Polymers in Confined Geometry.pdf
Polymers in Confined Geometry.pdf
Polymers in Confined Geometry.pdf
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Chapter 1<br />
Introduction<br />
<strong>Polymers</strong> are one of the ma<strong>in</strong> constituents of cells. The cytoskeleton is formed by<br />
a set of prote<strong>in</strong> filaments (microtubules, act<strong>in</strong> filaments, <strong>in</strong>termediate filaments).<br />
It provides mechanic stability and a railway network for <strong>in</strong>tracellular transport.<br />
Genetic <strong>in</strong>formation is also stored <strong>in</strong> a macromolecule, deoxyribonucleic acid<br />
(DNA). As the basic ‘cookbook’ of life it provides the recipe for sequenc<strong>in</strong>g all<br />
the other biopolymers.<br />
DNA is not only carrier of genetic <strong>in</strong>formation, but its mechanic properties<br />
(such as bend<strong>in</strong>g and torsional stiffness) are also essential for how this <strong>in</strong>formation<br />
is processed. For example some processes <strong>in</strong> gene expression are regulated by loop<br />
formation and other conformational changes of DNA.<br />
These few examples are supposed to give a flavor of the manifold role biopolymers<br />
play <strong>in</strong> cellular processes (cf. [3, 5, 6, 14]).<br />
Biopolymers differ from synthetic polymers <strong>in</strong> one important aspect. They are<br />
stiff on length scales relevant for the biophysical processes they are <strong>in</strong>volved <strong>in</strong>.<br />
This stiffness is characterized <strong>in</strong> terms of the persistence length which measures<br />
the length scale (along the backbone) over which correlations of the tangents<br />
(describ<strong>in</strong>g the polymer configuration) decay. For DNA the persistence length is<br />
approximately lp ≈ 50 nm. This is much larger than a typical microscopic length<br />
scale of DNA, e.g. the diameter h ≈ 2 nm:<br />
lp ≫ h semi-flexible polymer.<br />
F-Act<strong>in</strong> is even stiffer, with lp ≈ 17 nm and h ≈ 7 nm. This unique feature<br />
gives rise to a multitude of <strong>in</strong>terest<strong>in</strong>g phenomena genu<strong>in</strong>ely different from those<br />
found for their synthetic cous<strong>in</strong>s (such as polyethylene), where lp is comparable<br />
to the microscopic scale h (cf. [17, 31]).<br />
Our focus <strong>in</strong> this thesis will be on biopolymers <strong>in</strong> conf<strong>in</strong>ed geometry. This is<br />
motivated by rapid grow<strong>in</strong>g <strong>in</strong>terest <strong>in</strong> observ<strong>in</strong>g and manipulat<strong>in</strong>g s<strong>in</strong>ge polymer<br />
cha<strong>in</strong>s <strong>in</strong> biotechnological applications us<strong>in</strong>g micro- and nanofluidic devices.<br />
Us<strong>in</strong>g optical tweezers, it is possible to exert small forces on polymers. By<br />
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