Perturbed dentate gyrus function in serotonin 5-HT2C receptor mutant mice

Serotonin systems have been implicated in the regulation of hippocampal function. Serotonin 5-HT2C receptors are widely expressed throughout the hippocampal formation, and these receptors have been proposed to modulate synaptic plasticity in the visual cortex. To assess the contribution of 5-HT2C receptors to the serotonergic regulation of hippocampal function, mice with a targeted 5-HT2C-receptor gene mutation were examined. An examination of long-term potentiation at each of four principal regions of the hippocampal formation revealed a selective impairment restricted to medial perforant path–dentate gyrus synapses of mutant mice. This deficit was accompanied by abnormal performance in behavioral assays associated with dentate gyrus function. 5-HT2C receptor mutants exhibited abnormal performance in the Morris water maze assay of spatial learning and reduced aversion to a novel environment. These deficits were selective and were not associated with a generalized learning deficit or with an impairment in the discrimination of spatial context. These results indicate that a genetic perturbation of serotonin receptor function can modulate dentate gyrus plasticity and that plasticity in this structure may contribute to neural mechanisms underlying hippocampus-dependent behaviors.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Low- and high-level transgenic expression of β2-adrenergic receptors differentially affect cardiac hypertrophy and function in Gαq-overexpressing mice

Transgenic overexpression of Gαq in the heart triggers events leading to a phenotype of eccentric hypertrophy, depressed ventricular function, marked expression of hypertrophy-associated genes, and depressed β-adrenergic receptor (βAR) function. The role of βAR dysfunction in the development of this failure phenotype was delineated by transgenic coexpression of the carboxyl terminus of the βAR kinase (βARK), which acts to inhibit the kinase, or concomitant overexpression of the β2AR at low (≈30-fold, Gαq/β2ARL), moderate (≈140-fold, Gαq/β2ARM), and high (≈1,000-fold, Gαq/β2ARH) levels above background βAR density. Expression of the βARK inhibitor had no effect on the phenotype, consistent with the lack of increased βARK levels in Gαq mice. In marked contrast, Gαq/β2ARL mice displayed rescue of hypertrophy and resting ventricular function and decreased cardiac expression of atrial natriuretic factor and α-skeletal actin mRNA. These effects occurred in the absence of any improvement in basal or agonist-stimulated adenylyl cyclase (AC) activities in crude cardiac membranes, although restoration of a compartmentalized β2AR/AC signal cannot be excluded. Higher expression of receptors in Gαq/β2ARM mice resulted in salvage of AC activity, but hypertrophy, ventricular function, and expression of fetal genes were unaffected or worsened. With ≈1,000-fold overexpression, the majority of Gαq/β2ARH mice died with cardiomegaly at 5 weeks. Thus, although it appears that excessive, uncontrolled, or generalized augmentation of βAR signaling is deleterious in heart failure, selective enhancement by overexpressing the β2AR subtype to limited levels restores not only ventricular function but also reverses cardiac hypertrophy.