Protein folding: a perspective for biology, medicine and biotechnology

At the present time, protein folding is an extremely active field of research including aspects of biology, chemistry, biochemistry, computer science and physics. The fundamental principles have practical applications in the exploitation of the advances in genome research, in the understanding of different pathologies and in the design of novel proteins with special functions. Although the detailed mechanisms of folding are not completely known, significant advances have been made in the understanding of this complex process through both experimental and theoretical approaches. In this review, the evolution of concepts from Anfinsen's postulate to the "new view" emphasizing the concept of the energy landscape of folding is presented. The main rules of protein folding have been established from in vitro experiments. It has been long accepted that the in vitro refolding process is a good model for understanding the mechanisms by which a nascent polypeptide chain reaches its native conformation in the cellular environment. Indeed, many denatured proteins, even those whose disulfide bridges have been disrupted, are able to refold spontaneously. Although this assumption was challenged by the discovery of molecular chaperones, from the amount of both structural and functional information now available, it has been clearly established that the main rules of protein folding deduced from in vitro experiments are also valid in the cellular environment. This modern view of protein folding permits a better understanding of the aggregation processes that play a role in several pathologies, including those induced by prions and Alzheimer's disease. Drug design and de novo protein design with the aim of creating proteins with novel functions by application of protein folding rules are making significant progress and offer perspectives for practical applications in the development of pharmaceuticals and medical diagnostics.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schr��dinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schr��dinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Probl��mes de premier passage et de commande optimale pour des cha��nes de Markov �� temps discret.

Nous consid��rons des processus de diffusion, d�����nis par des ��quations diff��rentielles stochastiques, et puis nous nous int��ressons �� des probl��mes de premier passage pour les cha��nes de Markov en temps discret correspon- dant �� ces processus de diffusion. Comme il est connu dans la litt��rature, ces cha��nes convergent en loi vers la solution des ��quations diff��rentielles stochas- tiques consid��r��es. Notre contribution consiste �� trouver des formules expli- cites pour la probabilit�� de premier passage et la dur��e de la partie pour ces cha��nes de Markov �� temps discret. Nous montrons aussi que les r��sultats ob- tenus convergent selon la m��trique euclidienne (i.e topologie euclidienne) vers les quantit��s correspondantes pour les processus de diffusion. En dernier lieu, nous ��tudions un probl��me de commande optimale pour des cha��nes de Markov en temps discret. L���objectif est de trouver la valeur qui mi- nimise l���esp��rance math��matique d���une certaine fonction de co��t. Contraire- ment au cas continu, il n���existe pas de formule explicite pour cette valeur op- timale dans le cas discret. Ainsi, nous avons ��tudi�� dans cette th��se quelques cas particuliers pour lesquels nous avons trouv�� cette valeur optimale.

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system ��n/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-k��n/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

Algorithmen f��r q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von gro��er Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen f��r q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen pr��sentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer L��sungen von q-holonomen Rekursionen beschrieben. Das f��nfte Kapitel besch��ftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung f��r die Koeffizienten ermittelt. Ferner k��nnen wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung f��r die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der n��tzlich ist, um q-holonome Rekursionen f��r bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schlie��lich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden k��nnen. ________________________________________________________________________________________________________________

Elimination in Operator Algebras

A large class of special functions are solutions of systems of linear difference and differential equations with polynomial coefficients. For a given function, these equations considered as operator polynomials generate a left ideal in a noncommutative algebra called Ore algebra. This ideal with finitely many conditions characterizes the function uniquely so that Gr��bner basis techniques can be applied. Many problems related to special functions which can be described by such ideals can be solved by performing elimination of appropriate noncommutative variables in these ideals. In this work, we mainly achieve the following: 1. We give an overview of the theoretical algebraic background as well as the algorithmic aspects of different methods using noncommutative Gr��bner elimination techniques in Ore algebras in order to solve problems related to special functions. 2. We describe in detail algorithms which are based on Gr��bner elimination techniques and perform the creative telescoping method for sums and integrals of special functions. 3. We investigate and compare these algorithms by illustrative examples which are performed by the computer algebra system Maple. This investigation has the objective to test how far noncommutative Gr��bner elimination techniques may be efficiently applied to perform creative telescoping.

