Effects of Macromolecular Crowding on the Collapse of Biopolymers

Experiments show that macromolecular crowding modestly reduces the size of intrinsically disordered proteins even at a volume fraction ($\varphi$) similar to that in the cytosol, whereas DNA undergoes a coil-to-globule transition at very small $\varphi$. We show using a combination of scaling arguments and simulations that the polymer size ${\overline{R}}_g(\varphi )$ depends on $x={\overline{R}}_g(0)/D$, where $D$ is the $\varphi$-dependent distance between the crowders. If $x\lesssim \mathcal{O}(1)$, there is only a small decrease in ${\overline{R}}_g(\varphi )$ as $\varphi$ increases. When $x\gg \mathcal{O}(1)$, a cooperative coil-to-globule transition is induced. Our theory quantitatively explains a number of experiments.

Figure 1

Crowding effect on the conformation of a SAW chain ($N=100$) for $\lambda \sim \mathcal{O}(1)$. (a) ${\overline{R}}_g(\varphi )$ as a function of crowder volume fraction ($\varphi$). The $\lambda$ values are shown in different colors. A snapshot of the SAW chain and the crowding particles on the top is for $\lambda =1.9$ at $\varphi =0.3$. (b) Distribution of $R_g$, $P[R_g(\varphi )]$ at $\lambda =3.8$. (c) Collapse of $P[R_g(\varphi )]$, with $\varphi =0.1–0.4$ and $\lambda =0.9–6.9$, onto a universal curve [Eq. (1), with $b=1.120$ and $\mathcal{N}=13.69$] obtained by rescaling $R_g(\varphi )$ by ${\overline{R}}_g(\varphi )$ justifies that the statistics of the polymer coil does not change. The corresponding result for the end-to-end distance is in [22]. (d) RDF of crowders from the center of the SAW chain at varying $\varphi$.

Figure 2

Dramatic compaction of the SAW chain ($N=50$, $\lambda =47$). (a) ${\overline{R}}_g(\varphi )/{\overline{R}}_g(0)$ of the SAW chain (the green square). The line with red circles is from Ref. [10], which simulated the effect of macromolecular crowding on the SAW polymer implicitly by using the effective depletion AO potential between two sites on a polymer. An ensemble of polymer conformations at each $\varphi$ and a snapshot of the simulation at $\lambda =47$ and $\varphi =0.2$ are shown at the top. (b) $P[R_g(\varphi )]$ at $\lambda =3.8$. (c) Shape parameter ($S$) and asphericity ($\mathrm{\Delta }$) of the SAW chain as a function of $\varphi$. (d) RDF of crowders from the center of the position in the SAW chain at varying $\varphi$.

Figure 3

Compaction of IDPs, ACTR, and IN in an increasing volume fraction of PEG 6000 [39], and $\lambda$N in BPTI or metmyoglobin (Mb) [40]. To compare experiments, we superimposed our simulation results with $N=100$ and $\lambda =0.9$, 1.9, 3.8. The compaction of IN, $\lambda \mathrm{N}$ (BPTI), and $\lambda \mathrm{N}$ (Mb) is described by $\lambda =0.9$, and ACTR by $\lambda =3.8$.

Figure 4

Diagram of a polymer collapse which varies depending on the value of parameter $x$. For $x\sim \mathcal{O}(1)<x_c$, the size of the polymer decreases with an increasing $\varphi$ while maintaining its coil statistics (${\overline{R}}_g\sim N^{3/5}$). By contrast, for $x_c\ll x$, the polymer undergoes a coil-globule transition. ${\varphi }_c$ greater than the volume fraction of close packing is not accessible ($\varphi \gtrsim {\varphi }_c^{\max }$). The difference between the crowding-induced dynamics in the two regimes of $x$ is illustrated with IDP and T4-DNA.