Anomalous Velocity Distributions in Active Brownian Suspensions

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f (v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

Transient dominance in a central African rain forest

The large-crowned emergent tree Microberlinia bisulcata dominates rain forest groves at Korup National Park, Cameroon, along with two codominants, Tetraberlinia bifoliolata and T. korupensis. M. bisulcata has a pronounced modal size frequency distribution around 110 cm stem diameter: its recruitment potential is very poor. It is a long-lived light-demanding species, one of many found in African forests. Tetraberlinia species lack modality, are more shade tolerant, and recruit better. All three species are ectomycorrhizal. M. bisulcata dominates grove basal area, even though it has similar numbers of trees (≥50 cm stem diameter) as each of the other two species. This situation presented a conundrum that prompted a long-term study of grove dynamics. Enumerations of two plots (82.5 and 56.25 ha) between 1990 and 2010 showed mortality and recruitment of M. bisulcata to be very low (both rates 0.2% per year) compared with Tetraberlinia (2.4% and 0.8% per year), and M. bisulcata grows twice as fast as the Tetraberlinia. Ordinations indicated that these three species determined community structure by their strong negative associations while other species showed almost none. Ranked species abundance curves fitted the Zipf-Mandelbrot model well and allowed “overdominance” of M. bisulcata to be estimated. Spatial analysis indicated strong repulsion by clusters of large (50 to <100 cm) and very large (≥100 cm) M. bisulcata of their own medium-sized (10 to <50 cm) trees and all sizes of Tetraberlinia. This was interpreted as competition by M. bisulcata increasing its dominance, but also inhibition of its own replacement potential. Stem coring showed a modal age of 200 years for M. bisulcata, but with large size variation (50–150 cm). Fifty-year model projections suggested little change in medium, decreases in large, and increases in very large trees of M. bisulcata, accompanied by overall decreases in medium and large trees of Tetraberlinia species. Realistically increasing very-large-tree mortality led to grove collapse without short-term replacement. M. bisulcata most likely depends on climatic events to rebuild its stands: the ratio of disturbance interval to median species' longevity is important. A new theory of transient dominance explains how M. bisulcata may be cycling in abundance over time and displaying nonequilibrium dynamics.

A study of oxygen isotopic fractionation during bio-induced calcite precipitation in eutrophic Baldeggersee, Switzerland

In order to better understand environmental factors controlling oxygen isotope shifts in autochthonous lacustrine carbonate sequences, we undertook an extensive one-year study (March, 1995 to February, 1996) of water-column chemistry and daily sediment trap material from a small lake in Central Switzerland. Comparisons between calculated equilibrium isotope values, using the fractionation equation of Friedman and O’Neil, (1977) and measured oxygen isotope ratios of calcite in the sediment-traps reveal that oxygen isotopic values of autochthonous calcite (δ18O) are in isotopic equilibrium with ambient water during most of the spring and summer, when the majority of the calcite precipitates. In contrast, small amounts of calcite precipitated in early-spring and again in late-autumn are isotopically depleted in 18O relative to the calculated equilibrium values, by as much as 0.8‰. This seasonally occurring apparent isotopic nonequilibrium is associated with times of high phosphorous concentrations, elevated pH (∼8.6) and increased [CO32−] (∼50 μmol/l) in the surface waters. The resulting weighted average δ18O value for the studied period is −9.6‰, compared with a calculated equilibrium δ18O value of −9.4‰. These data convincingly demonstrate that δ18O of calcite are, for the most part, a very reliable proxy for temperature and δ18O of the water.

Stable isotope response to lake eutrophication: Calibration of a high-resolution lacustrine sequence from Baldeggersee, Switzerland

