In vivo, DNA forms loops over a broad range of length scales: from several thousand base pairs (bp) down to about 100 bp. In loops shorter than the DNA persistence length (150 bp), thermal fluctuations can be neglected, and the molecule assumes approximately its minimal-energy shape. It is well-known that for a simple isotropic wormlike chain model, the minimal-energy shape of a loop can be derived exactly and is expressed as a combination of inverse elliptic integrals. Here, we construct a simple explicit two-parameter variational solution, referred to as harmonic loop, which reproduces the exact loop energy up to the fourth significant digit . The harmonic-loop solution is easier to handle than the exact one, simplifying the analytical calculation of several quantities. We generalize this solution to a twistable DNA model with anisotropic bending and twist-bend coupling, and show that the loop shape thus derived is in excellent agreement with simulations of two different coarse-grained DNA models. As recently found for DNA minicircles and observed in nucleosomal DNA data, twist-bend coupling induces twist oscillations in bent DNA. Here, we show that twist waves in DNA loops have a modulated amplitude, which is maximal in the middle of the loop and decaying at the loop edges, following the curvature modulation. We, finally, simulate the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations , and perform a normal diffusive motion, whose origin is briefly discussed.
By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100 base pairs (bp) . We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape, that reproduces the exact loop energy up to the fourth significant digit , and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations . They perform a normal diffusive motion, whose origin is briefly discussed.
R
In vivo, DNA forms loops over a broad range of length scales: from several thousand
By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100
R
down to about 100 bp. In loops shorter than the DNA persistence length (150 bp), thermal fluctuations can be neglected, and the molecule assumes approximately its minimal-energy shape. It is well-known that for a simple isotropic wormlike chain model,
. We show that in these loops
R
minimal-energy shape of a loop can be derived exactly and is expressed as a combination of inverse elliptic integrals. Here, we construct a simple explicit two-parameter variational solution, referred to as harmonic loop, which
excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape, that
R
. The harmonic-loop solution is easier to handle than the exact one, simplifying the analytical calculation of several quantities. We generalize this solution to a twistable DNA model with anisotropic bending and twist-bend coupling, and show that the loop shape thus derived is in excellent agreement with simulations of two different
, and is in very good agreement with shapes obtained from
R
DNA models. As recently found for DNA minicircles and observed in nucleosomal DNA data, twist-bend coupling induces twist oscillations in bent DNA. Here, we show that twist waves in DNA loops have a modulated amplitude, which is maximal in the middle of the loop and decaying at the loop edges, following the curvature modulation.
simulations.
R
simulate
analyze
R
, and
. They