Conformational entropy of a pseudoknot polymer

The thermodynamics and kinetics of ABAB pseudoknot formation owing to reversible intrachain reactions are investigated for a flexible polymer based on the off-lattice Monte Carlo simulations. The polymer is made of N hard spheres tethered by inextensible bonds and consists of two reactive pairs AA and BB with binding energies - ε1 and - ε2, respectively, and three loop lengths (ℓ1, ℓ2, and ℓ3). Although two intermediate states, loops A and B, may be formed, the folding path goes mainly through the intermediate loop whose free energy reduction associated with coil-to-loop crossover is greater. The conformational entropy loss is found to follow ΔS=α ln N+G, where α≃2.48 for coil-loop crossover and α≃2.43 for loop-pseudoknot crossover. The constant G depends on the three loop lengths and the two end-to-reactive site lengths (L1 and L2). For a given total loop length, G is maximum when the three loop lengths are equal (ℓ1 = ℓ2 = ℓ3). When ℓ1 = ℓ3, the entropy loss is minimum if ℓ2 =0. However, the condition ℓ1 ≠ ℓ3 makes G even smaller. This consequence indicates that asymmetry in loop lengths is thermodynamically favorable and this fact is consistent with observations of pseudoknotted RNA structures.