Figure 1.
The distribution of kinetic energy of a DNA molecule of length
µm at thermal equilibrium is plotted as a function of the dimensionless kinetic energy
for both global (left panel) and local (right panel) thermostats. The DNA molecule is composed of
rigid cylinders of radius
and
. The other parameters of the simulation are given in Table 1. According to Eq. (33) the number of degrees of freedom is
with
the number of non-redundant holonomic constraints (3 per ball-and socket joint, hence
). The factor
ensures the normalization of
(
is the Euler Gamma function).
Figure 2.
Global thermostat efficiency test.
Complementary autocorrelation function of the end-to-end distance of a DNA molecule simulated with the global Langevin thermostat (black) compared with the same function simulated with the local Langevin thermostat (red).
is the dimensionless lag-time with
the thermostat coupling frequency. The DNA molecule is composed of
rigid cylinders of radius
and
. The other parameters of the simulation are given in Table 1. Cylinders are connected by ball-and-socket joints. The chain ends are free to diffuse here.
Table 1.
Main set of parameters used for the DNA model and for the numerical simulations.
Figure 3.
Comparison to force-extension curves.
Red circles: dimensionless stretching force as a function of the mean relative extension
. Here the radius of the cylinders is
corresponding to the
mmol monovalent salt buffer used in [1]. The other parameters of the simulation are given in Table 1. For comparison, the black solid line reproduces the analytical Worm-Like-Chain force-extension approximation formula [35]. Black triangles correspond to a numerical fit of the exact Worm-Like-Chain model [34] with the same persistence length
. Blue crosses: we also show simulations in the limit case
, with no torsional rigidity (
) and no collisions, and compare it to the theoretical force-extension curve of a Freely-Jointed-Chain (FJC, blue solid line). The statistical error bars on the simulation points are all smaller than the symbol size.
Figure 4.
Comparison to experimental extension-rotation curves.
Mean relative extension as a function of the imposed overtwist
for different stretching forces
in the range of
pN. We superimpose on to the simulation results (symbols) the experimental results from [32] (lines). The statistical error bars on the simulation points are smaller than the symbol size.
Figure 5.
Twisting torque as a function of the average overtwist
for stretching forces
,
and
pN. Symbols are the simulation results. Horizontal lines show the values of the critical torques estimated from the experimental results at the corresponding stretching forces [32]. Oblique black dotted line: experimental results in the pure extended state (low
). Oblique blue dotted line: asymptotic behavior of the twisting torque as a function of the simulated average overtwist in the pure plectonemic state (high
):
with
and
;
is the pitch of the DNA double helix.
Figure 6.
Buckling instability with stretching force of pN and six different torques
. (Blue) DNA relative extension. (Red) DNA overtwist. DNA relative extension and overtwist are monitored as a function of the number of simulation steps. All these recordings have been obtained after thermal equilibrium has been reached.