Dissertations / Theses on the topic 'Folding system'

Thesis: S.B., Massachusetts Institute of Technology, Department of Architecture, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-58).
In architecture, natural light is one of the main factors to consider when designing a building or a room. A building has to be designed in such a way to allow the right amount of natural light in which influences the building occupants' visual and thermal comfort level. Curtains, blinds, shades, or shutters are the most common static shading methods currently used to regulate the amount of sunlight coming into a room. However, traditional blinds or shades cannot be customized with respect to fine-grain localized control, which can result in suboptimal indoor lighting levels when the blinds or shades are down. While static window treatments are practical low-cost options, they cannot offer the level of adjustment that dynamic shadings can provide. Majority of the time, occupants of a room have the freedom to adjust the shades; however, the shades are often left in one position since occupants are not willing to constantly adjust the shutters every time the outside environmental conditions change. Unlike traditional blinds, adaptive fac̦ades are designed to automatically adjust positions depending on the environmental changes or have the ability to be fine-grain controlled by the occupant. Because of the ability to respond to fluctuating weather conditions, adaptive fac̦ades can provide optimal indoor day lit space. The purpose of this thesis is to design and build a proof-of-concept prototype of a folding fan-shaped actuated adaptive facade system. Because of the scope of this thesis, the prototype is designed to fit in one of the windows at McCormick Hall instead of a full scale building fac̦ade. There are 13 fan-shaped shades units that can be individually controlled to reduce direct sunlight coming into the indoor space. The results demonstrate that this technology can be designed and built with a modest budget and commonly available tools to achieve high quality results for customized daylight control.
by June Kim.
S.B.

Approved for public release; distribution is unlimited
Analog-To-Digital Converters (ADCs) are integral building blocks of most sensor and communication systems today. As the need for ADCs with faster conversion speeds and lower power dissipation increases, there is a growing motivation to reduce the number of power-consuming components by employing folding circuits to fold the input analog signal symmetrically prior to quantization by high-speed comparators. These properties of low-power consumption, compactness, high-resolution and fast conversion speeds make folding ADCs an attractive concept to be used for defense applications, such as unmanned systems, direction-finding antenna architectures and system-on-a-chip applications. In this thesis, a prototype of an optical folding ADC was implemented using the Robust Symmetrical Number System (RSNS). The architecture employs a three-modulus (Moduli 7, 8, 9) scheme to preprocess the antenna signal. This thesis focuses on the simulation and hardware implementation of this ADC architecture, including the bank of comparators and the RSNS-to-Binary Conversion within a Field Programmable Gate Array (FPGA), to achieve an eight-bit dynamic range of 133. This is then integrated with the front-end photonics implementation (designed under a separate thesis). Low frequency analyses of the results using a 1-kHz input signal indicate a 5.39 Effective Number of Bits (ENOB), a Signal-to-Noise Ratio plus Distortion (SINAD) of 34.21 dB, and a Total Harmonic Distortion (THD) of -61.68 dB.

