Structural Characterizations of the Dimeric Anti-HIV Antibody 2G12 and the HIV-2 Envelope Glycoprotein

More than thirty years after the discovery that Human Immunodeficiency Virus (HIV) was the causative agent of Acquired Immunodeficiency Syndrome (AIDS), the disease remains pandemic as long as no effective universal vaccine is found. Over 34 million individuals in the world are infected with the virus, and the vast majority of them have no access to the antiretroviral therapies that have largely reduced HIV to a chronic disease in the developed world. The first chapter of this thesis introduces the history of the virus. The key to the infectious mechanism of the virus lies in its envelope glycoprotein (Env), a trimeric spike on the viral surface that utilizes host T cell receptors for entry. Though HIV-1 Env is immunogenic, most infected patients do not mount an effective neutralizing antibody response against it. Broadly-neutralizing anti-Env antibodies (bNAbs) present in the serum of a minority of infected individuals are usually sufficient to prevent the progression to full blown AIDS. Thus, the molecular details of these bNAbs as well as the antibody-antigen interface are of prime interest for structural studies, as insight gained would contribute to the design of a more effective immunogen and potential vaccine candidate. The second chapter of this thesis describes the low-resolution crystal structure of one such antibody, 2G12 dimer, which targets a high mannose epitope on the surface of Env. Patients infected with HIV-2, a related virus with ~35% sequence identity in the Env region, can generally mount a robust antibody response sufficient for viral control for reasons still unknown. The final two chapters of this thesis focus on the first reported structural studies of HIV-2 Env, the molecular details of which may inform HIV-1 therapy and immunogen design.

The conjugate representation of signal envelope

The problem of the representation of signal envelope is treated, motivated by the classical Hilbert representation in which the envelope is represented in terms of the received signal and its Hilbert transform. It is shown that the Hilbert representation is the proper one if the received signal is strictly bandlimited but that some other filter is more appropriate in the bandunlimited case. A specific alternative filter, the conjugate filter, is proposed and the overall envelope estimation error is evaluated to show that for a specific received signal power spectral density the proposed filter yields a lower envelope error than the Hilbert filter.

I. Exact solution of some nonlinear evolution equations. II. The similarity solution for the Korteweg-De Vries equation and the related Painleve Transcendent

In Part I, a method for finding solutions of certain diffusive dispersive nonlinear evolution equations is introduced. The method consists of a straightforward iteration procedure, applied to the equation as it stands (in most cases), which can be carried out to all terms, followed by a summation of the resulting infinite series, sometimes directly and other times in terms of traces of inverses of operators in an appropriate space.

We first illustrate our method with Burgers' and Thomas' equations, and show how it quickly leads to the Cole-Hopft transformation, which is known to linearize these equations.

We also apply this method to the Korteweg and de Vries, nonlinear (cubic) Schrödinger, Sine-Gordon, modified KdV and Boussinesq equations. In all these cases the multisoliton solutions are easily obtained and new expressions for some of them follow. More generally we show that the Marcenko integral equations, together with the inverse problem that originates them, follow naturally from our expressions.

Only solutions that are small in some sense (i.e., they tend to zero as the independent variable goes to ∞) are covered by our methods. However, by the study of the effect of writing the initial iterate u_1 = u_(1)(x,t) as a sum u_1 = ^∼/u_1 + ^≈/u_1 when we know the solution which results if u_1 = ^∼/u_1, we are led to expressions that describe the interaction of two arbitrary solutions, only one of which is small. This should not be confused with Backlund transformations and is more in the direction of performing the inverse scattering over an arbitrary “base” solution. Thus we are able to write expressions for the interaction of a cnoidal wave with a multisoliton in the case of the KdV equation; these expressions are somewhat different from the ones obtained by Wahlquist (1976). Similarly, we find multi-dark-pulse solutions and solutions describing the interaction of envelope-solitons with a uniform wave train in the case of the Schrodinger equation.

