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Abstract
The equilibrium dissociation constant (Kd) characterizes stability of binding complexes. The classic way of Kd determination involves finding the dependence of a fraction of unbound ligand on the total concentration of target (T0) when the total concentration of ligand (L0) remains constant. It is known that Kd determination for highly stable complexes is notoriously inaccurate; however, what the accuracy of Kd depends on fundamentally, i.e., method-independently, is largely unknown. Here we present an error-propagation analysis that answers this question in detail. This analysis explains the critical importance of the L0/Kd value for the accuracy of Kd and allows one to define the range of L0/Kd values required for accurate Kd determination. Our analysis creates a theoretical foundation for improving the accuracy of Kd determination.
Supplementary materials
Title
Mathematical derivations and experimental details
Description
Derivation of the theoretical dependence of fraction of unbound ligand (R) on total target concentration (T0) (Note S1); Derivation of the dependence of relative systematic error of Kd (deltaKd/Kd) on L0/Kd ratio (Note S2); Derivation of the dependence of Kd,det on L0 (Note S3); Derivation of the signal to noise ratio for any ligand concentration L0 (Note S4); Materials and solutions (Note S5); Details of NECEEM experiments (Note S6, Figure S1, Figure S2, and Table S1).
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