Nearly free molecular heat transfer from a sphere

Consider a sphere immersed in a rarefied monatomic gas with zero mean flow. The distribution function of the molecules at infinity is chosen to be a Maxwellian. The boundary condition at the body is diffuse reflection with perfect accommodation to the surface temperature. The microscopic flow of particles about the sphere is modeled kinetically by the Boltzmann equation with the Krook collision term. Appropriate normalizations in the near and far fields lead to a perturbation solution of the problem, expanded in terms of the ratio of body diameter to mean free path (inverse Knudsen number). The distribution function is found directly in each region, and intermediate matching is demonstrated. The heat transfer from the sphere is then calculated as an integral over this distribution function in the inner region. Final results indicate that the heat transfer may at first increase over its free flow value before falling to the continuum level.

Search for color transparency in A(e,e'p) at high momentum transfer

Rates for A(e, e'p) on the nuclei ^2H, C, Fe, and Au have been measured at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV fc)^2 . We extract the nuclear transparency T, a measure of the importance of final state interactions (FSI) between the outgoing proton and the recoil nucleus. Some calculations based on perturbative QCD predict an increase in T with momentum transfer, a phenomenon known as Color Transparency. No statistically significant rise is seen in the present experiment.

Preparation, characterization and intramolecular electron-transfer studies of ruthenium-modified cytochromes c

Redox-active ruthenium complexes have been covalently attached to the surface of a series of natural, semisynthetic and recombinant cytochromes c. The protein derivatives were characterized by a variety of spectroscopic techniques. Distant Fe^(2+) - Ru^(3+) electronic couplings were extracted from intramolecular electron-transfer rates in Ru(bpy)_2(im)HisX (where X= 33, 39, 62, and 72) derivatives of cyt c. The couplings increase according to 62 (0.0060) < 72 (0.057) < 33 (0.097) < 39 (0.11 cm^(-1)); however, this order is incongruent with histidine to heme edge-edge distances [62 (14.8) > 39 (12.3) > 33 (11.1) > =72 (8.4 Å)]. These results suggest the chemical nature of the intervening medium needs to be considered for a more precise evaluation of couplings. The rates (and couplings) correlate with the lengths of a-tunneling pathways comprised of covalent bonds, hydrogen bonds and through-space jumps from the histidines to the heme group. Space jumps greatly decrease couplings: one from Pro71 to Met80 extends the σ-tunneling length of the His72 pathway by roughly 10 covalent bond units. Experimental couplings also correlate well with those calculated using extended Hiickel theory to evaluate the contribution of the intervening protein medium.

Two horse heart cyt c variants incorporating the unnatural amino acids (S)-2- amino-3-(2,2'-bipyrid-6-yl)-propanoic acid (6Bpa) and (S)-2-amino-3-(2,2'-bipyrid-4-yl)propanoic acid ( 4Bpa) at position 72 have been prepared using semisynthetic protocols. Negligible perturbation of the protein structure results from this introduction of unnatural amino acids. Redox-active Ru(2,2'-bipyridine)_2^(2+) binds to 4Bpa72 cyt c but not to the 6Bpa protein. Enhanced ET rates were observed in the Ru(bpy)_2^(2+)-modified 4Bpa72 cyt c relative to the analogous His72 derivative. The rapid (< 60 nanosecond) photogeneration of ferrous Ru-modified 4Bpa72 cyt c in the conformationally altered alkaline state demonstrates that laser-induced ET can be employed to study submicrosecond protein-folding events.