Mitochondrial protein biogenesis depends on the import of nucleus-encoded precursors from the cytosol. Import is highly regulated and specific for different subcompartments, with intermembrane space (IMS) import driven by an oxidative mechanism on conserved cysteine residues. Oxidative folding in the IMS is facilitated by the mitochondria import and assembly (MIA) pathway. Proteins can only be imported into the IMS in Cys-reduced unfolded forms, as oxidation prevents translocation into the IMS. How the import-competent forms are maintained in the cytoplasm is lesser characterised compared to the MIA pathway. Two recent studies suggest that the cytosolic Thioredoxin (Trx) and Glutaredoxin (Grx) reductase systems play a role in facilitating IMS protein import, with previous evidence identifying a role for yeast Trxs in small Tim protein biogenesis. In this study, the redox properties of the yeast Trx and Grx systems were investigated, as well as whether the yeast Grx system play a role in the biogenesis of two typical types of IMS precursor proteins. First, in vitro studies were carried out to determine the standard redox potentials (E°’) of the Trx and Grx enzymes. This was a quantifiable parameter of reducing activity and the results were described in Chapter 3. This study determined the E°’Trx1 value, which was shown to be a more effective reductant compared to other orthologs. Experimental limitations prevented the Grx system E°’ values being determined. Next, whether the Grx plays a role in the biogenesis of the CX3C motif-containing small Tim proteins were investigated using yeast genetic in vivo and biochemical analysis methods. The results were described in Chapter 4. There, Grxs were observed to not affect cell growth, but in using overexpressed Tim9 as an import model, significant differences were observed for the Grx system as GRX deletion significantly decreased overexpressed Tim9 levels. Study on the isolated mitochondria and cytosol with overexpressed Tim9 was unclear however. This study also observed a genetic interaction between GRX andYME1 that recovered cell functioning under respiratory conditions. Finally, whether the Grx system plays a role in the biogenesis of CX9C motif-containing proteins (Mia40, Mia40C and Cox17) was studied in Chapter 5. Whilst Mia40C (C-domain of Mia40) and Cox17 are imported into mitochondria via the MIA pathway, the full-length Mia40 is a substrate of the presequence-targeted TIM23 pathway. The results indicated that import of the full-length Mia40 was unaffected by GRX deletion. However, studies of an overexpressed Mia40C as a substrate of the MIA pathway, showed strong mitochondrial protein level decreases caused by deletion of the Grx proteins. This decrease was also accompanied by an accumulation of unimported Mia40C in the cytosol. Cox17 as an alternative MIA pathway substrate also showed decreased mitochondrial levels in the GRX deletion mutants. These results altogether suggest that the cytosolic Grx system can function in the biogenesis of CX9C motif-containing IMS proteins imported through the MIA pathway, as well as the CX3C small Tim proteins. The topic of how IMS proteins are degraded in the cell was also raised by the study of Yme1.

The main aim of this thesis is to design electric scooter, which is ideally adapted for urban mobility and which will be a practical, attractive and environmental friendly alternative to the car with a combustion engine. Emphasis is given to proposal of ergonomic, aesthetic and functional solution of the system, which makes that scooter can be folded into a mobile compact shape. Folded scooter can be carried at public transportation vehicles and park right at home or in the office. The unique design and practical features of a scooter should be attractive not only in terms of personal mobility, but also as a utility vehicle for private companies and public institutions.

Cu, Zn superoxide dismutase (SOD1) is a dimeric, β-sandwich, metalloenzyme responsible for the dismutation of superoxide. Mutations covering nearly 50% of the amino acid sequence of SOD1 have been found to acquire a toxic gain-of-function leading to amyotrophic lateral sclerosis. A hallmark of this disease is the presence of insoluble aggregates containing SOD1 found in the brain and spinal cord. While it is unclear how these aggregates or smaller, precursor oligomeric species may be the source of the toxicity, mutations leading to increased populations of unstable, partially folded species along the folding pathway of SOD1 may be responsible for seeding and propagating aggregation. In an effort to determine the responsible species, we have systematically characterized the stability and folding kinetics of five well studied ALS variants: A4V, L38V, G93A, L106V and S134N. The effect of the amino acid substitutions was determined on a variety of different constructs characterizing the various post-translational maturation steps of SOD1: folding, disulfide bond formation and Zn binding. Zn was found to bind progressively tighter along the folding pathway of SOD1, minimizing populations of monomeric species. In contrast, ALS variants were found to have the greatest perturbation in the equilibrium populations of the folded and unfolded state for the most immature, disulfide-reduced metal-free SOD1. In this species, at physiological temperature, four out of five ALS variants were >50% unfolded. Finally the energetic barriers in the folding and unfolding reaction were studied to investigate the unusually slow folding of SOD1. These results reveal that both unfolding and refolding are dominated by enthalpic barriers which may be explained by the desolvation of the chain and provide insights into the role of sequence in governing the folding pathway and rate.

