Toward a statistical theory of catenanes. 2. Calculation of size and chain-ring-catenane distributions with DNA-like polymers

Abstract

Theory of the author is applied to polymer systems resulting from equilibria between DNA-like monomers with reactive ends with Kuhn segment (KS) length of 1000 Á. Computations are made for monomer sizes containing from 1.5 to 600 KS, corresponding to molecular weights from 3 x 106 to 1.2 X 10® daltons, at concentrations from undiluted polymer to mass dilution of 1:109 and over the entire range of possible extents of reaction. Molecular size distributions, weight and number fractions and molecular weight for chains, rings, and simplest catenanes, and overall MW's are computed. Maximum catenane yields are shown to occur, for given fraction of reaction, at intermediate concentration of monomers, growing larger with extent of reaction. For less general systems, current theory gives higher catenane predictions than previous Monte Carlo and overlap calculations. Gelation due to catenane linking is estimated not to occur for the general system, but in the special case of ring-catenane equilibrium alone may (and does, in topoisomerase experiments).

Statistical Ring Catenation under Thermodynamic Control: Should the Jacobson–Stockmayer Cyclization Theory Take into Account Catenane Formation?

“…22,23 However, the JS theory considers only ring−chain equilibria and neglects the formation of catenanes, knots, and other topological complex molecules that, in the experimental practice, could remain hidden within the mass of the supposed linear polymer. Jacobson tried to correct the JS theory for the presence of catenanes, 24,25 but his model largely overestimates catenane formation. 26 Recently, we have critically reviewed models and simulations of the catenation process and obtained a reliable expression for the molar catenation constant.…”

“…The reversible formation of large polymeric rings was studied theoretically by Jacobson and Stockmayer (JS) as early as 1950, but for many years their theory was largely confined among the specialists of polymer chemistry. − In the 1990s, owing to the increasing interest in macrocyclic chemistry, their theory was re-evaluated and popularized to make it more understandable to chemists of other disciplines. , However, the JS theory considers only ring–chain equilibria and neglects the formation of catenanes, knots, and other topological complex molecules that, in the experimental practice, could remain hidden within the mass of the supposed linear polymer. Jacobson tried to correct the JS theory for the presence of catenanes, , but his model largely overestimates catenane formation . Recently, we have critically reviewed models and simulations of the catenation process and obtained a reliable expression for the molar catenation constant .…”

Use of cohesive-ended DNA "monomers" as models for the study of polymeric systems: a perspective

“…Varying the concentrations similarly gives a range of ring/chain/catenane ratios. 16 Given these variables, DNA chain flexibility17 is the primary contributor to size distributions. Its high stiffness furnishes a minimal though significant contribution of chain thickness to steric hindrance.18 Solvent variability, particularly ionic strength, influences the thermodynamics of cohesive-end pairing6 and, less dramatically, the effective chain diameter19 and persistence length;20 after ligation, effects of supercoiling21 become apparent.…”