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In this paper, aiming at the nonlinear equations, a new two-step Levenberg–Marquardt method was proposed. We presented a new Levenberg–Marquardt parameter to obtain the trial step. A new modified Metropolis criterion was used to adjust the upper bound of the approximate step. The convergence of the method was analyzed under the H$ \ddot{\rm o} $lderian local error bound condition and the H$ \ddot\rm o $lderian continuity of the Jacobian. Numerical experiments showed that the new algorithm is effective and competitive in the numbers of functions, Jacobian evaluations and iterations.

Abstract Background Medullary sponge kidney (MSK)is rare in association with glomerulonephritis. We report a patient with medullary sponge kidney, and the kidney biopsy revealed a diagnosis of IgA nephropathy. Case presentation A 27-year-old female presented with hematuria and proteinuria, and imaging studies indicated the presence of medullary spongy kidney. With appropriate preparation, a kidney biopsy was performed. Considering the patient’s clinical and pathological characteristics, the final diagnosis was determined to be medullary sponge kidney associated by IgA nephropathy. The combination of corticosteroids and angiotensin receptor blockers (ARBs) proved to be significantly effective in reducing proteinuria in the current case. To the best of our knowledge, this is the first reported case that demonstrates the coexistence of MSK and IgA nephropathy. Conclusions Administering precise therapy based on renal pathology can potentially enhance outcomes for patients with renal conditions, necessitating the need for clinicians to be vigilant about differential diagnosis in order to reduce the rates of missed diagnoses and misdiagnosis.

Background Diabetic nephropathy (DN) is a frequent microvascular complication of diabetes. Glomerular mesangial cell (MC) hypertrophy occurs at the initial phase of DN and plays a critical role in the pathogenesis of DN. Given the role of long non coding RNA (lncRNA) in regulating MC hypertrophy and extracellular matrix (ECM) accumulation, our aim was to identify functional lncRNAs during MC hypertrophy. Methods Here, an lncRNA, C920021L13Rik (L13Rik for short), was identified to be up-regulated in DN progression. The expression of L13Rik in DN patients and diabetic mice was assessed using quantitative real-time PCR (qRT-PCR), and the function of L13Rik in regulating HG-induced MC hypertrophy and ECM accumulation was assessed through flow cytometry and western blotting analysis. Results The L13Rik levels were significantly increased while the miR-2861 levels were decreased in the peripheral blood of DN patients, the renal tissues of diabetic mice, and HG-treated MCs. Functionally, both L13Rik depletion and miR-2861 overexpression effectively reduced HG-induced cell hypertrophy and ECM accumulation. Mechanistically, L13Rik functioned as a competing endogenous RNA (ceRNA) to sponge miR-2861, resulting in the de-repression of cyclin-dependent kinase inhibitor 1B (CDKN1B), a gene known to regulate cell cycle and MC hypertrophy. Conclusions Collectively, the current results demonstrate that up-regulated L13Rik is correlated with DN and may be a hopeful therapeutic target for DN.

Podocyte injury is a critical factor in the pathogenesis of diabeticnephropathy (DN). Emerging evidence has demonstrated that breviscapine (Bre) exerts a renoprotective effect on diabetic rats. However, the effects of Bre on regulating podocyte injury under high glucose (HG) conditions remain unclear. In this study, an experimental mouse model of DN was induced by intraperitoneal injections of streptozotocin (STZ) in vivo. The effects of Bre on podocyte injury were assessed using cell counting kit-8 (CCK-8) assay, TdT-mediated dUTPnick-endlabelling (TUNEL) staining, quantitative real-time PCR (qRT‒PCR) and western blot analysis. We found that renal function was significantly decreased in diabetic mice, and this effect was blocked by Bre treatment. Bre effectively increased podocyte viability and inhibited HG-induced cell apoptosis. Furthermore, Bre ameliorated HG-induced podocyte injury, as evidenced by decreased α-smooth muscle actin (α-SMA) expression and increased podocin and synaptopodin expression. Mechanistically, Bre inhibited HG-induced nuclear factorkappaB (NF-κB) signalling activation and subsequently decreased NLR family pyrin domain containing 3 (NLRP3) inflammasome activation, resulting in a decrease in pyroptosis. Pharmacological inhibition of NLRP3 decreased HG-induced podocyte injury, whereas the NLRP3 agonist abrogated the effects of Bre on inhibiting podocyte injury. In summary, these results demonstrate that Bre alleviates HG-induced podocyte injury and improves renal function in diabetic mice, at least in part by inhibiting NF-κB/NLRP3-mediated pyroptosis.