The hallmark feature of many neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS), is the accumulation of cytoplasmic inclusions of key disease-linked proteins. Two of these proteins, TDP-43 and SOD1, represent a significant proportion of sporadic and familial ALS cases, respectively. The population of potentially aggregation-prone partially-folded states on the folding free-energy landscape may serve as a common mechanism for ALS pathogenesis. A detailed biophysical understanding of the folding and misfolding energy landscapes of TDP-43 and SOD1 can provide critical insights into the design of novel therapeutics to delay onset and progression in ALS. Equilibrium unfolding studies on the RNA recognition motif (RRM) domains of TDP-43 revealed the population of a stable RRM intermediate in RRM2, with residual structure localized to the N-terminal half of the domain. Other RRM domains from FUS/TLS and hnRNP A1 similarly populate RRM intermediates, suggesting a possible connection with disease. Mutations, which enhance the population of the RRM2 intermediate, could serve as tools for deciphering the functional and misfolding roles of this partially-folded state in disease models, leading to the development of new biomarkers to track ALS progression. ALS mutations in SOD1 have been shown to destabilize the stable homodimer to result in increased populations of the monomeric and unfolded forms of SOD1. Mechanistic insights into the misfolding of SOD1 demonstrated that the unfolded state is a key species in the initiation and propagation of aggregation, suggesting that limiting these populations may provide therapeutic benefit to ALS patients. An in vitro time-resolved Förster Resonance Energy Transfer assay to screen small molecules that stabilize the native state of SOD1 has identified several lead compounds, providing a pathway to new therapeutics to treat ALS.

The hallmark feature of many neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS), is the accumulation of cytoplasmic inclusions of key disease-linked proteins. Two of these proteins, TDP-43 and SOD1, represent a significant proportion of sporadic and familial ALS cases, respectively. The population of potentially aggregation-prone partially-folded states on the folding free-energy landscape may serve as a common mechanism for ALS pathogenesis. A detailed biophysical understanding of the folding and misfolding energy landscapes of TDP-43 and SOD1 can provide critical insights into the design of novel therapeutics to delay onset and progression in ALS. Equilibrium unfolding studies on the RNA recognition motif (RRM) domains of TDP-43 revealed the population of a stable RRM intermediate in RRM2, with residual structure localized to the N-terminal half of the domain. Other RRM domains from FUS/TLS and hnRNP A1 similarly populate RRM intermediates, suggesting a possible connection with disease. Mutations, which enhance the population of the RRM2 intermediate, could serve as tools for deciphering the functional and misfolding roles of this partially-folded state in disease models, leading to the development of new biomarkers to track ALS progression. ALS mutations in SOD1 have been shown to destabilize the stable homodimer to result in increased populations of the monomeric and unfolded forms of SOD1. Mechanistic insights into the misfolding of SOD1 demonstrated that the unfolded state is a key species in the initiation and propagation of aggregation, suggesting that limiting these populations may provide therapeutic benefit to ALS patients. An in vitro time-resolved Förster Resonance Energy Transfer assay to screen small molecules that stabilize the native state of SOD1 has identified several lead compounds, providing a pathway to new therapeutics to treat ALS.

