Codes over rings of size four, Hermitian lattices, and corresponding theta functions

Let be an imaginary quadratic field with ring of integers , where is a square free integer such that , and let is a linear code defined over . The level theta function of is defined on the lattice , where is the natural projection. In this paper, we prove that:

i) for any such that , and have the same coefficients up to ,

ii) for , determines the code uniquely,

iii) for , there is a positive dimensional family of symmetrized weight enumerator polynomials corresponding to .

     

Spectral Features of Canthaxanthin in HCP2. A QM/MM Approach

The increased interest in sequencing cyanobacterial genomes has allowed the identification of new homologs to both the N-terminal domain (NTD) and C-terminal domain (CTD) of the Orange Carotenoid Protein (OCP). The N-terminal domain homologs are known as Helical Carotenoid Proteins (HCPs). Although some of these paralogs have been reported to act as singlet oxygen quenchers, their distinct functional roles remain unclear. One of these paralogs (HCP2) exclusively binds canthaxanthin (CAN) and its crystal structure has been recently characterized. Its absorption spectrum is significantly red-shifted, in comparison to the protein in solution, due to a dimerization where the two carotenoids are closely placed, favoring an electronic coupling interaction. Both the crystal and solution spectra are red-shifted by more than 50 nm when compared to canthaxanthin in solution. Using molecular dynamics (MD) and quantum mechanical/molecular mechanical (QM/MM) studies of HCP2, we aim to simulate these shifts as well as obtain insight into the environmental and coupling effects of carotenoid–protein interactions.