Stable isotope analyses of discrete seasonal layers from a 108-yr annually laminated freeze-core from Baldeg-gersee, a small, eutrophic lake in central Switzerland, provide information on the climatological and environmental factors, including lake eutrophication, that control oxygen and carbon isotopic composition of epilimnic biologically induced calcite precipitate. During the last 100 yr, Baldeggersee has undergone major increases in productivity and eutrophication in response to nutrient loading from agriculture and industrialization in the lake's watershed. Calibration of the isotopic signal in Baldeggersee to historical limnological data quantitatively links evidence of isotopic depletion in the sedimented calcite to trophic state of the lake. δ18O values from the spring/summer “light” sediment layers steadily diverged to more depleted values in response to historical eutrophication: measured δ18O values were up to 21.5‰ more negative than calculated equilibrium δ18O values. Evidence for 13C depletion in the calcite, relative to equilibrium values, is more difficult to ascertain because of an overall dominance of isotopic enrichment in the dissolved inorganic pool as productivity in Baldeggersee increases. A positive association exists between the degree of oxygen-18 depletion and the calcite crystal size. Thus, large amorphous calcite grains can be used as a proxy for recognizing apparent isotopic nonequilibrium in sediment sequences from highly productive lacustrine environments from all geologic time scales. In contrast to the light layers, the oxygen isotopic composition of the calcite in the late summer/fall “dark” sediment layers is unaffected by the apparent isotope nonequilibrium. Oxygen and carbon isotope values from the dark laminae in the Baldeggersee sediment therefore provide environmental and climatological proxies that can be calibrated with known environmental and regional climate data for the last century.

(Table 3) Chemical composition of phosphatized rocks from the Kammu Seamount

Phosphatized biogenic limestones and phosphorites with initial Fe-Mn mineralization dredged from the summit surface of the Kammu Seamount (Milwaukee Seamounts, northwestern Pacific) are studied. The rocks are largely composed of nannofossils and planktonic foraminifers with an admixture of benthic foraminifers, bryozoans, and other organic remains, presumably including bacterial ones. The nannofosssil and foraminiferal assemblages indicate Quaternary age of sediments, and their phosphatization is consistent with the phosphatization age determined previously based on nonequilibrium uranium (within the limits of 1 My). The age of phosphatization and the Fe-Mn mineralization in the sediments from Pacific seamounts that young implies dependence of these ore-forming processes on oceanic environments favorable for ore accumulation rather than on their age.

Chemical and isotopic compositions of rocks, ores, and hydrothermal minerals from the Rainbow and Logachev-2 hydrothermal fields

The aim of this paper is to analyze and compare mineralogy and geochemistry of copper-zinc sulfide ores from the Logachev-2 and Rainbow hydrothermal fields of the Mid-Atlantic Ridge (MAR) confined to serpentinite protrusions. It was found that Zn(Fe) and Cu, Fe(Zn) sulfides had been deposited in black smokers pipes almost simultaneously from intermittently flowing, nonequilibrium H2S-low solutions of different temperatures. Pb isotope composition confirmed that the deep oceanic crust had been a source of lead. The ores from the Rainbow field are 20-fold higher in Co than ores restricted to basalts and show a high ratio of Co/Ni=46. The ores from the Rainbow field are enriched in 34S isotope (aver. d34S=10 per mil) because of constant flow of cold sea water into the subsurface zone of the hydrothermal system. Ores from the Logachev-2 field are 8 times higher in gold compared to other MAR regions. Sulfide ores from the Rainbow and Logachev-2 fields have no analogues among MAR ore occurrences in terms of enrichment in valuable components (Zn, Cd, Co, and Au).

(Table 3) Stable oxagen isotope record of planktonic foraminifera from Central Walvish Ridge

Above the Walvis Ridge, in the SE Atlantic Ocean, we collected living plantkic foraminifera from the upper water column using depth stratified plantkon tows. The oxygen isotope composition (d18Oc) in shells of foraminifera and shell concentration profiles show seasonal and depth habitats of individual species. The tow results are compared with the average annual deposition d18Oc from sediment traps and the interannual average d18Oc of fossil specimens in top sediments at the same site. The species Globigerinita glutinata best reflects the austral winter/spring sea surface temperature (SST). Its d18Oc signal in top sediments remains pristine. In contrast, tow results also show that Globigerinoides ruber continues to calcify below the surface mixed layer (SML), i.e., down to the deep chlorophyll maximum (DCM); hence its d18Oc signature of exported specimens reflects the SST only when SML incorporates the DCM. Deep tow and sediment trap results show that both Globorotalia truncatulinoides and Globorotalia inflata record the temperature between 150 and 350 m, depending on the season and the shell size. However, for all fossil taxa in sediments apart from Globigerinita glutinata, we observe a positive d18Oc shift with respect to the sediment trap and plankton tow values, likely related to the interannual flux changes and deep encrustation.

