Coronal fluid-dynamics in laser fusion

The fluid-dynamics of the corona ejected by laser-fusion targets in the direct-drive approach (thermal radiation and atomic physics unimportant) is discussed. A two-fluid model involves inverse bremsstrahlung absorption, refraction, different ion and electron temperatures with energy exchange, different ion and electron velocities and magnetic field generation, and their effect on ion-electron friction and heat flux. Four dimensionless parameters determine coronal regimes for one-dimensional flows under uniform irradiation. One additional parameter is involved in two-dimensional problems,including the stability of one-dimensional flows, and the smoothing of nonuniform driving.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

Contraste de las formulaciones existentes para la estimación de la tasa de rebase en diques de abrigo portuario

The research that is summarized in this article, resultant of diverse studies realized in the CEDEX, has for object a comparative analysis of methods of overtopping rates developed by different authors. For that, the summary was realized first and the analysis of the existing formulations to estimate the rate of overtopping on rubble mound and vertical breakwaters. Later, there was carried out the contrast of the above mentioned formulations by the results obtained in two hydraulic model tests of the Hydraulic Research Laboratory (Center of Studies of Ports and Coasts of the CEDEX, Madrid, Spain).

A 2D computational parametric analysis of the sheltering effect of fences on a railway vehicle standing on a bridge and experiencing crosswinds

In a crosswind scenario, the risk of high-speed trains overturning increases when they run on viaducts since the aerodynamic loads are higher than on the ground. In order to increase safety, vehicles are sheltered by fences that are installed on the viaduct to reduce the loads experienced by the train. Windbreaks can be designed to have different heights, and with or without eaves on the top. In this paper, a parametric study with a total of 12 fence designs was carried out using a two-dimensional model of a train standing on a viaduct. To asses the relative effectiveness of sheltering devices, tests were done in a wind tunnel with a scaled model at a Reynolds number of 1 × 105, and the train’s aerodynamic coefficients were measured. Experimental results were compared with those predicted by Unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of flow, showing that a computational model is able to satisfactorily predict the trend of the aerodynamic coefficients. In a second set of tests, the Reynolds number was increased to 12 × 106 (at a free flow air velocity of 30 m/s) in order to simulate strong wind conditions. The aerodynamic coefficients showed a similar trend for both Reynolds numbers; however, their numerical value changed enough to indicate that simulations at the lower Reynolds number do not provide all required information. Furthermore, the variation of coefficients in the simulations allowed an explanation of how fences modified the flow around the vehicle to be proposed. This made it clear why increasing fence height reduced all the coefficients but adding an eave had an effect mainly on the lift force coefficient. Finally, by analysing the time signals it was possible to clarify the influence of the Reynolds number on the peak-to-peak amplitude, the time period and the Strouhal number.

Sistema de adquisición de datos para una aplicación de detección del ruido de reversa en tiempo real