Other equations tractable by our method are presented. These include the following equations: Self-induced transparency, reduced Maxwell-Bloch, and a two-dimensional nonlinear Schrodinger. Higher order and matrix-valued equations with nonscalar dispersion functions are also presented.

In Part II, the second Painleve transcendent is treated in conjunction with the similarity solutions of the Korteweg-de Vries equat ion and the modified Korteweg-de Vries equation.

Terahertz time domain spectroscopy of amino acids and sugars

A time-domain spectrometer for use in the terahertz (THz) spectral range was designed and constructed. Due to there being few existing methods of generating and detecting THz radiation, the spectrometer is expected to have vast applications to solid, liquid, and gas phase samples. In particular, knowledge of complex organic chemistry and chemical abundances in the interstellar medium (ISM) can be obtained when compared to astronomical data. The THz spectral region is of particular interest due to reduced line density when compared to the millimeter wave spectrum, the existence of high resolution observatories, and potentially strong transitions resulting from the lowest-lying vibrational modes of large molecules.

The heart of the THz time-domain spectrometer (THz-TDS) is the ultrafast laser. Due to the femtosecond duration of ultrafast laser pulses and an energy-time uncertainty relationship, the pulses typically have a several-THz bandwidth. By various means of optical rectification, the optical pulse carrier envelope shape, i.e. intensity-time profile, can be transferred to the phase of the resulting THz pulse. As a consequence, optical pump-THz probe spectroscopy is readily achieved, as was demonstrated in studies of dye-sensitized TiO₂, as discussed in chapter 4. Detection of the terahertz radiation is commonly based on electro-optic sampling and provides full phase information. This allows for accurate determination of both the real and imaginary index of refraction, the so-called optical constants, without additional analysis. A suite of amino acids and sugars, all of which have been found in meteorites, were studied in crystalline form embedded in a polyethylene matrix. As the temperature was varied between 10 and 310 K, various strong vibrational modes were found to shift in spectral intensity and frequency. Such modes can be attributed to intramolecular, intermolecular, or phonon modes, or to some combination of the three.

Nonstationary response of structures and its application to earthquake engineering

This thesis presents a simplified state-variable method to solve for the nonstationary response of linear MDOF systems subjected to a modulated stationary excitation in both time and frequency domains. The resulting covariance matrix and evolutionary spectral density matrix of the response may be expressed as a product of a constant system matrix and a time-dependent matrix, the latter can be explicitly evaluated for most envelopes currently prevailing in engineering. The stationary correlation matrix of the response may be found by taking the limit of the covariance response when a unit step envelope is used. The reliability analysis can then be performed based on the first two moments of the response obtained.

The method presented facilitates obtaining explicit solutions for general linear MDOF systems and is flexible enough to be applied to different stochastic models of excitation such as the stationary models, modulated stationary models, filtered stationary models, and filtered modulated stationary models and their stochastic equivalents including the random pulse train model, filtered shot noise, and some ARMA models in earthquake engineering. This approach may also be readily incorporated into finite element codes for random vibration analysis of linear structures.

A set of explicit solutions for the response of simple linear structures subjected to modulated white noise earthquake models with four different envelopes are presented as illustration. In addition, the method has been applied to three selected topics of interest in earthquake engineering, namely, nonstationary analysis of primary-secondary systems with classical or nonclassical dampings, soil layer response and related structural reliability analysis, and the effect of the vertical components on seismic performance of structures. For all the three cases, explicit solutions are obtained, dynamic characteristics of structures are investigated, and some suggestions are given for aseismic design of structures.

