Antibody multivalency effects in the direct binding model for vesicle immunolysis assays

The influence of rigid or flexible linkage between two ligands on the effective affinity and avidity for reversible interactions with bivalent receptors

Bivalent or polyvalent cooperative binding between ligand and receptor is much tighter and more efficient than monovalent binding of the same counterparts. Because of this, many biological processes involve polyvalent binding for realization of regulatory mechanisms. For this reason it is necessary to develop a general formalism for prediction of the relationship between the binding affinities of each ligand subunits, the length of the flexible linker between them and avidity of the interaction. Here, we consider an approach that is based on the description of the state of equilibrium for the reaction of mono- and multivalent ligand-receptor binding of algebraic equation systems. This approach allows the evaluation of the avidity of bivalent binding and to determine the concentrations of ligand-receptor complexes, which will be obtained at the equilibrium state. The analysis presented here may be useful in analysing the binding behaviour of a bivalent receptor and a ligand consisting of two subunits covalently connected with a rigid or flexible linker.

Biosensor immunosurface engineering inspired by B-cell membrane-bound antibodies: modeling and analysis of multivalent antigen capture by immobilized antibodies

Immobilized antibodies are used by many biosensors and diagnostic tests as specific receptors for the presence of targeted substances in clinical, biological, or environmental samples. The antibodies used in these devices are the soluble form of the antibodies presented on the B-cell membrane: they have the same specificity, but they may differ from those presented on the B cell in orientation, flexibility, mobility, and support-membrane properties. These properties influence the formation of noncovalent bonds between the pathogen antigenic determinants (epitopes) and the amino acids of the antibodies. This paper extends the theoretical modeling foundation addressing multivalent antigen binding to cell surface receptors to account for local and far-field antibody surface density effects, immobilized antibodies, and the flexibility and range of motion of immobilized antibodies. An analysis of the derived model provides insight into the design of biosensor immunosurfaces to enhance pathogen capture capability.

Computational models in immunological methods: an historical review

The utilization of computational models in immunology dates from the birth of the science. From the description of antibody-antigen binding to the structural models of receptors, models are utilized to bring fundamental understandings of the processes together with laboratory measurements to uncover implications of these data. In this review, an historical view of the role of computational models in the immunology laboratory is presented, and short mathematical descriptions are given of fundamental assays. In addition, the range of current uses of models is explored -- especially as seen through papers which have appeared in the Journal of Immunological Methods from volume 1 (1971/1972) to volume 208 (1997). Each paper which introduced a new mathematical, statistical, or computer simulation model, or introduced an enhancement to an instrument through a model in those volumes is cited and the type of computational model noted.