Codification of genetic information; regulation of gene expression; transport of nutrients inside cells; immune protection against infectious agents; transduction of external signals... These are some of the crucial processes that take place in living organisms at the molecular level. A deep understanding of how these phenomena occur is vital to get a precise knowledge of the laws governing the microscopic world and understand, prevent and even find cures for many illnesses with an origin in the molecular scale. Single-molecule experiments emerge as a powerful and versatile tool to investigate molecular processes at the level of individual molecules and trajectories with unprecedented spatial and temporal resolution. A paradigmatic experimental technique is given by “optical tweezers” (OT), which consist of a laser beam that captures micron-sized plastic beads using light momentum conservation. This instrument makes it possible to manipulate with nanometric precision a biomolecule and exert forces on it in the range of [0-100] pN. The diversity of systems being studied using optical tweezers increases every day. In this thesis, OT are used to unravel the mechanisms of unfolding and folding of several small nucleic acid hairpins and a protein when a force is applied to their ends. Moreover, single antigen-antibody bonds are investigated by qualitatively measuring the correlation between bond affinity and bond elasticity. All single-molecule experiments have in common the relevant role played by thermal fluctuations. These are crucial at the microscopic scale and contain overriding thermodynamic and kinetic information of molecular systems. The study of the characteristic forces at which molecular cooperative transitions occur, such as molecular unfolding or bond dissociation, is known as dynamic force spectroscopy (DFS). In this thesis DFS combined with Markov models are widely used to characterize the unfolding/folding reaction pathway, the transition states present in the molecular free-energy landscape, and the elastic, kinetic and thermodynamic properties of a protein, the antigen-antibody bond and nucleic acid hairpins under different conditions. A general result is that non-equilibrium DFS methods provide an excellent platform to extract thermodynamic properties of molecular states that can only be observed under dynamical conditions (that is, they are never observed in equilibrium at reasonable time scales), such as intermediate or bound configurations. An alternative method to extract thermodynamic properties of molecular systems is the use of fluctuation relations (FR). These are mathematical identities that relate non-equilibrium work measurements to free-energy differences. When an irreversible transformation is mechanically induced in an otherwise full-equilibrated molecular system, a work is performed between an initial and a final state that differs in each independent repetition of the experiment. FR relate a collection of these work measurements to the difference in free energy between the initial and the final states, independently of the molecular reaction pathway. If the system is initially found at a partially equilibrated state, an extended version of FR can be used to measure its free energy of formation. This grants access to the thermodynamic properties of misfolded and intermediate states that are rarely sampled in full equilibrium. Additionally, the extended FR allow us to reconstruct the free-energy branches of molecular states observed during non-equilibrium experiments from irreversible work measurements. Hence, relative stabilities between molecular native, unfolded, misfolded an intermediate states can be compared at different stages of the irreversible experiment. Results in this thesis pave the way to characterize the thermodynamics and kinetics of complex molecular process that occur under partial equilibrium conditions (as is the case in living organisms), using both DFS and FR. Examples are found in many kinetic states related to intermolecular binding or in transient non-equilibrium states occurring in polymerization reactions (e.g. translocating). Hence the influence of the findings and methods developed in this thesis remains to be seen.
La codificació de la informació genètica, la regulació de l'expressió dels gens, el transport de nutrients dins la cèl·lula, la protecció immunològica contra agents infecciosos... Aquests són alguns dels processos moleculars que s'esdevenen en organismes vius i són crucials per la seva supervivència. Entendre el funcionament d'aquests fenòmens és vital per conèixer les lleis que governen l'escala microscòpica i per entendre, preveure, o fins i tot trobar cures de malalties amb origen molecular, com el Parkinson, l'Alzheimer, o alguns càncers. Els experiments amb una única molècula són una eina molt poderosa i versàtil que permet investigar molts processos moleculars a escala de molècula i trajectòria individual, amb una resolució espaio-temporal sense precedents. Una eina paradigmàtica per dur a terme aquest tipus d'estudis són les “pinces òptiques”, consistents en un feix de llum coherent focalitzat capaç d'atrapar partícules de plàstic microscòpiques utilitzant la conservació del moment. Aquest instrument permet manipular una única biomolècula amb precisió nanomètrica, i exercir-hi forces en el rang entre 0 i 100 pN. La diversitat de sistemes estudiats amb les pinces òptiques augmenta cada dia. En aquesta tesi, s'utilitzen per desxifrar els mecanismes del plegament i desplegament d'àcids nucleics i d'una proteïna quan s'hi aplica una força. A més, les propietats d'un únic enllaç entre un antigen i un anticòs s'investiguen de manera qualitativa, mesurant la correlació entre l'afinitat i l'elasticitat de la unió. Els resultats d'aquesta tesi obren la porta a la caracterització termodinàmica i cinètica de processos moleculars complexos que s'esdevenen en condicions d'equilibri parcial (com ocorre en organismes vius) utilitzant l'espectroscòpia dinàmica de forces (és a dir, l'estudi de les forces característiques per induir transicions moleculars) i els teoremes de fluctuació (que proporcionen estimacions de l'energia lliure mitjançant mesures irreversibles). Alguns exemples poden trobar-se en els estats cinètics i metaestables relacionats amb el plegament mecànic -com els estats intermedis i mal plegats-, en la interacció intermolecular, o en estats metaestables que es donen en reaccions de polimerització -com la translocació dels motors moleculars.

