A system of linear equations for the identification of DNA binding affinity of zinc fingers

In a recent article (1), the authors examined biophysical characteristics in the interaction between methylated DNA and ZBTB38 protein, which possesses five zinc finger domains (ZFs 6–10) in the C-terminal region. While the authors identified that ZFs 6–9 were minimal structural elements for high-affinity DNA binding, the role of ZF 10 remained inconclusive. Here, we show that the binding data shown in Fig. 1 of the paper can be used to predict the role of ZF 10 in regard to binding to methylated DNA with an algebraic technique of solving a system of linear equations (2).

Fig. 1 of the paper reports dissociation constants (K_D) of 5.3 nm, 5.0 nm, and 40.6 nm for ZFs 6–10, ZFs 6–9, and ZFs 7–10, respectively. From this information, a system of linear equations of binding affinity (ΔG⁰) with three unknowns can be established using the thermodynamic relation, ΔG⁰ = RT × ln K_D (3), with an assumption of additivity in the binding (4).

• ZFs 6–10: ΔG⁰(ZF 6) + ΔG⁰(ZFs 7–9) + ΔG⁰(ZF 10) = −46.7 kJ/mol

• ZFs 6–9: ΔG⁰(ZF 6) + ΔG⁰(ZFs 7–9) = −46.9 kJ/mol

• ZFs 7–10: ΔG⁰(ZFs 7–9) + ΔG⁰(ZF 10) = −41.7 kJ/mol

By solving the three equations, we obtained that ΔG⁰(ZF 6) = −5.0 kJ/mol, ΔG⁰(ZF 7–9) = −41.9 kJ/mol, and ΔG⁰(ZF 10) = 0.2 kJ/mol. Our calculation clearly suggests that ZF 10 in ZBTB38 protein does not contribute to binding affinity in agreement with the speculation made in the paper (1).