NaB may restore the dysbiosis of gut microbiota to attenuate steatohepatitis, which is suggested to be a potential gut microbiota modulator and therapeutic substance for NAFLD.

In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. The latter result can be viewed as an analog of the well-known theorem of Bishop that a complete noncompact Riemannian manifold with nonnegative Ricci curvature has at most Euclidean volume growth.Combining Theorem 1.1 and Theorem 1.2, we also have the following consequence, which was obtained previously in [10] and [15] respectively. Corollary 1.1. Let (M n , g ij , f ) be a complete noncompact gradient shrinking Ricci soliton. Then we have M |u|e −f dV < +∞ for any function u on M with |u(x)| ≤ Ae αr 2 (x) , 0 ≤ α < 1 4 and A > 0. In particular, the weighted volume of M is finite, M e −f dV < +∞.

Non-alcoholic steatohepatitis (NASH) is an epidemic metabolic disease with limited therapeutic strategies. Cumulative data support the pivotal role of gut microbiota in NASH. Here, we investigated the hypothesis regarding whether fecal microbiota transplantation (FMT) is effective in attenuating high-fat diet (HFD)-induced steatohepatitis in mice. Mice were randomized into control, HFD and HFD + FMT groups. After an 8-week HFD, FMT treatment was initiated and carried out for 8 weeks. The gut microbiota structure, butyrate concentrations of the cecal content, liver pathology and intrahepatic lipid and cytokines were examined. Our results showed that after FMT, the gut microbiota disturbance was corrected in HFD-fed mice with elevated abundances of the beneficial bacteria Christensenellaceae and Lactobacillus. FMT also increased butyrate concentrations of the cecal content and the intestinal tight junction protein ZO-1, resulting in relief of endotoxima in HFD-fed mice. Steatohepatitis was alleviated after FMT, as indicated by a significant decrease in intrahepatic lipid accumulation (reduced Oli-red staining, decreased intrahepatic triglyceride and cholesterol), intrahepatic pro-inflammatory cytokines, and the NAS score. Accordingly, intrahepatic IFN-γ and IL-17 were decreased, but Foxp3, IL-4 and IL-22 were increased after FMT intervention. These data indicate that FMT attenuated HFD-induced steatohepatitis in mice via a beneficial effect on the gut microbiota.