Glassy Dynamics and Memory Effects in an Intrinsically Disordered Protein Construct

Glassy, nonexponential relaxations in globular proteins are typically attributed to conformational behaviors that are missing from intrinsically disordered proteins. Yet, we show that single molecules of a disordered-protein construct display two signatures of glassy dynamics, logarithmic relaxations and a Kovacs memory effect, in response to changes in applied tension. We attribute this to the presence of multiple independent local structures in the chain, which we corroborate with a model that correctly predicts the force dependence of the relaxation. The mechanism established here likely applies to other disordered proteins.

Figure 1

(a) Experimental setup: A polymer consisting of multiple NFL IDRs joined by disulfide bonds is stretched with a force $f$ while its extension $L$ is tracked. Stuck beads are tracked to remove drift. (b) Example force-quench experiment on a single polymer: at $t=0$, the force was decreased from $f_1=50$ to $f_2=9\mathrm{pN}$, resulting in a rapid elastic response followed by a slow logarithmic relaxation (inset). (c) Typical force dependence of the logarithmic relaxation after quench from $f_1=50\mathrm{pN}$, plotted as the compaction, $\mathrm{\Delta }L\equiv L(t)-L(t_0)$, after a reference time $t_0=1\mathrm{s}$. At higher $f_2$ (labeled, in pN), the relaxation slows due to hindering of chain shortening by tension. Data points and error bars are the mean and standard error of the mean after logarithmic binning in time (error bars are smaller than points); lines are best fits to $b\log (t/t_0)$.

Figure 2

(a) Typical two-step experiment: The force was initially $f_1=60\mathrm{pN}$, then held at $f_2=7\mathrm{pN}$ for $t_w=10\mathrm{s}$, then increased to $f_3=19\mathrm{pN}$. (b) Detail of extension dynamics at $f_3$ from the data in (a), showing a nonmonotonic change in $L$, i.e., a Kovacs hump [18]. Data points and error bars are the mean and standard error of the mean after logarithmic binning in time (error bars are smaller than points). (c) Cartoon of heterogeneous dynamics within a single IDR domain that result in the Kovacs hump: Incubation at $f_2$ for $t_w$ (left) allows folding of fast segments, but is not long enough to allow folding of slow segments. Application of the higher force $f_3$ causes unfolding of some fast segments, leading to the increase, $L_2>L_1$. At long times, the slow segments finally fold, causing the slow decrease, $L_3<L_2$.

Figure 3

Bottom: Dependence of the normalized logarithmic relaxation rate $\overline{b}$ on the force-quench magnitude, $\overline{f}\equiv f_2/f_1$. Each data point represents a single force quench on a single polymer, with error estimated from the uncertainty in the measured slope. 248 data points, from 16 separate polymers, are shown. The line is a fit to Eq. (3) with best-fit parameter $\rho =0.108\pm 0.004$ (error estimated from bootstrapping, as described in the Supplemental Material [23]). Top: standardized residuals of the fit, $\mathrm{\Delta }\overline{b}/{\sigma }_{\overline{b}}$, where $\mathrm{\Delta }\overline{b}$ is the difference between the data and the fit, and ${\sigma }_{\overline{b}}$ is the error estimate of the data. Inset: The data are linearized by plotting $\overline{b}$ vs $1/\overline{f}$.