Internal friction of single polypeptide chains at high stretch

Abstract

Experiments that measure the viscoelasticity of single molecules from the Brownian fluctuations of an atomic force microscope (AFM) have provided a new window onto their internal dynamics in an underlying conformational landscape. Here we develop and apply these methods to examine the internal friction of unfolded polypeptide chains at high stretch. The results reveal a power law dependence of internal friction with tension (exponent 1.3 +/- 0.5) and a relaxation time approximately independent of force. To explain these results we develop a frictional worm-like chain (FWLC) model based on the Rayleigh dissipation function of a stiff chain with dynamical resistance to local bending. We analyse the dissipation rate integrated over the chain length by its Fourier components to calculate an effective tension-dependent friction constant for the end-to-end vector of the chain. The result is an internal friction that increases as a power law with tension with an exponent 3/2, consistent with experiment. Extracting the intrinsic bending friction constant of the chain it is found to be approximately 7 orders of magnitude greater than expected from solvent friction alone; a possible explanation we offer is that the underlying energy landscape for bending amino acids and/or peptide bond is rough, consistent with recent results on both proteins and polysaccharides.

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

“…We can directly compare our results with those of Khatri et al (13), who reported a value of k i L i y1 À 2 nN (a spring constant normalized on the stretched module length L i ) for the same protein. Correspondingly, taking the value of L i to be~20-30 nm, we obtain a much larger value, not smaller than~30 mN/m, for the spring constant of the I27 protein.…”

“…Note also that a persistence length of the protein as small as 0.25 nm (we believe this is too small; cf. the data given in (39)) was invoked by Khatri et al (13) to explain their observation.…”

“…Dextran and I27 protein molecules were chosen for these starting experiments because both of these molecules can be regarded as standard (if not calibrating) samples for single-molecule force spectroscopy, and have been widely studied (see, e.g., (8,13,18,19,(23)(24)(25)(26)(27)(28)(29)(30)). The dissipative properties of both of these molecules have been described elsewhere (8,13).…”

“…The dissipative properties of both of these molecules have been described elsewhere (8,13). An additional advantage is provided by the characteristic fingerprints of both dextran (a pronounced force plateau occurring at stretching forces of 800 pN) and I27 (modular nature of the protein, with the characteristic unfolding force of 100-200 pN for a module) molecules.…”

“…A number of experiments to measure the dissipative properties of single molecules (i.e., their internal friction) have been reported (see, e.g., (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)). One of the most straightforward methods employs small-amplitude dithering of an atomic force microscope (AFM) tip and measurements of the phase changes of this oscillatory system in the course of molecule stretching.…”