The structural dynamics of proteins and other macromolecules typically serve crucial roles for their respective biological function. While rigid protein structures are used in classic “lock and key” descriptions of enzymology and receptor-ligand interactions, more and more evidence suggest that the majority of molecular interactions occur on the spectrum between induced-fit binding and conformational selection binding. This model of biomolecular interaction requires, to differing degrees, conformation plasticity and dynamics of the protein itself. To characterize the determinants and implications of protein dynamics, there exists no more suited biophysical technique than nuclear magnetic resonance (NMR) spectroscopy. This method is capable of probing the individual atomic nuclei of proteins in a site-specific manner. Furthermore, NMR spectroscopy is unique in being able to access timescales from picoseconds to seconds, providing information on events from bond vibration and libration to protein folding and ligand binding. The breadth of biophysical information accessible by NMR spectroscopy has led to its widespread use in the study of protein dynamics. The work presented herein involves i) the use of NMR for investigation of structure and dynamics in two separate biological systems that demonstrate a high degree of flexibility for folded proteins and ii) the improvement of pulse sequences and methodology for better characterizing picosecond to nanosecond backbone and side-chain dynamics. The organizing principle of this work, which is best exemplified in the structural studies of the piRNA-pathway protein Gametocyte-specific factor 1, is the unmatched capability of NMR spectroscopy to decipher molecular details within dynamic protein systems. First, the molecular structure and RNA-binding properties of gametocyte-specific factor 1 (GTSF1) of the piRNA effector pathway were investigated. A partially disordered protein with two Zn finger domains, the work presented here describes the isolation of a GTSF1 protein construct amendable to study by NMR spectroscopy. Chemical shift assignment of GTSF1 allowed site-specific observation of amide correlations, which established the basis for NMR structure calculation of GTSF1 and the evaluation of binding to candidate RNA sequences, with goal of the identification of an in vivo RNA binding partner for GTSF1. The work presents compelling data that indicate GTSF1 Zn finger 1 specifically binds a motif GGUUC(G/A) RNA, which in this study was found in the T-arm loop of transfer RNA. Zn finger 2 is affected by the interaction with RNA, but the available structural and binding data indicate that the second Zn finger is a more dynamic, breathable entity, supported by cysteine chemical shift and structural differences between the two GTSF1 Zn fingers. Although it’s currently speculative, the function of GTSF1 might first require binding of RNA to the more stable Zn finger 1, which then leaves Zn finger 2 poised for binding to another molecular species. tRNA-derived fragments that include the T-arm TC loop have been recently implicated in silencing of transposable elements in mammalian cells. GTSF1, which was identified in a genetic screen for piRNA-pathway proteins as vitally required for gene silencing, might plausibly act as a sensor of transcription of transposable elements and help initiate Piwi-piRISCs-mediated chromatin modification and heterochromatin formation. Next, NMR spectroscopy is used to investigate protein thermostability in psychrophilic (cold-loving) cytochrome c552. Isolated from the bacterium Colwellia psychrerythraea (Cp), previous work has implicated two conserved Cpcyt c552 methionine residues, which are both conserved across psychrophilic and psychrotolerant cytochromes, as acting in dynamical ligand substitution with a third methionine that is the axial heme ligand. It is proposed that elevated backbone dynamics in these methionine residues and the ability for them swap into the axial ligand position accounts for an uncharacteristically high melting temperature (Tm) compared to meso- and thermophile c-type cytochromes. Progress was made in NMR sample preparation and backbone chemical shift assignment of both redox states of Cpcyt c552, and insight from 1D 1H NMR experiments focused on the heme group bound to Cp cytochrome c552 is discussed. Additionally, chemical shifts are used to predict protein dynamics as a first test of a multiple methionine axial ligand hypothesis. Initial data analysis predicts relatively large measures of Random Coil Index for residues surrounding the native axial heme ligand, and shows the hyperfine shifts localized to the residues surrounding the heme. Future experiments will selectively record methyl group dynamics of methionine residues for elucidation of rate constants of methionine substitution and to determine the structural properties of this minor conformation. Finally, two NMR methodology studies are presented in this thesis: a novel simultaneous-acquisition TROSY pulse sequence for measurement of backbone spin relaxation rates (R1 and {1H}-15N heteronuclear NOE) and a side-chain 2H spin relaxation method for using multifield experimental datasets for better sampling of the spectral density function. Together, these pulse sequences represent significant advancements in NMR measurement of microscopic rate constants and more nuanced detail of protein dynamics.

