Transient high-level expression of ß-galactosidase after transfection of fibroblasts from GM1 gangliosidosis patients with plasmid DNA

GM1 gangliosidosis is an autosomal recessive disorder caused by the deficiency of lysosomal acid hydrolase ß-galactosidase (ß-Gal). It is one of the most frequent lysosomal storage disorders in Brazil, with an estimated frequency of 1:17,000. The enzyme is secreted and can be captured by deficient cells and targeted to the lysosomes. There is no effective treatment for GM1 gangliosidosis. To determine the efficiency of an expression vector for correcting the genetic defect of GM1 gangliosidosis, we tested transfer of the ß-Gal gene (Glb1) to fibroblasts in culture using liposomes. ß-Gal cDNA was cloned into the expression vectors pSCTOP and pREP9. Transfection was performed using 4 µL lipofectamine 2000 and 1.5-2.0 µg DNA. Cells (2 x 10(5)/well) were harvested 24 h, 48 h, and 7 days after transfection. Enzyme specific activity was measured in cell lysate and supernatant by fluorometric assay. Twenty-four hours after transfection, treated cells showed a higher enzyme specific activity (pREP9-ß-Gal: 621.5 ± 323.0, pSCTOP-ß-Gal: 714.5 ± 349.5, pREP9-ß-Gal + pSCTOP-ß-Gal: 1859.0 ± 182.4, and pREP9-ß-Gal + pTRACER: 979.5 ± 254.9 nmol·h-1·mg-1 protein) compared to untreated cells (18.0 ± 3.1 for cell and 32.2 ± 22.2 nmol·h-1·mg-1 protein for supernatant). However, cells maintained in culture for 7 days showed values similar to those of untreated patients. In the present study, we were able to transfect primary patients' skin fibroblasts in culture using a non-viral vector which overexpresses the ß-Gal gene for 24 h. This is the first attempt to correct fibroblasts from patients with GM1 gangliosidosis by gene therapy using a non-viral vector.

Inférence topologique

Les données provenant de l'échantillonnage fin d'un processus continu (champ aléatoire) peuvent être représentées sous forme d'images. Un test statistique permettant de détecter une différence entre deux images peut être vu comme un ensemble de tests où chaque pixel est comparé au pixel correspondant de l'autre image. On utilise alors une méthode de contrôle de l'erreur de type I au niveau de l'ensemble de tests, comme la correction de Bonferroni ou le contrôle du taux de faux-positifs (FDR). Des méthodes d'analyse de données ont été développées en imagerie médicale, principalement par Keith Worsley, utilisant la géométrie des champs aléatoires afin de construire un test statistique global sur une image entière. Il s'agit d'utiliser l'espérance de la caractéristique d'Euler de l'ensemble d'excursion du champ aléatoire sous-jacent à l'échantillon au-delà d'un seuil donné, pour déterminer la probabilité que le champ aléatoire dépasse ce même seuil sous l'hypothèse nulle (inférence topologique). Nous exposons quelques notions portant sur les champs aléatoires, en particulier l'isotropie (la fonction de covariance entre deux points du champ dépend seulement de la distance qui les sépare). Nous discutons de deux méthodes pour l'analyse des champs anisotropes. La première consiste à déformer le champ puis à utiliser les volumes intrinsèques et les compacités de la caractéristique d'Euler. La seconde utilise plutôt les courbures de Lipschitz-Killing. Nous faisons ensuite une étude de niveau et de puissance de l'inférence topologique en comparaison avec la correction de Bonferroni. Finalement, nous utilisons l'inférence topologique pour décrire l'évolution du changement climatique sur le territoire du Québec entre 1991 et 2100, en utilisant des données de température simulées et publiées par l'Équipe Simulations climatiques d'Ouranos selon le modèle régional canadien du climat.

