Renewal theory, Geiger counters, and the maximum number of receptors bound to a randomly haptenated polymer chain.

摘要: Polymers containing small chemical groups (haptens) covalently attached at random along the chain are commonly used to initiate an immune response. Properties of polymer such as its length, spacing haptens, and total number haptens chain, correlate with reactivity. Here we model ability many finite-sized cell surface receptors bind simultaneously conjugated a chain. The binding sites on two different or separate parts multivalent receptor cannot be arbitrarily close one another; so, in general, not all can bound by receptors. We develop analogy between steric hindrance among detecting randomly placed temporary locking Geiger counter that has detected radioactive decay. Using renewal theory, compute probability distribution, moments, for maximum monovalent also flexible bivalent obtain mean variance haptenated polymers, bound. demonstrate importance our results applying them immunological data showing that, polymers immunology, effective valence may much 50% smaller than nominal valence.