2.2
Experimental binding affinities
Testing the interaction between two molecules, is one of the most common ex- periments in biochemistry and molecular biology. For this reason, there are a vast amount of different techniques used to measure these interactions [26]. Our interest is focused on the interaction of a ligand with a protein, and in this domain, there are several techniques that are preferred. Binding affinity experiments fall into two categories. Direct methods, which measure the actual concentrations within the sample, and indirect methods, which measures a signal from an external source, and is subsequently converted into a binding affinity value. The most common methods are described below.
2.2.1
Isothermal titration calorimetry
The gold standard of experimental binding affinity measurements is isothermal titatration calorimetry (ITC, [27]). This quantitative thermodynamic approach is the only protocol that can directly measure physical properties, like ∆G, ∆H
and ∆S, in addition to the Ka constant. In addition, when ITC experiments are
conducted on the same protein-ligand system, with variations in temperature, the
heat capacity (∆Cp) can also be measured.
First, the ligand of interest is injected, in small aliquots, into a solution containing the protein. The aliquots are precisely titrated into the sample cell which trig- gers a change in temperature relative to a reference cell. Then, the cell heater responds by heating or cooling, depending on whether the reaction is exothermic or endothermic, to return the sample cell to base temperature. The power applied by the cell heater to the sample cell after each titration of ligand, can be converted into the heat produced by the cell.
2.2. EXPERIMENTAL BINDING AFFINITIES
The energy required decreases as the titration proceeds, as there is less protein on to which the ligand can bind. Finally, the change in heat over the entire reaction time can be used to calculate ∆H directly, using Eqn. 2.19, where v is the volume
of the cell, qi is the heat generated for each aliqout of ligand titrated into the
sample, and [L]i is the concentration of ligand for each aliquot. The Ka can also
be calculated from the total amount of heat produced which can, in turn, be used to calculate ∆G and and ∆S via Eqns. 2.5 and 2.7a.
2.2.2
Fluorescence spectroscopy techniques
This group of techniques measure the rate of product formation, or the rate at which the substrate is associating with the enzyme, through the use of fluorescence. The general idea of fluorescence-based experiments is to label either the ligand or substrate with a marker that has fluorescent properties. A fluorometer detects the strength of this signal. The reaction between the competing ligand and substrate is initiated, resulting in a change of strength in fluorescence signal. For example, a protein and substrate are allowed to interact where initially, there is no fluorescent signal. Upon the addition of a known concentration of a competitive inhibitor, which has been labelled with a fluorescent marker, the strength of the fluorescent signal indicates the concentration of inhibitor occupying the binding site.
The two main techniques are fluorescence polarisation (FP, [28, 29]) and fluores- cence resonance energy transfer (FRET, [30, 31]). FP uses the idea of polarised fluorescence emission which becomes unpolarised faster in the bound state, than the unbound state. Here the inhibitor is excited using polarisable light, and the speed at which it becomes unpolarised indicates the amount of ligand bound to the enzyme. FRET requires a double labelling of the enzyme and inhibitor. When apart, the labels do not emit fluorescent light, but when the inhibitor binds to the enzyme, the energy transfer between the two labelled molecules emits a fluorescent signal. The strength of this signal corresponds to the amount of inhibit occupying
2.2. EXPERIMENTAL BINDING AFFINITIES the enzyme. Ki= IC50 1 + [S] Km (2.20)
The results of these techniques are usually reported as the concentration of inhibitor
required to reduce the enzyme activity by half (IC50). This value can be related
to the Ki due to the reasoning that at low values of [S], the Ki equals the IC50.
The Cheng-Prussoff equation [32], in Eqn 2.20, demonstrates this relationship.
2.2.3
Surface plasmon resonance
Surface plasmon resonance (SPR, [33]) is an optical based technique that measures the change in refractive index due to ligand association and dissociation. Protein molecules are immobilsed on a sensor surface and the analyte molecules, that is the inhibitor, is injected onto the surface allowing for inhibitor association. This association of inhibitor to the immobilised protein is accompanied by an increase
in refractive index, yielding the rate of ligand association, k1. After some time, a
solution that dissociates the ligand (usually the sample buffer) from the protein is introduced, and the refractive index is measured, giving rise to the rate of ligand
dissociation (k−1). Using Eqn. 2.3, the association constant, Ka, can be deduced.
2.2.4
Experimental error
Experimental techniques are associated with errors due to a number of factors, and the difficulty in controlling them. Here, potential sources of error [34, 35, 36, 37, 28, 38] will be outlined for the approaches that have been explained in section 2.2 .
Although ITC is highly sensitive, the detection of heat from protein-ligand asso- ciation, for systems that report very low enthalpies, is difficult to measure accu-