Comparative energy measurements in single molecule interactions

Abstract

Single molecule experiments have opened promising new avenues of investigations in biology, but the quantitative interpretation of results remains challenging. In particular, there is a need for a comparison of such experiments with theoretical methods. We experimentally determine the activation free energy for single molecule interactions between two synaptic proteins syntaxin 1A and synaptobrevin 2, using an atomic force microscope and the Jarzynski equality of nonequilibrium thermodynamics. The value obtained is shown to be reasonably consistent with that from single molecule reaction rate theory. The temperature dependence of the spontaneous dissociation lifetime along with different pulling speeds is used to confirm the approach to the adiabatic limit. This comparison of the Jarzynski equality for intermolecular interactions extends the procedure for calculation of activation energies in nonequilibrium processes.

FIGURE 1

Schematic of experimental setup. Recombinant syntaxin 1A and synaptobrevin 2 cytoplasmic tails are attached to the cantilever tip and coverslip, respectively, through a Ni²⁺-six histidine residue coordination at the C-termini of these proteins. The picture is not to scale. The piezo is used to first move the coverslip up toward the cantilever tip to bring about the interaction and then down to exert force on the intermolecular bond. The work parameter λ is the distance from the bottom of the cantilever holder to the top of the coverslip, x_i is the extension of the bound intermolecular complex, and F_i/k is the distance bent by the tip of a cantilever of spring constant k in response to a force F_i.

FIGURE 2

(a) A typical force curve obtained for the intermolecular interaction of the syntaxin 1A-synaptobrevin 2 pair. The force on the cantilever tip is plotted as a function of the distance moved by the coverslip. The segment de represents the bond rupture force. The net intermolecular extension to the point of rupture can be calculated from the distance moved by the piezo from point c to d, and subtracting from it the rupture force divided by the spring constant, which is the decrease in tip-coverslip separation distance due to the bending of the cantilever tip from the applied force at rupture. The segment ab is due to direct contact between the cantilever tip and coverslip. (b) Force and (c) extension histograms at the point of rupture for the intermolecular interaction of the syntaxin 1A-synaptobrevin 2 pair. The arrowheads on the histogram show mean values.

FIGURE 3

(a) The bound state is represented by the solid circle at the bottom of the potential well. (b) The lowering of the energy barrier due to the application of the force.

FIGURE 4

The mean rupture force as a function of the rate of applied force dF/dt, for three different temperatures of 277 K, 287 K, and 297 K, are shown as triangles, circles, and squares, respectively. The corresponding best-fit straight lines are indicated as dotted, dashed, and solid lines. Based on the phenomenological model, the mean lifetime τ_o of the bound system under zero force is found from the intercept and the slope of the lines to be 1.95, 0.4, and 0.18 s, respectively. Points indicate mean ± SE values.

FIGURE 5

The natural logarithm of the mean lifetime τ_o of the bound system plotted as a function of inverse temperature. From the slope, the activation energy ΔG_PM can be found based on the phenomenological model.

FIGURE 6

(a) The distribution of W_i obtained from the force extension curves recorded at a pulling velocity of 40 nm/s for experiments done at 297 K. (b) Values of ΔG plotted as a function of the reciprocal pulling velocity using the JE for three different temperatures. For experiments at 297 K (squares), the asymptotic behavior of ΔG_JE approaches the adiabatic limit at low pulling velocities. At lower temperatures of 277 K (triangles) and 287 K (circle), the adiabatic limit is not achieved due to the longer lifetimes. The lines connecting the data points can be used as an aid to the eye. Points indicate mean ± SE values.