Deterministic Error Propagation in Kinetic K_d Determination: General Theory with Application to Surface-Based Assays

Area of Science:

• Biophysical Chemistry
• Molecular Interactions
• Kinetic Analysis

Background:

• Accurate determination of equilibrium dissociation constants (Kd) from kinetic measurements is crucial for understanding molecular interactions.
• Systematic errors in concentration and signal can propagate into rate constants (kon, koff) and affect the calculated Kd (koff/kon).
• Existing methods often require extensive data or specific conditions, limiting their applicability.

Purpose of the Study:

• To present a deterministic, platform-independent framework for error propagation in kinetic binding measurements.
• To analyze the impact of systematic errors on Kd determination under pseudo-first-order conditions.
• To provide a theoretical foundation for optimizing experimental strategies in molecular interaction analysis.

Main Methods:

• Developed a general framework for error propagation applicable to reversible 1:1 binding kinetics.
• Derived closed-form expressions for relative error in Kd based on kinetic equations.
• Applied the framework to surface-based binding assays, including independent determination of maximal signal (Smax).

Main Results:

• Revealed a triphasic dependence of the relative Kd error on the ratio of total target concentration to Kd (T0/Kd).
• Identified a low T0/Kd regime where Kd is intrinsically robust to systematic error.
• Demonstrated that accurate kinetic parameters can be obtained from data acquired at T0 values significantly below the true Kd.

Conclusions:

• The presented framework provides a general theoretical basis for understanding accuracy constraints in kinetic Kd determination.
• Independent Smax determination enables robust Kd determination from minimal data, enhancing compatibility with various experimental strategies.
• The findings clarify how theoretical principles apply to practical surface-based measurements widely used in molecular interaction analyses.