Rapid conformational fluctuations in a model of methylcellulose

Methylcellulose is a thermoresponsive polymer that undergoes a morphological transition at elevated temperature, forming uniform diameter fibrils. However, the gelation mechanism is still unclear, in particular, at higher polymer concentrations. We use Langevin dynamics simulations to investigate a coarse-grained model for methylcellulose that produces collapsed ringlike structures in dilute solution with a radius close to the fibrils observed in experiments. We show that the competition between the dihedral potential and self-attraction causes these collapsed states to undergo a rapid conformational change, which helps the chain to avoid kinetic traps by permitting a transition between collapsed states. If the dihedral potential is removed, the chains do not escape from their collapsed configuration, whereas at high dihedral potentials, the chains cannot stabilize the collapsed state. We provide systematic data on the effect of the dihedral potential in a model of methylcellulose, and discuss the implication of these previously overlooked rapid conformational fluctuations on the spontaneous formation of high-aspect-ratio fibrils.

Figure 1

Snapshots of a flipping event of a 1000-mer MC chain at $50{}^{\circ }\mathrm{C}$. The time lag between each snapshot is 7 ns, corresponding to $250\tau$.

Figure 2

Radius of gyration and the relative difference of $R_{\text{g}}$ for a 1000-mer MC chain as a function of simulation time. (a) $R_{\text{g}}$ vs time for three independent trajectories with 1000 monomers. The three trajectories are of total duration $3.16\times {10}^4\tau ,3.475\times {10}^4\tau$, and $5\times {10}^4\tau$. Before $t=0$, the chain was equilibrated at room temperature. At $t=0$, the temperature was elevated to $50{}^{\circ }\mathrm{C}$. (b) $\mathrm{\Delta }{R}_{\text{g}}/R_{\text{g}}$ vs time for the same three trajectories. An offset of 0.5 on the $y$ axis for each trajectory has been made for clarity. A total of 14, 18, and 25 flipping events are identified for top to bottom trajectories, respectively.

Figure 3

Histogram of the time between two flipping events for 1000-mer MC chain at $50{}^{\circ }\mathrm{C}$. The data correspond to a total 65 flipping events obtained from five independent trajectories.

Figure 4

(a) Shape anisotropy ${\kappa }^2$ and (b) the individual eigenvalues of the gyration tensor ${\lambda }_i$ vs time for a 1000-mer MC chain. The temperature jumps from $25{}^{\circ }\mathrm{C}$ to $50{}^{\circ }\mathrm{C}$ at the time $t=0$ (not indicated on the figure). The (red) dots indicate flipping events. (c) Snapshots at (i) 731, (ii) 889, and (iii) 1054 ns, which correspond to $2.61\times {10}^4\tau ,3.18\times {10}^4\tau$, and $3.77\times {10}^4\tau$, respectively. The corresponding time points in panels (a) and (b) are indicated by the dashed vertical lines.

Figure 5

Ternary plot of the rescaled eigenvalues ${(\lambda /R_{\text{g}})}^2$ for 1000-mer MC chains at $50{}^{\circ }\mathrm{C}$. The eigenvalues are ordered as ${\lambda }_x\le {\lambda }_y\le {\lambda }_z$ and satisfy ${\lambda }_x^2+{\lambda }_y^2+{\lambda }_z^2=R_{\text{g}}^2$. Data points are sampled every $50\tau$. The data correspond to the second half of five independent trajectories to remove the effects of the initial configuration and make sure the MC chain has already reached or visited a collapsed state. The 2006 data points are binned with bin size of 0.01. The colormap shows the probability of observing the combination of eigenvalues in a given bin. A representative MC conformation within the highest probability bin is included.

Figure 6

Box plot of the time between two flipping events with respect to the strength of the dihedral potential, $K_{\text{d}}$, at $50{}^{\circ }\mathrm{C}$. The box represents the interquartile range, which contains $50\%$ of the values. The whiskers extend to cover $99.3\%$ of the values. The line across the box is the median value. Each circle shows one data point, with the ones above the whiskers denoting outliers.

Figure 7

Box plots showing the eigenvalues of the gyration tensor $\left({\lambda }_x\le {\lambda }_y\le {\lambda }_z\right)$ as a function of the dihedral potential $K_{\text{d}}$. The description of the box plots are similar to Fig. 6, except here the outliers are plotted with the (red) cross symbols. (a) ${\lambda }_x$, (b) ${\lambda }_y$, and (c) ${\lambda }_z$.

Figure 8

Snapshots of initial, intermediate, and final structures in the five-chain simulation at $50{}^{\circ }\mathrm{C}$. The ring is formed from a single-chain simulation with $N=1000$. The initial configuration was constructed by placing five replicas of a ring with the spacing of 5.4 nm. Each color represents one MC chain.