Electron transfer in cytochrome c oxidase : the rate of electron equillibration between cytochrome a and copper A

Intramolecular electron transfer in partially reduced cytochrome c oxidase has been studied by means of perturbed equilibrium techniques. We have prepared a three electron reduced, CO inhibited form of the enzyme in which cytochrome a and copper A are partially reduced an in intramolecular redox equilibrium. When these samples were photolyzed using a nitrogen laser (0.6 µs, 1.0 mJ pulses) changes in absorbance at 598 nm and 830 nm were observed which are consistent with a fast electron from cytochrome a to copper A. The absorbance changes at 598 nm have an apparent rate of 17,200 ± 1,700 s^(-1) (1σ), at pH 7.0 and 25.5 °C. These changes were not observed in either the CO mixed valence or CO inhibited fully reduced forms of the enzyme. The rate is fastest at about pH 8.0, and falls off in either direction, and there is a small, but clear temperature dependence. The process was also observed in the cytochrome c -- cytochrome c oxidase high affinity complex.

This rate is far faster than any rate measured or inferred previously for the cytochrome a -- copper A electron equilibration, but the interpretation of these results is hampered by the fact that the relaxation could only be followed during the time before CO became rebound to the oxygen binding site. The meaning of our our measured rate is discussed, along with other reported rates for this process. In addition, a temperature-jump experiment on the same system is discussed.

We have also prepared a partially reduced, cyanide inhibited form of the enzyme in which cytochrome a, copper A and copper B are partially reduced and in redox equilibrium. Warming these samples produced absorbance changes at 605 nm which indicate that cytochrome a was becoming more oxidized, but there were no parallel changes in absorbance at 830 nm as would be expected if copper A was becoming reduced. We concluded that electrons were being redistributed from cytochrome a to copper B. The kinetics of the absorbance changes at 605 nm were investigated by temperature-jump methods. Although a rate could not be resolved, we concluded that the process must occur with an (apparent) rate larger than 10,000 s^(-1).

During the course of the temperature-jump experiments, we also found that non-redox related, temperature dependent absorbance changes in fully reduced CO inhibited cytochrome c oxidase, and in the cyanide mixed valence enzyme, took place with an (apparent) rate faster that 30,000 s^(-1).

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.

An experimental investigation of the heat transfer from a buoyant gas plume to a horizontal unobstructed ceiling

This thesis presents an experimental investigation of the axisymmetric heat transfer from a small scale fire and resulting buoyant plume to a horizontal, unobstructed ceiling during the initial stages of development. A propane-air burner yielding a heat source strength between 1.0 kW and 1.6 kW was used to simulate the fire, and measurements proved that this heat source did satisfactorily represent a source of buoyancy only. The ceiling consisted of a 1/16" steel plate of 0.91 m. diameter, insulated on the upper side. The ceiling height was adjustable between 0.5 m and 0.91 m. Temperature measurements were carried out in the plume, ceiling jet, and on the ceiling.

Heat transfer data were obtained by using the transient method and applying corrections for the radial conduction along the ceiling and losses through the insulation material. The ceiling heat transfer coefficient was based on the adiabatic ceiling jet temperature (recovery temperature) reached after a long time. A parameter involving the source strength Q and ceiling height H was found to correlate measurements of this temperature and its radial variation. A similar parameter for estimating the ceiling heat transfer coefficient was confirmed by the experimental results.

This investigation therefore provides reasonable estimates for the heat transfer from a buoyant gas plume to a ceiling in the axisymmetric case, for the stagnation region where such heat transfer is a maximum and for the ceiling jet region (r/H ≤ 0.7). A comparison with data from experiments which involved larger heat sources indicates that the predicted scaling of temperatures and heat transfer rates for larger scale fires is adequate.

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.

Preparation and characterization of an intramolecular electron transfer in a pentaammineruthenium derivative of Candida krisei cytochrome c

A semisynthetic binuclear metalloprotein has been prepared by appending the pentaammineruthenium moiety to histidine 39 of the cytochrome c from the yeast Candida krusei. The site of ruthenium binding was identified by peptide mapping. Spectroscopic and electrochemical properties of the derivative indicate the protein conformation is unperturbed by the modification. A preliminary (minimum) rate constant of 170s^(-1) has been determined for the intramolecular electron transfer from ruthenium(II) to iron(III), which occurs over a distance of at least 13Å (barring major conformational changes). Electrochemical studies indicate that this reaction should proceed with a driving force of ~170mV. The rate constant is an order of magnitude faster than that observed in horse heart cytochrome c for intramolecular electron transfer from pentaammineruthenium(II)(histidine 33) to iron(III) (over a similar distance, and with a similar driving force), suggesting a medium or orientation effect makes the Candida intramolecular electron transfer more favorable.

Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

The theory of long distance electron transfer reactions

The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.

The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.

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.

Hydrogen-Atom Transfer Photochemistry of Tetrakis(µ-pyrophosphito)diplatinate(II)

In many senses, the hydrogen-atom transfer reactions observed with the triplet excited state of pyrophosphito-bridged platinum(II) dimers resemble the reactions of organic ketone nπ* states. The first two chapters describe our attempts to understand the reactivity differences between these two chromophores. Reactivity of the metal dimers is strongly regulated by the detailed nature of the ligands that ring the axial site, the hydrogen-abstraction center. A hydrogen-bonded network linking the ligands facilitates H-atom transfer quenching with alcohols through the formation of a hydrogen-bonded complex between the alcohol and a dimer. For substrates of equal C-H bond strength that lack a hydroxyl group (e.g., benzyl hydrocarbons), the quenching rate is several orders of magnitude slower.

The shape and size of the axial site, as determined by the ligands, also discriminate among quenchers by their steric characteristics. Very small quenchers quench slowly because of high entropies of activation, while very large ones have large enthalpic barriers. The two effects find a balance with quenchers of "just the right size."

The third chapter discusses the design of a mass spectrometer that uses positron annihilation to ionize neutral molecules. The mass spectrometer creates positron-molecule adducts whose annihilation produces fragmentation products that may yield information on the bonding of positrons in such complexes.

Direct simulation of proton-coupled electron transfer reaction dynamics and mechanisms

Proton-coupled electron transfer (PCET) reactions are ubiquitous throughout chemistry and biology. However, challenges arise in both the the experimental and theoretical investigation of PCET reactions; the rare-event nature of the reactions and the coupling between quantum mechanical electron- and proton-transfer with the slower classical dynamics of the surrounding environment necessitates the development of robust simulation methodology. In the following dissertation, novel path-integral based methods are developed and employed for the direct simulation of the reaction dynamics and mechanisms of condensed-phase PCET.

Engineering and Characterization of Cytochrome P450 Enzymes for Nitrogen-Atom Transfer Reactions

The creation of novel enzyme activity is a great challenge to protein engineers, but nature has done so repeatedly throughout the process of natural selection. I begin by outlining the multitude of distinct reactions catalyzed by a single enzyme class, cytochrome P450 monooxygenases. I discuss the ability of cytochrome P450 to generate reactive intermediates capable of diverse reactivity, suggesting this enzyme can also be used to generate novel reactive intermediates in the form of metal-carbenoid and nitrenoid species. I then show that cytochrome P450 from Bacillus megaterium (P450_BM3) and its isolated cofactor can catalyze metal-nitrenoid transfer in the form of intramolecular C–H bond amination. Mutations to the protein sequence can enhance the reactivity and selectivity of this transformation significantly beyond that of the free cofactor. Next, I demonstrate an intermolecular nitrene transfer reaction catalyzed by P450_BM3 in the form of sulfide imidation. Understanding that sulfur heteroatoms are strong nucleophiles, I show that increasing the sulfide nucleophilicity through substituents on the aryl sulfide ring can dramatically increase reaction productivity. To explore engineering nitrenoid transfer in P450BM3, active site mutagenesis is employed to tune the regioselectivity intramolecular C–H amination catalysts. The solution of the crystal structure of a highly selective variant demonstrates that hydrophobic residues in the active site strongly modulate reactivity and regioselectivity. Finally, I use a similar strategy to develop P450-based catalysts for intermolecular olefin aziridination, demonstrating that active site mutagenesis can greatly enhance this nitrene transfer reaction. The resulting variant can catalyze intermolecular aziridination with more than 1000 total turnovers and enantioselectivity of up to 99% ee.