Student Theses and Dissertations

In Search of Generic Properties of Evolved Systems: From Elasticity of Proteins to Structure of Metabolic Networks

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

RU Laboratory

Leibler Laboratory


In many proteins - especially allosteric proteins that couple regulatory state at allosteric sites to function at active sites - structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Structural displacements can be difficult to analyze and interpret. Static structural information, although more limited than dynamical analysis, is much more experimentally accessible. The large quantity of available static protein structural data makes more effective analysis and interpretation of such data a valuable tool to supplement experimental study of protein mechanics. Although underused for protein analysis, strain is the natural quantity for studying local deformations. I calculated strain tensor fields in proteins deformed by ligand binding or thermal fluctuations using X-ray crystallography, NMR, and electron microscopy structure ensembles. Strains - primarily shears - show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. Moreover, other transformations of displacements yield additional insights. I studied divergence and curl of deformations of the transmembrane channel KcsA. In addition, I introduced quantities analogous to bend, splay, and twist deformation energies of nematic liquid crystals. These transformations enable decomposition of displacements into distinct modes of deformation, helping characterize the types of deformation a protein undergoes. I applied these calculations to study the filter and gating regions of KcsA. I identified a continuous path of rotational deformations that physically couples these two regions and, I propose, underlies the allosteric interaction between these regions. Bend, splay, and twist distinguish KcsA gate opening, filter opening, and filter-gate coupling, respectively. I argue that strain - particularly shear - is the most appropriate quantity for analysis of local protein deformations. More generally, physically meaningful representations of deformations such as strain, curl, bend, splay, and twist can make testable predictions and provide insights into protein mechanics, augmenting experimental methods and more fully exploiting available structural data. Separately, I worked to better understand the consequences of environmental fluctuations on evolved systems. Previous work by several groups in addition to my own preliminary investigations, has shown that a variety of interesting effects - including evolution of noise-robust phenotypes and increased speed of evolutionary adaptation in fluctuating environments - can occur as a result of environmental changes. However, these results are model-dependent, resulting in need for a biologically plausible model system. Previous work has employed flux balance analysis to predict the metabolic phenotypes of synthetic genotypes sampled from a genotype space determined by empirical metabolic databases. That work identified intriguing properties of the set of viable genotypes: the viable fraction of genotypes is very small, yet the set is connected and spans the genotype space. Seeking to better understand the organization of the viable set in that model, I investigated the geometry of the viable set. I found that the viable set has a very small effective dimension (approximately 3, in an 8000-dimensional genotype space) and exhibits significant spatial correlations. In contrast, the embedding dimension of the viable set is large (at least 1000-dimensions in cases studied here). While further work to better understand the relationship between the small effective dimension and large embedding dimension is ongoing, I studied random walk dynamics on the viable set to test how its geometry could affect evolutionary dynamics. The drift speed of biased random walks increases monotonically with the bias, suggesting a lack of trapping. Consequently and in contrast to some model systems, evolutionary dynamics in alternating environmental conditions are not faster than dynamics in fixed environments in this metabolic model. Better understanding of the geometry of the viable set in the metabolic genotype space could yield insight into the degree to which these properties were evolutionarily selected or were generic properties of high-dimensional fitness landscapes.


A Thesis Presented to the Faculty of The Rockefeller University in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy

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