Rate limit of protein elastic response is tether dependent

Abstract

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D eff ∼ 1,200 nm 2 ∕s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D eff ∼ 10 8 nm 2 ∕s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D eff ∼ 10 4 -10 6 nm 2 ∕s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.force spectroscopy | protein diffusion | viscoelasticity | single molecule

Elasticity, structure, and relaxation of extended proteins under force

“…1A) at any force suggests that diffusion occurs on a very fast D ∼ 2 × 10 8 nm 2 /s timescale (using a very approximate estimation detailed in SI Text, later confirmed by more precise calculations as detailed below). These values are in close agreement to that measured in fluorescence techniques (15,16), but five to six orders of magnitude faster than observed in atomic force spectroscopy measurements (12)(13)(14). We and collaborators have recently suggested that the observed slow diffusion coefficients seen in force spectroscopies experiments result from the viscous drag on the microscopic objects (beads, tips, surfaces) they are necessarily tethered to (14), and do not correspond to an intrinsic property of the protein.…”

“…These values are in close agreement to that measured in fluorescence techniques (15,16), but five to six orders of magnitude faster than observed in atomic force spectroscopy measurements (12)(13)(14). We and collaborators have recently suggested that the observed slow diffusion coefficients seen in force spectroscopies experiments result from the viscous drag on the microscopic objects (beads, tips, surfaces) they are necessarily tethered to (14), and do not correspond to an intrinsic property of the protein. Diffusion is much faster in the simulations because in the usual steered MD setup force is directly applied to one extremity of the protein, the other one being fixed, without any intermediate tethering agent.…”

“…A joint experimental and theoretical study has suggested that increasing force greatly enhances internal friction along the end-toend coordinate with a power law dependence (12). Indeed force spectroscopy measurements have reported values on the order of 10 2 -10 4 nm 2 /s (12)(13)(14) about five orders of magnitude slower than that obtained for unfolded protein in the absence of force as measured by fluorescence techniques (15,16). However, we recently suggested that the slow diffusion coefficients of proteins estimated by force spectroscopies are due to the viscous drag on the microscopic objects (beads, tips, surfaces) they are necessarily tethered to (14).…”

“…Indeed force spectroscopy measurements have reported values on the order of 10 2 -10 4 nm 2 /s (12)(13)(14) about five orders of magnitude slower than that obtained for unfolded protein in the absence of force as measured by fluorescence techniques (15,16). However, we recently suggested that the slow diffusion coefficients of proteins estimated by force spectroscopies are due to the viscous drag on the microscopic objects (beads, tips, surfaces) they are necessarily tethered to (14). Diffusion of untethered protein under force as studied in molecular dynamics (MD) simulations occur on a much faster timescale (typically 10 8 nm 2 /s), close to that obtained from fluorescence techniques where the probes are of molecular size.…”

“…This observation may seem in contrast with some force-ramp and constant-velocity measurements showing a static disorder of p on a second timescale among different collapse or extension trajectories (17,26), especially at the lower forces. Possible explanations include the effect of the ionic environment of the experimental buffer solutions that could alter the dihedral free-energy profile, or the strong effect of tethering on the protein internal diffusion (14) that could result in different pathways in the Ramachandran space and in out-of-equilibrium states.…”