Identifikation spezieller Funktionen, die durch Rodriguesformeln gegeben sind

Es ist allgemein bekannt, dass sich zwei gegebene Systeme spezieller Funktionen durch Angabe einer Rekursionsgleichung und entsprechend vieler Anfangswerte identifizieren lassen, denn computeralgebraisch betrachtet hat man damit eine Normalform vorliegen. Daher hat sich die interessante Forschungsfrage ergeben, Funktionensysteme zu identifizieren, die ��ber ihre Rodriguesformel gegeben sind. Zieht man den in den 1990er Jahren gefundenen Zeilberger-Algorithmus f��r holonome Funktionenfamilien hinzu, kann die Rodriguesformel algorithmisch in eine Rekursionsgleichung ��berf��hrt werden. Falls die Funktionenfamilie ��berdies hypergeometrisch ist, sogar laufzeiteffizient. Um den Zeilberger-Algorithmus ��berhaupt anwenden zu k��nnen, muss es gelingen, die Rodriguesformel in eine Summe umzuwandeln. Die vorliegende Arbeit beschreibt die Umwandlung einer Rodriguesformel in die genannte Normalform f��r den kontinuierlichen, den diskreten sowie den q-diskreten Fall vollst��ndig. Das in Almkvist und Zeilberger (1990) angegebene Vorgehen im kontinuierlichen Fall, wo die in der Rodriguesformel auftauchende n-te Ableitung ��ber die Cauchysche Integralformel in ein komplexes Integral ��berf��hrt wird, zeigt sich im diskreten Fall nun dergestalt, dass die n-te Potenz des Vorw��rtsdifferenzenoperators in eine Summenschreibweise ��berf��hrt wird. Die Rekursionsgleichung aus dieser Summe zu generieren, ist dann mit dem diskreten Zeilberger-Algorithmus einfach. Im q-Fall wird dargestellt, wie Rekursionsgleichungen aus vier verschiedenen q-Rodriguesformeln gewonnen werden k��nnen, wobei zun��chst die n-te Potenz der jeweiligen q-Operatoren in eine Summe ��berf��hrt wird. Drei der vier Summenformeln waren bislang unbekannt. Sie wurden experimentell gefunden und per vollst��ndiger Induktion bewiesen. Der q-Zeilberger-Algorithmus erzeugt anschlie��end aus diesen Summen die gew��nschte Rekursionsgleichung. In der Praxis ist es sinnvoll, den schnellen Zeilberger-Algorithmus anzuwenden, der Rekursionsgleichungen f��r bestimmte Summen ��ber hypergeometrische Terme ausgibt. Auf dieser Fassung des Algorithmus basierend wurden die ��berlegungen in Maple realisiert. Es ist daher sinnvoll, dass alle hier aufgef��hrten Prozeduren, die aus kontinuierlichen, diskreten sowie q-diskreten Rodriguesformeln jeweils Rekursionsgleichungen erzeugen, an den hypergeometrischen Funktionenfamilien der klassischen orthogonalen Polynome, der klassischen diskreten orthogonalen Polynome und an der q-Hahn-Klasse des Askey-Wilson-Schemas vollst��ndig getestet werden. Die Testergebnisse liegen tabellarisch vor. Ein bedeutendes Forschungsergebnis ist, dass mit der im q-Fall implementierten Prozedur zur Erzeugung einer Rekursionsgleichung aus der Rodriguesformel bewiesen werden konnte, dass die im Standardwerk von Koekoek/Lesky/Swarttouw(2010) angegebene Rodriguesformel der Stieltjes-Wigert-Polynome nicht korrekt ist. Die richtige Rodriguesformel wurde experimentell gefunden und mit den bereitgestellten Methoden bewiesen. Hervorzuheben bleibt, dass an Stelle von Rekursionsgleichungen analog Differential- bzw. Differenzengleichungen f��r die Identifikation erzeugt wurden. Wie gesagt geh��rt zu einer Normalform f��r eine holonome Funktionenfamilie die Angabe der Anfangswerte. F��r den kontinuierlichen Fall wurden umfangreiche, in dieser Gestalt in der Literatur noch nie aufgef��hrte Anfangswertberechnungen vorgenommen. Im diskreten Fall musste f��r die Anfangswertberechnung zur Differenzengleichung der Petkovsek-van-Hoeij-Algorithmus hinzugezogen werden, um die hypergeometrischen L��sungen der resultierenden Rekursionsgleichungen zu bestimmen. Die Arbeit stellt zu Beginn den schnellen Zeilberger-Algorithmus in seiner kontinuierlichen, diskreten und q-diskreten Variante vor, der das Fundament f��r die weiteren Betrachtungen bildet. Dabei wird geb��hrend auf die Unterschiede zwischen q-Zeilberger-Algorithmus und diskretem Zeilberger-Algorithmus eingegangen. Bei der praktischen Umsetzung wird Bezug auf die in Maple umgesetzten Zeilberger-Implementationen aus Koepf(1998/2014) genommen. Die meisten der umgesetzten Prozeduren werden im Text dokumentiert. Somit wird ein vollst��ndiges Paket an Algorithmen bereitgestellt, mit denen beispielsweise Formelsammlungen f��r hypergeometrische Funktionenfamilien ��berpr��ft werden k��nnen, deren Rodriguesformeln bekannt sind. Gleichzeitig kann in Zukunft f��r noch nicht erforschte hypergeometrische Funktionenklassen die beschreibende Rekursionsgleichung erzeugt werden, wenn die Rodriguesformel bekannt ist.