Succinate:ubiquinone oxidoreductase from Paracoccus denitrificans and particulate methane monooxygenase from Methylococcus capsulatus (Bath): experimental and theoretical EPR studies of the metal cofactors

This thesis summarizes the application of conventional and modern electron paramagnetic resonance (EPR) techniques to establish proximity relationships between paramagnetic metal centers in metalloproteins and between metal centers and magnetic ligand nuclei in two important and timely membrane proteins: succinate:ubiquinone oxidoreductase (SQR) from Paracoccus denitrificans and particulate methane monooxygenase (pMMO) from Methylococcus capsulatus. Such proximity relationships are thought to be critical to the biological function and the associated biochemistry mediated by the metal centers in these proteins. A mechanistic understanding of biological function relies heavily on structure-function relationships and the knowledge of how molecular structure and electronic properties of the metal centers influence the reactivity in metalloenzymes. EPR spectroscopy has proven to be one of the most powerful techniques towards obtaining information about interactions between metal centers as well as defining ligand structures. SQR is an electron transport enzyme wherein the substrates, organic and metallic cofactors are held relatively far apart. Here, the proximity relationships of the metallic cofactors were studied through their weak spin-spin interactions by means of EPR power saturation and electron spin-lattice (T_1) measurements, when the enzyme was poised at designated reduction levels. Analysis of the electron T_1 measurements for the S-3 center when the b-heme is paramagnetic led to a detailed analysis of the dipolar interactions and distance determination between two interacting metal centers. Studies of ligand environment of the metal centers by electron spin echo envelope modulation (ESEEM) spectroscopy resulted in the identication of peptide nitrogens as coupled nuclei in the environment of the S-1 and S-3 centers.

Finally, an EPR model was developed to describe the ferromagnetically coupled trinuclear copper clusters in pMMO when the enzyme is oxidized. The Cu(II) ions in these clusters appear to be strongly exchange coupled, and the EPR is consistent with equilateral triangular arrangements of type 2 copper ions. These results offer the first glimpse of the magneto-structural correlations for a trinuclear copper cluster of this type, which, until the work on pMMO, has had no precedent in the metalloprotein literature. Such trinuclear copper clusters are even rare in synthetic models.

A cocktail of thermally stable, chemically synthesized capture agents for the efficient detection of anti-gp41 antibodies from human sera and techniques

This thesis reports on a method to improve in vitro diagnostic assays that detect immune response, with specific application to HIV-1. The inherent polyclonal diversity of the humoral immune response was addressed by using sequential in situ click chemistry to develop a cocktail of peptide-based capture agents, the components of which were raised against different, representative anti-HIV antibodies that bind to a conserved epitope of the HIV-1 envelope protein gp41. The cocktail was used to detect anti-HIV-1 antibodies from a panel of sera collected from HIV-positive patients, with improved signal-to-noise ratio relative to the gold standard commercial recombinant protein antigen. The capture agents were stable when stored as a powder for two months at temperatures close to 60°C.

Chemical studies of viral entry mechanisms: I. Hydrophobic protein-lipid interactions during sendai virus membrane fusion. II. Kinetics of bacteriophage λ DNA injection.

Viruses possess very specific methods of targeting and entering cells. These methods would be extremely useful if they could also be applied to drug delivery, but little is known about the molecular mechanisms of the viral entry process. In order to gain further insight into mechanisms of viral entry, chemical and spectroscopic studies in two systems were conducted, examining hydrophobic protein-lipid interactions during Sendai virus membrane fusion, and the kinetics of bacteriophage λ DNA injection.

Sendai virus glycoprotein interactions with target membranes during the early stages of fusion were examined using time-resolved hydrophobic photoaffinity labeling with the lipid-soluble carbene generator3-(trifluoromethyl)-3-(m-^(125 )I] iodophenyl)diazirine (TID). The probe was incorporated in target membranes prior to virus addition and photolysis. During Sendai virus fusion with liposomes composed of cardiolipin (CL) or phosphatidylserine (PS), the viral fusion (F) protein is preferentially labeled at early time points, supporting the hypothesis that hydrophobic interaction of the fusion peptide at the N-terminus of the F_1 subunit with the target membrane is an initiating event in fusion. Correlation of the hydrophobic interactions with independently monitored fusion kinetics further supports this conclusion. Separation of proteins after labeling shows that the F_1 subunit, containing the putative hydrophobic fusion sequence, is exclusively labeled, and that the F_2 subunit does not participate in fusion. Labeling shows temperature and pH dependence consistent with a need for protein conformational mobility and fusion at neutral pH. Higher amounts of labeling during fusion with CL vesicles than during virus-PS vesicle fusion reflects membrane packing regulation of peptide insertion into target membranes. Labeling of the viral hemagglutinin/neuraminidase (HN) at low pH indicates that HN-mediated fusion is triggered by hydrophobic interactions, after titration of acidic amino acids. HN labeling under nonfusogenic conditions reveals that viral binding may involve hydrophobic as well as electrostatic interactions. Controls for diffusional labeling exclude a major contribution from this source. Labeling during reconstituted Sendai virus envelope-liposome fusion shows that functional reconstitution involves protein retention of the ability to undergo hydrophobic interactions.