Uranium and thorium isotopes and sedimentation rates in metalliferous sediments from the western flank of the East Pacific Rise at 21°-22°S

Isotopic compositions of uranium (234U and 238U) and thorium (230Th and 232Th) were measured in metalliferous sediments from the western flank of the East Pacific Rise at 21°-22°S, in the area of hydrothermal activity and massive sulfide accumulation at the axis of the EPR. Concentration of 232Th (on the carbonate-free base) is consistent with composition of mafic extrusive rocks; isotope ratios 232Th/238U and 234U/238U indicate that about 70% of uranium passes into sediments from sea water with hydrothermal iron hydroxide. Mean sedimentation rates are calculated for seven cores by the nonequilibrium 230Th method with use of the constant concentration model. Flux of 230Th to bottom sediments is calculated and its mean value is used to determine sedimentation rate in four other cores. The constant flux model is used to calculate change of sedimentation rate with depth for seven cores over time interval of 100-300 ky. Sedimentation rates varied not much (0.3-0.6 cm/ky). The greatest changes occurred in two cores: one located near massive sulfide structures, and another near the spreading axis. Determinations of mean rates by the radiocarbon method and the nonequilibrium thorium method are in good agreement.

Composition and crystal parameters of carbonate-apatites from animal teeth and bones and from phosphate rocks of the ocean bottom

Samples of recent to Miocene fish and marine mammal bones from the bottom of the Atlantic and Pacific Oceans and Miocene Maikop deposits (Transcaspian region) are studied by X-ray diffraction technique combined with chemical and energy-dispersive analyses. Changes of lattice parameters and chemical composition of bioapatite during fossilization and diagenesis suggest that development of skeletal apatite proceeds from dahllite-type hydroxyapatite to francolite-type carbonate-fluorapatite. It is assumed that jump-type transition from dahllite to francolite during initial fossilization reflects replacement of biogeochemical reactions in living organisms, which are subject to nonlinear laws of nonequilibrium thermodynamics, by physicochemical processes according to the linear equilibrium thermodynamics.

Geochemistry and fluxes at DSDP Hole 83-504B

This chapter documents the chemical changes produced by hydrothermal alteration of basalts drilled on Leg 83, in Hole 504B. It interprets these chemical changes in terms of mineralogical changes and alteration processes and discusses implications for geochemical cycling. Alteration of Leg 83 basalts is characterized by nonequilibrium and is heterogeneous on a scale of centimeters to tens or hundreds of meters. The basalts exhibit trends toward losses of SiO2, CaO, TiO2; decreases in density; gains of MnO, Na2O, CO2, H2O+ , S; slight gains of MgO; increased oxidation of Fe; and variable changes in A12O3. Some mobility of rare earth elements (REE) also occurred, especially the light REE and Eu. The basalts have lost Ca in excess of Mg + Na gains. Variations in chemical trends are due to differing water/rock ratios, substrate control of secondary mineralogy, and superimposition of greenschist and zeolite facies mineralogies. Zeolitization resulted in uptake of Ca and H2O and losses of Si, Al, and Na. These effects are different from the Na uptake observed in other altered basalts from the seafloor attributed to the zeolite facies and are probably due to higher temperatures of alteration of Leg 83 basalts. Basalts from the transition zone are enriched in Mn, S, and CO2 relative to the pillow and dike sections and contain a metal-sulfide-rich stockwork zone, suggesting that they once were located within or near a hydrothermal upflow zone. Samples from the bottom of the dike section are extensively fractured and recrystallized indicating that alteration was significantly affected by local variations in permeability.

Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (mesoreservoir). The mesoreservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of noninteracting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.

Particle and energy transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.

Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surfacefilm of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological nonequilibrium thermodynamics for a general nonisothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analyzed.

