Fig. 5

Analysis reveals quantitative relations between model parameters and circadian period. a Parameters extracted from fitting locomotor data of wild type (N = 11), per ^S (N = 22), per ^L (N = 19) and tim ^UL (N = 11) flies measured in constant darkness for 5–7 days. Plotted parameter is indicated in the adjacent box for each graph, with curvatures shown for \(b_{MD} ,b_{MR} ,b_{ER} ,b_{ED} > 0\). The data show that the exponential rate constants are independent of \(T_{0}\), while parameters \(T_{M}\) and \(T_{E}\) grow roughly linearly with \(T_{0}\). Dashed lines are visual guides (top and middle panels) or linear fits (bottom panels). b Sketch of two locomotor patterns where the red locomotion is driven by a faster clock (shorter \(T_{0}\)). If increase in \(T_{0}\) results in lengthening of activity peak widths from \(T_{M,short}\) to \(T_{M,long}\) without altering the exponential rates, our model predicts that the activity amplitude must also increase from \(h_{short}\) to \(h_{long}\). The first M peaks are shown to overlap to emphasize constancy of the exponential rates. The red sketched activity has been vertically shifted for visual clarity. c Data from flies in a demonstrate a positive correlation between average activity amplitude h and the circadian period \(T_{0}\). Dashed line is a linear fit to the data giving \({\text{h}} \approx 1.4T_{0}\)