Conformational dynamics of an unfolded biopolymer : theory and simulation

The conformational dynamics of an unfolded biopolymer such as a polypeptide or DNA has attracted a significant amount of attention in the context of protein folding and the design of biomimetic technologies. To this end, recent advances in single-molecule experiments have allowed for biomolecules to be probed with an unprecedented level of detail, shedding light on their dynamics. Motivated by the need to interpret experimental data and to help guide future studies, we use concepts from polymer physics, computer simulations, and experimental data to study the timescales in which an unfolded biopolymer undergoes conformational rearrangement.

First, we examine the end-to-end loop formation time in the experimentally relevant scenario where the dynamics are probed using a fluorescence probe and quencher. We show that the loop formation time in the experimentally relevant case is quantitatively dissimilar from the predictions of previous theoretical studies that neglect the quenching kinetics, which are often used to interpret experimental data.

We additionally find that the loop formation times can be re-casted in a simple, universal dependence that is characteristic of random-coils. Furthermore, deviations from this universal dependence can be used as a sensitive tool for detecting structural order in unfolded biopolymers.

We also consider a surface-tethered polymer chain and investigate the rate of a reaction between the free end and the surface. We explore this rate in the reaction-controlled limit and the diffusion-controlled limit, providing evidence for near-universal dependences of the rate in the respective limits.

Next, we examine the transit time of end-to-end loop formation in a case study. We find that approximating the end-to-end dynamics as diffusion in a 1D potential of mean force fails dramatically to describe the transit time. Furthermore, we find that the transit time is uninfluenced by the average entropic force imposed by the polymer chain and is well described by a simple free-diffusion model.

Finally, we explore the role of internal friction in the dynamics of an unfolded protein. Using simple polymer models that incorporate internal friction as an adjustable free parameter, we mimic typical single-molecule experiments that probe the unfolded state dynamics and make several experimentally verifiable predictions.