Entre todas las fuentes de ruido, la activación de la propulsión en reversa de un avión después de aterrizar es conocida por las autoridades del aeropuerto como una causa importante de impacto acústico, molestias y quejas en las proximidades vecinas de los aeropuertos. Por ello, muchos de los aeropuertos de todo el mundo han establecido restricciones en el uso de la reversa, especialmente en las horas de la noche. Una forma de reducir el impacto acústico en las actividades aeroportuarias es implementar herramientas eficaces para la detección de ruido en reversa en los aeropuertos. Para este proyecto de fin de carrera, aplicando la metodología TREND (Thrust Reverser Noise Detection), se pretende desarrollar un sistema software capaz de determinar que una aeronave que aterrice en la pista active el frenado en reversa en tiempo real. Para el diseño de la aplicación se plantea un modelo software, que se compone de dos módulos:  El módulo de adquisición de señales acústicas, simula un sistema de captación por señales de audio. Éste módulo obtiene muestra de señales estéreo de ficheros de audio de formato “.WAV” o del sistema de captación, para acondicionar las muestras de audio y enviarlas al siguiente módulo. El sistema de captación (array de micrófonos), se encuentra situado en una localización cercana a la pista de aterrizaje.  El módulo de procesado busca los eventos de detección aplicando la metodología TREND con las muestras acústicas que recibe del módulo de adquisición. La metodología TREND describe la búsqueda de dos eventos sonoros llamados evento 1 (EV1) y evento 2 (EV2); el primero de ellos, es el evento que se activa cuando una aeronave aterriza discriminando otros eventos sonoros como despegues de aviones y otros sonidos de fondo, mientras que el segundo, se producirá después del evento 1, sólo cuando la aeronave utilice la reversa para frenar. Para determinar la detección del evento 1, es necesario discriminar las señales ajenas al aterrizaje aplicando un filtrado en la señal capturada, después, se aplicará un detector de umbral del nivel de presión sonora y por último, se determina la procedencia de la fuente de sonido con respecto al sistema de captación. En el caso de la detección del evento 2, está basada en la implementación de umbrales en la evolución temporal del nivel de potencia acústica aplicando el modelo de propagación inversa, con ayuda del cálculo de la estimación de la distancia en cada instante de tiempo mientras el avión recorre la pista de aterrizaje. Con cada aterrizaje detectado se realiza una grabación que se archiva en una carpeta específica y todos los datos adquiridos, son registrados por la aplicación software en un fichero de texto. ABSTRACT. Among all noise sources, the activation of reverse thrust to slow the aircraft after landing is considered as an important cause of noise pollution by the airport authorities, as well as complaints and annoyance in the airport´s nearby locations. Therefore, many airports around the globe have restricted the use of reverse thrust, especially during the evening hours. One way to reduce noise impact on airport activities is the implementation of effective tools that deal with reverse noise detection. This Final Project aims to the development of a software system capable of detecting if an aircraft landing on the runway activates reverse thrust on real time, using the TREND (Thrust Reverser Noise Detection) methodology. To design this application, a two modules model is proposed: • The acoustic signals obtainment module, which simulates an audio waves based catchment system. This module obtains stereo signal samples from “.WAV” audio files or the catchment system in order to prepare these audio samples and send them to the next module. The catchment system (a microphone array) is located on a place near the landing runway. • The processing module, which looks for detection events among the acoustic samples received from the other module, using the TREND methodology. The TREND methodology describes the search of two sounds events named event 1 (EV1) and event 2 (EV2). The first is the event activated by a landing plane, discriminating other sound events such as background noises or taking off planes; the second one will occur after event one only when the aircraft uses reverse to slow down. To determine event 1 detection, signals outside the landing must be discriminated using a filter on the catched signal. A pressure level´s threshold detector will be used on the signal afterwards. Finally, the origin of the sound source is determined regarding the catchment system. The detection of event 2 is based on threshold implementations in the temporal evolution of the acoustic power´s level by using the inverse propagation model and calculating the distance estimation at each time step while the plane goes on the landing runway. A recording is made every time a landing is detected, which is stored in a folder. All acquired data are registered by the software application on a text file.

UMA ANÁLISE DA RELAÇÃO ENTRE VARIÁVEIS MACROECONÔMICAS E O COMPORTAMENTO DAS AÇÕES DE MAIOR LIQUIDEZ DO ÍNDICE IBOVESPA

As ações de maior liquidez do índice IBOVESPA, refletem o comportamento das ações de um modo geral, bem como a relação das variáveis macroeconômicas em seu comportamento e estão entre as mais negociadas no mercado de capitais brasileiro. Desta forma, pode-se entender que há reflexos de fatores que impactam as empresas de maior liquidez que definem o comportamento das variáveis macroeconômicas e que o inverso também é uma verdade, oscilações nos fatores macroeconômicos também afetam as ações de maior liquidez, como IPCA, PIB, SELIC e Taxa de Câmbio. O estudo propõe uma análise da relação existente entre variáveis macroeconômicas e o comportamento das ações de maior liquidez do índice IBOVESPA, corroborando com estudos que buscam entender a influência de fatores macroeconômicos sobre o preço de ações e contribuindo empiricamente com a formação de portfólios de investimento. O trabalho abrangeu o período de 2008 a 2014. Os resultados concluíram que a formação de carteiras, visando a proteção do capital investido, deve conter ativos com correlação negativa em relação às variáveis estudadas, o que torna possível a composição de uma carteira com risco reduzido.

Aggregate community properties and the strength of species’ interactions

Although humanity depends on the continued, aggregate functioning of natural ecosystems, few studies have explored the impact of community structure on the stability of aggregate community properties. Here we derive the stability of the aggregate property of community biomass as a function of species’ competition coefficients for a two-species model. The model predicts that the stability of community biomass is relatively independent of the magnitude of the interaction strengths. Instead, the degree of asymmetry of the interactions appears to be key to community stability.

Saccharomyces cerevisiae MPS2 Encodes a Membrane Protein Localized at the Spindle Pole Body and the Nuclear Envelope

The MPS2 (monopolar spindle two) gene is one of several genes required for the proper execution of spindle pole body (SPB) duplication in the budding yeast Saccharomyces cerevisiae (Winey et al., 1991). We report here that the MPS2 gene encodes an essential 44-kDa protein with two putative coiled-coil regions and a hydrophobic sequence. Although MPS2 is required for normal mitotic growth, some null strains can survive; these survivors exhibit slow growth and abnormal ploidy. The MPS2 protein was tagged with nine copies of the myc epitope, and biochemical fractionation experiments show that it is an integral membrane protein. Visualization of a green fluorescent protein (GFP) Mps2p fusion protein in living cells and indirect immunofluorescence microscopy of 9xmyc-Mps2p revealed a perinuclear localization with one or two brighter foci of staining corresponding to the SPB. Additionally, immunoelectron microscopy shows that GFP-Mps2p localizes to the SPB. Our analysis suggests that Mps2p is required as a component of the SPB for insertion of the nascent SPB into the nuclear envelope.

