Biological clocks with a period of Ϸ24 h (circadian) exist in most organisms and time a variety of functions, including sleep-wake cycles, hormone release, bioluminescence, and core body temperature fluctuations. Much of our understanding of the clock mechanism comes from the identification of specific mutations that affect circadian behavior. A widely studied mutation in casein kinase I (CKI), the CKI tau mutant, has been shown to cause a loss of kinase function in vitro, but it has been difficult to reconcile this loss of function with the current model of circadian clock function. Here we show that mathematical modeling predicts the opposite, that the kinase mutant CKI tau increases kinase activity, and we verify this prediction experimentally. CKI tau is a highly specific gain-of-function mutation that increases the in vivo phosphorylation and degradation of the circadian regulators PER1 and PER2. These findings experimentally validate a mathematical modeling approach to a complex biological function, clarify the role of CKI in the clock, and demonstrate that a specific mutation can be both a gain and a loss of function depending on the substrate.kinase ͉ systems biology ͉ phosphorylation ͉ PER ͉ degradation C ircadian rhythms govern key physiologic processes including sleep-wake cycles; glucose, lipid, and drug metabolism; heart rate; stress and growth hormones; and immunity, as well as basic cellular processes such as timing of the cell division cycle (1-6). The disruption of circadian rhythm causes significant physiologic stress, is frequently experienced in jet lag and night-shift work, and has been linked to bipolar disorder (7). Thus, circadian regulation of physiology has important consequences for health. A detailed quantitative model that makes clear, testable, and accurate predictions about the clock and how we may manipulate it can therefore have benefits for human health.Much of our understanding of clock components and their interactions began with the identification of mutations that affect circadian behavior (8, 9). In mammals, the original and most extensively studied circadian rhythm mutation is the semidominant tau, first described in 1988. Hamsters with this mutation show phase-advanced activity and have a circadian period of 20 h when homozygous mutant animals are isolated from time cues (9). This tau mutation has been identified as a missense mutation within the substrate recognition site of casein kinase I (denoted CKI tau ) (10). CKI and the closely related CKI␦ are widely expressed serine-threonine protein kinases implicated in development, circadian rhythms, and DNA metabolism (11). When tested in vitro on multiple substrates, CKI tau was shown to have a much reduced overall catalytic activity (10,12,13). This partial loss-of-function mutation and its phenotype have been difficult to reconcile with our current understanding of the molecular feedback loop that governs timing in mammalian cells (13) and recent empirical observations on clock function (14-16). For example, Dey et al. (1...