Surface Plasmon Resonance (SPR), a method pleasurable not only linguistically, but mostly due to its unique precision in the characterization of protein-protein kinetics. The underlying optical physics behind one of the smallest scales on earth — as well as its possible trademark collisions with the Star Wars franchise — shall not be discussed here. For the data analyst, it is enough to understand that a solution containing purified protein passes at high speed over a surface covered in possible binding sites, and that mass changes at said surface are recorded over time. As shown below, signal changes either increase in the presence of protein in the passing solution (association phase) or decrease when absent (dissociation phase).
Signal changes follow the integrated forms of separate differential equations, involving characteristic variables, including the on-rate, which describes the likelyhood of successful binding, as well as the off-rate, highly useful in calculating the half-life of successfully formed complexes. Together, they can be used to calculate the affinity, allowing for the calculation of binding site occupation in dependence of the binding partner's concentrations.
These differential equations can only be analytically solved (resulting in mathematical equations) in their simplest form, i.e., if only a 1-to-1 binding model without accounting for possible deviations, such as experimental error or changed interaction dynamics by the presence of contaminants. Numerical integration on the other hand, is not limited by mathematical complexity, but only computation power, which is nowadays not rate-limiting with data encountered in SPR experiments. In the simplest form of such algorithms, such as the Euler Method [1], one can imagine walking through the timeline, each time calculating what the next signal timepoint would look like in dependence of the current timepoint.
Single-Cycle Kinetics. [2] This contemporary experimental approach for evaluating binding kinetics using SPR is based on consecutive injections of diverse binder concentrations without returning to baseline in between, as illustrated below. This method proves particularly advantageous when dealing with high-affinity binders or unstable surfaces. Model fitting for such data requires the application of distinct differential equations within segments of the dataset. While such analyses have been incorporated into commercially available software, they often become unwieldy and lack flexibility, as the utilized models frequently cannot be configured independently. Our R-package "spR" is tailored to SPR data analysis, created with the intent to simplify and render SPR data analysis comprehensible.
