On the Riemann-Roch formula without projective hypotheses

Navarro, Alberto; Navarro, José

doi:10.1090/tran/8107

Cited by 1 publication

(1 citation statement)

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“…The Chow groups carry rich information about an algebraic variety and are generally hard to compute. In mathematics, specifically in algebraic geometry, the Grothendieck-Riemann-Roch theorem is an example of coherent cohomology [19]. It is a generalization of the Hirzebruch-Riemann-Roch theorem about complex manifolds, which is itselfa generalization of the classical Riemann-Roch theorem for line bundles on compact Riemann surfaces [20].…”

Section: Introductionmentioning

confidence: 99%

SARS-CoV-2 Spike Protein Interaction Space

Lungu

Putz

2023

IJMS

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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a +sense single-strand RNA virus. The virus has four major surface proteins: spike (S), envelope (E), membrane (M), and nucleocapsid (N), respectively. The constitutive proteins present a high grade of symmetry. Identifying a binding site is difficult. The virion is approximately 50–200 nm in diameter. Angiotensin-converting enzyme 2 (ACE2) acts as the cell receptor for the virus. SARS-CoV-2 has an increased affinity to human ACE2 compared with the original SAR strain. Topological space, and its symmetry, is a critical component in molecular interactions. By exploring this space, a suitable ligand space can be characterized accordingly. A spike protein (S) computational model in a complex with ACE 2 was generated using silica methods. Topological spaces were probed using high computational throughput screening techniques to identify and characterize the topological space of both SARS and SARS-CoV-2 spike protein and its ligand space. In order to identify the symmetry clusters, computational analysis techniques, together with statistical analysis, were utilized. The computations are based on crystallographic protein data bank PDB-based models of constitutive proteins. Cartesian coordinates of component atoms and some cluster maps were generated and analyzed. Dihedral angles were used in order to compute a topological receptor space. This computational study uses a multimodal representation of spike protein interactions with some fragment proteins. The chemical space of the receptors (a dimensional volume) suggests the relevance of the receptor as a drug target. The spike protein S of SARS and SARS-CoV-2 is analyzed and compared. The results suggest a mirror symmetry of SARS and SARS-CoV-2 spike proteins. The results show thatSARS-CoV-2 space is variable and has a distinct topology. In conclusion, surface proteins grant virion variability and symmetry in interactions with a potential complementary target (protein, antibody, ligand). The mirror symmetry of dihedral angle clusters determines a high specificity of the receptor space.

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Section: Introductionmentioning

confidence: 99%