Recent work has highlighted an intimate link between the internal friction of single biopolymers and dynamics on an underlying energy landscape of conformational change. Here, we examine the coarse-grained dynamics of flexible biopolymers by incorporating local internal friction sources into the successful Rouse model of polymer dynamics. Our main result is a closed-form expression of the frequency response function of a Rouse chain with and without internal friction. We find that the regimes in which internal friction and solvent friction dominate are characterized by single-mode dumbbell (|J(ω → ∞)| ∼ ω-1) and Rouse-like behavior (|J(ω → ∞)| ∼ ω-1/2), respectively. A real-space analysis shows these behaviors are due to a frequency-dependent length of chain that can respond to perturbations. By distinguishing dissipation due to internal conformational change with that from the solvent, the RIF model provides a simple and generic basis for probing the structure and dynamics of single biomolecules in stretching experiments.

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.

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.

We report on single molecule measurements of the viscoelastic properties of the polysaccharide dextran using a new approach which involves acquiring the power spectral density of the thermal noise of an atomic force microscope cantilever while holding the single molecule of interest under force-clamp conditions. The attractiveness of this approach when compared with techniques which use forced oscillations under constant loading rate conditions is that it is a near-equilibrium measure of mechanical response which provides a more relevant probe of thermally driven biomolecular dynamics. Using a simple harmonic oscillator model of the cantilever-molecule system and by subtracting the response of the free cantilever taking into account hydrodynamic effects, the effective damping zetamol and elastic constant kmol of a single molecule are obtained. The molecular elasticity measured by this new technique shows a dependence on applied force that reflects the chair-boat conformational transition of the pyranose rings of the dextran molecule which is in good agreement with values obtained directly from the gradient of a conventional constant loading rate force-extension curve. The molecular damping is also seen to follow a nontrivial dependence on loading which we suggest indicates that it is internal friction and not work done on the solvent that is the dominant dissipative process.