Solid-state synthesis and mechanical unfolding of polymers of T4 lysozyme

Recent advances in single molecule manipulation methods offer a novel approach to investigating the protein folding problem. These studies usually are done on molecules that are naturally organized as linear arrays of globular domains. To extend these techniques to study proteins that normally exist as monomers, we have developed a method of synthesizing polymers of protein molecules in the solid state. By introducing cysteines at locations where bacteriophage T4 lysozyme molecules contact each other in a crystal and taking advantage of the alignment provided by the lattice, we have obtained polymers of defined polarity up to 25 molecules long that retain enzymatic activity. These polymers then were manipulated mechanically by using a modified scanning force microscope to characterize the force-induced reversible unfolding of the individual lysozyme molecules. This approach should be general and adaptable to many other proteins with known crystal structures. For T4 lysozyme, the force required to unfold the monomers was 64 ± 16 pN at the pulling speed used. Refolding occurred within 1 sec of relaxation with an efficiency close to 100%. Analysis of the force versus extension curves suggests that the mechanical unfolding transition follows a two-state model. The unfolding forces determined in 1 M guanidine hydrochloride indicate that in these conditions the activation barrier for unfolding is reduced by 2 kcal/mol.

Mg-chelatase of tobacco: The role of the subunit CHL D in the chelation step of protoporphyrin IX

The Mg-chelation is found to be a prerequisite to direct protoporphyrin IX into the chlorophyll (Chl)-synthesizing branch of the tetrapyrrol pathway. The ATP-dependent insertion of magnesium into protoporphyrin IX is catalyzed by the enzyme Mg-chelatase, which consists of three protein subunits (CHL D, CHL I, and CHL H). We have chosen the Mg-chelatase from tobacco to obtain more information about the mode of molecular action of this complex enzyme by elucidating the interactions in vitro and in vivo between the central subunit CHL D and subunits CHL I and CHL H. We dissected CHL D in defined peptide fragments and assayed for the essential part of CHL D for protein–protein interaction and enzyme activity. Surprisingly, only a small part of CHL D, i.e., 110 aa, was required for interaction with the partner subunits and maintenance of the enzyme activity. In addition, it could be demonstrated that CHL D is capable of forming homodimers. Moreover, it interacted with both CHL I and CHL H. Our data led to the outline of a two-step model based on the cooperation of the subunits for the chelation process.

A decrease of reelin expression as a putative vulnerability factor in schizophrenia

Postmortem prefrontal cortices (PFC) (Brodmann’s areas 10 and 46), temporal cortices (Brodmann’s area 22), hippocampi, caudate nuclei, and cerebella of schizophrenia patients and their matched nonpsychiatric subjects were compared for reelin (RELN) mRNA and reelin (RELN) protein content. In all of the brain areas studied, RELN and its mRNA were significantly reduced (≈50%) in patients with schizophrenia; this decrease was similar in patients affected by undifferentiated or paranoid schizophrenia. To exclude possible artifacts caused by postmortem mRNA degradation, we measured the mRNAs in the same PFC extracts from γ-aminobutyric acid (GABA)A receptors α1 and α5 and nicotinic acetylcholine receptor α7 subunits. Whereas the expression of the α7 nicotinic acetylcholine receptor subunit was normal, that of the α1 and α5 receptor subunits of GABAA was increased when schizophrenia was present. RELN mRNA was preferentially expressed in GABAergic interneurons of PFC, temporal cortex, hippocampus, and glutamatergic granule cells of cerebellum. A protein putatively functioning as an intracellular target for the signal-transduction cascade triggered by RELN protein released into the extracellular matrix is termed mouse disabled-1 (DAB1) and is expressed at comparable levels in the neuroplasm of the PFC and hippocampal pyramidal neurons, cerebellar Purkinje neurons of schizophrenia patients, and nonpsychiatric subjects; these three types of neurons do not express RELN protein. In the same samples of temporal cortex, we found a decrease in RELN protein of ≈50% but no changes in DAB1 protein expression. We also observed a large (up to 70%) decrease of GAD67 but only a small decrease of GAD65 protein content. These findings are interpreted within a neurodevelopmental/vulnerability “two-hit” model for the etiology of schizophrenia.