No description available.

Intracellular protein-protein interactions (PPIs) play a vital role in many biological processes. Although they are viewed as of high biological interest they prove difficult to explore as potential targets for drug discovery. Numerous studies have shown α- helical peptides 'locked' in their respective bioactive structure can greatly increase their performance by increasing their target affinity, resistance to proteolysis as well as facilitating cellular uptake. A striking feature of literature to date is how few studies utilise different stapling techniques when developing inhibitors for PPIs. Current methods generally exploit ruthenium catalysed ring closing metathesis (RCM) or copper catalysed alkyne/azide click (CuAAC) chemistry to generate geometrically constrained peptides. Even though these methods have shown great potential they both share a fundamental limitation as the chemistry can only be employed on small synthetic peptides and cannot be extended to larger proteins. Thiol-ene coupling (TEC) chemistry (Chapter 1) which is often described as a 'click' reaction due to its fast reaction rates, high yields, wide functional group tolerance and insensitivity to ambient oxygen and water has the potential to solve this challenge. Thiol-ene chemistry was investigated as an alternative stapling strategy by employing the naturally occurring amino acid L-cysteine (Cys) as a source of the thiyl radical and L-homoallylglycine (Hag), a non-natural amino acid shown to act as a methionine surrogate in protein synthesis to act as a source of an alkene functionality to form a potentially expressible thioether tether in Chapter 2. However, due to unsatisfactory results from the intramolecular thiol-ene cyclisation at the molar concentrations required for peptide or protein modification, and a promising new lead, the closely related thiol-yne reaction was investigated as an alternative in Chapter 3. Using a small library of peptides (14 mers) derived from α-Synuclein (αSyn), a protein mainly found in the presynaptic terminals in the brain and is believed to be key to the pathological progress of Parkinson's disease, a successful macrocyclisation was achieved between the side chains of cysteine (Cys) and homopropargylglycine (Hpg). Although the vinyl-thioether tether did not confer any helical conformation on the stapled peptides, the results clearly demonstrate a potential route for the development of expressible staples. Electron paramagnetic resonance (EPR) spectroscopy in combination with site-directed spin labelling (SDSL) of biomolecules has become a powerful tool for studying the structure and conformational dynamics of biomolecules. Typically, proteins are modified in a site-specific manner by utilising the side chains of cysteine residues to form disulphide bonds with spin active compounds, however, this strategy has its limitations. In Chapter 3 thiol-ene chemistry was investigated as an alternative biorthogonal method to spin label proteins and peptides. The newly synthesised sulfhydryl bearing nitroxide spin label was found to degrade upon exposure to radical promoting conditions, however, an alternative strategy was explored using more classical thiol-Michael chemistry to spin label dehydroalanine (Dha) modified peptides giving the desired spin labelled complex.

Au Yuen-yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 140-152). / Abstracts in English and Chinese. / Abstract --- p.iii / Acknowledgements --- p.v / Chapter Chapter One: --- General Background and Introduction --- p.1 / Chapter 1 -1 --- Introduction --- p.1 / Chapter 1-2 --- Three-Bond Coupling Constants (3J) --- p.1 / Chapter 1-2-1 --- Development of the Karplus Equation --- p.1 / Chapter 1-2-2 --- Application of3J in the Conformational Analysis of Nucleic Acid --- p.4 / Chapter 1-2-3 --- Problem of Accuracy for3 J Measurement --- p.7 / Chapter 1-3 --- Two-Bond Coupling Constants (2J) --- p.7 / Chapter 1-3-1 --- The Use of the Projection Method --- p.7 / Chapter 1-3-2 --- 2J Coupling Constant Involving Hydrogen Bonds --- p.8 / Chapter 1-4 --- One-Bond Coupling Constants (1J) --- p.10 / Chapter 1-5 --- Conclusion --- p.11 / Chapter Chapter Two: --- Experimental Section / Chapter 2-1 --- Introduction --- p.12 / Chapter 2-2 --- Heteronuclear Multiple-Quantum Coherence (HMQC) Experiment --- p.12 / Chapter 2-3 --- Experimental Section --- p.15 / Chapter 2-3-1 --- Sample Preparation --- p.15 / Chapter 2-3-2 --- NMR Spectroscopy --- p.16 / Chapter Chapter Three: --- Theory of Nuclear Spin-Spin Coupling Constants --- p.18 / Chapter 3-1 --- Introduction --- p.18 / Chapter 3-2 --- Application of Finite Perturbation Theory on Nuclear Spin-Spin Coupling --- p.18 / Chapter 3-3 --- Methodology --- p.22 / Chapter Chapter Four: --- DFT and NMR Study of1JCH Coupling Constants --- p.28 / Chapter 4-1 --- Introduction --- p.28 / Chapter 4-2 --- Nomenclature and Definition of Structural Parametersin DNA and RNA --- p.28 / Chapter 4-2-1 --- "Nomenclature, Symbols and Atomic Numbering Schemes" --- p.28 / Chapter 4-2-2 --- Definition of Torsion Angles and their Rangesin Nucleotides --- p.31 / Chapter 4-2-3 --- Description of the Furanose Ring --- p.31 / Chapter 4-3 --- Results and Discussion --- p.37 / Chapter 4-3-1 --- Basis Set Effect --- p.37 / Chapter 4-3-2 --- Relative Conformational Energy Profiles --- p.37 / Chapter 4-3-3 --- Comparison of the Dependence of 1JCH Coupling Constants on Conformational Changes With and Without the DNA Backbone --- p.40 / Chapter 4-3-4 --- Effect of Backbone 3'- and 5'-Phosphate --- p.42 / Chapter 4-3-5 --- Effect of Glycosidic Torsion Anglex --- p.49 / Chapter 4-3-6 --- Effect of Ring Conformation with Fixed Glycosidic Torsion Anglex --- p.52 / Chapter 4-3-7 --- Effect of Torsion Angle α --- p.52 / Chapter 4-3-8 --- Effect of Torsion Angle β --- p.53 / Chapter 4-3-9 --- Effect of Torsion Angle γ --- p.56 / Chapter 4-3-10 --- Effect of Torsion Angle ε --- p.59 / Chapter 4-3-11 --- Effect of Torsion Angle ζ --- p.61 / Chapter 4-3-12 --- Effect of Base Pairing --- p.65 / Chapter 4-3-13 --- Effect of Base Stacking from the (n-1) and (n+1) Base --- p.65 / Chapter 4-3-14 --- Comparison of Experimental and Theoretical Data --- p.68 / Chapter 4-4 --- Conclusion --- p.74 / Chapter Chapter Five: --- DFT Study of 2JCH and 3JCH Coupling Constants --- p.79 / Chapter 5-1 --- Introduction --- p.79 / Chapter 5-2 --- Results and Discussion on 2JCH Coupling Constants --- p.79 / Chapter 5-2-1 --- Effect of Backbone 3'- and 5'-Phosphate --- p.79 / Chapter 5-2-2 --- Effect of Ring Conformation with Fixed Glycosidic Torsion Anglex --- p.82 / Chapter 5-2-3 --- Effect of Glycosidic Torsion Anglex --- p.87 / Chapter 5-2-4 --- Effect of Torsion Angleγ --- p.87 / Chapter 5-2-5 --- Effect of Torsion Angle ε --- p.90 / Chapter 5-2-6 --- Effect of Base Pairing --- p.90 / Chapter 5-2-7 --- Effect of Base Stacking from the (n-1) and (n+1) Base --- p.90 / Chapter 5-3 --- Results and Discussion on 3JCH Coupling Constants --- p.95 / Chapter 5-3-1 --- Effect of Backbone 3'- and 5'-Phosphate --- p.95 / Chapter 5-3-2 --- Effect of Ring Conformation with Fixed Glycosidic Torsion Anglex --- p.95 / Chapter 5-3-3 --- "Effect of Different Torsion Angles (X,α,β,γ,ε,and ζ)" --- p.100 / Chapter 5-3-4 --- Effect of Base Pairing --- p.100 / Chapter 5-3-5 --- Effect of Base Stacking from the (n-1) and (n+1) Base --- p.105 / Chapter 5-4 --- Conclusion --- p.105 / Chapter Chapter Six: --- Conclusion --- p.111 / Appendix A Product Operator Formalism on HMQC Pulse Scheme --- p.113 / Appendix B Finite Perturbation Theory --- p.115 / Appendix C Supplementary Figures of Chapter Four --- p.118 / Appendix D Some of the NMR Spectra --- p.134 / References --- p.140

