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ORIGINAL RESEARCH article

Front. Immunol.

Sec. Systems Immunology

Volume 16 - 2025 | doi: 10.3389/fimmu.2025.1657633

This article is part of the Research TopicMathematical Modeling in Discovery and Analysis of Immune ResponsesView all 12 articles

Application of the Richards function to serum antibody titration

Provisionally accepted
Ágnes  KovácsÁgnes Kovács1,2Krisztian  PappKrisztian Papp3,4József  PrechlJózsef Prechl3*Tamás  PfeilTamás Pfeil2,5*
  • 1Department of Biostatistics, University of Veterinary Medicine Budapest, Budapest, Hungary
  • 2Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Budapest, Hungary
  • 3R&D Laboratory, Diagnosticum Zrt, Budapest, Hungary
  • 4Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary
  • 5HUN-REN--ELTE Numerical Analysis and Large Networks Research Group, Budapest, Hungary

The final, formatted version of the article will be published soon.

Conventional approaches to the titration of serum antibody binding use mid-point or end-point titers that are in a relative space and are therefore difficult to standardize. Here we propose the use of the thermodynamic titer, which, under appropriate measurement conditions, is a universal measure of the thermodynamic activity of serum antibodies. We show that the interpretation of the generalized logistic function as applied to biochemical binding events is possible using analogies to relative and absolute growth rates and size, which applies to the products of the reaction. Such deeper interpretation reveals the biological meaning of the asymmetry parameter of the function as a proportionality factor to ideal binding conditions. The use of a universally applicable and thermodynamically meaningful serum antibody titer could improve systematic mapping and understanding of antibody function.

Keywords: logistic function, Richards function, Growth, Serum antibody, binding, antigen, Affinity, titration

Received: 01 Jul 2025; Accepted: 16 Oct 2025.

Copyright: © 2025 Kovács, Papp, Prechl and Pfeil. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence:
József Prechl, jprechl@diagnosticum.hu
Tamás Pfeil, tamas.pfeil@ttk.elte.hu

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