Article does not explain the origin of free-solution protein interaction signals

Bornhop et al. (1) had shown that interactions between protein molecules in solution can be detected by measuring the solution refractive index shifts using a technique referred to as backscattering interferometry (BSI). The origin of the BSI signal was unclear. In a recent article in PNAS, Bornhop et al. (2) claim to provide an explanation of its origin. Based on a large body of published literature, they argue that solvation and conformational changes during protein interactions could have a large effect on BSI signal. However, other than pointing out this possibly important fact, this article does not really provide an explanation of the BSI signal origin for the following reasons.

• i)Instead of developing a model from first principles, Bornhop et al. (2) simply construct a linear function of four variables, namely, the average values and change upon binding of solvent-addressable surface area, the radius of gyration of the interacting proteins, and a constant term (equation 5 of ref. 2). They obtain the five unknown coefficients of this function by fitting it to experimentally obtained BSI signals. They then claim this linear function to be an explanation of the BSI signal. Simply providing a function that fits experimental data without providing any insight into its origin, starting from first principles, cannot be considered a proper explanation of any phenomena. One can easily construct many functions that fit the data perfectly but have no conceivable physical basis.
• ii)This so-called “explanation” is also a rather poor one because the numerical value of the constant term (“E” in equation 5 of ref. 2) exceeds the other terms in the equation by as much as two orders of magnitude (calculated using data from tables S4 and S5 of ref. 2). This result means that the constant term is the most significant one in the proposed function. By the authors’ own admission, this constant term cannot be associated with any identifiable physical property. A function resting on a quantity that cannot even be properly defined can hardly be considered explanatory.
• iii)A first principles approach to explain BSI signal origin must start from optical effective medium theory, specifically the Maxwell–Garnett formulation (3), because the protein volume fractions involved in BSI are smaller than 10⁻⁴. Such a formulation permits the inclusion of solvation and conformational changes through the dielectric constant and volume, respectively, of the protein complex formed during the interaction. Using typical values for proteins in a Maxwell–Garnett model, I estimated the refractive index changes in reported BSI experiments to be two to three orders of magnitude below the detection limit of BSI.

In conclusion, there is significant discrepancy between first principles estimates and experimentally observed magnitudes of the BSI signal. The current article merely provides a curve-fitting function of dubious origin and not a proper theoretical model of BSI signal origin. The difficulties in replicating BSI experiments (4) would hopefully be resolved by the recently recommended guidelines (2), permitting the generation of larger datasets that may help elucidate the origin of BSI signal.