Inference for dynamic systems and conformational sampling for protein folding are two problems motivated by applied data, which pose computational challenges from a statistical perspective. Dynamic systems are often described by a set of coupled differential equations, and methods of parametric estimation for these models from noisy data can require repeatedly solving the equations numerically. Many of these models also lead to rough likelihood surfaces, which makes sampling difficult. We introduce a method for Bayesian inference on these models, using a multiple chain framework that exploits the underlying mathematical structure and interpolates the posterior to improve efficiency. In protein folding, a large conformational space must be searched for low energy states, where any energy function constructed on the states is at best approximate. We propose a method for sampling fragment conformations that accounts for geometric and energetic constraints, and explore ideas for folding entire proteins that account for uncertain energy landscapes and learning from data more effectively. These ingredients are combined into a framework for tackling the problem of generating improvements to protein structure predictions.
Statistics

Proteins present at the synapse need to be multitasking in order to perform all vital functions in this limited space. In this thesis I have analyzed the function and evolution of such proteins, focusing on the PDZ domain and the paralemmin family. The PDZ domains bind to a wide variety of interaction partners. The affinity for each partner is regulated by residues at the binding site, but also through intradomain allostery. How this intradomain allostery is transferred to the binding site is not established. I here show that side chain interactions can explain all transfer of intradomain allostery in three analyzed PDZ domains. A circularly permuted PDZ domain has an identical set of amino acids as the original protein and a very similar structure with only a few perturbed side chains. By using the circular permutant I show that a slight alteration in the position of a side chain leads to a corresponding change in allosteric signal. I further study the folding of several PDZ domains and show that they all fold via a conserved folding mechanism, supporting the notion that the final structure has a part in deciding folding mechanism. The folding mechanism of the circularly permuted PDZ domain is conserved compared to the original protein illustrating how circular permutations can be tolerated through evolution. The multifunctionality of paralemmins probably lies in their highly flexible structures. I have studied the evolution of the paralemmins and found that the four mammalian paralemmins arose in the two whole-genome duplications that occurred early in the vertebrate evolution. The fact that all four paralemmins have survived evolution since the gene duplications suggests that they have important functions, possibly in the development of the nervous system. Synaptic proteins are crucial for many biological processes, and their misfolding implicated in many diseases. The results presented here shed light on the mechanisms of action of the synaptic proteins and will help us to understand how they generate disease.

