Figure 1.

The loop closure probability P (y axis) for different loop lengths (x axis): experimental results (○) and two-dimensional lattice results (●). Experiments are from hairpin loop initiation parameters (32) using ln(P) = −ΔG/kT, where ΔG is the closure free energy. We assume ΔG is dominated by the loss of conformational entropy. The two-dimensional lattice results are from exact computer enumerations, where P is the ratio of conformation counts for the closed and open conformations. This factor that is needed to convert the lattice conformation count to the experimental data is approximately independent of chain length. For a self-avoiding chain on a two-dimensional lattice, there are three possible bond angles, which closely resemble three rotational isomeric states for each of the seven dihedral angle degrees of freedom per nucleotide. This simple relationship (one bond angle to seven angles) suggests the existence of a constant scaling factor μ to scale up the conformational count for realistic molecules. The numerical value of μ cannot be directly determined from the scaling in Fig. 1, because μ is defined for “loops” that do not contain any intra-loop contacts, whereas a loop measured in the experiment can contain unstacked (unstable) base–base contacts. We treat μ as a global constant for all loops because different loops, although possibly containing different details in geometry, share the same scaling relationship in chain conformational statistics, no matter how large the loop is and where the loop appears.