Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Identification of fucose-α(1-2)-galactose binding proteins in the mammalian brain

Fucose-α(1-2)-galactose (Fucα(1-2)Gal) carbohydrates have been implicated in cognitive functions. However, the underlying molecular mechanisms that govern these processes are not well understood. While significant progress has been made toward identifying glycoconjugates bearing this carbohydrate epitope, a major challenge remains the discovery of interactions mediated by these sugars. Here, we employ the use of multivalent glycopolymers to enable the proteomic identification of weak affinity, low abundant Fucα(1-2)Gal-binding proteins (i.e. lectins) from the brain. End-biotinylated glycopolymers containing photoactivatable crosslinkers were used to capture and enrich potential Fucα(1-2)Gal-specific lectins from rat brain lysates. Candidate lectins were tested for their ability to bind Fucα(1-2)Gal, and the functional significance of the interaction was investigated for one such candidate, SV2a, using a knock-out mouse system. Our results suggest an important role for this glycan-lectin interaction in facilitating synaptic changes necessary for neuronal communication. This study highlights the use of glycopolymer mimetics to discover novel lectins and identify functional interactions between fucosyl carbohydrates and lectins in the brain.

A measurement of inclusive quasi-elastic electron scattering cross sections at high momentum transfer

We have measured inclusive electron-scattering cross sections for targets of ^(4)He, C, Al, Fe, and Au, for kinematics spanning the quasi-elastic peak, with squared, four­ momentum transfers (q^2) between 0.23 and 2.89 (GeV/c)^2. Additional data were measured for Fe with q^2's up to 3.69 (GeV/c)^2 These cross sections were analyzed for the y-scaling behavior expected from a simple, impulse-approximation model, and are found to approach a scaling limit at the highest q^2's. The q^2 approach to scaling is compared with a calculation for infinite nuclear matter, and relationships between the scaling function and nucleon momentum distributions are discussed. Deviations from perfect scaling are used to set limits on possible changes in the size of nucleons inside the nucleus.

Engineering multi-step electron tunneling systems in proteins

Multi-step electron tunneling, or “hopping,” has become a fast-developing research field with studies ranging from theoretical modeling systems, inorganic complexes, to biological systems. In particular, the field is exploring hopping mechanisms in new proteins and protein complexes, as well as further understanding the classical biological hopping systems such as ribonuclease reductase, DNA photolyases, and photosystem II. Despite the plethora of natural systems, only a few biologically engineered systems exist. Engineered hopping systems can provide valuable information on key structural and electronic features, just like other kinds of biological model systems. Also, engineered systems can harness common biologic processes and utilize them for alternative reactions. In this thesis, two new hopping systems are engineered and characterized.

The protein Pseudomonas aeruginosa azurin is used as a building block to create the two new hopping systems. Besides being well studied and amenable to mutation, azurin already has been used to successfully engineer a hopping system. The two hopping systems presented in this thesis have a histidine-attached high potential rhenium 4,7-dimethyl-1,10-phenanthroline tricarbonyl [Re(dmp)(CO)3] + label which, when excited, acts as the initial electron acceptor. The metal donor is the type I copper of the azurin protein. The hopping intermediates are all tryptophan, an amino acid mutated into the azurin at select sites between the photoactive metal label and the protein metal site. One system exhibits an inter-molecular hopping through a protein dimer interface; the other system undergoes intra-molecular multi-hopping utilizing a tryptophan “wire.” The electron transfer reactions are triggered by excitation of the rhenium label and monitored by UV-Visible transient absorption, luminescence decays measurements, and time-resolved Infrared spectroscopy (TRIR). Both systems were structurally characterized by protein X-ray crystallography.

Isolation and characterization of proteins that bind to yeast origins of DNA replication

Yeast chromosomes contain sequences called ARSs which function as origins of replication in vitro and in vivo. We have carried out a systematic deletion analysis of ARS1, allowing us to define three functionally distinct domains, designated A, B, and C. Domain A is a sequence of 11 to 19bp, containing the core consensus element that is required for replication. The core consensus sequence, A/TTTTATPuTTTA/T, is conserved at all ARSs sequenced to date. A fragment containing only element A and 8 flanking nucleotides enables autonomous replication of centromeric plasmids. These plasmids replicate very inefficiently, suggesting that flanking sequences must be important for ARS function. Domain B also provides important sequences needed for efficient replication. Deletion of domain B drastically increases the doubling times of transformants and reduces plasmid stability. Domain B contains a potential consensus sequence conserved at some ARSs which overlaps a region of bent DNA. Mutational analysis suggests this bent DNA may be important for ARS function. Deletion of domain C has only a slight effect on replication of plasmids carrying those deletions.