Previous studies have reported altered glutamate (Glu) concentrations in the blood and brain of individuals with autism spectrum disorder (ASD) compared to neurotypical controls (NC), but the direction (increased or decreased) of metabolite differences is still unclear. Moreover, the relationship between Glu and both brain function and clinical manifestations of the disorder require further investigation. Within this study, we investigated metabolite concentrations within the dorsal anterior cingulate cortex (dACC), a brain region functionally associated with inhibitory executive control tasks and also part of the salience network. There were 19 participants with ASD and 20 NCs between the ages of 23 and 58 years who participated in this study. A study clinician administered the Autism Diagnostic Observation Schedule (ADOS) to individuals with ASD to further confirm their diagnosis. In addition, all participants in this study completed assessments of general intelligence and attention, which included an inhibitory executive control task. Researchers also acquired in vivo single-voxel proton magnetic resonance spectroscopy (1H-MRS) in the dACC to quantify both Glu and combined Glu and glutamine (Glx) concentrations. We hypothesised that these metabolite concentrations would be altered (decreased or increased) in adult participants with ASD compared to NCs and would correlate with inhibitory performance and ASD severity in individuals with ASD. Participants also underwent a resting-state functional magnetic resonance imaging (fMRI) scan to assess the relationship between functional connectivity and Glu and Glx concentrations. We also hypothesised that there would be an altered relationship between local Glu and Glx concentrations and seed-based functional connectivity in adults with ASD compared to NCs. There were no significant group differences in Glu or Glx concentrations between individuals with ASD and NCs. Furthermore, we did not find any relationship between metabolite concentrations and either inhibitory performance or clinical symptoms of the disorder. This evidence suggests that increased or decreased Glu and Glx concentrations were not a core marker of altered brain function in the dACC in this group of adult individuals with ASD. When individuals taking psychotropic medications were excluded from the analysis, there was a significant interaction between age and group for Glx concentrations. This evidence weakly suggests disease-specific variations in Glx concentrations over the lifespan of an individual with ASD. Nevertheless, this result did not survive correction for multiple comparisons and requires further replication. In our final experiment, we reported that Glu concentrations were negatively correlated with right and left dACC seed-based resting-state functional connectivity to the left medial temporal lobe only in individuals with ASD. We also reported an interaction between groups in the association between Glx concentrations and both left and right dACC functional connectivity to other salience network regions including the insular cortex. This evidence suggests that local Glu and Glx concentrations were incongruent with long-distance functional connectivity in individuals with ASD. This analysis was largely exploratory, but further investigation and replication of these relationships may further explain the pathophysiology of the disorder as well as provide a useful marker for therapeutic intervention.

Lai, Kin Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 92-97). / Abstracts in English and Chinese. / Title Page --- p.i / Thesis Committee --- p.ii / Abstract (In English) --- p.iv / Abstract (In Chinese) --- p.v / Acknowledgement --- p.vi / List of Figures --- p.xii / List of Tables --- p.xiv / List of Symbols and Abbreviations --- p.xvi / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Chemical Shift Predictions of Nucleic Acids --- p.1 / Chapter 1.1.1 --- Chemical Shift --- p.1 / Chapter 1.1.2 --- Chemical Shift Prediction of Double Helical DNA and RNA --- p.1 / Chapter 1.1.3 --- Chemical Shift Prediction of Random Coil DNA --- p.2 / Chapter 1.1.4 --- Applications of Nucleic Acid Chemical Shift Prediction --- p.4 / Chapter 1.2 --- General Review of DNA Structure --- p.4 / Chapter 1.2.1 --- Structure and Nomenclature of Nucleotide --- p.4 / Chapter 1.2.2 --- Structure of Polynucleotide --- p.5 / Chapter 1.2.3 --- Sugar Conformation in Nucleotide --- p.5 / Chapter 1.2.4 --- Double Helical DNA Conformation --- p.7 / Chapter 1.3 --- A.A Mismatches in DNA Duplexes --- p.8 / Chapter 1.3.1 --- Mismatches in DNA Duplexes --- p.8 / Chapter 1.3.2 --- Biological Significance of A． A Mismatches --- p.9 / Chapter 1.4 --- Purpose of the Work --- p.9 / Chapter 2 --- Materials and Method --- p.10 / Chapter 2.1 --- Overview of the Proposed Prediction Method --- p.10 / Chapter 2.1.1 --- Nearest Neighbor Model --- p.10 / Chapter 2.1.2 --- Base Pair Replacement Approach --- p.10 / Chapter 2.2 --- Sample Design --- p.11 / Chapter 2.2.1 --- Reference Sequences for Obtaining Triplet Values and Correction Factors --- p.11 / Chapter 2.2.2 --- Sequences for Verifying the Base Pair Replacement Approach --- p.12 / Chapter 2.2.3 --- Sequences for Testing Chemical Shift Prediction Accuracy --- p.12 / Chapter 2.3 --- Sample Preparation --- p.13 / Chapter 2.4 --- NMR Experiments --- p.14 / Chapter 2.4.1 --- Non-labile Proton Resonance Assignment --- p.14 / Chapter 2.4.2 --- Labile Proton Resonance Assignment --- p.16 / Chapter 2.5 --- Validating the Assumption in Reference Hairpin Model Samples --- p.17 / Chapter 3 --- Establishment of Proton Chemical Shift Prediction method of A.A Mismatches in B-DNA Duplexes --- p.18 / Chapter 3.1 --- Resonance Assignment --- p.18 / Chapter 3.1.1 --- Non-labile Protons --- p.18 / Chapter 3.1.2 --- Labile Protons --- p.20 / Chapter 3.2 --- Validating the Assumption in Reference Hairpin Model Samples --- p.21 / Chapter 3.3 --- Extraction of A.A Mismatch Triplet Chemical Shift Values --- p.22 / Chapter 3.4 --- Calculation of the 5´ة- and 3´ة-Correction Factors --- p.24 / Chapter 3.5 --- Chemical Shift Prediction Using Triplet Values and Correction Factors Extracted from Top Strands of refA.A(XAY) and refA．T(XAY) --- p.27 / Chapter 3.6 --- Chemical Shift Prediction Using Triplet Values and Correction Factors Extracted from Bottom Strands of refA.A(XAY) and refA．T(XAY) --- p.28 / Chapter 4 --- Testing of Proton Chemical Shift Prediction of A.A Mismatches in B- DNA --- p.29 / Chapter 4.1 --- Prediction Result Using Triplet Values and Correction Factors Extracted from the Top Strands of refA.A(XAY) and refA.T(XAY) --- p.29 / Chapter 4.2 --- Prediction Result Using Triplet Values and Correction Factors Extracted from Bottom Strands of refA.A(XAY) and refAT(XAY) --- p.30 / Chapter 4.3 --- Applicability of the Base Pair Replacement Approach --- p.31 / Chapter 4.3.1 --- Chemical Shifts and 3JH1´ةH2´ة of refT.A(XTY) Sequences --- p.31 / Chapter 4.3.2 --- Correction factors Extracted from the Top Strands of refA.A(XAY) and refT.A(XTY) --- p.31 / Chapter 4.3.3 --- Prediction Result Using Correction Factors Extracted from the Top Strands of refA.A(XAY) and refT.A(XTY) --- p.33 / Chapter 5 --- Conclusion --- p.35 / Appendix I NOE Sequential Assignment of refA.T(XAY) - (A) Aromatic Protons at 25 °C; (B) Labile Protons at 25 °C --- p.36 / Appendix II NOE Sequential Assignment of refA.A(XAY) - (A) Aromatic Protons at 25 °C; (B) Labile Protons at 5 °C --- p.40 / Appendix III H1'-H2'/H2´ح region of DQF-COSY Spectra of refA.T(XAY) at 25 °C --- p.44 / Appendix IV H1'- H2'/H2´ح region of DQF-COSY Spectra of refA.A(XAY) at 25 °C --- p.46 / Appendix V H3' region of HSQC Spectra of refA T(XAY) at 25 °C --- p.48 / Appendix VI H3' region of 1H-31̐ư HSQC Spectra of refA.A(XAY) at 25 °C --- p.50 / Appendix VII 3JH1'h2'1H and 31P Chemical Shifts of refA T(XAY) --- p.52 / Appendix VIII 3JH1'H2'and 31P Chemical Shifts of refA.A(XTY) --- p.60 / Appendix IX NOE Sequential Assignment of refT .A(XTY) - (A) Aromatic Protons at 25 °C; (B) Labile Protons at 25 °C --- p.68 / Appendix X H1'-H2'/H2''region of DQF-COSY Spectra of refT.A(XTY) --- p.72 / Appendix XI H3'region of H-31P HSQC Spectra of refT.A(XTY) --- p.74 / Appendix XII 3JH1'H2'1H and 31P Chemical Shifts of refT.A(XTY) --- p.76 / Appendix XIII Chemical Shifts of Testing Sequences --- p.84 / Reference --- p.92

