This dissertation consists of three parts. The first part considers the archetypical multiterminal source coding problem with logarithmic loss distortion constraints. A single-letter description of the achievable rate distortion region is given for finite-alphabet sources. In the course of doing so, the rate distortion region for the m-encoder CEO problem is also characterized. Several applications and examples are given, and a variety of related problems are discussed.

The second part of this dissertation considers the combinatorial problem of Coded Cooperative Data Exchange. In this problem, data which is originally distributed in a network is exchanged among nodes until universal recovery is achieved (i.e., all terminals recover all data initially present in the network). This dissertation characterizes the minimum number of exchanges which must take place in order to permit universal recovery. Explicit algorithms and tight concentration results are given for several special cases of interest.

Finally, three new lemmas are provided, each of which is interesting in its own right. Applications to multiterminal information theory are discussed.

Microorganisms like bacteria have evolved over billions of years to survive in diverse environments and have developed unique functions and metabolic pathways as a result. Manipulating and harnessing their abilities has been a hallmark of the biotechnology revolution and has the potential to solve problems in areas as diverse as health, environmental remediation and energy production. With genetic engineering we now have the ability to install in microbes beneficial functionalities and chemical production processes, but have really just scratched the surface of what is possible. Truly disruptive innovations will come from controllably interfacing these microscopic workhorses with non- living systems in an effort that will likely require both genetic engineering and materials science approaches.

It is with this premise that I present my research on a class of synthetic small molecules known as conjugated oligoelectrolytes (COEs). These water-soluble oligomers spontaneously intercalate into biological membranes and in turn modify the ionic and electronic transport properties of this ubiquitous interface in a variety of microorganisms.

COEs have previously been shown to improve the performance of microbial electronic devices for power production and contaminant removal in wastewater. The research presented here demonstrates the use of COEs for the inverse process of powering a microbe, Shewanella, in order to drive metabolic activity, specifically the reduction of fumarate to succinate. A mechanistic investigation of this process utilizing various voltammetry techniques, microscopy, liquid chromatography, and visible spectroscopy reveals possible membrane permeabilization and enzyme excretion, contradicting a previous hypothesis of COEs acting like transmembrane “molecular wires.” In addition, structure-function relationships for COEs are developed through examination of the effects of different molecular features on various biological systems. Using microscopy and electrochemistry, some effects of ionic group type and arrangement on the biological interactions of COEs are revealed. It is determined that cationic charges are necessary for interaction with E. coli and that a terminal end-only arrangement of charges is beneficial for lipid membrane intercalation. Finally through visible spectroscopy and zeta potential measurements it is determined that longer COEs associate in less quantity with E. coli but affect the cell surface charge to a greater degree than do shorter COEs. It is these relationships that will ultimately lead to new biological applications and inform future molecular design of this exciting class of molecules.

Solar energy storage is critical to combatting anthropogenic climate change and transitioning to renewable sources of energy. Billions of years ago, plants evolved the ability to harvest and store energy from the sun in a process initiated by Photosystems I and II, wherein the oxygen evolving complex oxidizes water to produce dioxygen. This heterocubane CaMn4O5 cluster serves as a source of inspiration for the Tilley group’s investigations into the chemistry of water oxidation by cobalt oxo cubanes. Chapter 1 briefly describes the current understanding of the mechanism for water oxidation by the oxygen evolving complex, and the challenges posed to synthetic inorganic chemists by this system. Chapter 2 details the first approach attempted to synthesize new heterometallic cobalt oxo cubanes starting from simple tricobalt precursors. While the primary aim of this study was to find rational synthetic routes to a wide library of MCo3O4 clusters, the electronic structure of the Co3O4 fragment provides insight into the role of the fourth cobalt in the parent cluster. Chapter 3 presents a near complete investigation into the metal-metal exchange reaction between the Co4O4 cubane and MnII/III complexes to give the MnCo3O4 cubane. This study provides mechanistic evidence for a pendant metal intermediate during the exchange process, details reactions with CoIII and CoIV materials, and also reports an array of substituted benzoate and pyridine ligated cobalt oxo cubanes. This manuscript is available publicly on ChemRxiv. Chapter 4 details the synthesis and properties of a vanadium-cobalt oxo cubane through the principles outlined in the metal-metal exchange study. The isostructural vanadium and ruthenium cobalt oxo cubanes allow for interrogation of the role of the tricobalt framework. This chapter continues to describe the oxidative reactivity of the vanadium-cobalt oxo system and attempts to observe the oxidized intermediate spectroscopically with in situ methods. Theory and experiment suggest a more localized hole compared to the all-cobalt system, which may have implications for vanadium-cobalt oxide materials.