The kinetics of bivalent ligand-bivalent receptor aggregation: Ring formation and the breakdown of the equivalent site approximation

Richard G Posner, Carla Wofsy, Byron Goldstein

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

When bivalent ligands capable of bridging binding sites on two different receptors interact with bivalent receptors, aggregates form. The aggregates can be of two types: chains (open structures containing n receptors, n - 1 doubly bound ligands and 0, 1, or 2 singly bound ligands) and rings (closed structures containing n receptors and n doubly bound ligands). Both types of aggregates have been detected experimentally. In general, to determine the time dependence of the concentration of any particular aggregate requires solving an infinite set of coupled ordinary differential equations (ODEs). Perelson and DeLisi [19] showed that great simplification results if all receptor binding sites are equivalent, i.e., the binding properties of a site on a receptor are independent of the size of the aggregate the receptor is in. If only chains form, the problem reduces to solving two coupled ODEs for the concentrations of singly and doubly bound ligands. From the solutions to these ODEs, the time dependence of the entire aggregate size distribution can be determined. We show that the equivalent site approximation as formulated by Perelson and DeLisi [19] is incompatible with ring formation. We then present a modified equivalent site approximation that is useful if chains of any size can form but rings above a certain size (k) cannot. We show how to reduce the resulting infinite set of coupled ODEs to a closed system of at most 4k + 2 ODEs for the ligand concentrations, the ring concentrations, and the concentrations of all chains up to size k. Although we can only predict the kinetics of aggregate formation for aggregates of size k or less, at equilibrium the modified equivalent site approximation yields the complete aggregate size distribution.

Original languageEnglish (US)
Pages (from-to)171-190
Number of pages20
JournalMathematical Biosciences
Volume126
Issue number2
DOIs
StatePublished - 1995

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Receptor Aggregation
protein aggregates
Receptor
ligand
Breakdown
Aggregation
Agglomeration
Kinetics
Ligands
Ring
kinetics
receptors
Ordinary differential equations
Approximation
Ordinary differential equation
aggregate size
Binding Sites
Time Dependence
Binding sites
binding sites

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Applied Mathematics
  • Modeling and Simulation
  • Statistics and Probability
  • Medicine(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

The kinetics of bivalent ligand-bivalent receptor aggregation : Ring formation and the breakdown of the equivalent site approximation. / Posner, Richard G; Wofsy, Carla; Goldstein, Byron.

In: Mathematical Biosciences, Vol. 126, No. 2, 1995, p. 171-190.

Research output: Contribution to journalArticle

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