Hydrodynamic Selection of the Kinetic Pathway of a Polymer Coil-Globule Transition

Recently, the role of hydrodynamic interactions in the selection of a kinetic pathway for phase transitions has attracted considerable attention. Here we study this problem numerically by taking as an example a coil-globule transition of a single polymer, which is a prototype model of protein folding. When a swollen polymer collapses into a globule state, hydrodynamic interactions accelerate the transition. We find, on the other hand, that when a rather compact polymer collapses into the same final state, hydrodynamic interactions decelerate the transition due to a slow squeezing process of the solvent. We reveal that the degree of the initial enhancement of anisotropy of the polymer configuration determines whether hydrodynamic interactions accelerate or decelerate the collapsing dynamics. We also discuss the possible relevance of squeezing flow effects in protein folding.

Figure 1

Temporal change of $R_g/R_g^{\theta }$ for a G-to-P (a) and a SP-to-P quench (c). Insets depict the CGT processes. Flow fields around the FPD polymer are shown in (b) and (d) for quenches (a) and (c), respectively. The darker (red) the arrow color, the stronger the flow.

Figure 2

(a) Comparison of polymer shapes at $t=100$ and 200 for BD and FPD. The surface color represents the Gaussian curvature $K$ (see the color bar). (b) Dependence of the relaxation time of mode $p$, ${\tau }_p$, on the mode number $p$ for BD and FPD polymers. The straight lines have slopes of $-2$ and $-2/3$, consistent with predictions of Rouse and Zimm models, respectively. The curves are to guide the eye.

Figure 3

Variation of $V_{sp}+V_{\mathrm{LJ}}$ per particle during the CGT for $R_g^i/R_g^{\theta }=1.66$ (a) and $R_g^i/R_g^{\theta }=0.81$ (b). Temporal changes of the scaled total potential energy for FPD (c) and BD (d) for $R_g^i/R_g^{\theta }=1.66$ (closed circles), $R_g^i/R_g^{\theta }=1.03$ (open circles), and $R_g^i/R_g^{\theta }=0.69$ (open triangles). The data in (a)–(d) were averaged over seven runs.

Figure 4

Dependences of (a) the relaxation times and (b) $A_{\mathrm{FPD}}/A_{\mathrm{BD}}$ on $R_g^i/R_g^{\theta }$. Curves are to guide the eye. The inset shows the $ϵ$ dependence of $R_g$. The error bars represent the dispersion of the data for seven independent runs.