Examination of Sendai virus fusion with erythrocyte membranes indicates that hydrophobic interactions also trigger fusion between biological membranes, and that HN binding may involve hydrophobic interactions as well. Labeling of the erythrocyte membranes revealed close membrane association of spectrin, which may play a role in regulating membrane fusion. The data show that hydrophobic fusion protein interaction with both artificial and biological membranes is a triggering event in fusion. Correlation of these results with earlier studies of membrane hydration and fusion kinetics provides a more detailed view of the mechanism of fusion.

The kinetics of DNA injection by bacteriophage λ. into liposomes bearing reconstituted receptors were measured using fluorescence spectroscopy. LamB, the bacteriophage receptor, was extracted from bacteria and reconstituted into liposomes by detergent removal dialysis. The DNA binding fluorophore ethidium bromide was encapsulated in the liposomes during dialysis. Enhanced fluorescence of ethidium bromide upon binding to injected DNA was monitored, and showed that injection is a rapid, one-step process. The bimolecular rate law, determined by the method of initial rates, revealed that injection occurs several times faster than indicated by earlier studies employing indirect assays.

It is hoped that these studies will increase the understanding of the mechanisms of virus entry into cells, and to facilitate the development of virus-mimetic drug delivery strategies.

Kinetic investigations of heterogeneously catalyzed reactions on the Ru(001) and Pt(110)-(1x2) surfaces

The initial probabilities of activated, dissociative chemisorption of methane and ethane on Pt(110)-(1 x 2) have been measured. The surface temperature was varied from 450 to 900 K with the reactant gas temperature constant at 300 K. Under these conditions, we probe the kinetics of dissociation via trapping-mediated (as opposed to 'direct') mechanism. It was found that the probabilities of dissociation of both methane and ethane were strong functions of the surface temperature with an apparent activation energies of 14.4 kcal/mol for methane and 2.8 kcal/mol for ethane, which implys that the methane and ethane molecules have fully accommodated to the surface temperature. Kinetic isotope effects were observed for both reactions, indicating that the C-H bond cleavage was involved in the rate-limiting step. A mechanistic model based on the trapping-mediated mechanism is used to explain the observed kinetic behavior. The activation energies for C-H bond dissociation of the thermally accommodated methane and ethane on the surface extracted from the model are 18.4 and 10.3 kcal/mol, respectively.

