Sheetlike structure in the proximity of compact DNA

We determine the phase diagram of DNA with inter- and intrastrand native-pair interactions that mimic the compaction of DNA. We show that DNA takes an overall sheetlike structure in the region where an incipient transition to a compact phase would have occurred. The stability of this phase is due to the extra entropy from the folding of the sheet, which is absent in the remaining polymerlike states of the phase diagram.

Figure 1

Schematic diagram for the native contacts: (a) intrastrand contacts (dotted lines) in each polymer chain (A or B) with energy ${\epsilon }_s$ and (b) base-pair contacts (dotted lines) between chains A and B with energy ${\epsilon }_p$.

Figure 2

The phase diagram shows the occurrence of various states in different regions of the ${\epsilon }_s\text{−}{\epsilon }_p$ plane. These states are state I (two free ssDNA), state II (dsDNA), state III (two folded ssDNA), state IV (folded dsDNA), and state V (sheet). The dashed line corresponds to ${\epsilon }_s={\epsilon }_p$ and goes through the intersection point of the phase boundaries.

Figure 3

The probability of occurrence of different states in the phase diagram. (a)–(d) The right panel shows four different states of polymer A (green) and polymer B (orange); state I (two free ssDNA), state II (one dsDNA), state III (two folded ssDNA), and state IV (folded dsDNA). In the left panel, the color map shows the probability of occurrence of a state (next to it) in different regions of the ${\epsilon }_s\text{−}{\epsilon }_p$ plane. (e) A sheet structure formed from polymer A (green) and polymer B (orange) (top panel) and their occurrence probability in different regions of the ${\epsilon }_s\text{−}{\epsilon }_p$ plane (bottom panel). The sheet structure occurs in the Y regions of the phase diagram.

Figure 4

Probability of occurrence of different states along the line with slope one (${\epsilon }_s/{\epsilon }_p=1$) in Fig. 2 (dashed line).