Les systèmes toxine-antitoxine (TA) sont de petits modules génétiques largement présents dans les génomes bactériens. Ils codent pour une petite protéine toxique et une antitoxine. Ils sont classés en six types en fonction de la nature et du mode d'action de l'antitoxine. Ce travail a porté sur l'étude du type I, pour lequel l'antitoxine est un ARN antisens qui cible l'ARNm de la toxine afin de réprimer son expression. Au cours de cette thèse, nous avons étudié le système aapA3/IsoA3, codé sur le chromosome du pathogène gastrique humain Helicobacter pylori. À ce jour, la plupart des systèmes TA ont été étudiés à l'aide de systèmes d'expression artificiels, qui ne permettent pas de caractériser la régulation transcriptionnelle ou post-transcriptionnelle. En utilisant la létalité induite par l’expression chromosomique de la toxine obtenue en absence d’antitoxine, nous avons développé une sélection génétique de mutants suppresseurs révélés par séquençage haut-débit. Cette approche, appelée FASTBAC-Seq, nous a permis de cartographier une myriade de déterminants de toxicité localisés dans les régions codantes et non codantes du gène de la toxine AapA3. En particulier, certaines de ces mutations ont révélé l'existence de tige-boucles ARN transitoires qui agissent de manière co-transcriptionnelle pour empêcher l'initiation de la traduction pendant la synthèse de l'ARNm codant pour la toxine. Ces structures ARN métastables fonctionnelles sont nécessaires pour découpler les processus de transcription et de traduction et permettent la présence de ces gènes toxiques sur le chromosome bactérien. Bien que les ARNm non traduits deviennent rapidement instables, nos travaux ont également révélé l'existence de deux tige-boucles protectrices situées aux deux extrémités de l'ARNm. Ces structures secondaires empêchent des activités exonucléolytiques agissant en 5' et 3'. Dans l’ensemble, notre travail met en évidence les conséquences de la forte pression de sélection pour limiter l'expression des toxines sous laquelle évoluent les systèmes TA. Cela nous a permis de mieux comprendre l’influence du repliement secondaire des ARNm, non seulement lors de la régulation posttranscriptionnelle, mais aussi co-transcriptionnelle de l’expression de cette famille particulière de gènes. Ces caractéristiques de régulation basées sur l'ARN peuvent être exploitées à l'avenir pour des applications biotechnologiques (p. ex., production accrue de protéines par stabilisation d'ARNm) ou biomédicales (p.ex., développement de stratégies antimicrobiennes alternatives pour l'activation de la synthèse de toxines)
Toxin-antitoxin (TA) systems are small genetic modules widely present in bacterial genomes. They usually code for a small toxic protein and its cognate antitoxin and can be classified into six types depending on the nature and mode of action of the antitoxin. This work focuses on the study of type I, for which the antitoxin is an antisense RNA that targets the toxin mRNA to inhibit its expression. We characterized the aapA3/IsoA3 system, encoded on the chromosome of the human gastric pathogen Helicobacter pylori. To date, most TAs have been studied using artificial expression systems, which do not allow the characterization of transcriptional or post-transcriptional regulation. Taking advantage of the lethality induced by the toxin chromosomal expression in the absence of antitoxin, we developed a high-throughput genetic selection of suppressor mutations revealed by Next-Generation Sequencing. This approach, named FASTBAC-Seq, allowed us to map a myriad of toxicity determinants located in both, coding and noncoding regions, of the aapA3 toxic gene. More precisely, some suppressor mutations revealed the existence of transient RNA hairpins that act co-transcriptionally to prevent translation initiation while the toxinencoding mRNA is being made. Such functional RNA metastable structures are essential to uncouple the transcription and translation processes and allow the presence of these toxic genes on bacterial chromosomes. Although untranslated mRNAs become rapidly unstable, our work also revealed the presence of two protective stem-loops located at both mRNA ends that prevent from both, 5’ and 3’ exonucleolytic activity. Altogether, our work evidenced the consequences of the strong selection pressure to silence toxin expression under which the TAs evolve, and highlighted the key role of mRNA folding in the co- and post-transcriptional regulation of this family of genes. These RNA-based regulatory mechanisms may be exploited in the future for biotechnological (e.g., increased protein production through mRNA stabilization) or biomedical (e.g., development of alternative antimicrobial strategies aiming at the activation of toxin synthesis) applications

