Immunogenicity and crossreactivity of antibodies to SARS-CoV-2 nucleocapsid protein

ABSTRACTCOVID-19 patients elicit strong responses to the nucleocapsid (N) protein of SARS-CoV-2 but binding antibodies are also detected in prepandemic individuals, indicating potential crossreactivity with common cold human coronaviruses (HCoV) and questioning its utility in seroprevalence studies. We investigated the immunogenicity of the full-length and shorter fragments of the SARS-CoV-2 N protein, and the crossreactivity of antibodies with HCoV. We indentified a C-terminus region in SARS-CoV2 N of minimal sequence homology with HCoV that was more specific and highly immunogenic. IgGs to the full-length SARS-CoV-2 N also recognised N229E N, and IgGs to HKU1 N recognised SARS-CoV-2 N. Crossreactivity with SARS-CoV-2 was stronger for alpha-rather than beta-HCoV despite having less sequence identity, revealing the importance of conformational recognition. Higher preexisting IgG to OC43 N correlated with lower IgG to SARS-CoV-2 in rRT-PCR negative individuals, reflecting less exposure and indicating a potential protective association. Antibodies to SARS-CoV-2 N were higher in patients with more severe and longer symptoms and in females. IgGs remained stable for at least 3 months, while IgAs and IgMs declined faster. In conclusion, N is a primary target of SARS-CoV-2-specific and HCoV crossreactive antibodies, both of which may affect the acquisition of immunity to COVID-19.

What is the least number of moves needed to solve the k-peg Towers of Hanoi problem?

We prove that the solutions to the [Formula: see text]-peg Tower of Hanoi problem given by Frame and Stewart are minimal. The proof relies on first identifying that for any [Formula: see text]-disk, [Formula: see text]-peg problem, there is at least one minimal sequence is symmetric. We show that if we order the number moved required for the disks in the minimal symmetric sequence in an increasing manner and obtain the sequence [Formula: see text], then [Formula: see text]. We also prove that the maximum number of disks that can be moved using [Formula: see text] steps is [Formula: see text]. We use these to lower bound the telescopic sum (2) that is a lower bound on the number of moves required for any minimal symmetric sequence. This gives us the required result.