RNA Hybridization and Protein Multimerization In and Out of Equilibrium

Abstract

Biological macromolecules such as proteins and nucleic acids often exert their roles in the cell through binding to one another and creating complex multimers. Modeling these self-assembly processes is an important goal towards both achieving a greater understanding of physiological systems and their pathogenic misregulation, as well as engineering biology-inspired synthetic systems. Such models typically employ the language of statistical physics, a framework which has been quite successful in quantitatively explaining diverse sets of biological phenomena. This success is in many ways surprising: statistical physics almost entirely describes equilibrium phenomena, while biology is--by definition--far from equilibrium. Here, I explore this tension, concentrating on biological self-assembly. How can we use our equilibrium understanding of self-assembly processes to understand the dynamical systems inherent to biology and to engineer new dynamic phenomena?

I focus on two classes of biological self-assembly: the binding of proteins to one another to form protein complexes, and the structures and hybridization properties of nucleic acids. First, I address open questions in the equilibrium descriptions of each system. For proteins, I describe how we can quantitatively predict the equilibrium yields of protein complexes comprised of non-identical building blocks. For nucleic acids, I demonstrate that: 1) we can enumerate the entire equilibrium landscape of secondary structures of small sets of short nucleic acids; and 2) we develop a minimal polymer physics-based model to predict complex structures known as pseudoknots which has been a long-standing challenge. I then build on these equilibrium models to address non-equilibrium phenomena in both systems. I show that we can expand upon the success of the de novo design of protein interactions to construct a synthetic protein-based oscillator that can operate independently of transcription and translation processes. Finally, I describe how the non-equilibrium aspect of nucleic-acid hybridization can allow us to probe the structures of large RNA molecules which have been difficult to model, and discuss recent work towards understanding the phase transition underlying RNA aggregation in repeat expansion disorders.