The studies of the catalytic decomposition of formic acid on the Ru(001) surface with thermal desorption mass spectrometry following the adsorption of DCOOH and HCOOH on the surface at 130 and 310 K are described. Formic acid (DCOOH) chemisorbs dissociatively on the surface via both the cleavage of its O-H bond to form a formate and a hydrogen adatom, and the cleavage of its C-O bond to form a carbon monoxide, a deuterium adatom and an hydroxyl (OH). The former is the predominant reaction. The rate of desorption of carbon dioxide is a direct measure of the kinetics of decomposition of the surface formate. It is characterized by a kinetic isotope effect, an increasingly narrow FWHM, and an upward shift in peak temperature with Ɵ_T, the coverage of the dissociatively adsorbed formic acid. The FWHM and the peak temperature change from 18 K and 326 K at Ɵ_T = 0.04 to 8 K and 395 K at Ɵ_T = 0.89. The increase in the apparent activation energy of the C-D bond cleavage is largely a result of self-poisoning by the formate, the presence of which on the surface alters the electronic properties of the surface such that the activation energy of the decomposition of formate is increased. The variation of the activation energy for carbon dioxide formation with Ɵ_T accounts for the observed sharp carbon dioxide peak. The coverage of surface formate can be adjusted over a relatively wide range so that the activation energy for C-D bond cleavage in the case of DCOOH can be adjusted to be below, approximately equal to, or well above the activation energy for the recombinative desorption of the deuterium adatoms. Accordingly, the desorption of deuterium was observed to be governed completely by the desorption kinetics of the deuterium adatoms at low Ɵ_T, jointly by the kinetics of deuterium desorption and C-D bond cleavage at intermediate Ɵ_T, and solely by the kinetics of C-D bond cleavage at high Ɵ_T. The overall branching ratio of the formate to carbon dioxide and carbon monoxide is approximately unity, regardless the initial coverage Ɵ_T, even though the activation energy for the production of carbon dioxide varies with Ɵ_T. The desorption of water, which implies C-O bond cleavage of the formate, appears at approximately the same temperature as that of carbon dioxide. These observations suggest that the cleavage of the C-D bond and that of the C-O bond of two surface formates are coupled, possibly via the formation of a short-lived surface complex that is the precursor to to the decomposition.

The measurement of steady-state rate is demonstrated here to be valuable in determining kinetics associated with short-lived, molecularly adsorbed precursor to further reactions on the surface, by determining the kinetic parameters of the molecular precursor of formaldehyde to its dissociation on the Pt(110)-(1 x 2) surface.

Overlayers of nitrogen adatoms on Ru(001) have been characterized both by thermal desorption mass spectrometry and low-energy electron diffraction, as well as chemically via the postadsorption and desorption of ammonia and carbon monoxide.

The nitrogen-adatom overlayer was prepared by decomposing ammonia thermally on the surface at a pressure of 2.8 x 10^(-6) Torr and a temperature of 480 K. The saturated overlayer prepared under these conditions has associated with it a (√247/10 x √247/10)R22.7° LEED pattern, has two peaks in its thermal desorption spectrum, and has a fractional surface coverage of 0.40. Annealing the overlayer to approximately 535 K results in a rather sharp (√3 x √3)R30° LEED pattern with an associated fractional surface coverage of one-third. Annealing the overlayer further to 620 K results in the disappearance of the low-temperature thermal desorption peak and the appearance of a rather fuzzy p(2x2) LEED pattern with an associated fractional surface coverage of approximately one-fourth. In the low coverage limit, the presence of the (√3 x √3)R30° N overlayer alters the surface in such a way that the binding energy of ammonia is increased by 20% relative to the clean surface, whereas that of carbon monoxide is reduced by 15%.

A general methodology for the indirect relative determination of the absolute fractional surface coverages has been developed and was utilized to determine the saturation fractional coverage of hydrogen on Ru(001). Formaldehyde was employed as a bridge to lead us from the known reference point of the saturation fractional coverage of carbon monoxide to unknown reference point of the fractional coverage of hydrogen on Ru(001), which is then used to determine accurately the saturation fractional coverage of hydrogen. We find that ƟSAT/H = 1.02 (±0.05), i.e., the surface stoichiometry is Ru : H = 1 : 1. The relative nature of the method, which cancels systematic errors, together with the utilization of a glass envelope around the mass spectrometer, which reduces spurious contributions in the thermal desorption spectra, results in high accuracy in the determination of absolute fractional coverages.

Observations of 1-6 MeV Jovian electrons at 1 AU and a study of their propagation

The 1-6 MeV electron flux at 1 AU has been measured for the time period October 1972 to December 1977 by the Caltech Electron/Isotope Spectrometers on the IMP-7 and IMP-8 satellites. The non-solar interplanetary electron flux reported here covered parts of five synodic periods. The 88 Jovian increases identified in these five synodic periods were classified by their time profiles. The fall time profiles were consistent with an exponential fall with τ ≈ 4-9 days. The rise time profiles displayed a systematic variation over the synodic period. Exponential rise time profiles with τ ≈ 1-3 days tended to occur in the time period before nominal connection, diffusive profiles predicted by the convection-diffusion model around nominal connection, and abrupt profiles after nominal connection.