Modelización de los Procesos de Cristalización en Poliolefinas

“Por lo tanto, la cristalización de polímeros se supone, y en las teorías se describe a menudo, como un proceso de múltiples pasos con muchos aspectos físico-químicos y estructurales influyendo en él. Debido a la propia estructura de la cadena, es fácil entender que un proceso que es termodinámicamente forzado a aumentar su ordenamiento local, se vea obstaculizado geométricamente y, por tanto, no puede conducirse a un estado de equilibrio final. Como resultado, se forman habitualmente estructuras de no equilibrio con diferentes características dependiendo de la temperatura, presión, cizallamiento y otros parámetros físico-químicos del sistema”. Estas palabras, pronunciadas recientemente por el profesor Bernhard Wunderlich, uno de los mas relevantes fisico-quimicos que han abordado en las ultimas décadas el estudio del estado físico de las macromoléculas, adelantan lo que de alguna manera se explicita en esta memoria y constituyen el “leitmotiv” de este trabajo de tesis. El mecanismo de la cristalización de polímeros esta aun bajo debate en la comunidad de la física de polímeros y la mayoría de los abordajes experimentales se explican a través de la teoría LH. Esta teoría clásica debida a Lauritzen y Hoffman (LH), y que es una generalización de la teoría de cristalización de una molécula pequeña desde la fase de vapor, describe satisfactoriamente muchas observaciones experimentales aunque esta lejos de explicar el complejo fenómeno de la cristalización de polímeros. De hecho, la formulación original de esta teoría en el National Bureau of Standards, a comienzos de la década de los 70, sufrió varias reformulaciones importantes a lo largo de la década de los 80, buscando su adaptación a los hallazgos experimentales. Así nació el régimen III de cristalización que posibilita la creacion de nichos moleculares en la superficie y que dio pie al paradigma ofrecido por Sadler y col., para justificar los experimentos que se obtenian por “scattering” de neutrones y otras técnicas como la técnica de “droplets” o enfriamiento rapido. Por encima de todo, el gran éxito de la teoría radica en que explica la dependencia inversa entre el tamaño del plegado molecular y el subenfriamiento, definido este ultimo como el intervalo de temperatura que media entre la temperatura de equilibrio y la temperatura de cristalización. El problema concreto que aborda esta tesis es el estudio de los procesos de ordenamiento de poliolefinas con distinto grado de ramificacion mediante simulaciones numéricas. Los copolimeros estudiados en esta tesis se consideran materiales modelo de gran homogeneidad molecular desde el punto de vista de la distribución de tamaños y de ramificaciones en la cadena polimérica. Se eligieron estas poliolefinas debido al gran interes experimental en conocer el cambio en las propiedades fisicas de los materiales dependiendo del tipo y cantidad de comonomero utilizado. Además, son modelos sobre los que existen una ingente cantidad de información experimental, que es algo que preocupa siempre al crear una realidad virtual como es la simulación. La experiencia en el grupo Biophym es que los resultados de simulación deben de tener siempre un correlato mas o menos próximo experimental y ese argumento se maneja a lo largo de esta memoria. Empíricamente, se conoce muy bien que las propiedades físicas de las poliolefinas, en suma dependen del tipo y de la cantidad de ramificaciones que presenta el material polimérico. Sin embargo, tal como se ha explicado no existen modelos teóricos adecuados que expliquen los mecanismos subyacentes de los efectos de las ramas. La memoria de este trabajo es amplia por la complejidad del tema. Se inicia con una extensa introducción sobre los conceptos básicos de una macromolecula que son relevantes para entender el contenido del resto de la memoria. Se definen los conceptos de macromolecula flexible, distribuciones y momentos, y su comportamiento en disolución y fundido con los correspondientes parametros caracteristicos. Se pone especial énfasis en el concepto de “entanglement” o enmaranamiento por considerarse clave a la hora de tratar macromoléculas con una longitud superior a la longitud critica de enmaranamiento. Finaliza esta introducción con una reseña sobre el estado del arte en la simulación de los procesos de cristalización. En un segundo capitulo del trabajo se expone detalladamente la metodología usada en cada grupo de casos. En el primer capitulo de resultados, se discuten los estudios de simulación en disolución diluida para sistemas lineales y ramificados de cadena única. Este caso mas simple depende claramente del potencial de torsión elegido tal como se discute a lo largo del texto. La formación de los núcleos “babys” propuestos por Muthukumar parece que son consecuencia del potencial de torsión, ya que este facilita los estados de torsión mas estables. Así que se propone el análisis de otros potenciales que son igualmente utilizados y los resultados obtenidos sobre la cristalización, discutidos en consecuencia. Seguidamente, en un segundo capitulo de resultados