Unbinding forces of single antibody-antigen complexes correlate with their thermal dissociation rates

Abstract

Point mutants of three unrelated antifluorescein antibodies were constructed to obtain nine different single-chain Fv fragments, whose on-rates, off-rates, and equilibrium binding affinities were determined in solution. Additionally, activation energies for unbinding were estimated from the temperature dependence of the off-rate in solution. Loading rate-dependent unbinding forces were determined for single molecules by atomic force microscopy, which extrapolated at zero force to a value close to the off-rate measured in solution, without any indication for multiple transition states. The measured unbinding forces of all nine mutants correlated well with the off-rate in solution, but not with the temperature dependence of the reaction, indicating that the same transition state must be crossed in spontaneous and forced unbinding and that the unbinding path under load cannot be too different from the one at zero force. The distance of the transition state from the ground state along the unbinding pathway is directly proportional to the barrier height, regardless of the details of the binding site, which most likely reflects the elasticity of the protein in the unbinding process. Atomic force microscopy thus can be a valuable tool for the characterization of solution properties of protein-ligand systems at the single molecule level, predicting relative off-rates, potentially of great value for combinatorial chemistry and biology.

Figure 1

Model structures of the scFv fragments c12 B5–6 (A), 4D5-Flu (B), and FITC-E2 (C) with bound fluorescein. Altered amino acid positions are indicated for the scFv fragments c12 B5–6 and FITC-E2 (e.g., His H58 Ala indicates that histidine at position 58 in the heavy chain is mutated to alanine).

Figure 2

Loading rate dependence of the unbinding forces for FITC-E2 wt and 4D5-Flu at 25°C. For each loading rate more than 100 unbinding events were recorded. The most probable unbinding force was determined by fitting a Gaussian to the distribution of unbinding forces. The statistical error of the unbinding force was estimated as the width of the distribution divided by the square root of the number of unbinding events. The off-rates at zero force, determined from linear fits to the data, agree well with the thermal off-rate, which are indicated by arrows. At zero force Eq. 2 gives a value for r = k_off⋅k_B⋅T/x_β, allowing the placement of the kinetic constants on the r axis.

Figure 3

Linear correlation between the force F and ln k_off. Forces and off-rates are expressed relative to the FITC-E2 wt.

Figure 4

The plot of Δx_β/x_{β_wt} vs. Δln(k_off)/ln(k_{off_wt}) shows the increase of x_β with increasing activation energy. The wt is the unmutated scFv FITC-E2. The slope of the linear fit is 0.3.