Simulating precursor steps for fibril formation in methylcellulose solutions

We use coarse-grained molecular dynamics simulations to study the precursor steps for fibril formation in methylcellulose solutions. Simulations of ring stacking between two collapsed methylcellulose chains demonstrate the existence of a capture radius that is much larger than that predicted by polymer diffusion alone. When two rings are in very close proximity, they stack together to form a fibril precursor. Simulations of stacks of such rings suggest that this structure is metastable. In contrast, chains that are within the capture radius but not in close proximity, as well as for systems containing both ringlike and relaxed chains, fibril-like structures form via a distinctly different mechanism. Irrespective of their initial arrangement, the chains undergo two specific conformational changes: (i) a part of either a ring or a randomly coiled chain splays out and (ii) the splayed chain subsequently engulfs a nearby chain if it is within a certain capture distance. The latter results are consistent with recent experimental measurements of fibril formation by short methylcellulose chains, which suggests the formation of a twisted bundle.

Figure 1

Representative initial conditions for (a) block, (b) alternating, and (c) jammed initial configuration.

Figure 2

Final structures of two-chain systems with the initial distance between their centers of mass $r_0$ being (a) $3\sigma$ and (b) $8\sigma$.

Figure 3

Snapshots for a four-chain system initiated in a jammed configuration. Snapshots are taken at (a) $0\tau$, (b) $1360\tau$, (c) $9265\tau$, and (d) $13695\tau$.

Figure 4

Difference in the shape anisotropy factor between successive frames ($\mathrm{\Delta }{\kappa }_i^2$) as a function of time for all chains for the jammed configuration. The labels for the vertical dashed lines correspond to the times of the snapshots in Fig. 3, with the text color corresponding to the particular chain referenced by the label.

Figure 5

Final structure of two-chain systems with $r_0$ = (a) $13\sigma$, (b) $18\sigma$, (c) $36\sigma$, and (d) $45\sigma$.

Figure 6

Mechanism of ring formation consisting of four chains and initiated in an alternating configuration. Snapshots are taken at (i) $0\tau$, (ii) $880\tau$, (iii) $1510\tau$, (iv) $5095\tau$, and (v) $9660\tau$ (last configuration for this simulation).

Figure 7

(a) Shape anisotropy factor obtained from the eigenvalues of the individual chain gyration tensors. The labels at the top of the plot correspond to the times of the snapshots in Fig. 6. (b) Global shape anisotropy obtained from the eigenvalues of the global gyration tensor. The dotted black line corresponds to a ringlike topology at ${\kappa }^2=0.25$.

Figure 8

Evolution of the shape anisotropy factor for (a) four-chain systems and (b) eight-chain systems. Each block of data corresponds to a single simulation. Simulations initiated in block configuration start with label B and those in alternating configuration start with label A. In each simulation, the first two (for four-chains) or four (for eight-chains) color maps from the left correspond to chains initiated in a ring configuration, and the others correspond to chains initiated in random coil configuration. (c) Zoomed version of A1 in (a); (d) zoomed version of B4 in (a). Representative movies pertaining to the time evolution of all the simulations can be found in [32].

Figure 9

(a) Snapshot showing splaying of all chains for case B4 at $2655\tau$. (b) Snapshot of the intermediate bundled structure at $11\hspace{0.17em}240\tau$. Other relevant snapshots for (b) are shown in Fig. S5 [32]. For both cases, orange and cyan colored chains were initiated in a ringlike configuration, whereas the other two chains were initiated in a random coil configuration.