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Fig. 6 | BMC Neuroscience

Fig. 6

From: A mathematical model provides mechanistic links to temporal patterns in Drosophila daily activity

Fig. 6

Our results make quantitative predictions about biochemical signals that may shape fly locomotor patterns. a Cartoon showing circadian genes and their products oscillate in a sinusoidal fashion (top row, left) and produce a power spectrum with a single peak (top row, right). We propose that efferent signal from the clock impinges on exponential processes that turn on/off stochastically in time. An example may be neuromodulator accumulation and release (middle rows, left). Without circadian regulation, the exponential process should result in noisy power spectra (middle rows, right). Integration of the sinusoidal with the exponential processes together with other signals (not shown) result in the observed shape of fly locomotion (bottom row, left). The resulting time series has multiple peaks in power spectrum by virtue of its non-sinusoidal shape (bottom row, right). b We suggest that the exponential processes that may underlie the observed shape in locomotion are temporally gated by the circadian clock. If so, then changing rhythm of the clock should cause corresponding changes both in the oscillatory period and the peak–peak amplitude of the gated signal. Shortening period of the clock (\(T_{long} \to T_{short}\)) predicts speeding up of the periodic exponential process and decrease of its amplitude of oscillation (\(A_{long} \to A_{short}\)). In these cartoons, it is assumed that the rate at which the exponential process occurs, for instance, the rate of neuromodulator release, is not affected by the circadian clock speed. To underscore the constant rate, the first decay phase of the fast and slow exponential waves are overlaid

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