Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.

Asymptotic optimality of RESTART estimators in highly dependable systems

Abstract We consider a wide class of models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multi-component systems in reliability settings. Repair times and component lifetimes are random variables that follow a general distribution, and the repair service adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly-dependable systems, the RESTART method is used for the estimation of steady-state unavailability and other reliability measures. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty involved in applying this method is finding a suitable function, called the importance function, to define the regions. In this paper we introduce an importance function which, for unbalanced systems, represents a great improvement over the importance function used in previous papers. We also demonstrate the asymptotic optimality of RESTART estimators in these models. Several examples are presented to show the effectiveness of the new approach, and probabilities up to the order of 10-42 are accurately estimated with little computational effort.

Impact of metal-organic vapor phase epitaxy environment on silicon bulk lifetime for III–V-on-Si multijunction solar cells

With the final goal of integrating III-V materials on silicon substrates for tandem solar cells, the influence of the Metal-Organic Vapor Phase Epitaxy (MOVPE) environment on the minority carrier properties of silicon wafers has been evaluated. These properties will essentially determine the photovoltaic performance of the bottom cell in a III-V-on-Si tandem solar cell. A comparison of the base minority carrier lifetimes obtained for different thermal processes carried out in a MOVPE reactor on Czochralski silicon wafers has been carried out. An important degradation of minority carrier lifetime during the surface preparation (i.e. H2 anneal) has been observed. Three different mechanisms have been proposed for explaining this behavior: 1) the introduction of extrinsic impurities coming from the reactor; 2) the activation of intrinsic lifetime killing impurities coming from the wafer itself; and finally, 3) the formation of crystal defects, which eventually become recombination centers. The effect of the emitter formation by phosphorus diffusion has also been evaluated. In this sense, it has been reported that lifetime can be recovered during the emitter formation either by the effect of the P on extracting impurities, or by the role of the atomic hydrogen on passivating the defects.

Material requirements for the adoption of unconventional silicon crystal and wafer growth techniques for high-efficiency solar cells

Silicon wafers comprise approximately 40% of crystalline silicon module cost, and represent an area of great technological innovation potential. Paradoxically, unconventional wafer-growth techniques have thus far failed to displace multicrystalline and Czochralski silicon, despite four decades of innovation. One of the shortcomings of most unconventional materials has been a persistent carrier lifetime deficit in comparison to established wafer technologies, which limits the device efficiency potential. In this perspective article, we review a defect-management framework that has proven successful in enabling millisecond lifetimes in kerfless and cast materials. Control of dislocations and slowly diffusing metal point defects during growth, coupled to effective control of fast-diffusing species during cell processing, is critical to enable high cell efficiencies. To accelerate the pace of novel wafer development, we discuss approaches to rapidly evaluate the device efficiency potential of unconventional wafers from injection-dependent lifetime measurements.

Static and dynamic lengths of neutrophil microvilli

Containing most of the L-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) on their tips, microvilli are believed to promote the initial arrest of neutrophils on endothelium. At the rolling stage following arrest, the lifetimes of the involved molecular bonds depend on the pulling force imposed by the shear stress of blood flow. With two different methods, electron microscopy and micropipette manipulation, we have obtained two comparable neutrophil microvillus lengths, both ≈0.3 μm in average. We have found also that, under a pulling force, a microvillus can be extended (microvillus extension) or a long thin membrane cylinder (a tether) can be formed from it (tether formation). If the force is ≤34 pN (± 3 pN), the length of the microvillus will be extended; if the force is >61 pN (± 5 pN), a tether will be formed from the microvillus at a constant velocity, which depends linearly on the force. When the force is between 34 pN and 61 pN (transition zone), the degree of association between membrane and cytoskeleton in individual microvilli will dictate whether microvillus extension or tether formation occurs. When a microvillus is extended, it acts like a spring with a spring constant of ≈43 pN/μm. In contrast to a rigid or nonextendible microvillus, both microvillus extension and tether formation can decrease the pulling force imposed on the adhesive bonds, and thus prolonging the persistence of the bonds at high physiological shear stresses.

Fluorescence and photobleaching dynamics of single light-harvesting complexes

Single light-harvesting complexes LH-2 from Rhodopseudomonas acidophila were immobilized on various charged surfaces under physiological conditions. Polarized light experiments showed that the complexes were situated on the surface as nearly upright cylinders. Their fluorescence lifetimes and photobleaching properties were obtained by using a confocal fluorescence microscope with picosecond time resolution. Initially all molecules fluoresced with a lifetime of 1 ± 0.2 ns, similar to the bulk value. The photobleaching of one bacteriochlorophyll molecule from the 18-member assembly caused the fluorescence to switch off completely, because of trapping of the mobile excitations by energy transfer. This process was linear in light intensity. On continued irradiation the fluorescence often reappeared, but all molecules did not show the same behavior. Some LH-2 complexes displayed a variation of their quantum yields that was attributed to photoinduced confinement of the excited states and thereby a diminution of the superradiance. Others showed much shorter lifetimes caused by excitation energy traps that are only ≈3% efficient. On repeated excitation some molecules entered a noisy state where the fluorescence switched on and off with a correlation time of ≈0.1 s. About 490 molecules were examined.

