Taming the Molecular Dance: Harnessing Statistical Mechanics to Quantitatively Characterize Allosteric Systems

Citation

Einav, Tal (2019) Taming the Molecular Dance: Harnessing Statistical Mechanics to Quantitatively Characterize Allosteric Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/S4CV-T162. https://resolver.caltech.edu/CaltechTHESIS:06082019-034706928

Abstract

The pace of biological research continues to grow at a staggering pace as high-throughput experimental techniques rapidly increase our ability to sequence DNA, quantify cell behavior, and image molecules of all types within the cellular milieu. Given this surge in experimental prowess, the time is ripe to examine how well our conceptual cartoons of biological phenomena can not only recapitulate the data but also successfully predict the outcomes of future experiments.

One of the fundamental challenges in biology is that the space of possible molecules is overwhelmingly large. The number of variants of a moderately-sized protein (20^300) is larger than the number of atoms in the universe, as is the space of possible bacterial genomes, protein interaction networks, and effector functions; progress in any of these fronts requires a theory-experiment dialogue that can extrapolate our small drop of data to explain large swaths of parameter space.

My thesis strives towards this goal by analyzing a number of central molecular players in biology including enzymes (biological catalysts that accelerate chemical reactions), transcription factors (proteins that bind to DNA and regulate its expression), and ion channels (signaling proteins that regulate ion transport). I develop a quantitative description in each context by harnessing the statistical mechanical Monod-Wyman-Changeux model of allostery which coarse-grains the behavior of a multi-state system into two effective states, demonstrating that these seemingly diverse molecules are all governed by the same fundamental equation.

Writ large, there are two overarching goals encompassed by these projects. The first is to translate our biological knowledge into concrete physical models, enabling us to quantitatively describe how the key molecular components in each system interact to carry out their function. The second goal is to analyze how mutations can be mapped into the fundamental biophysical parameters governing each system. In my opinion, predicting the effects of mutations remains one of the great unsolved problems in biology, and it has been incredibly exciting to make progress on this front.

Looking back at my amazing graduate school experience, one of the most surprising aspects of my PhD was how closely each of my projects revolved around experiments. I entered graduate school as a theoretical physicist expecting to work on esoteric mathematical models, yet the direct connection with data provided a window into the exhilarating world of biology. While I have never physically manipulated these biological systems in the lab, my models allow me to push and prod and examine their behavior from the most mundane to the utterly extreme limits. Through modeling, I test our assumptions of how these systems work and tease out insights into their underlying biophysical mechanism. Most importantly, these models enable me to harness the incredible wealth of hard-won data to weave a few more threads of understanding into our tapestry of how these incredible living systems operate.

Thesis Files