Minimal models for proteins and RNA: From folding to function

We present a panoramic view of the utility of coarse-grained (CG) models to study folding and functions of proteins and RNA. Drawing largely on the methods developed in our group over the last twenty years, we describe a number of key applications ranging from folding of proteins with disulfide bonds to functions of molecular machines. After presenting the theoretical basis that justifies the use of CG models, we explore the biophysical basis for the emergence of a finite number of folds from lattice models. The lattice model simulations of approach to the folded state show that non-native interactions are relevant only early in the folding process - a finding that rationalizes the success of structure-based models that emphasize native interactions. Applications of off-lattice $C_{\alpha}$ and models that explicitly consider side chains ($C_{\alpha}$-SCM) to folding of $\beta$-hairpin and effects of macromolecular crowding are briefly discussed. Successful application of a new class of off-lattice model, referred to as the Self-Organized Polymer (SOP), is shown by describing the response of Green Fluorescent Protein (GFP) to mechanical force. The utility of the SOP model is further illustrated by applications that clarify the functions of the chaperonin GroEL and motion of the molecular motor kinesin. We also present two distinct models for RNA, namely, the Three Site Interaction (TIS) model and the SOP model, that probe forced unfolding and force quench refolding of a simple hairpin and {\it Azoarcus} ribozyme. The predictions based on the SOP model show that force-induced unfolding pathways of the ribozyme can be dramatically changed by varying the loading rate. We conclude with a discussion of future prospects for the use of coarse-grained models in addressing problems of outstanding interest in biology.