Cooperative monomer binding by polynucleotides. Effect of multiple‐loop configurations on formation of triple‐stranded complexes

Simulated binding curves for the reaction 2 polymer + monomer = triple‐stranded complex are presented, in which loop formation and sliding degeneracy of the polymer adsorption surface are considered. Exact calculations for a polymer chain length N of 11 units suggest that configurations of two or more loops have negligible effect on the isotherm when SW > 1, where S and W are exponential weighting factors for monomer–monomer S and polymer–polymer W nearest neighbor interactions. There is a pronounced effect, however, when SW ≪ 1. Limiting expressions ( N ≫ 1, but finite) for the single‐loop configurations suggest these configurations are negligible at any degree of saturation θ if θ (1 − θ) 2– k N 3– k ≪ SW , where k is defined by the weighting factor ( j + 1) − k for a ring of j units. This expression suggests that single monomer‐stack configurations are the only significant contributors to the grand partition function at the midpoint of the isotherm if N 3– k ≪ SW . Furthermore, single‐loop configurations are negligible below θ = 0.5 but become dominant above the isotherm midpoint when SW ∼ 1 (random binding) if 2 < k < 3. For k > 3 and N → ∞, loop configurations have no effect in any region of the random binding isotherm usually analyzed experimentally (θ < 0.95). Equivalence of matrix and sequence generating methods is also demonstrated.