Reconstructing Past Depositional and Diagenetic Processes through Quantitative Stratigraphic Analysis of the Martian Sedimentary Rock Record

High-resolution orbital and in situ observations acquired of the Martian surface during the past two decades provide the opportunity to study the rock record of Mars at an unprecedented level of detail. This dissertation consists of four studies whose common goal is to establish new standards for the quantitative analysis of visible and near-infrared data from the surface of Mars. Through the compilation of global image inventories, application of stratigraphic and sedimentologic statistical methods, and use of laboratory analogs, this dissertation provides insight into the history of past depositional and diagenetic processes on Mars. The first study presents a global inventory of stratified deposits observed in images from the High Resolution Image Science Experiment (HiRISE) camera on-board the Mars Reconnaissance Orbiter. This work uses the widespread coverage of high-resolution orbital images to make global-scale observations about the processes controlling sediment transport and deposition on Mars. The next chapter presents a study of bed thickness distributions in Martian sedimentary deposits, showing how statistical methods can be used to establish quantitative criteria for evaluating the depositional history of stratified deposits observed in orbital images. The third study tests the ability of spectral mixing models to obtain quantitative mineral abundances from near-infrared reflectance spectra of clay and sulfate mixtures in the laboratory for application to the analysis of orbital spectra of sedimentary deposits on Mars. The final study employs a statistical analysis of the size, shape, and distribution of nodules observed by the Mars Science Laboratory Curiosity rover team in the Sheepbed mudstone at Yellowknife Bay in Gale crater. This analysis is used to evaluate hypotheses for nodule formation and to gain insight into the diagenetic history of an ancient habitable environment on Mars.

Computational microscopy: turning megapixels into gigapixels

The layout of a typical optical microscope has remained effectively unchanged over the past century. Besides the widespread adoption of digital focal plane arrays, relatively few innovations have helped improve standard imaging with bright-field microscopes. This thesis presents a new microscope imaging method, termed Fourier ptychography, which uses an LED to provide variable sample illumination and post-processing algorithms to recover useful sample information. Examples include increasing the resolution of megapixel-scale images to one gigapixel, measuring quantitative phase, achieving oil-immersion quality resolution without an immersion medium, and recovering complex three dimensional sample structure.

I. The 3.7 Å crystal structure of horse heart ferricytochrome C. II. The application of the Karle-Hauptman tangent formula to protein phasing

I. The 3.7 Å Crystal Structure of Horse Heart Ferricytochrome C.

The crystal structure of horse heart ferricytochrome c has been determined to a resolution of 3.7 Å using the multiple isomorphous replacement technique. Two isomorphous derivatives were used in the analysis, leading to a map with a mean figure of merit of 0.458. The quality of the resulting map was extremely high, even though the derivative data did not appear to be of high quality.

Although it was impossible to fit the known amino acid sequence to the calculated structure in an unambiguous way, many important features of the molecule could still be determined from the 3.7 Å electron density map. Among these was the fact that cytochrome c contains little or no α-helix. The polypeptide chain appears to be wound about the heme group in such a way as to form a loosely packed hydrophobic core in the molecule.

The heme group is located in a cleft on the molecule with one edge exposed to the solvent. The fifth coordinating ligand is His 18 and the sixth coordinating ligand is probably neither His 26 nor His 33.

The high resolution analysis of cytochrome c is now in progress and should be completed within the next year.

II. The Application of the Karle-Hauptman Tangent Formula to Protein Phasing.

The Karle-Hauptman tangent formula has been shown to be applicable to the refinement of previously determined protein phases. Tests were made with both the cytochrome c data from Part I and a theoretical structure based on the myoglobin molecule. The refinement process was found to be highly dependent upon the manner in which the tangent formula was applied. Iterative procedures did not work well, at least at low resolution.

The tangent formula worked very well in selecting the true phase from the two possible phase choices resulting from a single isomorphous replacement phase analysis. The only restriction on this application is that the heavy atoms form a non-centric cluster in the unit cell.

Pages 156 through 284 in this Thesis consist of previously published papers relating to the above two sections. References to these papers can be found on page 155.

Computational Microscopy: Breaking the Limit of Conventional Optics

Computational imaging is flourishing thanks to the recent advancement in array photodetectors and image processing algorithms. This thesis presents Fourier ptychography, which is a computational imaging technique implemented in microscopy to break the limit of conventional optics. With the implementation of Fourier ptychography, the resolution of the imaging system can surpass the diffraction limit of the objective lens's numerical aperture; the quantitative phase information of a sample can be reconstructed from intensity-only measurements; and the aberration of a microscope system can be characterized and computationally corrected. This computational microscopy technique enhances the performance of conventional optical systems and expands the scope of their applications.

A geometric analysis of convex demixing

Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components; and (iii) identifying a binary codeword with impulsive corruptions. This thesis describes and analyzes a convex optimization framework for solving an array of demixing problems.

Our framework includes a random orientation model for the constituent signals that ensures the structures are incoherent. This work introduces a summary parameter, the statistical dimension, that reflects the intrinsic complexity of a signal. The main result indicates that the difficulty of demixing under this random model depends only on the total complexity of the constituent signals involved: demixing succeeds with high probability when the sum of the complexities is less than the ambient dimension; otherwise, it fails with high probability.

The fact that a phase transition between success and failure occurs in demixing is a consequence of a new inequality in conic integral geometry. Roughly speaking, this inequality asserts that a convex cone behaves like a subspace whose dimension is equal to the statistical dimension of the cone. When combined with a geometric optimality condition for demixing, this inequality provides precise quantitative information about the phase transition, including the location and width of the transition region.

Quantitative, Time-Resolved Proteomic Analysis Using Bio-Orthogonal Non-Canonical Amino Acid Tagging

Bio-orthogonal non-canonical amino acid tagging (BONCAT) is an analytical method that allows the selective analysis of the subset of newly synthesized cellular proteins produced in response to a biological stimulus. In BONCAT, cells are treated with the non-canonical amino acid L-azidohomoalanine (Aha), which is utilized in protein synthesis in place of methionine by wild-type translational machinery. Nascent, Aha-labeled proteins are selectively ligated to affinity tags for enrichment and subsequently identified via mass spectrometry. The work presented in this thesis exhibits advancements in and applications of the BONCAT technology that establishes it as an effective tool for analyzing proteome dynamics with time-resolved precision.

Chapter 1 introduces the BONCAT method and serves as an outline for the thesis as a whole. I discuss motivations behind the methodological advancements in Chapter 2 and the biological applications in Chapters 2 and 3.

Chapter 2 presents methodological developments that make BONCAT a proteomic tool capable of, in addition to identifying newly synthesized proteins, accurately quantifying rates of protein synthesis. I demonstrate that this quantitative BONCAT approach can measure proteome-wide patterns of protein synthesis at time scales inaccessible to alternative techniques.

In Chapter 3, I use BONCAT to study the biological function of the small RNA regulator CyaR in Escherichia coli. I correctly identify previously known CyaR targets, and validate several new CyaR targets, expanding the functional roles of the sRNA regulator.

In Chapter 4, I use BONCAT to measure the proteomic profile of the quorum sensing bacterium Vibrio harveyi during the time-dependent transition from individual- to group-behaviors. My analysis reveals new quorum-sensing-regulated proteins with diverse functions, including transcription factors, chemotaxis proteins, transport proteins, and proteins involved in iron homeostasis.

Overall, this work describes how to use BONCAT to perform quantitative, time-resolved proteomic analysis and demonstrates that these measurements can be used to study a broad range of biological processes.