, based on a stochastic priority queuing model, we explained the power-law nature of resting period distributions, as well as its alterations shared with human depressive patients and Per2 mutant mice. Our findings lead to the development of a novel mathematical model for abnormal behaviors in psychiatric disorders.