Effects of macromolecular crowding on the collapse of biopolymers

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