Exponential


The exponential

The first thing what you see from your data is the sensorgram. Each sensorgram contains a world of information for the trained eye. Therefore, it is essential for you to recognize the good from the bad curves. A bad curve represents a bad experiment, producing bad results from which conclusions cannot be made. And be sure, there is a lot of rubbish in the SPR literature. Please read the articles from D.G. Myszka and R.L. Rich (1),(2).

A good understanding of the binding curves is the first step in understanding the data. Let’s start with the binding between two molecules. One molecule, the analyte (A) binds to one molecule, the ligand (L) in a reversible way. The speed or rate of binding (association) is denoted by the association rate constant ka. The breaking up of the complex (dissociation) is denoted by the dissociation rate constant kd.

Interaction
Eq 1: Interaction
Protein interaction
Protein interaction

The response generated by the interaction can be calculated with equation 2.

ComplecFormationn
Eq 2: Complex formation

Integrating equation 2, gives an integrated rate equation, which describes the whole interaction curve. In the equation, Rt is the response at time t and Req is the maximal response which can be reached with this analyte concentration.

ResponseCalculation
Eq 3: Response calculation

Equation 3 describes a simple-exponential binding profile. No other curve shapes such as parabolic, hyperbolic, concave and convex can describe the binding profile. Therefore, you have to train yourself to recognise an exponential binding curve!

To start, some sensorgrams are given as an overview of the possible curve shapes, which are all still exponential but differ in kinetics. The curves differ in association and dissociation rate, but the shape is always an exponential.

Simple exponential
Simple exponential curves
Exponential curve
Exponential curve

Look now at the following curves.

MasstransportCurves
Mass transfer curves

The sensorgrams have a binding profile with an initial binding, which appears to be linear. This is an example of (partially) mass transport limited kinetics. Directly after the analyte injection starts, the binding of the analyte to the ligand is faster than diffusion, creating a shortage of analyte at the surface. Therefore, the interaction is diffusion limited instead of kinetic limited. It is easy to incorporate mass transport limitation in the fitting models but it is better to avoid this by proper design of the experiment. For instance by lowering the ligand density or increasing the flow rate.

Masstransport
Interaction with mass transport

The next sensorgrams are often referred to as having biphasic binding responses. Biphasic responses are said to consist of a fast and slow interaction. And because a biphasic response can be described equally well by different models (1) it is virtually impossible to solve the interaction mechanism by modelling alone. In case of a biphasic curve, more optimisation of the experimental conditions is necessary. Don’t try to fit these curves!

Biphasic curves
Biphasic curves

The next two sets of curves are seen in cases like buffer jumps, spikes and drift. Although drift can be added to the fitting model, it is better to avoid drift by proper equilibration of the system. After immobilisation, drift is often very strong. The easiest way to equilibrate is to run flow buffer overnight. When starting your measurements, incorporate several dummy injections (running buffer) to validate the stability of the system. Always try to match the flow and sample buffer to avoid buffer jumps at the beginning and the end of the injections. The spiky and wobbly sensorgrams are a warning to clean your system. Make new degassed reagents and start over designing your experiment.

Wrong curves
'Wrong' curves

References

(1)Rich, R. L. and Myszka, D. G. Survey of the year 2007 commercial optical biosensor literature. J.Mol.Recognit. 21: 355-400; (2008). Goto reference
(2)Rich, R. L. and Myszka, D. G. Grading the commercial optical biosensor literature-Class of 2008: 'The Mighty Binders'. J.Mol.Recognit. 23: 1-64; (2010). Goto reference