Statistical mechanics of protein complexed and condensed DNA
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Abstract
In this thesis I treat various biophysical questions arising in the context of complexed /
”protein-packed” DNA and DNA in confined geometries (like in viruses or toroidal DNA
condensates). Using diverse theoretical methods I consider the statistical mechanics as
well as the dynamics of DNA under these conditions.
In the first part of the thesis (chapter 2) I derive for the first time the single molecule
”equation of state”, i.e. the force-extension relation of a looped DNA (Eq. 2.94) by using
the path integral formalism. Generalizing these results I show that the presence of
elastic substructures like loops or deflections caused by anchoring boundary conditions
(e.g. at the AFM tip or the mica substrate)
gives rise to a significant renormalization of
the apparent persistence length as extracted from single molecule experiments (Eqs. 2.39
and 2.98). As I show the experimentally observed apparent persistence length reduction
by a factor of 10 or more is naturally explained by this theory.
In chapter 3 I theoretically consider the thermal motion of nucleosomes along a DNA
template. After an extensive analysis of available experimental data and theoretical
modelling of two possible mechanisms I conclude that the ”corkscrew-motion” mechanism
most consistently explains this biologically important process.
In chapter 4 I demonstrate that DNA-spools (architectures in which DNA circumferentially
winds on a cylindrical surface, or onto itself) show a remarkable ”kinetic
inertness” that protects them from tension-induced disruption on experimentally and
biologically relevant timescales (cf. Fig. 4.1 and Eq. 4.18). I show that the underlying
model establishes a connection between the
seemingly unrelated and previously
unexplained force peaks in single molecule nucleosome and DNA-toroid stretching experiments.
Finally in chapter 5 I show that toroidally confined DNA (found in viruses, DNAcondensates
or sperm chromatin) undergoes a transition to a twisted, highly entangled
state provided that the aspect ratio of the underlying torus crosses a certain critical
value (cf. Eq. 5.6 and the phase diagram in Fig. 5.4). The presented mechanism
could rationalize several experimental mysteries, ranging from entangled and supercoiled
toroids released from virus capsids to the unexpectedly short cholesteric pitch in
the (toroidaly wound) sperm chromatin. I propose that the ”topological encapsulation”
resulting from our model may have some practical implications for the gene-therapeutic
DNA delivery process.