The purpose of this thesis was two fold: (i) The synthesis and characterization of SF5 containing dienes. (ii) The characterization of hydro/fluorocarbon compounds containing SF5/S02F groups via their 13C NMR spectra. A new SF5CH2CHBrCH2CF=CF2 was prepared and characterized as a precursor to new dielectric polymers. This new adduct was made from the reaction of pentafluorothio bromide with l,l,2-trifluoro-1,4-pentadiene. A SF5-diene was prepared from the reaction of pentafluorothio chloride with acetylene. This reaction involves a radical addition mechanism. The SF5 group is bonded to the carbon atom carrying the most hydrogens. SF5 - dienes are capable of undergoing different reactions, such as polymerization. Fluorocarbon sulfonyl fluorides (RS02F), which have been synthesized in our lab, were characterized by their 13C NMR spectra. The 13C NMR data of these sulfonyl fluorides show chemical shift values for the methyl and methylene groups next to a fluoroalkyl sulfonyl fluoride group in the 52.8-65.7 ppm range. The spectra showed that the inductive effect of electronegative substituents has a major influence on the 1Jc-F and 1Jc-H coupling. Infrared, 1H, 19F and 13C nuclear magnetic resonance and mass spectra are presented to support the assigned structure for the new compounds, SF5CH=CHCH=CHC1 and SF5CH2CHBrCH2CF=CF2.

The behavior of surfactants in solution has been and still is of scientific, technological, and industrial interest. The micelle forming compounds sodium N( octyloxycarbonyl)sarcosinate (NaOcSarc), and sodium N-(decyloxycarbonyl)sarcosinate (NaDecSarc) show in aqueous solution two lH NMR N-methyl peaks arising from a possible cis- or trans-conformation. The relative population of the N-methyl peaks depends mostly on the concentration of surfactant indicating micelle formation. Upon heating the two peaks start to coalesce and finally appear as one single peak . The temperature range in which this phenomenon occurs is from 25°C to 65°C. The primary interest of this study was to determine the activation parameters of rotation about the carbonyl-nitrogen (C-N) bond. Dynamic nuclear magnetic resonance spectroscopy was employed to approach this problem. A complete bandshape analysis was performed in order to calculate the free energy (G++), enthalpy (H++), and entropy (S++) of activation. The effect of a different counter ion (Li+) and sodium chloride salt addition were tested for possible changes of the activation parameters. Studies in nonaqeous solvents were conducted with the free acid form of the mentioned carbarnates. Dimethylsulfoxide and chloroform were chosen as organic solvents for these particular experiments. The critical micellar concentrations of all surfactants were determined, and the assignment of the individual N-methyl peaks to the correspondend conformation could be unambiguously shown by a two dimensional NMR experiment. The cmc's show strong salt dependence. The effect of a lithium as an alternative counter ion has a less drastic effect. Micellization seems not to occur in the free acid cases. Interestingly, the surfactants show stronger salt dependence than micellization dependence upon the activation parameters, indicating that solvent exposure occurs at the C-N partial double bond and considerable deformation of the ideal spherical shape.

[by] M.W.P. Strandberg ... [et al.]. / "May 10, 1955." "Reprinted from the Review of scientific instruments, vol. 27, no. 8, 596-605, August, 1956." / Includes bibliographical references. / Army Signal Corps Contract No. DA36-039 sc-64637, Project 102B. Dept. of the Army Project No. 3-99-10-022.

C.F. Davis, Jr., and M.W.P. Strandberg. / "December 9, 1955"--Cover. "Reprinted from The Physical review, vol. 105, no. 2, 447-455, January 15, 1957." / Includes bibliographical references. / Army Signal Corps Contract DA36-039 SC-64637 Project 102B Dept. of the Army Project 3-99-10-022