## Equilibrium Thermodynamics of Biopolymers

### professor M. Schulz (Ulm University)

### Abstract

Biopolymers, as proteins and DNA-molecules may be interpreted from a
theoretical point of view as macromolecules with quenched random disorder
along the chain. This idealzed model requires that monomer sequences show
pronounced Markovian behaviour. Furthermore, the thermodynamic behaviour
of compositionally randomized polymer chains is mainly controlled by the
monomer-monomer interaction. In this talk we may distinguish between short
and long range interactions.

In the first section of the present talk we focus on the thermodynamic
properties of linear biopolymers with long and short range interactions
on the basis of a generalized charge model. We demonstrate by application
of a perturbation expansion and a proper subsummation of the leading
terms that such models describe the main properties of biopolymers, for
instance the swelling-collaps transition, very well.
In the second part of this talk we investigate diluted solutions and dense
melts of such biopolymers by numerical Monte Carlo simulations. The
equilibrium structural properties of such systems are characterized by the
mean square end-to-end distance and the static structure factor of the
polymer chains. Both temperature and density determine the structure
(collapse, swelling or screening regime). A description of this behavior
is given using generalized scaling arguments and proven by the numerical
MC--simulations.

Finally, we analyze of the thermodynamic properties of random cross-linked
polymer networks made of phantom chains with compositional disorder. We
start our investigations from an extended Edwards Hamiltonian and end with
the discussion of the free energy and mechanical properties. Using replica
field theory we determine and solve the saddle point equations. The
physically relevant ground state is invariant against translations in the
real space, but it depends strongly on the coupling parameters for
interactions, topology and compositional disorder of the network. We
predict three different thermodynamic states for random copolymer
networks. For two regimes the saddle point shows a rotational symmetry
after elimination of translation effects. Here the network behaves similar
to a homogeneous network. The third regime corresponds to a ground state
with broken replica symmetry similar. Here, the behavior of the random
copolymer network shows similarities to the thermodynamical properties of
spin glasses and the network state is comparable to diluted proteins.