We have identified a protein called ARS binding factor I (ABF-I) that binds to the HMR-E ARS and ARS1. We have purified this protein to homogeneity using conventional and oligonucleotide affinity chromatography. The protein has an apparent molecular weight of 135kDa and is present at about 700 molecules per diploid cell, based on the yield of purified protein and in situ antibody staining. DNaseI footprinting reveals that ABF-I binds sequence-specifically to an approximately 24bp sequence that overlaps element Bat ARSl. This same protein binds to and protects a similar size region at the HMR-E ARS.

We also find evidence for another ARS binding protein, ABF-III, based on DN asei footprint analysis and gel retardation assays. The protein protects approximately 22bp adjacent to the ABF-I site. There appears to be no interaction between ABF-I and ABF-III despite the proximity of their binding sites.

To address the function of ABF-I in DNA replication, we have cloned the ABF-I gene using rabbit polyclonal anti-sera and murine monoclonal antibodies against ABF-I to screen a λgt11 expression library. Four EcoRI restriction fragments were isolated which encoded proteins that were recognized by both polyclonal and monoclonal antibodies. A gene disruption can now be constructed to determine the in vivo function of ABF-I.

Revealing, illuminating, and modifying proteins in human diseases using noncanonical amino acids

To better understand human diseases, much recent work has focused on proteins to either identify disease targets through proteomics or produce therapeutics via protein engineering. Noncanonical amino acids (ncAAs) are tools for altering the chemical and physical properties of proteins, providing a facile strategy not only to label proteins but also to engineer proteins with novel properties. My thesis research has focused on the development and applications of noncanonical amino acids in identifying, imaging, and engineering proteins for studying human diseases. Chapter 1 introduces the concept of ncAAs and reveals insights to how I chose my thesis projects.

ncAAs have been incorporated to tag and enrich newly synthesized proteins for mass spectrometry through a method termed BONCAT, or bioorthogonal noncanonical amino acid tagging. Chapter 2 describes the investigation of the proteomic response of human breast cancer cells to induced expression of tumor suppressor microRNA miR-126 by combining BONCAT with another proteomic method, SILAC or stable isotope labeling by amino acids in cell culture. This proteomic analysis led to the discovery of a direct target of miR-126, shedding new light on its role in suppressing cancer metastasis.

In addition to mass spectrometry, ncAAs can also be utilized to fluorescently label proteins. Chapter 3 details the synthesis of a set of cell-permeant cyclooctyne probes and demonstration of selective labeling of newly synthesized proteins in live mammalian cells using azidohomoalanine. Similar to live cell imaging, the ability to selectively label a particular cell type within a mixed cell population is important to interrogating many biological systems, such as tumor microenvironments. By taking advantage of the metabolic differences between cancer and normal cells, Chapter 5 discusses efforts to develop selective labeling of cancer cells using a glutamine analogue.

Furthermore, Chapter 4 describes the first demonstration of global replacement at polar amino acid positions and its application in developing an alternative PEGylation strategy for therapeutic proteins. Polar amino acids typically occupy solvent-exposed positions on the protein surface, and incorporation of noncanonical amino acids at these positions should allow easier modification and cause less perturbation compared to replacements at the interior positions of proteins.

Electrochemical and electron transfer investigations of copper proteins

A study of the pH and temperature dependence of the redox potentials of azurins from five species of bacteria has been performed. The variations in the potentials with pH have been interpreted in terms of electrostatic interactions between the copper site and titrating histidine residues, including the effects of substitutions in the amino acid sequences of the proteins on the electrostatic interactions. A comparison of the observed pH dependences with predictions based on histidine pK_a values known for Pseudomonas aeruginosa (Pae), Alcaligenes denitrificans (Ade), and Alcaligenes faecalis (Afa) azurins indicates that the Pae and Ade redox potentials exhibit pH dependences in line with electrostatic arguments, while Afa azurin exhibits more complex behavior. Redox enthalpies and entropies for four of the azurins at low and high pH values have also been obtained. Based on these results in conjuction with the variable pH experiments, it appears that Bordetella bronchiseptica azurin may undergo a more substantial conformational change with pH than has been observed for other species of azurin.

