Reply to Varma: Elucidation of the signal origin for label-free, free-solution interactions

In response to the letter submitted by Varma (1), we respectfully disagree with the assertion that our proposed free-solution response function (FreeSRF) model (2) does not explain the signal origin for free-solution measurements. His theoretical considerations are appreciated; however, as we have shown (2), they do not apply here.

• i)Our empirical model is informative, experimentally consistent, and a reasonable starting point for further elucidating interferometric free-solution, label-free assays. Our approach exhibits a strong correlation (Spearman’s rank) between signal magnitude with binding-induced conformation and hydration changes. This correlation held true for a diverse set of binding pairs, ranging widely in affinity and molecular mass. FreeSRF is supported by the published modeling literature that substantiates the use of radius of gyration, R_gyr, and solvent-accessible surface area (SASA) as physical parameters to represent intrinsic solution property changes for protein–ligand binding (3, 4). Marsh and Teichmann (4) validate our use of avgSASA in χ, showing it provides an excellent estimation of structural change upon binding. Because SASA also correlates with the amplitude of conformational change, it is reasonable to ascribe the refractive index (RI) signal to this property. We do admit that the dependence on structural and dynamical parameters may be more complex than our linear fit model, so an expanded model may emerge for predicting RI changes in free-solution measurements.
• ii)Having a large constant term is not reason to discount the validity of an expression, particularly if the physical parameters used in the equation vary widely with respect to the intrinsic property being measured. Although suitable currently, we do anticipate the emergence of a better definition for “E” (the error or disturbance term).
• iii)Varma’s approach, using the Maxwell–Garnett formulation (1), and that used by others (5, 6) predicted ΔRI signal for protein–ligand binding to be below the detection limit (DL) for BSI. This observation is not disputed (2), because we also predicted undetectable binding signals by BSI (<5 × 10⁻⁷) using a widely accepted relationship (7) for refractive index increment (RII) calculations (equations S13–S17 and figures S2 and S3 of ref. 2). However, quantification of the actual ΔRI signal produced for a binding pair (table S1 of ref. 2) confirms that ΔRI for a binding event is well within the DL for BSI (table S1 and figures S2 and S3 of ref. 2). Further, the predicted signal and experimentally measured value for ρ correlate well. Varma’s and RII approaches likely fail because (a) they overlook significant literature showing it is incorrect to assume a uniform dielectric constant for the protein (3, 8), (b) they lack reasonable consideration for the importance of hydration toward determining RI (8) and (c) the effect of the medium on the dielectric constant of the protein (and vice versa) (9) is ignored.

We conclude that the currently accepted model (5–7) does not accurately predict the signal for free-solution RI measurements. FreeSRF considers hydration and conformation changes and is predictive of both magnitude and directionality for the relative RI change. We hope the “difficulties in replicating BSI experiments” (5, 6) can be reconciled, allowing its successful use, as others have independently shown (10, 11).