Beside receptor-ligand binding mechanisms, folding and aggregation of proteins belong to the biologically most relevant molecular structure formation processes. While the specific binding between receptors and ligands is not necessarily accompanied by global structural changes, protein folding and oligomerization of peptides are typically cooperative conformational transitions [246]. Proteins and their aggregates are comparatively small systems. A typical protein consists of a sequence of some hundred amino acids and aggregates are often formed by only a few peptides. A very prominent example is the extracellular aggregation of the Aβ peptide, which is associated with Alzheimer's disease. Following the amyloid hypothesis, it is believed that these aggregates (which can also take fibrillar forms [247]) are neurotoxic, i.e., they are able to fuse into cell membranes of neurons and create pores that are penetrable to calcium ions. It is known that extracellular Ca2+ ions intruding into a neuron can promote its degeneration [248–250].

In this chapter, we will investigate thermodynamic properties of aggregation transitions of polymers and peptides from different perspectives of statistical analysis.

Pseudophase separation in nucleation processes of polymers

We have already discussed why conformational transitions polymers experience in structure formation processes are not phase transitions in the strict thermodynamic sense. This will be similar for the aggregation of a finite number of finitely long polymers, because surface effects are also not negligible in these cases.