The temperature dependence of the redox potential of bovine erythrocyte superoxide dismutase (SOD) has been determined at pH 7.0, with potassium ferricyanide as the mediator. The following thermodynamic parameters have been obtained (T = 25°C): E°' = 403±5 mV vs. NHE, ΔG°' = -9.31 kcal/mol, ΔH°' = -21.4 kcal/mol, ΔS°' = -40.7 eu, ΔS°'_(rc) = -25.1 eu. It is apparent from these results that ΔH°', rather than ΔS°', is the dominant factor in establishing the high redox potential of SOD. The large negative enthalpy of reduction may also reflect the factors which give SOD its high specificity toward reduction and oxidation by superoxide.

Structural and mechanistic motifs in membrane proteins: the three-dimensional modelling of rhodopsin, band 3, and the nicotinic acetylcholine receptor

Because so little is known about the structure of membrane proteins, an attempt has been made in this work to develop techniques by which to model them in three dimensions. The procedures devised rely heavily upon the availability of several sequences of a given protein. The modelling procedure is composed of two parts. The first identifies transmembrane regions within the protein sequence on the basis of hydrophobicity, β-turn potential, and the presence of certain amino acid types, specifically, proline and basic residues. The second part of the procedure arranges these transmembrane helices within the bilayer based upon the evolutionary conservation of their residues. Conserved residues are oriented toward other helices and variable residues are positioned to face the surrounding lipids. Available structural information concerning the protein's helical arrangement, including the lengths of interhelical loops, is also taken into account. Rhodopsin, band 3, and the nicotinic acetylcholine receptor have all been modelled using this methodology, and mechanisms of action could be proposed based upon the resulting structures.

Specific residues in the rhodopsin and iodopsin sequences were identified, which may regulate the proteins' wavelength selectivities. A hinge-like motion of helices M3, M4, and M5 with respect to the rest of the protein was proposed to result in the activation of transducin, the G-protein associated with rhodopsin. A similar mechanism is also proposed for signal transduction by the muscarinic acetylcholine and β-adrenergic receptors.

The nicotinic acetylcholine receptor was modelled with four trans-membrane helices per subunit and with the five homologous M2 helices forming the cation channel. Putative channel-lining residues were identified and a mechanism of channel-opening based upon the concerted, tangential rotation of the M2 helices was proposed.

Band 3, the anion exchange protein found in the erythrocyte membrane, was modelled with 14 transmembrane helices. In general the pathway of anion transport can be viewed as a channel composed of six helices that contains a single hydrophobic restriction. This hydrophobic region will not allow the passage of charged species, unless they are part of an ion-pair. An arginine residue located near this restriction is proposed to be responsible for anion transport. When ion-paired with a transportable anion it rotates across the barrier and releases the anion on the other side of the membrane. A similar process returns it to its original position. This proposed mechanism, based on the three-dimensional model, can account for the passive, electroneutral, anion exchange observed for band 3. Dianions can be transported through a similar mechanism with the additional participation of a histidine residue. Both residues are located on M10.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

A measurement of the proton elastic form factors for 1 ≤ Q^2 ≤ 3 (GeV/c)^2

We report measurements of the proton form factors, G^p_E and G^p_M, extracted from elastic electron scattering in the range 1 ≤ Q^2 ≤ 3 (GeV/c)^2 with uncertainties of <15% in G^p_E and <3% in G^p_M. The results for G^p_E are somewhat larger than indicated by most theoretical parameterizations. The ratio of Pauli and Dirac form factors, Q^2(F^p_2/F^p_1), is lower in value and demonstrates less Q^2 dependence than these parameterizations have indicated. Comparisons are made to theoretical models, including those based on perturbative QCD, vector-meson dominance, QCD sum rules, and diquark constituents to the proton. A global extraction of the form factors, including previous elastic scattering measurements, is also presented.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

Physical characterization of the rack effect and hydrogen bond networks in blue copper proteins

A summary of previous research is presented that indicates that the purpose of a blue copper protein's fold and hydrogen bond network, aka, the rack effect, enforce a copper(II) geometry around the copper(I) ion in the metal site. In several blue copper proteins, the C-terminal histidine ligand becomes protonated and detaches from the copper in the reduced forms. Mutants of amicyanin from Paracoccus denitrificans were made to alter the hydrogen bond network and quantify the rack effect by pK_a shifts.

The pK_a's of mutant amicyanins have been measured by pH-dependent electrochemistry. P94F and P94A mutations loosen the Northern loop, allowing the reduced copper to adopt a relaxed conformation: the ability to relax drives the reduction potentials up. The measured potentials are 265 (wild type), 380 (P94A), and 415 (P94F) mV vs. NHE. The measured pK_a's are 7.0 (wild type), 6.3 (P94A), and 5.0 (P94F). The additional hydrogen bond to the thiolate in the mutants is indicated by a red-shift in the blue copper absorption and an increase in the parallel hyperfine splitting in the EPR spectrum. This hydrogen bond is invoked as the cause for the increased stability of the C-terminal imidazole.

