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In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis. To gain insight into the dynamics of these interactions, new components need to be integrated into the(More)
Blocking of potassium channels by internally and externally applied barium ions has been studied in squid giant axons. Internal Ba (3-5 mM) causes rapid decay or "inactivation" of potassium current (IK). The kinetics and degree of block are strongly voltage-dependent. Large positive voltages speed blocking and make it more profound. Raising the external(More)
We have studied the interactions of Ba ion with K channels. Ba2+ blocks these channels when applied either internally or externally in millimolar concentrations. Periodic depolarizations enhance block with internal Ba2+, but diminish the block caused by external Ba2+. At rest, dissociation of Ba2+ from blocked channels is very slow, as ascertained by(More)
The mammalian suprachiasmatic nuclei (SCN) contain thousands of neurons capable of generating near 24-h rhythms. When isolated from their network, SCN neurons exhibit a range of oscillatory phenotypes: sustained or damping oscillations, or arrhythmic patterns. The implications of this variability are unknown. Experimentally, we found that cells within SCN(More)
Vital physiological behaviors exhibited daily by bacteria, plants, and animals are governed by endogenous oscillators called circadian clocks. The most salient feature of the circadian clock is its ability to change its internal time (phase) to match that of the external environment. The circadian clock, like many oscillators in nature, is regulated at the(More)
Systems theoretic tools (i.e. mathematical modelling, control, and feedback design) advance the understanding of robust performance in complex biological networks. We highlight phase entrainment as a key performance measure used to investigate dynamics of a single deterministic circadian oscillator for the purpose of generating insight into the behaviour of(More)
Circadian clocks drive endogenous oscillations in organisms across the tree of life. The Earth's daily light/dark cycle entrains these clocks to the environment. Two major theories of light entrainment have been presented in the literature. The discrete theory emphasizes the instantaneous phase-shifting behavior of short pulses of light, and the continuous(More)
Mathematical model reduction is a long-standing technique used both to gain insight into model subprocesses and to reduce the computational costs of simulation and analysis. A reduced model must retain essential features of the full model, which, traditionally, have been the trajectories of certain state variables. For biological clocks, timing, or phase,(More)
Systems theoretic tools, including mathematical modeling, control theoretic analysis, and feedback design, advance the understanding of the circadian clock: a set of noisy oscillators that communicate to ensure its function as a reliable pacemaker. The clock's internal time, or phase, is a key performance measure used to investigate dynamics of a single(More)