### Abstract

A general expression for the binding isotherm of divalent antibodies to antigens bound to solid lattices with excluded volume effects is derived by using a statistical mechanical approach. The method is based on matrix generation of the partition function for the system, from which the degree of saturation of the antigen lattice may be computed directly. The saturation function has a simple form that under appropriate conditions reduces to forms derived previously for simpler cases (such as monovalent binding with and without excluded volume effects). Solution by numerical techniques of a simple secular equation for each concentration of antibody allows computation of the saturation function. Thus, the binding expression derived is easily fit to any set of binding data obtained and results in the determination of such parameters as intrinsic affinity, length of excluded space (and hence molecular size), and number of sites. It predicts that under conditions wherein divalent binding is favored over univalent binding, biphasic adsorption isotherms will be obtained.

Original language | English |
---|---|

Pages (from-to) | 5924-5927 |

Number of pages | 4 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 78 |

Issue number | 10 II |

State | Published - 1981 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- General
- Genetics

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*78*(10 II), 5924-5927.

**General quantitative treatment for the binding of divalent antibodies to antigens immobilized on a solid phase.** / Pincus, M. R.; Rendell, M.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 78, no. 10 II, pp. 5924-5927.

}

TY - JOUR

T1 - General quantitative treatment for the binding of divalent antibodies to antigens immobilized on a solid phase

AU - Pincus, M. R.

AU - Rendell, M.

PY - 1981

Y1 - 1981

N2 - A general expression for the binding isotherm of divalent antibodies to antigens bound to solid lattices with excluded volume effects is derived by using a statistical mechanical approach. The method is based on matrix generation of the partition function for the system, from which the degree of saturation of the antigen lattice may be computed directly. The saturation function has a simple form that under appropriate conditions reduces to forms derived previously for simpler cases (such as monovalent binding with and without excluded volume effects). Solution by numerical techniques of a simple secular equation for each concentration of antibody allows computation of the saturation function. Thus, the binding expression derived is easily fit to any set of binding data obtained and results in the determination of such parameters as intrinsic affinity, length of excluded space (and hence molecular size), and number of sites. It predicts that under conditions wherein divalent binding is favored over univalent binding, biphasic adsorption isotherms will be obtained.

AB - A general expression for the binding isotherm of divalent antibodies to antigens bound to solid lattices with excluded volume effects is derived by using a statistical mechanical approach. The method is based on matrix generation of the partition function for the system, from which the degree of saturation of the antigen lattice may be computed directly. The saturation function has a simple form that under appropriate conditions reduces to forms derived previously for simpler cases (such as monovalent binding with and without excluded volume effects). Solution by numerical techniques of a simple secular equation for each concentration of antibody allows computation of the saturation function. Thus, the binding expression derived is easily fit to any set of binding data obtained and results in the determination of such parameters as intrinsic affinity, length of excluded space (and hence molecular size), and number of sites. It predicts that under conditions wherein divalent binding is favored over univalent binding, biphasic adsorption isotherms will be obtained.

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UR - http://www.scopus.com/inward/citedby.url?scp=0019791177&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0019791177

VL - 78

SP - 5924

EP - 5927

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 10 II

ER -