Innovaci��n de un nuevo sistema de gesti��n empresarial aplicaci��n e implementaci��n nuevo software a nivel nacional METROKIA S.A.

Kia Motors Corporation (KMC) tiene como objetivo desde hace algunos a��os, la creaci��n e implementaci��n de una soluci��n de negocios enfocada en una gesti��n empresarial estandarizada a todos los distribuidores de Kia a nivel latinoamericano: Colombia, Per��, Ecuador y Chile. El proceso actual con el que cuentan los distribuidores en Am��rica Latina con sus concesionarios es enviar toda la informaci��n relacionada con los estatutos financieros a trav��s de correo electr��nico junto con una base de datos f��sica, la cual se va archivando. El proceso es manual siendo de mucha dedicaci��n y tiempo requerido para cumplir con las funciones pedidas. El enfoque actual de este proceso es claro: analizar el desempe��o y rendimiento de cada uno de los concesionarios de la red junto con la identificaci��n de oportunidades para mejorar. KMC junto con todos sus distribuidores est��n interesados en buscar un sistema de gesti��n empresarial sencillo, adecuado y de f��cil manejo que permitir�� ��nicamente a todos los concesionarios presentar sus estados de cuenta y desarrollo de una manera estandarizada a su distribuidor directamente. Entonces, el sistema deseado debe ser capaz de generar resultados bas��ndose en lo comunicado por los distribuidores y proporcionar un conjunto de caracter��sticas bajo una adecuada funcionalidad para permitir a todos los usuarios de la red (concesionarios, distribuidores y KMC) analizar el rendimiento y desempe��o de la empresa e identificar las ��reas que requieren una mejora. En el siguiente documento, podremos ver el desarrollo que ha tenido METROKIA S.A para la creaci��n y aplicaci��n de una herramienta tecnol��gica (software) enfocada en lo mencionado anteriormente. Ha sido un proceso de varias etapas en donde tanto las variables como los indicadores de desempe��o han tenido correcciones con el fin de poder ser le��dos y entendidos f��cilmente por toda la organizaci��n y red de concesionarios afiliados.

Pad�� approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with ���xed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coef���cients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade�� approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

LOGO2VHDL: modelos descritos em VHDL a partir da linguagem do LOGO!Soft Comfort da Siemens

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

Radia����o emitida por uma carga el��trica orbitando um buraco negro de Schwarzschild segundo Teoria Qu��ntica de Campos

Desenvolvemos a quantiza����o do campo vetorial n��o massivo no espa��o-tempo de Schwarzschild, e calculamos a pot��ncia irradiada por uma carga el��trica em ��rbita circular em torno de um objeto com massa M em ambos os espa��os-tempos. Em Minkowski �� encontrada a express��o anal��tica da pot��ncia irradiada utilizando teoria qu��ntica de campos e assumindo gravita����o newtoniana. O resultado obtido �� equivalente ao resultado cl��ssico, dado que o c��lculo �� realizado em n��vel de ��rvore. Dadas as dificuldades matem��ticas encontradas ao se tentar obter solu����es expressas em termos de fun����es especiais conhecidas, em Schwarzschild o problema �� abordado de duas formas: solu����o anal��tica no limite de baixas freq����ncias, e resolu����o num��rica. O primeiro caso serviu como cheque de consist��ncia para o m��todo num��rico. Em Schwarzschild, o c��lculo tamb��m �� realizado utilizando teoria qu��ntica de campos em n��vel de ��rvore, e a express��o da pot��ncia �� encontrada analiticamente na aproxima����o de baixas freq����ncias e atrav��s de m��todos num��rico. Ap��s a compara����o dos resultados, conclu��mos que, para uma mesma velocidade angular de rota����o da carga (medida por observadores estat��sticos assint��ticos), a pot��ncia irradiada em Minkowski �� maior que a pot��ncia irradiada em Schwarzschild.

C��lculo fracion��rio aplicado em din��mica tumoral: m��todo da Transformada Diferencial generalizada

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

Chaperone activity and structure of monomeric polypeptide binding domains of���GroEL

The chaperonin GroEL is a large complex composed of 14 identical 57-kDa subunits that requires ATP and GroES for some of its activities. We find that a monomeric polypeptide corresponding to residues 191 to 345 has the activity of the tetradecamer both in facilitating the refolding of rhodanese and cyclophilin A in the absence of ATP and in catalyzing the unfolding of native barnase. Its crystal structure, solved at 2.5 ��� resolution, shows a well-ordered domain with the same fold as in intact GroEL. We have thus isolated the active site of the complex allosteric molecular chaperone, which functions as a ���minichaperone.��� This has mechanistic implications: the presence of a central cavity in the GroEL complex is not essential for those representative activities in vitro, and neither are the allosteric properties. The function of the allosteric behavior on the binding of GroES and ATP must be to regulate the affinity of the protein for its various substrates in vivo, where the cavity may also be required for special functions.