The times of enhancements in the magnetic field, │B│, at 1 AU showed a better correlation than corotating interaction regions (CIR's) with Jovian increases and other changes in the electron flux at 1 AU, suggesting that │B│ enhancements indicate the times that barriers to electron propagation pass Earth. Time sequences of the increases and decreases in the electron flux at 1 AU were qualitatively modeled by using the times that CIR's passed Jupiter and the times that │B│ enhancements passed Earth.

The electron data observed at 1 AU were modeled by using a convection-diffusion model of Jovian electron propagation. The synodic envelope formed by the maxima of the Jovian increases was modeled by the envelope formed by the predicted intensities at a time less than that needed to reach equilibrium. Even though the envelope shape calculated in this way was similar to the observed envelope, the required diffusion coefficients were not consistent with a diffusive process.

Three Jovian electron increases at 1 AU for the 1974 synodic period were fit with rise time profiles calculated from the convection-diffusion model. For the fits without an ambient electron background flux, the values for the diffusion coefficients that were consistent with the data were k_x = 1.0 - 2.5 x 10²¹ cm²/sec and k_y = 1.6 - 2.0 x 10²² cm²/sec. For the fits that included the ambient electron background flux, the values for the diffusion coefficients that were consistent with the data were k_x = 0.4 - 1.0 x 10²¹ cm²/sec and k_y = 0.8 - 1.3 x 10²² cm²/sec.

Self-healing Techniques for RF and mm-Wave Transmitters and Receivers

With continuing advances in CMOS technology, feature sizes of modern Silicon chip-sets have gone down drastically over the past decade. In addition to desktops and laptop processors, a vast majority of these chips are also being deployed in mobile communication devices like smart-phones and tablets, where multiple radio-frequency integrated circuits (RFICs) must be integrated into one device to cater to a wide variety of applications such as Wi-Fi, Bluetooth, NFC, wireless charging, etc. While a small feature size enables higher integration levels leading to billions of transistors co-existing on a single chip, it also makes these Silicon ICs more susceptible to variations. A part of these variations can be attributed to the manufacturing process itself, particularly due to the stringent dimensional tolerances associated with the lithographic steps in modern processes. Additionally, RF or millimeter-wave communication chip-sets are subject to another type of variation caused by dynamic changes in the operating environment. Another bottleneck in the development of high performance RF/mm-wave Silicon ICs is the lack of accurate analog/high-frequency models in nanometer CMOS processes. This can be primarily attributed to the fact that most cutting edge processes are geared towards digital system implementation and as such there is little model-to-hardware correlation at RF frequencies.

All these issues have significantly degraded yield of high performance mm-wave and RF CMOS systems which often require multiple trial-and-error based Silicon validations, thereby incurring additional production costs. This dissertation proposes a low overhead technique which attempts to counter the detrimental effects of these variations, thereby improving both performance and yield of chips post fabrication in a systematic way. The key idea behind this approach is to dynamically sense the performance of the system, identify when a problem has occurred, and then actuate it back to its desired performance level through an intelligent on-chip optimization algorithm. We term this technique as self-healing drawing inspiration from nature's own way of healing the body against adverse environmental effects. To effectively demonstrate the efficacy of self-healing in CMOS systems, several representative examples are designed, fabricated, and measured against a variety of operating conditions.

We demonstrate a high-power mm-wave segmented power mixer array based transmitter architecture that is capable of generating high-speed and non-constant envelope modulations at higher efficiencies compared to existing conventional designs. We then incorporate several sensors and actuators into the design and demonstrate closed-loop healing against a wide variety of non-ideal operating conditions. We also demonstrate fully-integrated self-healing in the context of another mm-wave power amplifier, where measurements were performed across several chips, showing significant improvements in performance as well as reduced variability in the presence of process variations and load impedance mismatch, as well as catastrophic transistor failure. Finally, on the receiver side, a closed-loop self-healing phase synthesis scheme is demonstrated in conjunction with a wide-band voltage controlled oscillator to generate phase shifter local oscillator (LO) signals for a phased array receiver. The system is shown to heal against non-idealities in the LO signal generation and distribution, significantly reducing phase errors across a wide range of frequencies.

