Application of NMR RDC’s, relaxation and self-diffusion for the study of dynamic processes of small molecules in solution

Spin-lattice Relaxation, self-Diffusion coefficients and Residual Dipolar Couplings (RDC’s) are the basis of well established Nuclear Magnetic Resonance techniques for the physicochemical study of small molecules (typically organic compounds and natural products with MW < 1000 Da), as they proved to be a powerful and complementary source of information about structural dynamic processes in solution. The work developed in this thesis consists in the application of the earlier-mentioned NMR techniques to explore, analyze and systematize patterns of the molecular dynamic behavior of selected small molecules in particular experimental conditions. Two systems were chosen to investigate molecular dynamic behavior by these techniques: the dynamics of ion-pair formation and ion interaction in ionic liquids (IL) and the dynamics of molecular reorientation when molecules are placed in oriented phases (alignment media). The application of NMR spin-lattice relaxation and self-diffusion measurements was applied to study the rotational and translational molecular dynamics of the IL: 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4]. The study of the cation-anion dynamics in neat and IL-water mixtures was systematically investigated by a combination of multinuclear NMR relaxation techniques with diffusion data (using by H1, C13 and F19 NMR spectroscopy). Spin-lattice relaxation time (T1), self-diffusion coefficients and nuclear Overhauser effect experiments were combined to determine the conditions that favor the formation of long lived [BMIM][BF4] ion-pairs in water. For this purpose and using the self-diffusion coefficients of cation and anion as a probe, different IL-water compositions were screened (from neat IL to infinite dilution) to find the conditions where both cation and anion present equal diffusion coefficients (8% water fraction at 25 ºC). This condition as well as the neat IL and the infinite dilution were then further studied by 13C NMR relaxation in order to determine correlation times (c) for the molecular reorientational motion using a mathematical iterative procedure and experimental data obtained in a temperature range between 273 and 353 K. The behavior of self-diffusion and relaxation data obtained in our experiments point at the combining parameters of molar fraction 8 % and temperature 298 K as the most favorable condition for the formation of long lived ion-pairs. When molecules are subjected to soft anisotropic motion by being placed in some special media, Residual Dipolar Couplings (RDCs), can be measured, because of the partial alignment induced by this media. RDCs are emerging as a powerful routine tool employed in conformational analysis, as it complements and even outperforms the approaches based on the classical NMR NOE or J3 couplings. In this work, three different alignment media have been characterized and evaluated in terms of integrity using 2H and 1H 1D-NMR spectroscopy, namely the stretched and compressed gel PMMA, and the lyotropic liquid crystals CpCl/n-hexanol/brine and cromolyn/water. The influence that different media and degrees of alignment have on the dynamic properties of several molecules was explored. Different sized sugars were used and their self-diffusion was determined as well as conformation features using RDCs. The results obtained indicate that no influence is felt by the small molecules diffusion and conformational features studied within the alignment degree range studied, which was the 3, 5 and 6 % CpCl/n-hexanol/brine for diffusion, and 5 and 7.5 % CpCl/n-hexanol/brine for conformation. It was also possible to determine that the small molecules diffusion verified in the alignment media presented close values to the ones observed in water, reinforcing the idea of no conditioning of molecular properties in such media.

The application of the equivalent annulus width concept in thermal diffusion separations

The equivalent annulus width concept is used to characterize a small commercial thermogravitational hermal diffusion column and its validity checked experimentally by separating batchwise in the column mixtures of n-heptanebenzene with different initial concentrations. The equation of Ruppell and Coull was used to analyse the data in the short separation times range and determine the equivalent annulus width. Good agreement was obtained between the experimental and predicted time-separation curves when using the equivalent annulus width value and on averaged value of the thermal diffusion constant. A new method is presented for the simultaneous determination of the equivalent annulus width and the thermal diffusion constant of a binary mixture from a single set of experimental data.

Confirmation of functional zones within the human subthalamic nucleus: patterns of connectivity and sub-parcellation using diffusion weighted imaging.

The subthalamic nucleus (STN) is a small, glutamatergic nucleus situated in the diencephalon. A critical component of normal motor function, it has become a key target for deep brain stimulation in the treatment of Parkinson's disease. Animal studies have demonstrated the existence of three functional sub-zones but these have never been shown conclusively in humans. In this work, a data driven method with diffusion weighted imaging demonstrated that three distinct clusters exist within the human STN based on brain connectivity profiles. The STN was successfully sub-parcellated into these regions, demonstrating good correspondence with that described in the animal literature. The local connectivity of each sub-region supported the hypothesis of bilateral limbic, associative and motor regions occupying the anterior, mid and posterior portions of the nucleus respectively. This study is the first to achieve in-vivo, non-invasive anatomical parcellation of the human STN into three anatomical zones within normal diagnostic scan times, which has important future implications for deep brain stimulation surgery.

