Studies in Confined Biopolymers

In this work we analyze the theoretical aspects of a single polymer confined inside a cavity. The problem is of biological relevance since it is known, for instance, that molecules like proteins need an isolated environment in order to quickly and correctly reach their folded native state. The polymer is considered in the Grand Canonical ensemble of its monomeric units, where its average length and the strength of the confinement are both regulated by an external chemical potential. We approach the problem under several different perspectives. We first investigate the “reference system” where only the set of interactions constituting the backbone of the polymer are considered. We then study two different approaches regarding the treatment the interactions between monomers which are distant along the chain. One consists of a diagrammatic expansion based on the Mayer function of the interaction potential. Interestingly the first terms of this expansion have the same patterns of distant monomers interactions, as the secondary structure interactions in RNA, corresponding respectively to molecules without pseudoknots and with pseudoknots. The second approach is a reformulation of the problem based on Gaussian variables, followed by a functional minimization of the resulting partition function. This is a potentially more general approach than the diagrammatic ex-