se estudian moleculas de alcanos de cadena larga lineales y ramificados en un fundido por simulaciones atomisticas como un modelo de polietileno. Los resultados atomisticos pese a ser de gran detalle no logran captar en su totalidad los efectos experimentales que se observan en los fundidos subenfriados en su etapa previa al estado ordenado. Por esta razon se discuten en los capítulos 3 y 4 de resultados sistemas de cadenas cortas y largas utilizando dos modelos de grano grueso (CG-PVA y CG-PE). El modelo CG-PE se desarrollo durante la tesis. El uso de modelos de grano grueso garantiza una mayor eficiencia computacional con respecto a los modelos atomísticos y son suficientes para mostrar los fenómenos a la escala relevante para la cristalización. En todos estos estudios mencionados se sigue la evolución de los procesos de ordenamiento y de fusión en simulaciones de relajación isoterma y no isoterma. Como resultado de los modelos de simulación, se han evaluado distintas propiedades fisicas como la longitud de segmento ordenado, la cristalinidad, temperaturas de fusion/cristalizacion, etc., lo que permite una comparación con los resultados experimentales. Se demuestra claramente que los sistemas ramificados retrasan y dificultan el orden de la cadena polimérica y por tanto, las regiones cristalinas ordenadas decrecen al crecer las ramas. Como una conclusión general parece mostrarse una tendencia a la formación de estructuras localmente ordenadas que crecen como bloques para completar el espacio de cristalización que puede alcanzarse a una temperatura y a una escala de tiempo determinada. Finalmente hay que señalar que los efectos observados, estan en concordancia con otros resultados tanto teoricos/simulacion como experimentales discutidos a lo largo de esta memoria. Su resumen se muestra en un capitulo de conclusiones y líneas futuras de investigación que se abren como consecuencia de esta memoria. Hay que mencionar que el ritmo de investigación se ha acentuado notablemente en el ultimo ano de trabajo, en parte debido a las ventajas notables obtenidas por el uso de la metodología de grano grueso que pese a ser muy importante para esta memoria no repercute fácilmente en trabajos publicables. Todo ello justifica que gran parte de los resultados esten en fase de publicación. Abstract “Polymer crystallization is therefore assumed, and in theories often described, to be a multi step process with many influencing aspects. Because of the chain structure, it is easy to understand that a process which is thermodynamically forced to increase local ordering but is geometrically hindered cannot proceed into a final equilibrium state. As a result, nonequilibrium structures with different characteristics are usually formed, which depend on temperature, pressure, shearing and other parameters”. These words, recently written by Professor Bernhard Wunderlich, one of the most prominent researchers in polymer physics, put somehow in value the "leitmotiv "of this thesis. The crystallization mechanism of polymers is still under debate in the physics community and most of the experimental findings are still explained by invoking the LH theory. This classical theory, which was initially formulated by Lauritzen and Hoffman (LH), is indeed a generalization of the crystallization theory for small molecules from the vapor phase. Even though it describes satisfactorily many experimental observations, it is far from explaining the complex phenomenon of polymer crystallization. This theory was firstly devised in the early 70s at the National Bureau of Standards. It was successively reformulated along the 80s to fit the experimental findings. Thus, the crystallization regime III was introduced into the theory in order to explain the results found in neutron scattering, droplet or quenching experiments. This concept defines the roughness of the crystallization surface leading to the paradigm proposed by Sadler et al. The great success of this theory is the ability to explain the inverse dependence of the molecular folding size on the supercooling, the latter defined as the temperature interval between the equilibrium temperature and the crystallization temperature. The main scope of this thesis is the study of ordering processes in polyolefins with different degree of branching by using computer simulations. The copolymers studied along this work are considered materials of high molecular homogeneity, from the point of view of both size and branching distributions of the polymer chain. These polyolefins were selected due to the great interest to understand their structure– property relationships. It is important to note that there is a vast amount of experimental data concerning these materials, which is essential to create a virtual reality as is the simulation. The Biophym research group has a wide experience in the correlation between simulation data and experimental results, being this idea highly alive along this work. Empirically, it is well-known that the physical properties of the polyolefins depend on the type and amount of branches presented in the polymeric