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Double-tagged fluorescent bacterial bioreporter for the study of polycyclic aromatic hydrocarbon diffusion and bioavailability.

Bacterial degradation of polycyclic aromatic hydrocarbons (PAHs), ubiquitous contaminants from oil and coal, is typically limited by poor accessibility of the contaminant to the bacteria. In order to measure PAH availability in complex systems, we designed a number of diffusion-based assays with a double-tagged bacterial reporter strain Burkholderia sartisoli RP037-mChe. The reporter strain is capable of mineralizing phenanthrene (PHE) and induces the expression of enhanced green fluorescent protein (eGFP) as a function of the PAH flux to the cell. At the same time, it produces a second autofluorescent protein (mCherry) in constitutive manner. Quantitative epifluorescence imaging was deployed in order to record reporter signals as a function of PAH availability. The reporter strain expressed eGFP proportionally to dosages of naphthalene or PHE in batch liquid cultures. To detect PAH diffusion from solid materials the reporter cells were embedded in 2 cm-sized agarose gel patches, and fluorescence was recorded over time for both markers as a function of distance to the PAH source. eGFP fluorescence gradients measured on known amounts of naphthalene or PHE served as calibration for quantifying PAH availability from contaminated soils. To detect reporter gene expression at even smaller diffusion distances, we mixed and immobilized cells with contaminated soils in an agarose gel. eGFP fluorescence measurements confirmed gel patch diffusion results that exposure to 2-3 mg lampblack soil gave four times higher expression than to material contaminated with 10 or 1 (mg PHE) g(-1).

l0-deconvolution for compressive diffusion MRI

Diffusion MRI is a well established imaging modality providing a powerful way to non-invasively probe the structure of the white matter. Despite the potential of the technique, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a wide variety of methods have been proposed to shorten acquisition times. [...] We here review a recent work where we propose to further exploit the versatility of compressed sensing and convex optimization with the aim to characterize the fiber orientation distribution sparsity more optimally. We re-formulate the spherical deconvolution problem as a constrained l0 minimization.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

High b-value Diffusion-weighted Imaging: A Sensitive Method to Reveal White Matter Changes in Schizophrenia

Background: b-value is the parameter characterizing the intensity of the diffusion weighting during image acquisition. Data acquisition is usually performed with low b value (b~1000 s/mm2). Evidence shows that high b-values (b>2000 s/mm2) are more sensitive to the slow diffusion compartment (SDC) and maybe more sensitive in detecting white matter (WM) anomalies in schizophrenia.Methods: 12 male patients with schizophrenia (mean age 35 +/-3 years) and 16 healthy male controls matched for age were scanned with a low b-value (1000 s/mm2) and a high b-value (4000 s/mm2) protocol. Apparent diffusion coefficient (ADC) is a measure of the average diffusion distance of water molecules per time unit (mm2/s). ADC maps were generated for all individuals. 8 region of interests (frontal and parietal region bilaterally, centrum semi-ovale bilaterally and anterior and posterior corpus callosum) were manually traced blind to diagnosis.Results: ADC measures acquired with high b-value imaging were more sensitive in detecting differences between schizophrenia patients and healthy controls than low b-value imaging with a gain in significance by a factor of 20- 100 times despite the lower image Signal-to-noise ratio (SNR). Increased ADC was identified in patient's WM (p=0.00015) with major contributions from left and right centrum semi-ovale and to a lesser extent right parietal region.Conclusions: Our results may be related to the sensitivity of high b-value imaging to the SDC believed to reflect mainly the intra-axonal and myelin bound water pool. High b-value imaging might be more sensitive and specific to WM anomalies in schizophrenia than low b-value imaging

Diffusion tensor echo planar imaging using surface coil transceiver with a semiadiabatic RF pulse sequence at 14.1T.

Diffusion magnetic resonance studies of the brain are typically performed using volume coils. Although in human brain this leads to a near optimal filling factor, studies of rodent brain must contend with the fact that only a fraction of the head volume can be ascribed to the brain. The use of surface coil as transceiver increases Signal-to-Noise Ratio (SNR), reduces radiofrequency power requirements and opens the possibility of parallel transmit schemes, likely to allow efficient acquisition schemes, of critical importance for reducing the long scan times implicated in diffusion tensor imaging. This study demonstrates the implementation of a semiadiabatic echo planar imaging sequence (echo time=40 ms, four interleaves) at 14.1T using a quadrature surface coil as transceiver. It resulted in artifact free images with excellent SNR throughout the brain. Diffusion tensor derived parameters obtained within the rat brain were in excellent agreement with reported values.

