An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-functions II

For the Lerch zeta-function $\phi(s, x, \lambda)$ defined below, the multiple mean square of the form (1.1), together with its discrete and hybrid analogues, (1.2) and (1.3), are investigated by means of Atkinson's [2] dissection method applied to the product $\phi(u, x, \lambda) \phi (v, x, -\lambda)$, where $u$ and $v$ are independent complex variables (see (4.2)). A complete asymptotic expansion of (1.1) as Im $s\rightarrow\pm\infty$ is deduced from Theorem 1, while those of (1.2) and (1.3) as $q\rightarrow\infty$ and (at the same time) as Im $s\rightarrow\pm\infty$ are deduced from Theorems 2 and 3 respectively. In the proofs, Atkinson's method above is enhanced by Mellin-Barnes type of integral formulae (see (4.1)), which further enable us systematic use of various properties of hypergeometric functions (see Section 5); especially in the proof of Theorem 1 crucial rôles are played by Lemmas 3 and 5

An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions

We shall establish full asymptotic expansions for the mean squares of Lerch zetafunctions, in the form (1.1) and (1.2) given below, based on F. V. Atkinson’s device (cf. [2], [4, Chapter 15] and [5, Chapter 2]). Mellin-Barnes’ type integral expression for an infinite double sum (see (3.2) and (3.5)) will play a central role in the derivation of our main formulae (2.1) and (2.2)

STAT1 regulates interferon-γ-induced angiotensinogen and MCP-1 expression in a bidirectional manner in primary cultured mesangial cells

Objective: Intrarenal interferon-γ significantly contributes to the development of glomerular injury in which angiotensinogen and monocyte chemoattractant protein 1 levels are elevated. However, the exact nature of the role that interferon-γ plays in regulating angiotensinogen and monocyte chemoattractant protein 1 expression has not been fully delineated. Therefore, the aim of this study was to investigate the role that interferon-γ plays in angiotensinogen and monocyte chemoattractant protein 1 expression. Methods: Primary cultured rat mesangial cells were treated with 0–20 ng/mL interferon-γ for 2, 8 or 24 hours. Expression levels of angiotensinogen, monocyte chemoattractant protein 1, suppressors of cytokine signaling 1, an intracellular suppressor of Janus kinase-signal transducers and activators of transcription signaling and activity of the Janus kinase-signal transducers and activators of transcription pathway were evaluated by reverse transcriptase polymerase chain reaction and western blot analysis. Results: Interferon-γ increased angiotensinogen expression in mesangial cells with maximal augmentation observed following 5 ng/mL interferon-γ at 8 hours of treatment (1.87 ± 0.05, mRNA, relative ratio). Further increases were reduced or absent using higher concentrations of interferon-γ. Following treatments, monocyte chemoattractant protein 1 expression was induced in a linear dose-dependent manner (6.85 ± 0.62-fold by 20 ng/mL interferon-γ at 24 hours). In addition, interferon-γ induced STAT1 phosphorylation and suppressors of cytokine signaling 1 expression in a linear dose-dependent manner. The suppression of STAT1 and suppressors of cytokine signaling 1 expression by small interference RNAs facilitated an increase in interferon-γ-induced angiotensinogen expression, indicating that these two factors negatively regulate angiotensinogen expression. In contrast, the increase in interferon-γ-induced monocyte chemoattractant protein 1 expression was attenuated in STAT1-deficient mesangial cells, suggesting that STAT1 positively regulates monocyte chemoattractant protein 1 expression in mesangial cells. Conclusion: These results demonstrate that while interferon-γ increases both angiotensinogen and monocyte chemoattractant protein 1 expression, STAT1 plays an opposing role in the regulation of each factor in mesangial cells

Central Glucagon-like Peptide-1 Receptor Signaling via Brainstem Catecholamine Neurons Counteracts Hypertension in Spontaneously Hypertensive Rats

Glucagon-like peptide-1 receptor (GLP-1R) agonists, widely used to treat type 2 diabetes, reduce blood pressure (BP) in hypertensive patients. Whether this action involves central mechanisms is unknown. We here report that repeated lateral ventricular (LV) injection of GLP-1R agonist, liraglutide, once daily for 15 days counteracted the development of hypertension in spontaneously hypertensive rats (SHR). In parallel, it suppressed urinary norepinephrine excretion, and induced c-Fos expressions in the area postrema (AP) and nucleus tractus solitarius (NTS) of brainstem including the NTS neurons immunoreactive to dopamine beta-hydroxylase (DBH). Acute administration of liraglutide into fourth ventricle, the area with easy access to the AP and NTS, transiently decreased BP in SHR and this effect was attenuated after lesion of NTS DBH neurons with anti-DBH conjugated to saporin (anti-DBH-SAP). In anti-DBH-SAP injected SHR, the antihypertensive effect of repeated LV injection of liraglutide for 14 days was also attenuated. These findings demonstrate that the central GLP-1R signaling via NTS DBH neurons counteracts the development of hypertension in SHR, accompanied by attenuated sympathetic nerve activity