Direct Measurement of Dissipation in a Single Protein using Small Amplitude Atomic Force Microscopy

Abstract

In Krammers theory, stiffness and dissipation coefficient of a protein determine the rate of their conformational change. Using atomic force microscope, it is possible to measure viscoelasticity of a single protein, wherein its dissipative and elastic nature is directly and independently measured. Such measurements are performed, either by measuring the thermal fluctuations of the protein held under a constant force, or by providing small modulations to the protein by dithering the cantilever and measuring its response. In small amplitude approximation, where dither amplitude is comparable to persistence length of polymers, it is possible to measure the proteins viscoelastic response accurately. We measured dissipation in I27 at extremely low pulling speeds ([~] 50 nm/s) and low dither frequencies ([~]100 Hz). At these experimental parameters the dissipation is found to be [~]10-5 kg/s, well above the detection limit of conventional AFM and upper limit predicted by Benedetti et al. Our stiffness data clearly reveals unfolding intermediate of titins individual immunoglobulin units. The intermediate is elongation of folded domains by [~]8 [A], wherein two hydrogen bonds are broken between beta sheets. It was possible to measure this elongation in our experiments. The directly measured internal friction of unfolded polymer chain shows a scaling with tension on the chain. The measurements show that it is possible to measure internal friction in single molecules unambiguously using small amplitude AFM. It suggests that systematic experiments to unravel the relation between directly measured internal friction and folding rates of proteins are possible.