Kinetics of the competitive response of receptors immobilised to ion-channels which have been incorporated into a tethered bilayer

Abstract

A competitive ion channel switch (ICS) biosensor has been modelled yielding ligand mediated monomer–dimer reaction kinetics of gramicidin (gA) ion-channels within a tethered bilayer lipid membrane. Through employing gramicidin A, functionalised with the water-soluble hapten digoxigenin, it is possible to cross-link gramicidin to antibody fragments tethered at the membrane/aqueous interface. The change in ionic conductivity of the channel dimers may then be used to measure the binding kinetics of hapten–protein interactions at the membrane surface. The approach involves measuring the time dependence of the increase in impedance following the addition of a biotinylated antibody fragment (b-Fab′), which cross-links the functionalised gramicidin monomers in the outer layer of the lipid bilayer to tethered membrane spanning lipid. The subsequent addition of the small molecule digoxin, (M_r 781 Da), competes with and reverses this interaction.

The model provides a quantitative description of the response to both the cross-linking following the addition of the b-Fab′ and the competitive displacement of the hapten by a water-soluble small analyte. Good agreement is obtained with independent measures of the cross-linking reaction rates of the gramicidin monomer–dimer and the b-Fab:hapten complex. The rate and amplitude of the competitive response is dependent on concentration and provides a fast and sensitive detection technique.

Estimates are made of the concentration of gramicidin monomers in both the inner and outer monolayer leaflets of the membrane. This is used in the calculation of the gramicidin monomer/dimer equilibrium constant, K_2D3. Other considerations include the membrane impedance limit set by the membrane leakage which is also a function of the concentration of the gA monomer concentration, and the two-dimensional kinetic association constant k_2D2, of the hapten:b-Fab′ complex. The gA dimer concentration is dependent on both the concentration of gA-dig and of the tethered streptavidin:b-Fab′ complexes.

The model shows that the 2D dissociation constant k_2D3^-1, must be at least 10 times faster than the 3D dissociation constant k_3D2^-1 for digoxin to completely reverse the cross-linked hapten–receptor interaction at the membrane interface.

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