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Binding rate

By virtue of continuous measurement of analyte binding, Biacore offers a further kind of concentration assay, based on determination of initial binding rates rather than bound amounts . Superficially, this may seem to be a trivial distinction, since the amount of analyte bound after a specified time of interaction is a measure of the binding rate. Under special conditions, however, initial binding rate measurements can provide advantages over assays based on binding levels, since the binding rates can be determined wholly by the analyte concentration and the diffusion rate of analyte to the surface. The assay is then independent of the rate or affinity of the interaction between analyte and detecting molecule. This can be valuable in situations where the concentration of a number of related molecules is to be measured, such as monoclonal antibodies or mutant forms of a protein. The advantage of the binding rate assay under these conditions is that a single standard curve is applicable to all variants of the protein, provided that the diffusion characteristics of the variants are similar.

Binding rate and binding level measurements.

Factors determining binding rates

Biochemical interaction rates

The rate at which an interaction proceeds is given by the difference between the forward (association) and reverse (dissociation) processes. For a 1:1 interaction

where k_a and k_d are the rate constants for the association and dissociation respectively.

The association rate is given by k_a[A][B], and the dissociation rate is given by k_d[AB]. The net rate of binding is

In Biacore systems, formation of complex is observed as an increase in response, measured in resonance units (RU). One interactant (the analyte, A) is supplied at a constant concentration during the sample injection. The available concentration of the second interactant (the ligand attached to the sensor surface, B) may be expressed in RU as the difference between the maximum analyte binding capacity R_max and the amount of complex formed R. Substituting these terms gives

where C is the concentration of analyte in the sample.

This represents the pseudo-first order kinetics observed for binding of analyte to surface-attached ligand with 1:1 stoichiometry. Similar model equations may be applied to more complex interaction models.

Mass transport processes

For analyte to bind to the sensor surface, the molecules must be transported from the bulk solution to the surface. This is a diffusion-controlled process. Under the conditions of laminar flow that apply in Biacore systems, the transport rate is directly proportional to the concentration of analyte in the bulk solution, with a proportionality constant called the mass transport coefficient km which is proportional to the cube root of the liquid flow rate.

Note that the transport rate is not influenced by the characteristics or amount of ligand immobilized on the surface.

What limits the observed binding?

In a given analysis situation, the observed rate of binding (i.e. the slope of the sensorgram) will be determined by the relative magnitudes of the biochemical interaction rate and the rate of mass transport. If interaction is much faster than transport, the observed binding will be limited entirely by the transport processes. Conversely, if transport is fast and interaction is slow, the observed binding will represent the interaction kinetics alone. When the rates of the two processes are of similar orders of magnitude, the binding will be determined by a combination of the two rate characteristics.

The net biochemical interaction rate varies with the amount of available ligand sites on the surface, and is highest at the beginning of the injection. The mass transport rate, on the other hand, is constant throughout the injection since the analyte concentration in solution is constant. As a result, the relative importance of mass transport and biochemical interaction can change during the course of an injection: mass transport processes can be limiting at the beginning of the injection while interaction limits the observed binding rate at later stages.

In a partially mass transport-limited situation, mass transport dominates at the beginning of the injection and interaction rate dominates late in the injection.

See also

List of help files

Calibration curves for concentration analysis