polymer adsorption onto the sphere can result in overcharging of the complex, even
in the mean-field description that might have relevance to overcharging of histone
proteins by DNA in nucleosome core particles, as discussed previously [79].
Other scenarios, such as tennis-ball-like [83–85], rosette-like [73, 79], and equatorwrapping [192, 196] structures, are also possible candidates of ordered (Wignercrystal-like) structures that minimize the electrostatic energy (see Figs. 2 and 12).
For all these structures, in the strong adsorption limit, we expect to see nearly neutral
or undercharged complexes within our model. At finite temperatures, the chain
fluctuations are expected to diminish the amount of adsorbed polyelectrolytes.
Inherently, the adsorption of a neutral fluctuating semiflexible polymer onto a spherical surface is a nontrivial problem [197, 198], and the presence of charges further
complicates the behavior of the adsorbed polymer chain. However, we would like
to point out that for uncharged polymers with large persistence lengths 4l p > a,
the optimal conformation obtained by Spakowitz and Wang [197] is similar to the
conformation treated in this section.
6.2.4 Experimental Results: DNA and Nucleosome
Our results on the formation of stable helical and solenoidal structures on cylinders
and spheres in the strong adsorption limit are applicable in a wide range of physical
systems. They include, e.g., the separation of carbon nanotubes by helical sequencespecific wrapping of single-stranded DNA molecules, which has been studied experimentally [199–203], theoretically [200, 204–208], and by computer simulations
[209–211], as well as in helical patterning of charged interfaces [80–82, 212].
Specifically, the discussed wrapping scenario mimics certain properties of
DNA–histone complexes in the nucleosome core particle (NCP), although various
important details are neglected in the present analysis. However, if realistic charge
patterns on the DNA, on the basic histone proteins, and on the highly charged histone
tails are considered, then an exact treatment of the electrostatic interactions of an
NCP becomes a complicated task, which is only likely to be solvable numerically
[213–217]. Moreover, our results can be applied to complexation of DNA with
synthetic colloidal oppositely charged nanoparticles, reminiscent of DNA–histone
complexation in chromatin. For instance, DNA complexed with silica polylysinecoated nanospheres of charge density r % e/nm
2 and with a diameter of 10–100 nm
has been studied recently [192, 196]. DNA was shown to wrap around a nanoparticle
from a few times up to about 40 times, depending on the sphere size and charge
density. For a small number of turns, DNA is wrapped on the sphere equator, where
the curvature is the smallest. The formation of large aggregates of DNA–nanoparticle
complexes with 5–50 spheres per T4-phage DNA has been observed [192, 196]. As
the nanoparticle concentration in solution increases, the aggregate becomes more and
more compact. In the fully compacted state, the ratio between the total charge of the
nanoparticles and the DNA charge depends on the particle size. Aggregates of
small nanoparticles are strongly undercharged by wrapped DNA, whereas for the
largest nanospheres at intermediate ionic strengths a small overcharging of the
aggregates has been detected. Most efficient compaction has been achieved at nearly
46
R.G. Winkler and A.G. Cherstvy
in the mean-field description that might have relevance to overcharging of histone
proteins by DNA in nucleosome core particles, as discussed previously [79].
Other scenarios, such as tennis-ball-like [83–85], rosette-like [73, 79], and equatorwrapping [192, 196] structures, are also possible candidates of ordered (Wignercrystal-like) structures that minimize the electrostatic energy (see Figs. 2 and 12).
For all these structures, in the strong adsorption limit, we expect to see nearly neutral
or undercharged complexes within our model. At finite temperatures, the chain
fluctuations are expected to diminish the amount of adsorbed polyelectrolytes.
Inherently, the adsorption of a neutral fluctuating semiflexible polymer onto a spherical surface is a nontrivial problem [197, 198], and the presence of charges further
complicates the behavior of the adsorbed polymer chain. However, we would like
to point out that for uncharged polymers with large persistence lengths 4l p > a,
the optimal conformation obtained by Spakowitz and Wang [197] is similar to the
conformation treated in this section.
6.2.4 Experimental Results: DNA and Nucleosome
Our results on the formation of stable helical and solenoidal structures on cylinders
and spheres in the strong adsorption limit are applicable in a wide range of physical
systems. They include, e.g., the separation of carbon nanotubes by helical sequencespecific wrapping of single-stranded DNA molecules, which has been studied experimentally [199–203], theoretically [200, 204–208], and by computer simulations
[209–211], as well as in helical patterning of charged interfaces [80–82, 212].
Specifically, the discussed wrapping scenario mimics certain properties of
DNA–histone complexes in the nucleosome core particle (NCP), although various
important details are neglected in the present analysis. However, if realistic charge
patterns on the DNA, on the basic histone proteins, and on the highly charged histone
tails are considered, then an exact treatment of the electrostatic interactions of an
NCP becomes a complicated task, which is only likely to be solvable numerically
[213–217]. Moreover, our results can be applied to complexation of DNA with
synthetic colloidal oppositely charged nanoparticles, reminiscent of DNA–histone
complexation in chromatin. For instance, DNA complexed with silica polylysinecoated nanospheres of charge density r % e/nm
2 and with a diameter of 10–100 nm
has been studied recently [192, 196]. DNA was shown to wrap around a nanoparticle
from a few times up to about 40 times, depending on the sphere size and charge
density. For a small number of turns, DNA is wrapped on the sphere equator, where
the curvature is the smallest. The formation of large aggregates of DNA–nanoparticle
complexes with 5–50 spheres per T4-phage DNA has been observed [192, 196]. As
the nanoparticle concentration in solution increases, the aggregate becomes more and
more compact. In the fully compacted state, the ratio between the total charge of the
nanoparticles and the DNA charge depends on the particle size. Aggregates of
small nanoparticles are strongly undercharged by wrapped DNA, whereas for the
largest nanospheres at intermediate ionic strengths a small overcharging of the
aggregates has been detected. Most efficient compaction has been achieved at nearly
46
R.G. Winkler and A.G. Cherstvy