| Summary: | <p>This thesis was inspired by an interest in the metalloenzymes: profoundly complex catalysts that perform the redox-mediated small molecule conversions that underpin the biosphere. The principal methodology is computational analysis of protein-film voltammetry (PFV), an experimental technique wherein an electro-active protein (such as a metalloenzyme) is chemically linked to an electrode, and subjected to a time-varying potential input, with a corresponding current response from two processes; double-layer capacitance and electron-hopping Faradaic reactions (catalytic processes also generate current, but are beyond the scope of the thesis). It is the latter that is of biological interest — electron-hopping Faradaic current arises from the reduction and oxidation of the metal atoms within the protein. The current generated from PFV experiments has a low Faradaic-to-background ratio and is not readily interpretable — hence the need for computational analysis. By using a model that describes the current response to a potential input as a function of the biochemical reaction parameters (rates and energetics), the aim is to fit experimental voltammetry data. Inferring the values of the parameters, given this experimental data is referred to as “solving the inverse problem”. Additionally, Bayesian statistical analysis methods are used to infer the likely distributions of these inferred parameters, which allows us to understand the degree of confidence we should have in our fits, as well as the degree of correlation between the various parameters. This is a computationally intensive process, requiring many simulations of the experimental current, and is complicated by the low signal-to-noise ratio and the fact that noise processes can obscure useful information. The choice of potential input is key; there are trade-offs between the amount of information that can be obtained about the(bio)chemical system under interrogation, complexity of analysis required, and simulation speed.</p>
<p>In chapter 1, we introduce the research problem, and provide a brief description of each chapter. In chapter 2 we lay out the necessary theory for understanding the thesis, along with a description of our approach to solving the inverse problem. In chapter 3, we detail theoretical work undertaken to validate the simulation and inference procedures described in chapter 2, and explore the impact of some assumptions made when deriving the simulation model. Chapter 4 detailsa quantitative characterisation of a voltammetry technique which we term “Purely Sinusoidal Voltammetry” (PSV). Using data acquired for a model chemical system, we demonstrate that PSV is faster to simulate than more information-rich techniques, while being more sensitive to the key electron-transfer reaction parameters than simpler voltammetry approaches. In chapter 5, we use this technique to infer parameters from data generated by a bacterial cytochrome, and detail the adaptations required when dealing with the lower signal-to-noise ratio inherent to PFV experiments, ultimately suggesting a framework for inferring parameters in this context. Finally, in chapter 6, we show that the methodology developed in chapter 5 can be used to capture the electrochemical impact of mutating key residues of the bacterial cytochrome.</p>
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