Rapid generation of incremental truncation libraries for protein engineering using α-phosphothioate nucleotides

Incremental truncation for the creation of hybrid enzymes (ITCHY) is a novel tool for the generation of combinatorial libraries of hybrid proteins independent of DNA sequence homology. We herein report a fundamentally different methodology for creating incremental truncation libraries using nucleotide triphosphate analogs. Central to the method is the polymerase catalyzed, low frequency, random incorporation of α-phosphothioate dNTPs into the region of DNA targeted for truncation. The resulting phosphothioate internucleotide linkages are resistant to 3′→5′ exonuclease hydrolysis, rendering the target DNA resistant to degradation in a subsequent exonuclease III treatment. From an experimental perspective the protocol reported here to create incremental truncation libraries is simpler and less time consuming than previous approaches by combining the two gene fragments in a single vector and eliminating additional purification steps. As proof of principle, an incremental truncation library of fusions between the N-terminal fragment of Escherichia coli glycinamide ribonucleotide formyltransferase (PurN) and the C-terminal fragment of human glycinamide ribonucleotide formyltransferase (hGART) was prepared and successfully tested for functional hybrids in an auxotrophic E.coli host strain. Multiple active hybrid enzymes were identified, including ones fused in regions of low sequence homology.

Efficient use of a small genome to generate antigenic diversity in tick-borne ehrlichial pathogens

Ehrlichiae are responsible for important tick-transmitted diseases, including anaplasmosis, the most prevalent tick-borne infection of livestock worldwide, and the emerging human diseases monocytic and granulocytic ehrlichiosis. Antigenic variation of major surface proteins is a key feature of these pathogens that allows persistence in the mammalian host, a requisite for subsequent tick transmission. In Anaplasma marginale pseudogenes for two antigenically variable gene families, msp2 and msp3, appear in concert. These pseudogenes can be recombined into the functional expression site to generate new antigenic variants. Coordinated control of the recombination of these genes would allow these two gene families to act synergistically to evade the host immune response.

Selective association of the methyl-CpG binding protein MBD2 with the silent p14/p16 locus in human neoplasia

DNA methylation of tumor suppressor genes is a common feature of human cancer. The cyclin-dependent kinase inhibitor gene p16/Ink4A is hypermethylated in a wide range of malignant tissues and the p14/ARF gene located 20 kb upstream on chromosome 9p21 is also methylated in carcinomas. p14/ARF (ARF, alternative reading frame) does not inhibit the activities of cyclins or cyclin-dependent kinase complexes; however, the importance of the two gene products in the etiology of cancer resides in their involvement in two major cell cycle regulatory pathways: p53 and the retinoblastoma protein, Rb, respectively. Distinct first exons driven from separate promoters are spliced onto the common exons 2 and 3 and the resulting proteins are translated in different reading frames. Both genes are expressed in normal cells but can be alternatively or coordinately silenced when their CpG islands are hypermethylated. Herein, we examined the presence of methyl-CpG binding proteins associated with aberrantly methylated promoters, the distribution of acetylated histones H3 and H4 by chromatin immunoprecipitation assays, and the effect of chemical treatment with 5-aza-2′-deoxycytidine (5aza-dC) and trichostatin A on gene induction in colon cell lines by quantitative reverse transcriptase–PCR. We observed that the methyl-CpG binding protein MBD2 is targeted to methylated regulatory regions and excludes the acetylated histones H3 and H4, resulting in a localized inactive chromatin configuration. When methylated, the genes can be induced by 5aza-dC but the combined action of 5aza-dC and trichostatin A results in robust gene expression. Thus, methyl-CpG binding proteins and histone deacetylases appear to cooperate in vivo, with a dominant effect of DNA methylation toward histone acetylation, and repress expression of tumor suppressor genes hypermethylated in cancers.

Dissection of the ion-induced folding of the hammerhead ribozyme using 19F NMR

We have used 19F NMR to analyze the metal ion-induced folding of the hammerhead ribozyme by selective incorporation of 5fluorouridine. We have studied the chemical shift and linewidths of 19F resonances of 5-fluorouridine at the 4 and 7 positions in the ribozyme core as a function of added Mg2+. The data fit well to a simple two-state model whereby the formation of domain 1 is induced by the noncooperative binding of Mg2+ with an association constant in the range of 100 to 500 M−1, depending on the concentration of monovalent ions present. The results are in excellent agreement with data reporting on changes in the global shape of the ribozyme. However, the NMR experiments exploit reporters located in the center of the RNA sections undergoing the folding transitions, thereby allowing the assignment of specific nucleotides to the separate stages. The results define the folding pathway at high resolution and provide a time scale for the first transition in the millisecond range.