Thermal dissociation of antigen-antibody-antigen-like systems

Abstract

The dissociation of antigen-antibody-antigen-like systems by random thermal motion is investigated for two-fold particles (dimers). The dimer is assumed to consist of two rigid spheres of radiusr joined by a loose inelastic string of extended lengthL. The spheres represent macromolecules and the string represents a bivalent molecular structure—such as an antibody—which is attached to active sites (e.g. antigen sites) on the spherical surfaces. The dimer dissociation rate constantr ₁₁ is calculated to be

$$r_{11} = (C/2L)(\sqrt {kT/m} ) \times erfc(\sqrt {E_B /kT} )$$

whereC=1.67 forL ≪r andC=0.92 forL>2r andE _B is the binding energy which holds the string fixed to the particle site. It is shown thatr ₁₁ plays a fundamental role in determining the manner and rate of higher order aggregate dissociations.