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. 2019 Mar;78(4):879-898.
doi: 10.1007/s00285-018-1295-x. Epub 2018 Oct 3.

Decoupled molecules with binding polynomials of bidegree (n, 2)

Yue Ren  1 , Johannes W R Martini  2 , Jacinta Torres  3
Affiliations

Decoupled molecules with binding polynomials of bidegree (n, 2)

Yue Ren et al. J Math Biol. 2019 Mar.

Abstract

We present a result on the number of decoupled molecules for systems binding two different types of ligands. In the case of n and 2 binding sites respectively, we show that there are [Formula: see text] decoupled molecules to a generic binding polynomial. For molecules with more binding sites for the second ligand, we provide computational results.

Keywords: Binding polynomials; Ligand binding; Numerical algebraic geometry.

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Figures

Fig. 1
Fig. 1
A molecule with 4 binding sites (e.g. hemoglobin)
Fig. 2
Fig. 2
A molecule with (4,4) sites
Fig. 3
Fig. 3
A decoupled molecule with (n,2) sites
Fig. 4
Fig. 4
Coefficients of the binding polynomial of bidegree (n,2)
Fig. 5
Fig. 5
A converging and a diverging solution path
Fig. 6
Fig. 6
Perturbation of normalized binding polynomials
Fig. 7
Fig. 7
Two complex conjugate solutions for (3, 2)
Fig. 8
Fig. 8
Mixed volumes of the Newton polytopes of (1), numbers in red resp. blue were verified symbolically using Gröbner bases resp. numerically using homotopy continuation (color figure online)
See this image and copyright information in PMC

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