The antigen-antibody reaction

Aladjem, Frederick; Palmiter, Michael T.

doi:10.1016/0022-5193(65)90087-1

Cited by 17 publications

(7 citation statements)

References 11 publications

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“…Hopefully, the methods which are presented here will be useful in other applications involving different integral equations of the general form (1). What should be clear is that a simple question: "Can you solve eq.…”

Section: Discussionmentioning

confidence: 99%

Integral equations of immunology

Hanson

1972

Commun. ACM

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The inversion of a particular integral equation of the first (Fredholm) kind is the basic problem considered. The strategy which yielded success consisted of three essential points: (1) fit the known experimental data by a curve with properties which derive from properties of the (as yet unknown) function; (2) stabilize the computation for the unknown function by using singular value decomposition; (3) constrain the unknown function approximation (since it represents a probability distribution) to be nonnegative. A number of test cases are presented. One set of actual experimental data is analyzed with the procedures presented.Key Words and Phrases: integral equations of the first kind, nonnegative constraints, singular value analysis.

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Section: Discussionmentioning

confidence: 99%

Integral equations of immunology

Hanson

1972

Commun. ACM

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“…Statistical Mechanical Basis Goldberg (1952Goldberg ( , 1953 seems to have been the first to adapt the statistical mechanical theories of polymer chemistry to antibody-antigen reactions. Palmiter and Aladjem (1963), Amano et al (1962), and Aladjem and Palmiter (1965) have made notable elaborations. The papers are indeed quite complex and require a high degree of mathematical sophistication on the part of the reader.…”

Section: Goldberg Most Probable Polymer Distribution Theorymentioning

confidence: 99%

“…(b) The statistical mechanical formulas are independent of heterogeneity. (c) The same statistical mechanical model was used by Palmiter and Aladjem (1963) and Aladjem and Palmiter (1965). (d) A second level of models is required for the evaluation of the parameters that were introduced at the statistical mechanical level.…”

Section: Goldberg Most Probable Polymer Distribution Theorymentioning

confidence: 99%

“…Numerous complications in this model can be visualized: (a) an antigen, instead of having identical combining sites, may have several different antigenic determinants so that the antiserum produced contains a mixed population of antibodies; (b) antibody sites, specific for the same determinant, may vary in reactivity; (c) the various sites on the same antigen molecule may overlap; (d) one antibody may attach by several sites to the same antigen molecule; and (e) the same bonds may not be formed in replicate final mixtures, especially if prepared stepwise. Nevertheless, Aladjem and Palmiter (1965) state that there are only two possibilities for each site: it is either filled, i.e. reacted, or it is empty.…”

Section: Introductionmentioning

confidence: 99%

“…The goal, then, is to find a suitable algorithm for computing the amounts of small complexes that permits any valence of antigen, any valence of antibody, heterogeneity of reagents, as well as cyclical complex formation. Fortunately, the ideas expressed mathematically by Heidelberger and Kendall (1935), Karush (1956), Goldberg (1952), Singer andCampbell (1953), Talmage and Cann (1961), Amano et al (1962), Palmiter and Aladjem (1963), Palmiter (1965), andHudson (1968) can be synthesized into an algorithm with several options. The proper names applied to the options are not intended to imply that the persons named consider the option either theirs or universally applicable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computer Simulation of Radial Immunodiffusion

Trautman¹

1973

Biophysical Journal

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An algorithm needed for computer simulation of immunodiffusion has been deduced from existing theories of the in vitro reaction between antibody and antigen. The "Goldberg most probable polymer distribution" theory provides a formula that gives the amount of free antibody, free antigen, and diffusible complexes from extreme antibody excess through extreme antigen excess for any valences of antibody and antigen. As is shown here, that formula can be used even for those reactions producing complexes, cyclical or otherwise, that may precipitate as well as for those reactions involving heterogeneity of binding avidities. It is necessary, however, to specify an extent of reaction parameter. Five limiting expressions for this parameter are proposed as options for the basic algorithm. These are identified as: (a) the "Heidelberger-Kendall complete reaction" option, (b) the "Singer-Campbell constant avidity" option, (c) the "Hudson extensive antibody heterogeneity" option, (d) a new "extensive antigen heterogeneity" option, and (e) the "Goldberg critical extent of reaction" option. Literature data showing need for the various options are presented.

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Sexual agglutination in yeast

Taylor¹,

Tobin²

1966

Archives of Biochemistry and Biophysics

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The antigen-antibody reaction

Cited by 17 publications

References 11 publications

Integral equations of immunology

Integral equations of immunology

Computer Simulation of Radial Immunodiffusion

Sexual agglutination in yeast

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