Signal Additivity as a Practical Criterion for Validating Kd Determination: Reconciling Conflicting Backscattering Interferometry Results
- 1Department of Chemistry
- 2York University
- 3Centre for Research on Biomolecular Interactions
Abstract
Backscattering interferometry (BSI) enables label-free, immobilization-free detection of molecular interactions in free solution, but published studies report conflicting outcomes, including saturable, nonsaturating, and poorly reproducible responses. Here, we develop a signal-additivity framework that distinguishes interaction detection from determination of the thermodynamic equilibrium dissociation constant, K d , and provides a basis for reconciling these reports. For a two-state system at fixed total target concentration, quantitative K d analysis requires the final referenced and control-subtracted response to be an affine function of equilibrium complex concentration over the fitted range. A general refractive-index expansion shows that nonlinear self-and crosscomponent contributions can survive control subtraction and generate composition-dependent residual signals. Illustrative simulations with a known input value, K d,true , show that such residuals can produce smooth, apparently saturable curves with biased apparent dissociation constants, K d,app , or strong concentration-range dependence of K d,app . Concentration-design analysis further illustrates, for a specified ligand-dependent residual model, a trade-off between upper-isotherm coverage and high-concentration residuals. Reinterpretation of representative BSI studies indicates that specificity, reproducibility, and apparent saturation support interaction detection but do not independently establish signal additivity. We therefore propose a workflow based on matched controls, concentration-range analysis, residual inspection, parameter-stability assessment, and binding-model evaluation, with measurements at different target concentrations when feasible. Although developed here using BSI, the underlying criterion applies more broadly to affinity studies in which a processed response is assumed to report equilibrium binding populations. BSI-derived values should be reported as K d,app unless signal additivity, adequate isotherm coverage, concentration accuracy, and binding-model adequacy are independently supported.
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BibTeX
@misc{che2026signal,
title = {{Signal Additivity as a Practical Criterion for Validating Kd Determination: Reconciling Conflicting Backscattering Interferometry Results}},
author = {Xingzhi Che and Alexander MacLellan and Ayesha Maqsood and Elyaa AlSafadi and Tong Ye Wang and Sergey N. Krylov},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009536/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009536/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Signal Additivity as a Practical Criterion for Validating Kd Determination: Reconciling Conflicting Backscattering Interferometry Results
AU - Xingzhi Che
AU - Alexander MacLellan
AU - Ayesha Maqsood
AU - Elyaa AlSafadi
AU - Tong Ye Wang
AU - Sergey N. Krylov
PY - 2026
DA - 2026/09/28
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009536/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009536/v1
AB - Backscattering interferometry (BSI) enables label-free, immobilization-free detection of molecular interactions in free solution, but published studies report conflicting outcomes, including saturable, nonsaturating, and poorly reproducible responses. Here, we develop a signal-additivity framework that distinguishes interaction detection from determination of the thermodynamic equilibrium dissociation constant, K d , and provides a basis for reconciling these reports. For a two-state system at fixed total target concentration, quantitative K d analysis requires the final referenced and control-subtracted response to be an affine function of equilibrium complex concentration over the fitted range. A general refractive-index expansion shows that nonlinear self-and crosscomponent contributions can survive control subtraction and generate composition-dependent residual signals. Illustrative simulations with a known input value, K d,true , show that such residuals can produce smooth, apparently saturable curves with biased apparent dissociation constants, K d,app , or strong concentration-range dependence of K d,app . Concentration-design analysis further illustrates, for a specified ligand-dependent residual model, a trade-off between upper-isotherm coverage and high-concentration residuals. Reinterpretation of representative BSI studies indicates that specificity, reproducibility, and apparent saturation support interaction detection but do not independently establish signal additivity. We therefore propose a workflow based on matched controls, concentration-range analysis, residual inspection, parameter-stability assessment, and binding-model evaluation, with measurements at different target concentrations when feasible. Although developed here using BSI, the underlying criterion applies more broadly to affinity studies in which a processed response is assumed to report equilibrium binding populations. BSI-derived values should be reported as K d,app unless signal additivity, adequate isotherm coverage, concentration accuracy, and binding-model adequacy are independently supported.
ER -