An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation

Hypoxic human proximal tubular epithelial cells undergo ferroptosis and elicit an NLRP3 inflammasome response in CD1c+ dendritic cells

Inflammasomes are multiprotein platforms responsible for the release of pro-inflammatory cytokines interleukin (IL)-1β and IL-18. Mouse studies have identified inflammasome activation within dendritic cells (DC) as pivotal for driving tubulointerstitial fibrosis and inflammation, the hallmarks of chronic kidney disease (CKD). However, translation of this work to human CKD remains limited. Here, we examined the complex tubular cell death pathways mediating inflammasome activation in human kidney DC and, thus, CKD progression. Ex vivo patient-derived proximal tubular epithelial cells (PTEC) cultured under hypoxic (1% O2) conditions modelling the CKD microenvironment showed characteristics of ferroptotic cell death, including mitochondrial dysfunction, reductions in the lipid repair enzyme glutathione peroxidase 4 (GPX4) and increases in lipid peroxidation by-product 4-hydroxynonenal (4-HNE) compared with normoxic PTEC. The addition of ferroptosis inhibitor, ferrostatin-1, significantly reduced hypoxic PTEC death. Human CD1c+ DC activated in the presence of hypoxic PTEC displayed significantly increased production of inflammasome-dependent cytokines IL-1β and IL-18. Treatment of co-cultures with VX-765 (caspase-1/4 inhibitor) and MCC950 (NLRP3 inflammasome inhibitor) significantly attenuated IL-1β/IL-18 levels, supporting an NLRP3 inflammasome-dependent DC response. In line with these in vitro findings, in situ immunolabelling of human fibrotic kidney tissue revealed a significant accumulation of tubulointerstitial CD1c+ DC containing active inflammasome (ASC) specks adjacent to ferroptotic PTEC. These data establish ferroptosis as the primary pattern of PTEC necrosis under the hypoxic conditions of CKD. Moreover, this study identifies NLRP3 inflammasome signalling driven by complex tubulointerstitial PTEC-DC interactions as a key checkpoint for therapeutic targeting in human CKD.</p