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Research on laser-plasma interaction in the quantum-electrodynamic (QED) regime has been greatly advanced by particle-in-cell & Monte-Carlo simulations (PIC-MC). While these simulations are widely used, we find that noticeable numerical error arises due to inappropriate implementation of the quantum process accounting for hard photon emission and pair production in the PIC-MC codes. The error stems from the low resolution of the QED table used to sample photon energy, which is generated in the logarithmic scale and cannot resolve high energy photons. We propose a new sampling method via Sigmoid function that handles both the low energy and high energy end of the photon emission spectrum. It guarantees the accuracy of PIC-MC algorithms for hard photon radiation and other related processes in the strong-field QED regime., 21 pages, 9 figures

BackgroundNeovasculogenesis is a characteristic of degenerative lumbar discs, which makes extruded tissues exposed to heme-iron cytotoxicity (increased oxidative stress by ferroptosis). However, the present analyses for neovascularization are very complicated, and its mechanism of action is rarely reported.MethodsMatrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) was performed to analyze human degenerative lumbar discs. Then, clinical relevance was analyzed between MALDI-TOF MS results and Pfirrmann classification of degenerative discs. In order to explore the mechanism, a heme-induced ferroptosis effect was evaluated both at tissue and cell levels using high-resolution MALDI-TOF MS and molecular biology methods. ResultsThe spectra revealed that hemoglobin (Hb) and heme signals were highly increased, thus serving as biomarkers of vasculogenesis in degenerative tissues. Clinical relevance analysis demonstrated that the intensity of Hb and heme peaks was closely related to Pfirrmann classification of degenerative discs. Mechanically, increased heme catabolism and down-regulation of glutathione peroxidase 4 (GPX4) levels were detected in degenerative discs, reflecting a iron-dependent cell death or ferroptosis. Further, accuracy mass measurements confirmed that the levels of ferroptosis-related metabolites such as glutathione, arachidonic acid (AA), sphinganine, polyunsaturated fatty acid (PUFA), and tricarboxylic acid (TCA) cycle were significantly different between the degenerative and normal tissues, indicating the interior of degenerative tissues was a prooxidant environment. Moreover, the heme-induced ferroptosis was verified in human nucleus pulposus cells, and the underlying mechanism might be associated with the Notch pathway. ConclusionsThe neovascularization in degenerative discs may expose the tissues to high heme toxicity, which further induces the ferroptosis effect within the tissues and accelerates the degeneration progression of discs. This study is beneficial for the pathological mechanism in degenerative discs and facilitate the development of non-operative intervention for lumbar disc herniation (LDH).

Additional file 2: Table S1. Identification results of potential biomarkers in human lumbar discs. Table S2. Identification results of potential biomarkers in nucleus pulposus cells.

Additional file 1: Fig. S1. Heme degeneration catalyzed by HO-1. Heme is formed by iron and porphyrin. The heme iron in Hb is very stable because of the tight arrangement of molecule. But, the non-protein-bound heme is hydrophobic and can enter cell membranes easily. As a result, heme is degraded by HO-1 to yield free iron, which is able to enhance oxidative stress and induce ferroptosis in cells. Fig. S2. A representative H&E stain of nucleus pulposus with Pfirrmann’s grade 1 (lower) and 3–4 (upper). Scale bar = 20 μm. Fig. S3. MS spectra of oxidative biomarkers in herniated nucleus pulposus and nonherniated nucleus pulposus measured by the high-resolution mass spectrometry. The tissue samples were obtained from the patients 14 and 4 in Table 1. Fig. S4. MS spectra of oxidative biomarkers in HNPCs after treatment with 20 μg/mL heme, 20 μg/mL FAC, and 10 μg/mL erastin for 24 h using high-resolution MALDI-TOF MS.