The circadian clocks that drive daily rhythms in animals are tightly coupled among the cells of some tissues. The coupling profoundly affects cellular rhythmicity and is central to contemporary understanding of circadian physiology and behavior. In contrast, studies of the clock in plant cells have largely ignored intercellular coupling, which is reported to be very weak or absent. We used luciferase reporter gene imaging to monitor circadian rhythms in leaves of Arabidopsis thaliana plants, achieving resolution close to the cellular level. Leaves grown without environmental cycles for up to 3 wk reproducibly showed spatiotemporal waves of gene expression consistent with intercellular coupling, using several reporter genes. Within individual leaves, different regions differed in phase by up to 17 h. A broad range of patterns was observed among leaves, rather than a common spatial distribution of circadian properties. Leaves exposed to light-dark cycles always had fully synchronized rhythms, which could desynchronize rapidly. After 4 d in constant light, some leaves were as desynchronized as leaves grown without any rhythmic input. Applying light-dark cycles to such a leaf resulted in full synchronization within 2-4 d. Thus, the rhythms of all cells were coupled to external light-dark cycles far more strongly than the cellular clocks were coupled to each other. Spontaneous desynchronization under constant conditions was limited, consistent with weak intercellular coupling among heterogeneous clocks. Both the weakness of coupling and the heterogeneity among cells are relevant to interpret molecular studies and to understand the physiological functions of the plant circadian clock. intercellular signaling | coupled oscillators | systems biology | plant physiology | gene regulatory networks
It is well known that internal or molecular noise induces concentration oscillations in chemical systems whose deterministic models exhibit damped oscillations. In this article we show, using the linear-noise approximation of the chemical master equation, that noise can also induce oscillations in systems whose deterministic descriptions admit no damped oscillations, i.e., systems with a stable node. This non-intuitive phenomenon is remarkable since, unlike noise-induced oscillations in systems with damped deterministic oscillations, it cannot be explained by noise excitation of the deterministic resonant frequency of the system. We here prove the following general properties of stable-node noise-induced oscillations for systems with two species: (i) the upper bound of their frequency is given by the geometric mean of the real eigenvalues of the Jacobian of the system, (ii) the upper bound of the Q-factor of the oscillations is inversely proportional to the distance between the real eigenvalues of the Jacobian, and (iii) these oscillations are not necessarily exhibited by all interacting chemical species in the system. The existence and properties of stable-node oscillations are verified by stochastic simulations of the Brusselator, a cascade Brusselator reaction system, and two other simple chemical systems involving auto-catalysis and trimerization. It is also shown how external noise induces stable node oscillations with different properties than those stimulated by internal noise.
Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production.
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