Jacob T. Schwartz

Linear Operators. Part I: General Theory.

This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.

REVEILLE1, a Myb-like transcription factor, integrates the circadian clock and auxin pathways.

The circadian clock modulates expression of a large fraction of the Arabidopsis genome and affects many aspects of plant growth and development. We have discovered one way in which the circadian system regulates hormone signaling, identifying a node that links the clock and auxin networks. Auxin plays key roles in development and responses to environmental cues, in part through regulation of plant growth. We have characterized REVEILLE1 (RVE1), a Myb-like, clock-regulated transcription factor that is homologous to the central clock genes CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY). Despite this homology, inactivation of RVE1 does not affect circadian rhythmicity but instead causes a growth phenotype, indicating this factor is a clock output affecting plant development. CCA1 regulates growth via the bHLH transcription factors PHYTOCHROME INTERACTING FACTOR4 (PIF4) and PIF5, but RVE1 acts independently of these genes. RVE1 instead controls auxin levels, promoting free auxin production during the day but having no effect during the night. RVE1 positively regulates the expression of the auxin biosynthetic gene YUCCA8 (YUC8), providing a mechanism for its growth-promoting effects. RVE1 is therefore a node that connects two important signaling networks that coordinate plant growth with rhythmic changes in the environment.

REVEILLE8 and PSEUDO-REPONSE REGULATOR5 form a negative feedback loop within the Arabidopsis circadian clock.

Circadian rhythms provide organisms with an adaptive advantage, allowing them to regulate physiological and developmental events so that they occur at the most appropriate time of day. In plants, as in other eukaryotes, multiple transcriptional feedback loops are central to clock function. In one such feedback loop, the Myb-like transcription factors CCA1 and LHY directly repress expression of the pseudoresponse regulator TOC1 by binding to an evening element (EE) in the TOC1 promoter. Another key regulatory circuit involves CCA1 and LHY and the TOC1 homologs PRR5, PRR7, and PRR9. Purification of EE–binding proteins from plant extracts followed by mass spectrometry led to the identification of RVE8, a homolog of CCA1 and LHY. Similar to these well-known clock genes, expression of RVE8 is circadian-regulated with a dawn phase of expression, and RVE8 binds specifically to the EE. However, whereas cca1 and lhy mutants have short period phenotypes and overexpression of either gene causes arrhythmia, rve8 mutants have long-period and RVE8-OX plants have short-period phenotypes. Light input to the clock is normal in rve8, but temperature compensation (a hallmark of circadian rhythms) is perturbed. RVE8 binds to the promoters of both TOC1 and PRR5 in the subjective afternoon, but surprisingly only PRR5 expression is perturbed by overexpression of RVE8. Together, our data indicate that RVE8 promotes expression of a subset of EE–containing clock genes towards the end of the subjective day and forms a negative feedback loop with PRR5. Thus RVE8 and its homologs CCA1 and LHY function close to the circadian oscillator but act via distinct molecular mechanisms.