Conformational fluctuations in single DNA molecules

Measurement of fluorescent lifetimes of dye-tagged DNA molecules reveal the existence of different conformations. Conformational fluctuations observed by fluorescence correlation spectroscopy give rise to a relaxation behavior that is described by “stretched” exponentials and indicates the presence of a distribution of transition rates between two conformations. Whether this is an inhomogeneous distribution, where each molecule contributes with its own reaction rate to the overall distribution, or a homogeneous distribution, where the reaction rate of each molecule is time-dependent, is not yet known. We used a tetramethylrhodamine-linked 217-bp DNA oligonucleotide as a probe for conformational fluctuations. Fluorescence fluctuations from single DNA molecules attached to a streptavidin-coated surface directly show the transitions between two conformational states. The conformational fluctuations typical for single molecules are similar to those seen in single ion channels in cell membranes.

Excitonic couplings and electronic coherence in bridged naphthalene dimers

The electronic excitations of naphthalene and a family of bridged naphthalene dimers are calculated and analyzed by using the Collective Electronic Oscillator method combined with the oblique Lanczos algorithm. All experimentally observed trends in absorption profiles and radiative lifetimes are reproduced. Each electronic excitation is linked to the corresponding real-space transition density matrix, which represents the motions of electrons and holes created in the molecule by photon absorption. Two-dimensional plots of these matrices help visualize the degree of exciton localization and explain the dependence of the electronic interaction between chromophores on their separation.

Nonequilibrium mechanism of transcription termination from observations of single RNA polymerase molecules

Cessation of transcription at specific terminator DNA sequences is used by viruses, bacteria, and eukaryotes to regulate the expression of downstream genes, but the mechanisms of transcription termination are poorly characterized. To elucidate the kinetic mechanism of termination at the intrinsic terminators of enteric bacteria, we observed, by using single-molecule light microscopy techniques, the behavior of surface-immobilized Escherichia coli RNA polymerase (RNAP) molecules in vitro. An RNAP molecule remains at a canonical intrinsic terminator for ≈64 s before releasing DNA, implying the formation of an elongation-incompetent (paused) intermediate by transcription complexes that terminate but not by those that read through the terminator. Analysis of pause lifetimes establishes a complete minimal mechanism of termination in which paused intermediate formation is both necessary and sufficient to induce release of RNAP at the terminator. The data suggest that intrinsic terminators function by a nonequilibrium process in which terminator effectiveness is determined by the relative rates of nucleotide addition and paused state entry by the transcription complex.

Tyrosine replacement in P-selectin glycoprotein ligand-1 affects distinct kinetic and mechanical properties of bonds with P- and L-selectin

Selectins are adhesion molecules that initiate tethering and rolling of leukocytes on the vessel wall. Rolling requires rapid formation and breakage of selectin–ligand bonds that must have mechanical strength to resist premature dissociation by the forces applied in shear flow. P- and L-selectin bind to the N-terminal region of P-selectin glycoprotein ligand-1 (PSGL-1), a mucin on leukocytes. To define determinants on PSGL-1 that contribute to the kinetic and mechanical properties of bonds with selectins, we compared rolling of transfected preB cells expressing P- or L-selectin on transfected cell monolayers expressing wild-type PSGL-1 or PSGL-1 constructs with substitutions in targeted N-terminal residues. Rolling through P- or L-selectin required a Thr or Ser at a specific position on PSGL-1, the attachment site for an essential O-glycan, but required only one of three nearby Tyr residues, which are sites for Tyr-SO3 formation. The adhesive strengths and numbers of cells rolling through P- or L-selectin were similar on wild-type PSGL-1 and on each of the three PSGL-1 constructs containing only a single Tyr. However, the cells rolled more irregularly on the single-Tyr forms of PSGL-1. Analysis of the lifetimes of transient tethers on limiting densities of PSGL-1 revealed that L-selectin dissociated faster from single-Tyr than wild-type PSGL-1 at all shears examined. In sharp contrast, P-selectin dissociated faster from single-Tyr than wild-type PSGL-1 at higher shear but not at lower shear. Thus, tyrosine replacements in PSGL-1 affect distinct kinetic and mechanical properties of bonds with P- and L-selectin.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Fractionation factors and activation energies for exchange of the low barrier hydrogen bonding proton in peptidyl trifluoromethyl ketone complexes of chymotrypsin

