Noninvasive Protein Structural Flexibility Mapping by Bimodal Dynamic Force Microscopy

Mapping of the protein structural flexibility with sub-2-nm spatial resolution in liquid is achieved by combining bimodal excitation and frequency modulation force microscopy. The excitation of two cantilever eigenmodes in dynamic force microscopy enables the separation between topography and flexibility mapping. We have measured variations of the elastic modulus in a single antibody pentamer from 8 to 18 MPa when the probe is moved from the end of the protein arm to the central protrusion. Bimodal dynamic force microscopy enables us to perform the measurements under very small repulsive loads (30–40 pN).

Figure 1

Experimental setup and bimodal FM AFM images of pentameric IgM (antibody) in liquid. (a) Bimodal FM AFM scheme in liquid. (b) Relevant distances in the experiment and theory. (c) Image of several antibody complexes taken in water at $\Delta f=40\mathrm{Hz}$. The peak force on the protein was 40 pN. The pentamer has a central protrusion surrounded by several arms ($F_{ab}$ domains). The apparent number of arms depends on the protein complex. The inset of (c) shows an atomic resolution image of the mica surface.

Figure 2

Bimodal FM AFM images of several isolated IgM pentamers. (a) Topography. (b) Cross section along the line marked in (a). (c) Topography. (d) Cross section along the line marked in (c). The measured height ($\sim 6\mathrm{nm}$) is very close to the nominal value of the relaxed molecule ($\sim 8\mathrm{nm}$). This is indicative of the noninvasive character of the measurement (peak force of 40 pN).

Figure 3

(a) Frequency shift on the mica and on top of the central region of an antibody as a function of the mean tip-surface distance. (b) Cantilever average deflection. (c) Force versus distance curve. (d) Peak force dependence on the frequency shift. The inset of (c) shows the points where the data were acquired. (e) Second mode amplitude dependence on the tip displacement. (f) Second mode phase shift.

Figure 4

Topography and flexibility map of a single IgM antibody. (a) Bimodal FM AFM image taken at $\Delta f=40\mathrm{Hz}$ (peak force of 40 pN), $A_1=4.5\mathrm{nm}$, and $A_{02}=0.5\mathrm{nm}$. (b) Flexibility map obtained simultaneously with the topography image by recording the bimodal parameters ($A_2$, ${\varphi }_2$). (c) Pentamer structure of the IgM antibody [32]. The locations of the lowest (L) and highest elastic moduli (H) are marked. (d) Topography (grey) and flexibility (black) profiles along the lines marked, respectively, in (a) and (b).