Energy and topology of heteropolymers

Abstract

The properties of biological polymers are controlled by two fundamental aspects: the energetic interactions, and the topological properties due to the fact that they are chains of connected monomers. In this thesis I study the interplay of topological and energetic properties in heteropolymers. We first study the problem of aggregation of polymers in solution. We find that aggregation is slowed by a transient topological force that exists on time scales shorter than the reptation time. We then study the translocation of a polymer through a membrane. Our key finding is that the dynamics of translocation occur on the same time scale as diffusion, and are affected only weakly by the entropic barrier created by the hole. Next we survey the energetics of random sequence heteropolymers, searching for "typical" properties of a sequence using lattice models. By enumerating the states and energies of compact 18, 27, and 36mers on a 3-d square lattice with an ensemble of random sequences, we test the validity of the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is a valid approximation at the length scale of real proteins. We then examine the validity of the Random Energy Model for these same lattice heteropolymers, through an analysis of the density of states. We see that the shape of the density of states is dependent on the sequence, and that this dependence is stronger for certain types of interactions between monomers.

(cont.) More generally, the validity of the random energy model depends strongly on the monomer-monomer interaction matrix. Finally, we consider a system in which the energy and topology of polymers can be quantified together more explicitly - a heteropolymer gel. We derive a theory for the affinity of heteropolymer gels for target molecules placed in solution with them, based on the the composition of the gel and solvent, and predict the composition of a gel which will switch from single-point to multi-point adsorption of target molecules as it undergoes its volume phase transition.