Simple and Analytical Model of RNA Collapse

An analytical model for the free energy change during collapse of an RNA molecule from an extended to a compact conformation is proposed. It considers explicit binding of water and ion molecules to the RNA and the exchange of these molecules with the aqueous solution. Microscopic states of the system are captured on a two-dimensional square lattice and evaluated using contact energies. We compute the free energy as a function of a collapse variable and the number of ions bound to the RNA. The major driving force to the collapse of the RNA chain is the gain in water entropy once expelled from the surface of the RNA molecule illustrated by decomposing the free energy into species contributions and their energy and entropy components. The sensitivity of the conclusions of the model to variations in parameters is computed and appears to be weak.