The isolation and partial biochemical analysis of Sindbis virus proteins

Recently, the amino acid sequences have been reported for several proteins, including the envelope glycoproteins of Sindbis virus, which all probably span the plasma membrane with a common topology: a large N-terminal, extracellular portion, a short region buried in the bilayer, and a short C-terminal intracellular segment. The regions of these proteins buried in the bilayer correspond to portions of the protein sequences which contain a stretch of hydrophobic amino acids and which have other common characteristics, as discussed. Reasons are also described for uncertainty, in some proteins more than others, as to the precise location of some parts of the sequence relative to the membrane.

The signal hypothesis for the transmembrane translocation of proteins is briefly described and its general applicability is reviewed. There are many proteins whose translocation is accurately described by this hypothesis, but some proteins are translocated in a different manner.

The transmembraneous glycoproteins E1 and E2 of Sindbis virus, as well as the only other virion protein, the capsid protein, were purified in amounts sufficient for biochemical analysis using sensitive techniques. The amino acid composition of each protein was determined, and extensive N-terminal sequences were obtained for E1 and E2. By these techniques E1 and E2 are indistinguishable from most water soluble proteins, as they do not contain an obvious excess of hydrophobic amino acids in their N-terminal regions or in the intact molecule.

The capsid protein was found to be blocked, and so its N-terminus could not be sequenced by the usual methods. However, with the use of a special labeling technique, it was possible to incorporate tritiated acetate into the N-terminus of the protein with good specificity, which was useful in the purification of peptides from which the first amino acids in the N-terminal sequence could be identified.

Nanomole amounts of PE2, the intracellular precursor of E2, were purified by an immuno-affinity technique, and its N-terminus was analyzed. Together with other work, these results showed that PE2 is not synthesized with an N-terminal extension, and the signal sequence for translocation is probably the N-terminal amino acid sequence of the protein. This N-terminus was found to be 80-90% blocked, also by Nacetylation, and this acetylation did not affect its function as a signal sequence. The putative signal sequence was also found to contain a glycosylated asparagine residue, but the inhibition of this glycosylation did not lead to the cleavage of the sequence.

Response of linear, viscous damped systems to excitations having time-varying frequency

The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time.

The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.

Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.

The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.

It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance.

One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon.

Observation and interpretation of tectonic strain release mechanisms

In four chapters various aspects of earthquake source are studied.

Chapter I

Surface displacements that followed the Parkfield, 1966, earthquakes were measured for two years with six small-scale geodetic networks straddling the fault trace. The logarithmic rate and the periodic nature of the creep displacement recorded on a strain meter made it possible to predict creep episodes on the San Andreas fault. Some individual earthquakes were related directly to surface displacement, while in general, slow creep and aftershock activity were found to occur independently. The Parkfield earthquake is interpreted as a buried dislocation.

Chapter II

The source parameters of earthquakes between magnitude 1 and 6 were studied using field observations, fault plane solutions, and surface wave and S-wave spectral analysis. The seismic moment, M_O, was found to be related to local magnitude, M_L, by log M_O = 1.7 M_L + 15.1. The source length vs magnitude relation for the San Andreas system found to be: M_L = 1.9 log L - 6.7. The surface wave envelope parameter AR gives the moment according to log M_O = log AR₃₀₀ + 30.1, and the stress drop, τ, was found to be related to the magnitude by τ = 0.54 M - 2.58. The relation between surface wave magnitude M_S and M_L is proposed to be M_S = 1.7 M_L - 4.1. It is proposed to estimate the relative stress level (and possibly the strength) of a source-region by the amplitude ratio of high-frequency to low-frequency waves. An apparent stress map for Southern California is presented.

