Tècniques per estudiar els gens i la seva expressió

La seqüenciació del DNA ens permet conèixer la composició química d'un determinat gen. Existeixen tècniques per comprovar si un gen s'expressa en una cèl·lula o teixit: són els protocols coneguts amb el nom de transferència northern (detecta la presència de RNA missatger) o la transferència western (que detecta la presència de proteïna). En els darrers deu anys han sorgit tot un seguit de tècniques que han permès passar de l'estudi individual dels gens a l'estudi global. Així, la genòmica estudia la seqüència de milers de gens alhora, la transcriptòmica comprova la presència de tots els missatgers presents en una cèl·lula en un moment determinat i la proteòmica fa el mateix, però analitzant el contingut global de proteïnes. En aquest capítol es presenten de manera resumida què són i què aporten cadascuna d'aquestes tècniques.The DNA sequencing allows us to know the chemistry composition of a gene. Otherwise, it can be evaluated if a gene is expressed in a cell by the northern blot protocol (which checks for the presence of a messenger RNA) or by the western blot (which evaluate the levels of a protein). In the past 10 years, the development of the new molecular biology techniques allowed us to study the genes of a genome in a more global view. Then, the genomics study the sequence of a thousands of genes at the same time, the transcriptomics check for the presence of all the messengers in a cell, and the proteomics do the same but analyzing the protein global content. In this chapter are presented the main concepts and the principal achievements of all these techniques

Bounding the distance of a controllable and observable system to an uncontrollable or unobservable one

Let $(A,B,C)$ be a triple of matrices representing a time-invariant linear system \left .\aligned \dot x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \} under similarity equivalence, corresponding to a realization of a prescribed transfer function matrix. In this paper we measure the distance between a irreducible realization, that is to say a controllable and observable triple of matrices $(A,B,C)$ and the nearest reducible one that is to say uncontrollable or unobservable one. Different upper bounds are obtained in terms of singular values of the controllability matrix $C(A,B,C)$, observability matrix $O(A,B,C)$ and controllability and observability matrix $CO(A,B,C)$ associated to the triple

El DNA es pot manipular

Per comprendre les possibilitats que ofereix l'enginyeria genètica, es necessita primer conèixer les eines que permeten la manipulació dels àcids nucleics. En la primera part d'aquest capítol es farà un repàs d'algunes d'aquestes eines: els plasmidis, petites molècules de DNA que podem trobar en determinats organismes unicel·lulars; els enzims de restricció, proteïnes típicament bacterianes que fragmenten el DNA per punts concrets; la DNA-ligasa, proteïna vírica amb la capacitat d'unir-los de nou; l'electroforesi en gels d'agarosa, que pot separar per mides diferents fragments de DNA, i, per acabar, la PCR, que ens permet amplificar qualsevol DNA de seqüència coneguda. En la segona part es presenten alguns exemples de les aplicacions que poden tenir aquestes tècniques.To better understand the possibilities that come from genetic engineering, it is useful to know the main tools for the nucleic acid manipulation. In the first part of this chapter it will be done a revision of some of this tools: the plasmids, a little pieces of DNA of some microorganisms; the restriction enzymes, a typical bacterial protein with the capability to fragment DNA molecules in appropriate points; the DNA ligase from T4 phagus, a protein with the ability to regenerate joints between two DNA fragments; the electrophoreses, that allows to see the DNA and to separate by size; and lastly the PCR that could amplify any DNA of known sequence. In the second part of this chapter it will be presented some examples of real applications of these techniques

Bounding the distance of a controllable system to an uncontrollable one

Let $(A,B)$ be a pair of matrices representing a time-invariant linear system $\dot x(t)=Ax(t)+Bu(t)$ under block-similarity equivalence. In this paper we measure the distance between a controllable pair of matrices $(A,B)$ and the nearest uncontrollable one. A bound is obtained in terms of singular values of the controllability matrix $C(A,B)$ associated to the pair. This bound is not simply based on the smallest singular value of $C(A,B)$ contrary to what one may expect. Also a lower bound is obtained using geometrical techniques expressed in terms of the singular values of a matrix representing the tangent space of the orbit of the pair $(A,B)$

Controllability of second order linear systems

Let (A1;A2;B) be a triple of matrices representing two-order time-invariant linear systems, ¨x = A1 ˙ x+A2x+Bu. Using linearization process we study the controllability of second order linear systems. We obtain su±cient conditions for controllability and we analyze the kind of systems verifying these conditions

Second order generalized linear systems. A geometric approach

Let (E;A1;A2;B) be a quadruple of matrices representing a two-order generalized time-invariant linear system, E¨x = A1 ˙ x + A2x + Bu. We study the controllability character under an algebraic point of view