Diffusion of isolated DNA molecules: Dependence on length and topology

Abstract

The conformation and dynamics of circular polymers is a subject of considerable theoretical and experimental interest. DNA is an important example because it occurs naturally in different topological states, including linear, relaxed circular, and supercoiled circular forms. A fundamental question is how the diffusion coefficients of isolated polymers scale with molecular length and how they vary for different topologies. Here, diffusion coefficients D for relaxed circular, supercoiled, and linear DNA molecules of length L ranging from Ϸ6 to 290 kbp were measured by tracking the Brownian motion of single molecules. A topology-independent scaling law D ϳ L ؊ was observed with L ‫؍‬ 0.571 ؎ 0.014, C ‫؍‬ 0.589 ؎ 0.018, and S ‫؍‬ 0.571 ؎ 0.057 for linear, relaxed circular, and supercoiled DNA, respectively, in good agreement with the scaling exponent of Х 0.588 predicted by renormalization group theory for polymers with significant excluded volume interactions. Our findings thus provide evidence in support of several theories that predict an effective diameter of DNA much greater than the Debye screening length. In addition, the measured ratio DCircular͞ DLinear ‫؍‬ 1.32 ؎ 0.014 was closer to the value of 1.45 predicted by using renormalization group theory than the value of 1.18 predicted by classical Kirkwood hydrodynamic theory and agreed well with a value of 1.31 predicted when incorporating a recently proposed expression for the radius of gyration of circular polymers into the Zimm model. circular ͉ polymer ͉ polyelectrolyte ͉ hydrodynamics ͉ excluded volume W hile many eukaryotic genomes are linear, prokaryotic genomes and most cloned DNA constructs are circular (1). Indeed, a commonly stated motivation for theoretical calculations on circular polymers is that they may be applicable to understanding the behavior of DNA. However, four of the five previously reported studies on the diffusion of circular polymers have used synthetic polymers, and only two of these, both using synthetic polymers, examined the dependence of the diffusion coefficient on molecular length. The dependence of D on length for relaxed circular DNA has never been measured. Here, we examine linear, relaxed circular, and supercoiled DNA molecules covering a wide range of lengths (Ϸ6 to 290 kbp).For long linear polymers in a good solvent, where excluded volume effects are appreciable, polymer physics theory (2) predicts D ϳ 1͞R G ϳ L Ϫ with Х 0.588, where R G is radius of gyration. The same scaling exponent has been calculated for both dynamic (D ϳ L Ϫ ) and static (R G ϳ L ) quantities, with nearly identical results determined by using a wide range of methods. Static scaling has been examined by using Monte Carlo simulations (3), bead-rod simulations (4), and cylindrical selfavoiding polygon models (5). Renormalization group theory methods have been used in both static (3, 6) and dynamic (7) calculations, and bond-fluctuation simulations (8) were used to measure and compare both scaling relationships. The predicted scaling exponent is close ...

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube

“…The values of solute diffusivity considered here are in the order of 10 À11 -10 À14 m 2 /s, which is typical for high molecular weight proteins and DNA. 52 This results in the Schmidt number in the order of 10 5 -10 8 . Since, mass transfer boundary layer thickness is inversely proportional to Schmidt number, it may be considered that thickness of mass transfer boundary layer would not more than 0.1-0.2% of the tube radius (typical microtube diameter are in the range of 50-500lm).…”

Monte Carlo simulation of a single ring among linear chains: Structural and dynamic heterogeneity

“…properties of ring polymers in the ring-linear blends. [24][25][26][27][28][29][30][31] Iyer et al 28 proposed a scaling model on the size of ring polymers in ring-linear blend and found that by gradually increasing the composition of linear chains, the ring molecules swell, with Flory's scaling exponent v increasing from 0.4 to 0.5 in the limit of infinite dilution for the rings. Using the BFM, Subramanian and Shanbhag 29,30 studied the dynamics of entangled ring polymers in ring-linear blends and found the self-diffusion coefficient and the primitive path length of ring polymers are more sensitive to volume fraction than that of linear chains.…”

“…This is in agreement with the results of Robertson et al on DNA. [25][26][27] By tracking the Brownian motion of individual tracer DNA molecules in blend of four topological combinations, Robertson et al found that the molecular topology, especially for the case of circular DNA molecules surrounded by linear molecules, have a strong effect on the diffusion at above certain concentration or molecular weight. Their findings suggest that free ends play a critical role in generating entanglements which retard diffusion.…”

Conformation of Ring Polymers in 2D Constrained Environments

“…Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box. DOI: 10.1103/PhysRevLett.106.248301 PACS numbers: 82.35.Gh, 87.64.Dz, 36.20.Ey, 87.14.gk Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”

“…Ring closure of a polymer is one of the important factors influencing its statistical mechanical properties [1], e.g., scaling [2,3], shape [4,5], and diffusion [6][7][8], because it restrains the accessible phase space. The theoretical description of circular chains (knots or catenanes) is a challenging problem, owing to the difficulties inherent to a systematic theoretical analysis of such objects constrained to a unique topology.…”