An official website of the United States government
Abstract Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulations of open knotted polymer chains, often parameterized to DNA, typically perform a closure operation and calculate the Alexander polynomial to assign a knot topology. This is limited in scenarios where the topology is less well-defined, for example when the chain is in the process of untying or is strongly confined. Here, we use a discretized version of the Second Vassiliev Invariant for open chains to analyze Langevin Dynamics simulations of untying and strongly confined polymer chains. We demonstrate that the Vassiliev parameter can accurately and efficiently characterize the knotted state of polymers, providing additional information not captured by a single-closure Alexander calculation. We discuss its relative strengths and weaknesses compared to standard techniques, and argue that it is a useful and powerful tool for analyzing polymer knot simulations.
more »
« less
Long-lived metastable knots in polyampholyte chains
Knots in proteins and DNA are known to have significant effect on their equilibrium and dynamic properties as well as on their function. While knot dynamics and thermodynamics in electrically neutral and uniformly charged polymer chains are relatively well understood, proteins are generally polyampholytes, with varied charge distributions along their backbones. Here we use simulations of knotted polymer chains to show that variation in the charge distribution on a polyampholyte chain with zero net charge leads to significant variation in the resulting knot dynamics, with some charge distributions resulting in long-lived metastable knots that escape the (open-ended) chain on a timescale that is much longer than that for knots in electrically neutral chains. The knot dynamics in such systems can be described, quantitatively, using a simple one-dimensional model where the knot undergoes biased Brownian motion along a “reaction coordinate”, equal to the knot size, in the presence of a potential of mean force. In this picture, long-lived knots result from charge sequences that create large electrostatic barriers to knot escape. This model allows us to predict knot lifetimes even when those times are not directly accessible by simulations.
more »
« less
- Award ID(s):
- 1955552
- PAR ID:
- 10499252
- Editor(s):
- Yong, Xin
- Publisher / Repository:
- PLOS
- Date Published:
- Journal Name:
- PLOS ONE
- Volume:
- 18
- Issue:
- 6
- ISSN:
- 1932-6203
- Page Range / eLocation ID:
- e0287200
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an “opening up process,” wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.more » « less
-
Herein we report the synthesis of ternary statistical methacrylate copolymers comprising cationic ammonium (amino-ethyl methacrylate: AEMA), carboxylic acid (propanoic acid methacrylate: PAMA) and hydrophobic (ethyl methacrylate: EMA) side chain monomers, to study the functional role of anionic groups on their antimicrobial and hemolytic activities as well as the conformation of polymer chains. The hydrophobic monomer EMA was maintained at 40 mol% in all the polymers, with different percentages of cationic ammonium (AEMA) and anionic carboxylate (PAMA) side chains, resulting in different total net charge for the polymers. The antimicrobial and hemolytic activities of the copolymer were determined by the net charge of +3 or larger, suggesting that there was no distinct effect of the anionic carboxylate groups on the antimicrobial and hemolytic activities of the copolymers. However, the pH titration and atomic molecular dynamics simulations suggest that anionic groups may play a strong role in controlling the polymer conformation. This was achieved via formation of salt bridges between cationic and anionic groups, transiently crosslinking the polymer chain allowing dynamic switching between compact and extended conformations. These results suggest that inclusion of functional groups in general, other than the canonical hydrophobic and cationic groups in antimicrobial agents, may have broader implications in acquiring functional structures required for adequate antimicrobial activity. In order to explain the implications, we propose a molecular model in which formation of intra-chain, transient salt bridges, due to the presence of both anionic and cationic groups along the polymer, may function as “adhesives” which facilitate compact packing of the polymer chain to enable functional group interaction but without rigidly locking down the overall polymer structure, which may adversely affect their functional roles.more » « less
-
Langevin dynamics simulations of double-knotted DNA molecules in a nanochannel reveal that the interactions between the two knots differ with the degree of channel confinement. In relatively wide channels, the two knots can intertwine with each other, forming a persistently intertwined knot. Moreover, the two knots can pass through each other in large channels. In contrast, for small channel sizes, the knots tend to remain separated, and their crossing is inhibited. The change in knot–knot interactions as the channel size decreases is rationalized through an analysis of the magnitude of the transverse fluctuations, which must be large enough to allow one knot to swell to accommodate the intertwined state.more » « less
-
The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length l p to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes – subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes–Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid ( i.e. as l p increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of l p , however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As l p is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1371/journal.pone.0287200
