Many mammalian peripheral tissues have circadian clocks; endogenous oscillators that generate transcriptional rhythms thought to be important for the daily timing of physiological processes. The extent of circadian gene regulation in peripheral tissues is unclear, and to what degree circadian regulation in different tissues involves common or specialized pathways is unknown. Here we report a comparative analysis of circadian gene expression in vivo in mouse liver and heart using oligonucleotide arrays representing 12,488 genes. We find that peripheral circadian gene regulation is extensive (> or = 8-10% of the genes expressed in each tissue), that the distributions of circadian phases in the two tissues are markedly different, and that very few genes show circadian regulation in both tissues. This specificity of circadian regulation cannot be accounted for by tissue-specific gene expression. Despite this divergence, the clock-regulated genes in liver and heart participate in overlapping, extremely diverse processes. A core set of 37 genes with similar circadian regulation in both tissues includes candidates for new clock genes and output genes, and it contains genes responsive to circulating factors with circadian or diurnal rhythms.
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice with open boundaries. The standard objects of quantum integrable models are identified with elements of classical nonlinear integrable difference equation. In particular, elliptic solutions of Hirota's equation give complete set of eigenvalues of the quantum transfer matrices. Eigenvalues of Baxter's Q-operator are solutions to the auxiliary linear problems for classical Hirota's equation. The elliptic solutions relevant to Bethe ansatz are studied. The nested Bethe ansatz equations for A k−1 -type models appear as discrete time equations of motions for zeros of classical τ -functions and Baker-Akhiezer functions. Determinant representations of the general solution to bilinear discrete Hirota's equation and a new determinant formula for eigenvalues of the quantum transfer matrices are obtained.
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice with open boundaries. The standard objects of quantum integrable models are identified with elements of classical nonlinear integrable difference equation. In particular, elliptic solutions of Hirota's equation give complete set of eigenvalues of the quantum transfer matrices. Eigenvalues of Baxter's Q-operator are solutions to the auxiliary linear problems for classical Hirota's equation. The elliptic solutions relevant to Bethe ansatz are studied. The nested Bethe ansatz equations for A k−1 -type models appear as discrete time equations of motions for zeros of classical τ -functions and Baker-Akhiezer functions. Determinant representations of the general solution to bilinear discrete Hirota's equation and a new determinant formula for eigenvalues of the quantum transfer matrices are obtained.
The structure of a genetic network is uncovered by studying its response to external stimuli (input signals). We present a theory of propagation of an input signal through a linear stochastic genetic network. We found that there are important advantages in using oscillatory signals over step or impulse signals and that the system may enter into a pure fluctuation resonance for a specific input frequency.systems biology ͉ synthetic biology ͉ stochastic processes
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