NMR investigations have been carried out of complexes between bovine chymotrypsin Aα and a series of four peptidyl trifluoromethyl ketones, listed here in order of increasing affinity for chymotrypsin: N-Acetyl-l-Phe-CF3, N-Acetyl-Gly-l-Phe-CF3, N-Acetyl-l-Val-l-Phe-CF3, and N-Acetyl-l-Leu-l-Phe-CF3. The D/H fractionation factors (φ) for the hydrogen in the H-bond between His 57 and Asp 102 (His 57-Hδ1) in these four complexes at 5°C were in the range φ = 0.32–0.43, expected for a low-barrier hydrogen bond. For this series of complexes, measurements also were made of the chemical shifts of His 57-Hɛ1 (δ2,2-dimethylsilapentane-5-sulfonic acid 8.97–9.18), the exchange rate of the His 57-Hδ1 proton with bulk water protons (284–12.4 s−1), and the activation enthalpies for this hydrogen exchange (14.7–19.4 kcal⋅mol−1). It was found that the previously noted correlations between the inhibition constants (Ki 170–1.2 μM) and the chemical shifts of His 57-Hδ1 (δ2,2-dimethylsilapentane-5-sulfonic acid 18.61–18.95) for this series of peptidyl trifluoromethyl ketones with chymotrypsin [Lin, J., Cassidy, C. S. & Frey, P. A. (1998) Biochemistry 37, 11940–11948] could be extended to include the fractionation factors, hydrogen exchange rates, and hydrogen exchange activation enthalpies. The results support the proposal of low barrier hydrogen bond-facilitated general base catalysis in the addition of Ser 195 to the peptidyl carbonyl group of substrates in the mechanism of chymotrypsin-catalyzed peptide hydrolysis. Trends in the enthalpies for hydrogen exchange and the fractionation factors are consistent with a strong, double-minimum or single-well potential hydrogen bond in the strongest complexes. The lifetimes of His 57-Hδ1, which is solvent shielded in these complexes, track the strength of the hydrogen bond. Because these lifetimes are orders of magnitude shorter than those of the complexes themselves, the enzyme must have a pathway for hydrogen exchange at this site that is independent of dissociation of the complexes.

Femtosecond dynamics of the forbidden carotenoid S1 state in light-harvesting complexes of purple bacteria observed after two-photon excitation

Time-resolved excited-state absorption intensities after direct two-photon excitation of the carotenoid S1 state are reported for light-harvesting complexes of purple bacteria. Direct excitation of the carotenoid S1 state enables the measurement of subsequent dynamics on a fs time scale without interference from higher excited states, such as the optically allowed S2 state or the recently discovered dark state situated between S1 and S2. The lifetimes of the carotenoid S1 states in the B800-B850 complex and B800-B820 complex of Rhodopseudomonas acidophila are 7 ± 0.5 ps and 6 ± 0.5 ps, respectively, and in the light-harvesting complex 2 of Rhodobacter sphaeroides ≈1.9 ± 0.5 ps. These results explain the differences in the carotenoid to bacteriochlorophyll energy transfer efficiency after S2 excitation. In Rps. acidophila the carotenoid S1 to bacteriochlorophyll energy transfer is found to be quite inefficient (φET1 <28%) whereas in Rb. sphaeroides this energy transfer is very efficient (φET1 ≈80%). The results are rationalized by calculations of the ensemble averaged time constants. We find that the Car S1 → B800 electronic energy transfer (EET) pathway (≈85%) dominates over Car S1 → B850 EET (≈15%) in Rb. sphaeroides, whereas in Rps. acidophila the Car S1 → B850 EET (≈60%) is more efficient than the Car S1 → B800 EET (≈40%). The individual electronic couplings for the Car S1 → BChl energy transfer are estimated to be approximately 5–26 cm−1. A major contribution to the difference between the energy transfer efficiencies can be explained by different Car S1 energy gaps in the two species.

Reversible encapsulation by self-assembling resorcinarene subunits

Encapsulation complexes are assemblies in which a reversibly formed host more or less completely surrounds guest molecules. Host structures held together by hydrogen bonds have lifetimes in organic solvents of milliseconds to hours, long enough to directly observe the encapsulated guest by NMR spectroscopy. We describe here the action of alkyl ammonium compounds as guests that gather up to six molecules of the host module to form encapsulation complexes. The stoichiometry of the complexes—the largest hydrogen-bonded host capsules to date—is determined by the size and concentration of the guest.

Conformational transitions monitored for single molecules in solution.

Phenomena that can be observed for a large number of molecules may not be understood if it is not possible to observe the events on the single-molecule level. We measured the fluorescence lifetimes of individual tetramethylrhodamine molecules, linked to an 18-mer deoxyribonucleotide sequence specific for M13 DNA, by time-resolved, single-photon counting in a confocal fluorescence microscope during Brownian motion in solution. When many molecules were observed, a biexponential fluorescence decay was observed with equal amplitudes. However, on the single-molecule level, the fraction of one of the amplitudes spanned from 0 to unity for a collection of single-molecule detections. Further analysis by fluorescence correlation spectroscopy made on many molecules revealed a process that obeys a stretched exponential relaxation law. These facts, combined with previous evidence of the quenching effect of guanosine on rhodamines, indicate that the tetramethylrhodamine molecule senses conformational transitions as it associates and dissociates to a guanosine-rich area. Thus, our results reveal conformational transitions in a single molecule in solution under conditions that are relevant for biological processes.