Chapter III

Seismic triggering and seismic shaking are proposed as two closely related mechanisms of strain release which explain observations of the character of the P wave generated by the Alaskan earthquake of 1964, and distant fault slippage observed after the Borrego Mountain, California earthquake of 1968. The Alaska, 1964, earthquake is shown to be adequately described as a series of individual rupture events. The first of these events had a body wave magnitude of 6.6 and is considered to have initiated or triggered the whole sequence. The propagation velocity of the disturbance is estimated to be 3.5 km/sec. On the basis of circumstantial evidence it is proposed that the Borrego Mountain, 1968, earthquake caused release of tectonic strain along three active faults at distances of 45 to 75 km from the epicenter. It is suggested that this mechanism of strain release is best described as "seismic shaking."

Chapter IV

The changes of apparent stress with depth are studied in the South American deep seismic zone. For shallow earthquakes the apparent stress is 20 bars on the average, the same as for earthquakes in the Aleutians and on Oceanic Ridges. At depths between 50 and 150 km the apparent stresses are relatively high, approximately 380 bars, and around 600 km depth they are again near 20 bars. The seismic efficiency is estimated to be 0.1. This suggests that the true stress is obtained by multiplying the apparent stress by ten. The variation of apparent stress with depth is explained in terms of the hypothesis of ocean floor consumption.

Robust Control of Evolutionary Dynamics

The application of principles from evolutionary biology has long been used to gain new insights into the progression and clinical control of both infectious diseases and neoplasms. This iterative evolutionary process consists of expansion, diversification and selection within an adaptive landscape - species are subject to random genetic or epigenetic alterations that result in variations; genetic information is inherited through asexual reproduction and strong selective pressures such as therapeutic intervention can lead to the adaptation and expansion of resistant variants. These principles lie at the center of modern evolutionary synthesis and constitute the primary reasons for the development of resistance and therapeutic failure, but also provide a framework that allows for more effective control.

A model system for studying the evolution of resistance and control of therapeutic failure is the treatment of chronic HIV-1 infection by broadly neutralizing antibody (bNAb) therapy. A relatively recent discovery is that a minority of HIV-infected individuals can produce broadly neutralizing antibodies, that is, antibodies that inhibit infection by many strains of HIV. Passive transfer of human antibodies for the prevention and treatment of HIV-1 infection is increasingly being considered as an alternative to a conventional vaccine. However, recent evolution studies have uncovered that antibody treatment can exert selective pressure on virus that results in the rapid evolution of resistance. In certain cases, complete resistance to an antibody is conferred with a single amino acid substitution on the viral envelope of HIV.

The challenges in uncovering resistance mechanisms and designing effective combination strategies to control evolutionary processes and prevent therapeutic failure apply more broadly. We are motivated by two questions: Can we predict the evolution to resistance by characterizing genetic alterations that contribute to modified phenotypic fitness? Given an evolutionary landscape and a set of candidate therapies, can we computationally synthesize treatment strategies that control evolution to resistance?

To address the first question, we propose a mathematical framework to reason about evolutionary dynamics of HIV from computationally derived Gibbs energy fitness landscapes -- expanding the theoretical concept of an evolutionary landscape originally conceived by Sewall Wright to a computable, quantifiable, multidimensional, structurally defined fitness surface upon which to study complex HIV evolutionary outcomes.

To design combination treatment strategies that control evolution to resistance, we propose a methodology that solves for optimal combinations and concentrations of candidate therapies, and allows for the ability to quantifiably explore tradeoffs in treatment design, such as limiting the number of candidate therapies in the combination, dosage constraints and robustness to error. Our algorithm is based on the application of recent results in optimal control to an HIV evolutionary dynamics model and is constructed from experimentally derived antibody resistant phenotypes and their single antibody pharmacodynamics. This method represents a first step towards integrating principled engineering techniques with an experimentally based mathematical model in the rational design of combination treatment strategies and offers predictive understanding of the effects of combination therapies of evolutionary dynamics and resistance of HIV. Preliminary in vitro studies suggest that the combination antibody therapies predicted by our algorithm can neutralize heterogeneous viral populations despite containing resistant mutations.