material. However, there are not suitable models to explain the underlying mechanisms associated to branching. This report is extensive due to the complexity of the topic under study. It begins with a general introduction to the basics concepts of macromolecular physics. This chapter is relevant to understand the content of the present document. Some concepts are defined along this section, among others the flexibility of macromolecules, size distributions and moments, and the behavior in solution and melt along with their corresponding characteristic parameters. Special emphasis is placed on the concept of "entanglement" which is a key item when dealing with macromolecules having a molecular size greater than the critical entanglement length. The introduction finishes with a review of the state of art on the simulation of crystallization processes. The second chapter of the thesis describes, in detail, the computational methodology used in each study. In the first results section, we discuss the simulation studies in dilute solution for linear and short chain branched single chain models. The simplest case is clearly dependent on the selected torsion potential as it is discussed throughout the text. For example, the formation of baby nuclei proposed by Mutukhumar seems to result from the effects of the torsion potential. Thus, we propose the analysis of other torsion potentials that are also used by other research groups. The results obtained on crystallization processes are accordingly discussed. Then, in a second results section, we study linear and branched long-chain alkane molecules in a melt by atomistic simulations as a polyethylene-like model. In spite of the great detail given by atomistic simulations, they are not able to fully capture the experimental facts observed in supercooled melts, in particular the pre-ordered states. For this reason, we discuss short and long chains systems using two coarse-grained models (CG-PVA and CG-PE) in section 3 and 4 of chapter 2. The CG-PE model was developed during the thesis. The use of coarse-grained models ensures greater computational efficiency with respect to atomistic models and is enough to show the relevant scale phenomena for crystallization. In all the analysis we follow the evolution of the ordering and melting processes by both isothermal and non isothermal simulations. During this thesis we have obtained different physical properties such as stem length, crystallinity, melting/crystallization temperatures, and so on. We show that branches in the chains cause a delay in the crystallization and hinder the ordering of the polymer chain. Therefore, crystalline regions decrease in size as branching increases. As a general conclusion, it seems that there is a tendency in the macromolecular systems to form ordered structures, which can grown locally as blocks, occupying the crystallization space at a given temperature and time scale. Finally it should be noted that the observed effects are consistent with both, other theoretical/simulation and experimental results. The summary is provided in the conclusions chapter along with future research lines that open as result of this report. It should be mentioned that the research work has speeded up markedly in the last year, in part because of the remarkable benefits obtained by the use of coarse-grained methodology that despite being very important for this thesis work, is not easily publishable by itself. All this justify that most of the results are still in the publication phase.

Definition of amide protection factors for early kinetic intermediates in protein folding

Hydrogen–deuterium exchange experiments have been used previously to investigate the structures of well defined states of a given protein. These include the native state, the unfolded state, and any intermediates that can be stably populated at equilibrium. More recently, the hydrogen–deuterium exchange technique has been applied in kinetic labeling experiments to probe the structures of transiently formed intermediates on the kinetic folding pathway of a given protein. From these equilibrium and nonequilibrium studies, protection factors are usually obtained. These protection factors are defined as the ratio of the rate of exchange of a given backbone amide when it is in a fully solvent-exposed state (usually obtained from model peptides) to the rate of exchange of that amide in some state of the protein or in some intermediate on the folding pathway of the protein. This definition is straightforward for the case of equilibrium studies; however, it is less clear-cut for the case of transient kinetic intermediates. To clarify the concept for the case of burst-phase intermediates, we have introduced and mathematically defined two different types of protection factors: one is Pstruc, which is more related to the structure of the intermediate, and the other is Papp, which is more related to the stability of the intermediate. Kinetic hydrogen–deuterium exchange data from disulfide-intact ribonuclease A and from cytochrome c are discussed to explain the use and implications of these two definitions.