A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity. Statement for broader audience We present a simple geometrical model of a chain, which captures the essential features of globular proteins, and explore its consequences. Our model marries the ideas of Kepler, of objects touching each other, and Pauling, of hydrogen bonds providing scaffolding for helices and sheets. We suggest a poking potential for a chain, whose deployment yields the correct structures of both helices and sheets, while promoting the assembly of the building blocks into the tertiary structure.