Connectivity and tissue microstructural alterations in right and left temporal lobe epilepsy revealed by diffusion spectrum imaging.

Focal epilepsy is increasingly recognized as the result of an altered brain network, both on the structural and functional levels and the characterization of these widespread brain alterations is crucial for our understanding of the clinical manifestation of seizure and cognitive deficits as well as for the management of candidates to epilepsy surgery. Tractography based on Diffusion Tensor Imaging allows non-invasive mapping of white matter tracts in vivo. Recently, diffusion spectrum imaging (DSI), based on an increased number of diffusion directions and intensities, has improved the sensitivity of tractography, notably with respect to the problem of fiber crossing and recent developments allow acquisition times compatible with clinical application. We used DSI and parcellation of the gray matter in regions of interest to build whole-brain connectivity matrices describing the mutual connections between cortical and subcortical regions in patients with focal epilepsy and healthy controls. In addition, the high angular and radial resolution of DSI allowed us to evaluate also some of the biophysical compartment models, to better understand the cause of the changes in diffusion anisotropy. Global connectivity, hub architecture and regional connectivity patterns were altered in TLE patients and showed different characteristics in RTLE vs LTLE with stronger abnormalities in RTLE. The microstructural analysis suggested that disturbed axonal density contributed more than fiber orientation to the connectivity changes affecting the temporal lobes whereas fiber orientation changes were more involved in extratemporal lobe changes. Our study provides further structural evidence that RTLE and LTLE are not symmetrical entities and DSI-based imaging could help investigate the microstructural correlate of these imaging abnormalities.

Un protocole de diffusion des messages dans les réseaux véhiculaires

De nos jours, la voiture est devenue le mode de transport le plus utilisé, mais malheureusement, il est accompagné d’un certain nombre de problèmes (accidents, pollution, embouteillages, etc.), qui vont aller en s’aggravant avec l’augmentation prévue du nombre de voitures particulières, malgré les efforts très importants mis en œuvre pour tenter de les réduire ; le nombre de morts sur les routes demeure très important. Les réseaux sans fil de véhicules, appelés VANET, qui consistent de plusieurs véhicules mobiles sans infrastructure préexistante pour communiquer, font actuellement l’objet d'une attention accrue de la part des constructeurs et des chercheurs, afin d’améliorer la sécurité sur les routes ou encore les aides proposées aux conducteurs. Par exemple, ils peuvent avertir d’autres automobilistes que les routes sont glissantes ou qu’un accident vient de se produire. Dans VANET, les protocoles de diffusion (broadcast) jouent un rôle très important par rapport aux messages unicast, car ils sont conçus pour transmettre des messages de sécurité importants à tous les nœuds. Ces protocoles de diffusion ne sont pas fiables et ils souffrent de plusieurs problèmes, à savoir : (1) Tempête de diffusion (broadcast storm) ; (2) Nœud caché (hidden node) ; (3) Échec de la transmission. Ces problèmes doivent être résolus afin de fournir une diffusion fiable et rapide. L’objectif de notre recherche est de résoudre certains de ces problèmes, tout en assurant le meilleur compromis entre fiabilité, délai garanti, et débit garanti (Qualité de Service : QdS). Le travail de recherche de ce mémoire a porté sur le développement d’une nouvelle technique qui peut être utilisée pour gérer le droit d’accès aux médias (protocole de gestion des émissions), la gestion de grappe (cluster) et la communication. Ce protocole intègre l'approche de gestion centralisée des grappes stables et la transmission des données. Dans cette technique, le temps est divisé en cycles, chaque cycle est partagé entre les canaux de service et de contrôle, et divisé en deux parties. La première partie s’appuie sur TDMA (Time Division Multiple Access). La deuxième partie s’appuie sur CSMA/CA (Carrier Sense Multiple Access / Collision Avoidance) pour gérer l’accès au medium. En outre, notre protocole ajuste d’une manière adaptative le temps consommé dans la diffusion des messages de sécurité, ce qui permettra une amélioration de la capacité des canaux. Il est implanté dans la couche MAC (Medium Access Control), centralisé dans les têtes de grappes (CH, cluster-head) qui s’adaptent continuellement à la dynamique des véhicules. Ainsi, l’utilisation de ce protocole centralisé nous assure une consommation efficace d’intervalles de temps pour le nombre exact de véhicules actifs, y compris les nœuds/véhicules cachés; notre protocole assure également un délai limité pour les applications de sécurité, afin d’accéder au canal de communication, et il permet aussi de réduire le surplus (overhead) à l’aide d’une propagation dirigée de diffusion.