This chapter discusses potential and free energy surfaces for molecules of biological interest, ranging from small peptides to proteins. Computer simulations and protein structure prediction are described in Section 9.1 and Section 9.2, respectively. Some theoretical aspects of protein folding are discussed in Section 9.3, and an introduction to the random energy model and the principle of minimal frustration is provided in Section 9.4. Two-dimensional free energy surfaces are considered in Section 9.5, with examples ranging from lattice and off-lattice bead representations to results obtained from biased sampling (Section 6.5.1) of all-atom models with explicit solvent.

Lattice models generally take a coarse-grained view of protein structure, as well as restricting the configuration space to a grid. The potential energy surface is also discretised: the catchment basins and transition states of a continuous PES are absent. These features are recovered in continuum bead models, where each amino acid is still represented by a single centre, but the configuration space is not restricted to a grid. One such model is discussed in detail in Section 9.6. Disconnectivity graphs for all-atom representations of two small molecules, IAN and NATMA, are analysed in Section 9.7 and Section 9.8, and both free energy and potential energy surfaces are considered for polyalanine peptides in Section 9.9.

While free energy surfaces have been calculated for all-atom protein representations, including explicit solvent, detailed analysis of potential energy surfaces has usually focused on smaller systems, particularly on the formation of elements of secondary structure.