10. Chemical bonds and anti-body-antigen interactions
The AFM lacks an intrinsic, controlled chemical sensitivity, but great progress has been made in functionalizing the probe tip in order to make it selectively sticky. In one approach, friction is measured through twisting of the cantilever as a functionalized tip is dragged over a heterogeneous surface (Frisbie, Rozsnyai et al. 1994). This approach has even been extended to carbon nanotube tips (Wong, Joselevich et al. 1998). Another method for detecting interactions is to record structure in the force-distance curve as a tip is pulled away from a surface, a technique often referred to as force spectroscopy. Hoh and coworkers used this method to detect hydrogen bonds between the tip and a glass surface in water (Hoh, Cleveland et al. 1992).
Figure 23: Antibody functional imaging. (a) is image taken with a bare tip over lysozyme on mica. (b) is image taken with a monoclonal antibody on the tip. (c) Shows the action of free antigen in blocking the sensing antibody and restoring contrast similar to the bare tip. All scans are 500 nm square. (From Raab et al. (Raab, Han et al. 1999) with permission.)
More recently, techniques have been developed for attaching large molecules to either the tip or a substrate (or both) and detecting the bonding between them as the tip is pulled away from the substrate. These measurements are important because they hold out the prospect of comparing binding parameters for single pairs of molecules with calorimetric data obtained on large populations. They are becoming easier to carry out and interpret and may offer a better path to systematic development of drugs in as much as total free energies and some kinetic data are available. Examples of such experiments are protein-ligand interactions (Florin, Moy et al. 1994; Lee, Kidwell et al. 1994; Dammer, Popescu et al. 1995; Nakajima, Kunioka et al. 1997; Moore, Stevens et al. 1999) and antibody-antigen binding (Dammer, Hegner et al. 1996; Hinterdorfer, Baumgartner et al. 1996; Allen, Chen et al. 1997; Hinterdorfer, Raab et al. 1998).
The basic arrangement of such experiments is outline in Fig. 22a. The receptor (shown as a circle with a wedge missing) may be bound covalently to a tip and the ligand (shown as a triangle) bound to a surface. Hinterdorfer et al. showed that measurements were greatly facilitated when a flexible linker was used to bind at least one of the receptor ligand pair, because it relaxes constraints on their alignment as the tip is docked on the target molecule (Hinterdorfer, Baumgartner et al. 1996). These workers used a flexible polymer chain (polyethylene glycol) of about 6nm in length. When the tip is pulled back from the surface (Fig. 22b) a characteristic adhesion peak is seen in the retrace force curve (shown in the figure to have a magnitude F>a). A flexible linker would result in a shift of the adhesion peak in the retraction curve to the right. A histogram of the values of Fa obtained from many such measurements may show a distinct peak which is taken to be the rapture force of the bond.
The rapture force is not unique. It depends on the dynamics of the process as discussed by Evans and Ritchie (Evans and Ritchie 1997) and more recently by Moore et al. (Moore, Stevens et al. 1999). There are several contributions to the rate dependence. At high rates of loading (rate of increase of force) molecular friction generates a force proportional to the velocity of the tip (Grubmuller, Heymann et al. 1996). At smaller rates the time dependence of the entropy term in the free energy dominates. This is because time is required for the system to explore different configurations, some of which will facilitate unbinding more readily. Moore et al. (Moore, Stevens et al. 1999) have used the following semi-empirical equation to fit force data taken as a function of loading rate over a wide range of scan speeds
Here, DH and DS are the transition state enthalpy and entropy
associated with the bond, r is the size of the binding pocket, v is the
velocity of the tip and t0 is an inverse attempt
frequency, on the order of 10-8s for biotin-streptavidin (Moore, Stevens et al.
1999). The factor 
accounts for the reduced contribution of
entropy to lowering the overall barrier at higher loading rates. Moore et al. (Moore,
Stevens et al. 1999) obtain excellent fits to experimental data using Eqn. 23, finding
logarithmic dependence on loading rates at small rates and linear behavior at higher
rates. The critical rate at which behavior turned from linear to logarithmic was on the
order of 100nN/s, related to the diffusivity of the of the ligand in the binding pocket by
Moore et al. At very small loading rates (0.1nN/s) the effective barrier fell to a value
close to that obtained from thermodynamic measurements.
A further development of these methods is functional imaging where a functionalized tip
is used to locate specific moeties in an image. This will be of utility in mapping
complicated surfaces, for example locating specific receptor proteins on a cell surface.
Raab et al. used magnetic DFM with an antibody functionalized tip to image the
distribution of antigen (lysozyme) on a mica substrate. The magnetic DFM permitted the tip
to be engaged gently so that the antibody (and its flexible tether) were not damaged on
approach to the surface. The use of magnetic DFM facilitates amplitude and frequency
control, which in turn permits control of the antibody-antigen binding during imaging.
Operated at a small amplitude A with a tether length L, the effective molar
concentration of antibody under the tip is 
while the binding time is
,
where kon is the binding constant in M-1s-1. The scan speed and
oscillation amplitude must be chosen so that the tip dwells over the target for times that
are long compared to t. Using kon=1.65x105M-1s-1,
L=6nm and A=2.5nm, Raab et al. obtained t on the order of millisecond (Raab, Han et al. 1999), permitting micron-sized
areas to be scanned in minutes.
Results of a functional imaging experiment are shown in Fig. 23. Fig. 23a shows a 500nm square area of a mica substrate imaged under buffer and covered by a sub-monolayer of lysozyme. It is imaged by magnetic DFM with a bare tip. Fig. 23b shows a similar area imaged with a functionalized tip. The features are characteristically higher and broader (broadened by approximately twice the tether length of 6nm). The specific nature of this enhanced contrast is demonstrated in Fig. 23c. Free antigen had been injected into the liquid cell prior to acquisition of this image. As the tip scanned up, it became blocked by antigen binding from solution at the point labeled by the arrow. The contrast reverts to that found with a bare tip. Subsequent washing of the cell restored the specific imaging, proving the antigenic sensitivity of the probe. It is interesting to note that the blocked tip gives images identical to the bare tip. Evidently, the blocked antibody diffuses around freely and does not interfere with the image, much as was found for the soluble protein domains of the membrane protein discussed in section 8 (and see Plate II). The inherent variation in tip geometry and chemistry and the heterogeneity of cell surfaces may well preclude functional imaging in a single sweep. The most promising approach is to carry out imaging before and after adding free antigen, having previously established that this does not affect the target image when a bare tip is used.
Figure 24: Showing STM images taken over a monolayer of protoporphyrin on graphite. The fraction of iron-containing molecules is 0 (A), 0.2 (B), 0.8 (C) and 1.0 (D). The largest enhancement of contrast for the iron-containing molecules occurs at the redox potential for the iron oxidation/reduction process corresponding to the peak in the cyclic voltammograms on the right. Here E is for 0, F for 0.2, G for 0.8 and H for 1.0 fraction of iron containing protoporphyrins. (Data from Tao (Tao 1996) with permission.)
