Narrow Results

Some special cases of Marchuk's model of an infectious disease are studied. A paralysis effect is neglected, and the model reduces to 3 ordinary differential equations with time delay and initial data corresponding to a healthy organism infected by some dose of the antigen at time 0. It is proved that, if the immune system is very strong and the antigen reproduction rate is not too large, then every solution has a finite limit, which is equal to the stationary state describing the healthy organism. If the antigen reproduction rate is large, then all solutions have average values equal to the values corresponding to the chronic form of the disease.

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

Antibodies are responsible for antigen recognition in vertebrate organisms. Practically any molecule can be bound by antibodies. In this work structures of 73 complexes of antibodies with small antigens were taken from PDB database and compared. The main epitope of studied ligands was an aromatic ring. Antibodies bound it with a deep cavity, lying between complementary determining regions (CDR) H3 and L3 and formed by aromatic residues. In most cases the aromatic ring of ligand was placed parallel to one or two aromatic sidechains of binding site at 3.5-4 Angstrom distance. This disposition of aromatic rings is a sign of the presence of π-stacking. It was found that small ligands with aromatics area percentage > 36% predominantly form π-stacking interaction with antibodies. Most often this interaction was observed for residues in positions H33, H95, L32 and L93.