Figure 2.

Excluded volume effects of crowders. (A) We approximate the disordered single-stranded DNA as a hard-sphere of radius r^u. The center-of-mass of the crowder is excluded from the (purple) shaded region of length r_c. Similarly, the center-of-mass of the DNA is excluded from a region (not shown) of length r^u around the crowder. (B) The DNA is placed into an environment consisting of spherical crowders with radius r_c, which shows the shaded regions of length r^u excluding the center-of-mass of the sphere representing the DNA strand. Hence, the DNA strand may only be placed into hashed regions and not shaded regions, as it would clash with one of the crowders. Therefore, when the open state of the DNA strand (C) folds up into a hairpin (D) having radius r^f < r^u, more hashed regions become available to the crowders and proteins in the solution (less volume is excluded), and the entropy of the solution goes up, thus making the system with the folded DNA state more free-energetically favorable. An analogous argument can be made for two complementary DNA strands forming a duplex.