Melting curves give a measure of the thermal stability of the protein. A thermodynamic intermediate with pH-dependent reversibility is revealed. Comparisons with the electrochemistry and apoamicyanin suggest that the intermediate involves the region of the protein near the metal site. This region is destabilized in the P94F mutant; coupled with the evidence that the imidazole is stabilized under the same conditions confirms an original concept of the rack effect: a high energy configuration is stabilized at a cost to the rest of the protein.

The Get3 ATPase drives unidirectional targeting of tail-anchored membrane proteins

Efficient and accurate localization of membrane proteins is essential to all cells and requires a complex cascade of interactions between protein machineries. This is exemplified in the recently discovered Guided Entry of Tail-anchored protein pathway, in which the central targeting factor Get3 must sequentially interact with three distinct binding partners (Get4, Get1 and Get2) to ensure the targeted delivery of Tail-anchored proteins to the endoplasmic reticulum membrane. To understand the molecular and energetic principles that provide the vectorial driving force of these interactions, we used a quantitative fluorescence approach combined with mechanistic enzymology to monitor the effector interactions of Get3 at each stage of Tail-anchored protein targeting. We show that nucleotide and membrane protein substrate generate a gradient of interaction energies that drive the cyclic and ordered transit of Get3 from Get4 to Get2 and lastly to Get1. These data also define how the Get3/Tail-anchored complex is captured, handed over, and disassembled by the Get1/2 receptor at the membrane, and reveal a novel role for Get4/5 in recycling Get3 from the endoplasmic reticulum membrane at the end of the targeting reaction. These results provide general insights into how complex cascades of protein interactions are coordinated and coupled to energy inputs in biological systems.

Biological electron transfer in copper proteins

Nature has used a variety of protein systems to mediate electron transfer. In this thesis I examine aspects of the control of biological electron transfer by two copper proteins that act as natural electron carriers.

In the first study, I have made a mutation to one of the ligand residues in the azurin blue copper center, methionine 121 changed to a glutamic acid. Studies of intramolecular electron transfer rates from that mutated center to covalently attached ruthenium complexes indicate that the weak axial methionine ligand is important not only for tuning the reduction potential of the blue copper site but also for maintaining the low reorganization energy that is important for fast electron transfer at long distances.

In the second study, I begin to examine the reorganization energy of the purple copper center in the CuA domain of subunit II of cytochrome c oxidase. In this copper center, the unpaired electron is delocalized over the entire binuclear site. Because long-range electron transfer into and out of this center occurs over long distances with very small driving forces, the reorganization energy of the CuA center has been predicted to be extremely low. I describe a strategy for measuring this reorganization energy starting with the construction of a series of mutations introducing surface histidines. These histidines can then be labeled with a series of ruthenium compounds that differ primarily in their reduction potentials. The electron transfer rates to these ruthenium compounds can then be used to determine the reorganization energy of the CuA site.

Computational design of self-assembling proteins and protein-DNA nanowires

Computational protein design (CPD) is a burgeoning field that uses a physical-chemical or knowledge-based scoring function to create protein variants with new or improved properties. This exciting approach has recently been used to generate proteins with entirely new functions, ones that are not observed in naturally occurring proteins. For example, several enzymes were designed to catalyze reactions that are not in the repertoire of any known natural enzyme. In these designs, novel catalytic activity was built de novo (from scratch) into a previously inert protein scaffold. In addition to de novo enzyme design, the computational design of protein-protein interactions can also be used to create novel functionality, such as neutralization of influenza. Our goal here was to design a protein that can self-assemble with DNA into nanowires. We used computational tools to homodimerize a transcription factor that binds a specific sequence of double-stranded DNA. We arranged the protein-protein and protein-DNA binding sites so that the self-assembly could occur in a linear fashion to generate nanowires. Upon mixing our designed protein homodimer with the double-stranded DNA, the molecules immediately self-assembled into nanowires. This nanowire topology was confirmed using atomic force microscopy. Co-crystal structure showed that the nanowire is assembled via the desired interactions. To the best of our knowledge, this is the first example of a protein-DNA self-assembly that does not rely on covalent interactions. We anticipate that this new material will stimulate further interest in the development of advanced biomaterials.