Conception et évaluation d’un nouveau système de transfection ciblée, basé sur l’utilisation du système E/Kcoil

Actuellement le polyéthylènimine (PEI) est l’agent de transfection transitoire le plus utilisé par l’industrie pharmaceutique pour la production de protéines recombinantes à grande échelle par les cellules de mammifères. Il permet la condensation de l’ADN plasmidique (ADNp) en formant spontanément des nanoparticules positives appelées polyplexes, lui procurant la possibilité de s’attacher sur la membrane cellulaire afin d’être internalisé, ainsi qu’une protection face aux nucléases intracellulaires. Cependant, alors que les polyplexes s’attachent sur la quasi-totalité des cellules seulement 5 à 10 % de l’ADNp internalisé atteint leur noyau, ce qui indique que la majorité des polyplexes ne participent pas à l’expression du transgène. Ceci contraste avec l’efficacité des vecteurs viraux où une seule particule virale par cellule peut être suffisante. Les virus ont évolués afin d’exploiter les voies d’internalisation et de routage cellulaire pour exprimer efficacement leur matériel génétique. Nous avons donc supposé que l’exploitation des voies d’internalisation et de routage cellulaire d’un récepteur pourrait, de façon similaire à plusieurs virus, permettre d’optimiser le processus de transfection en réduisant les quantités d’ADNp et d’agent de transfection nécessaires. Une alternative au PEI pour transfecter les cellules de mammifèreest l’utilisation de protéines possédant un domaine de liaison à l’ADNp. Toutefois, leur utilisation reste marginale à cause de la grande quantité requise pour atteindre l’expression du transgène. Dans cette étude, nous avons utilisé le système E/Kcoil afin de cibler un récepteur membranaire dans le but de délivrer l’ADNp dans des cellules de mammifères. Le Ecoil et le Kcoil sont des heptapeptides répétés qui peuvent interagir ensemble avec une grande affinité et spécificité afin de former des structures coiled-coil. Nous avons fusionné le Ecoil avec des protéines capables d’interagir avec l’ADNp et le Kcoil avec un récepteur membranaire que nous avons surexprimé dans les cellules HEK293 de manière stable. Nous avons découvert que la réduction de la sulfatation de la surface cellulaire permettait l’attachement ciblé sur les cellules par l’intermédiaire du système E/Kcoil. Nous démontrons dans cette étude comment utiliser le système E/Kcoil et une protéine interagissant avec l’ADNp pour délivrer un transgène de manière ciblée. Cette nouvelle méthode de transfection permet de réduire les quantités de protéines nécessaires pour l’expression du transgène.

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

Review of bio-particle manipulation using dielectrophoresis

During the last decade, large and costly instruments are being replaced by system based on microfluidic devices. Microfluidic devices hold the promise of combining a small analytical laboratory onto a chip-sized substrate to identify, immobilize, separate, and purify cells, bio-molecules, toxins, and other chemical and biological materials. Compared to conventional instruments, microfluidic devices would perform these tasks faster with higher sensitivity and efficiency, and greater affordability. Dielectrophoresis is one of the enabling technologies for these devices. It exploits the differences in particle dielectric properties to allow manipulation and characterization of particles suspended in a fluidic medium. Particles can be trapped or moved between regions of high or low electric fields due to the polarization effects in non-uniform electric fields. By varying the applied electric field frequency, the magnitude and direction of the dielectrophoretic force on the particle can be controlled. Dielectrophoresis has been successfully demonstrated in the separation, transportation, trapping, and sorting of various biological particles.

Exercises A

Exercises and solutions in LaTex

Exercises B

Exercises and solutions in LaTex

Exercises A pdf

Exercises and solutions in PDF

Exercises B pdf

Exercises and solutions in PDF

Exercises B

Exercises and solutions in LaTex

Exercises B pdf

Exercises and solution in PDF

A note on atmospheric predictability

Using the method of Lorenz (1982), we have estimated the predictability of a recent version of the European Center for Medium-Range Weather Forecasting (ECMWF) model using two different estimates of the initial error corresponding to 6- and 24-hr forecast errors, respectively. For a 6-hr forecast error of the extratropical 500-hPa geopotential height field, a potential increase in forecast skill by more than 3 d is suggested, indicating a further increase in predictability by another 1.5 d compared to the use of a 24-hr forecast error. This is due to a smaller initial error and to an initial error reduction resulting in a smaller averaged growth rate for the whole 7-d forecast. A similar assessment for the tropics using the wind vector fields at 850 and 250 hPa suggests a huge potential improvement with a 7-d forecast providing the same skill as a 1-d forecast now. A contributing factor to the increase in the estimate of predictability is the apparent slow increase of error during the early part of the forecast.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.