A Study on How Conformation Entropy of Attached Macromolecules Drives Polymeric Collapse and Protein Folding

The conformation of macromolecules attached to a surface is influenced by both their excluded volume and steric forces. Here, self-avoiding random walk simulations are used to evaluate the occurrence of various conformations as a function of the number of monomeric units to estimate the effect of conformational entropy of a tethered chain. Then, a more realistic scenario is assessed, which can more accurately reproduce the shape of a tethered macromolecule. The simulations presented here confirm that it is more likely for a polymer to undergo a collapse conformation rather than a stretched one, as a collapse conformation can be realized in more different ways. Also, they confirm the “mushroom” shape of polymers close to a surface. From this simple approach, the conformation entropy of a model 100-unit polymer close to a surface is estimated to contribute with over 129 $k_{B}T$ toward its collapse. This conformation entropy is higher than that of typical hydrogen bonds and even barriers that keep proteins folded. As such, entropic collapse of macromolecules plays an important role in realizing the mushroom shape of attached polymers and can be the driving force in protein folding, while the polypeptide chain emerges from the ribosome.