Protein folding is the process during which an extended and unstructured polypeptide converts to its compact folded structure that is most often the functional state. The process has been characterized extensively in dilute buffer in-vitro during the last decades but the actual biological place for this process is the inside of living cells. The cytoplasm of a cell is filled with a plethora of different macromolecules that together occupy up to 40% of the total volume. This large amount of macromolecules restricts the available space to each individual molecule, which has been termed macromolecular crowding. Macromolecular crowding results in excluded volume effects and also increases chances for non-specific interactions. Macromolecular crowding should favor reactions that lead to a decrease in the total occupied volume by all molecules, such as folding reactions. Theoretical models have predicted that the stability of protein folded states should increase in presence of macromolecular crowding due to unfavorable effects on the extended unfolded state. To understand protein folding and function in living systems, we need to have a defined quantitative link between in-vitro dilute conditions (where most biophysical experiments are made) and in-vivo crowded conditions. An important question is thus how macromolecular crowding modifies the biophysical properties of a protein. The work underlying this thesis focused on how macromolecular crowding tunes protein equilibrium stability and kinetic folding processes. To mimic the crowded cellular environment, synthetic sugar-based polymers (Dextrans of different sizes and Ficoll 70) were used as crowding agents (crowders) in controlled in-vitro experiments. In contrast to previous studies which often have focused on one protein and one crowder at a time, the goal here was to make systematic analyses of how size, shape and concentration of the crowders affect both equilibrium and kinetic properties of structurally-different proteins. Three model proteins (cytochrome c, apoazurin and apoflavodoxin) were investigated under crowding by Ficoll 70 and different-size Dextrans, using various spectroscopic techniques such as far-UV circular dichroism and intrinsic tryptophan fluorescence. Thermodynamic models were applied to explain the experimental results. It was discovered that equilibrium stability of all three proteins increased in presence of crowding agents in a crowder concentration dependent manner. The stabilization effect was around 2-3 kJ/mol, larger for the various Dextrans than for Ficoll 70 at the same g/l, but independent of Dextran size (in the range 20 to 70 kDa). To further investigate the cause for the stabilization a theoretical crowding model was applied. In this model, Dextran and Ficoll were modeled as elongated rods and the protein was represented as a sphere, where the folded sphere representation was smaller than the unfolded sphere representation. It is notable that the observed stability changes could be reproduced by this model taking only steric interactions into account. This correlation showed that when using sugar-based crowding agents, excluded volume effects could be studied in isolation and there were no contributions from nonspecific interactions. Time-resolved experiments with apoazurin and apoflavodoxin revealed an increase in the folding rate constants while the unfolding rates were invariant in the presence of crowding agents. For apoflavodoxin and cytochrome c, the presence of crowding agents also altered the folding pathway such that it became more homogeneous (cytochrome c) and it gave less misfolding (apoflavodoxin). These results showed that macromolecular crowding restricts the conformational space of the unfolded polypeptide chain, makes the conformations more compact which, in turn, eliminates access to certain pathways. The results from kinetic and equilibrium measurements on three model proteins, together with available data from the literature, demonstrate that macromolecular crowding effects due to volume exclusion are in the order of a few kJ/mol. Considering the numerous concentration balances and cross-dependent reactions of the cellular machinery, small changes in energetics/kinetics of the magnitudes found here can still have dramatic consequences for cellular fitness. In fact local and transient changes in macromolecular crowding levels may be a way to tune biochemical reactions without invoking gene expression.

Soit Γ un sous-groupe fini de SU2(ℂ). Alors le quotient ℂ2/Γ peut être plongé dans ℂ3 sous la forme d'une surface munie d'une singularité isolée. Le quotient ℂ2/Γ est appelé singularité de Klein, d'après F. Klein qui fut le premier à les décrire en 1884. A travers leurs résolutions minimales, ces singularités ont un lien étroit avec les diagrammes de Dynkin simplement lacés de types Ar, Dr et Er. Dans les années 1970, E. Brieskorn et P. Slodowy ont tiré profit de cette connection pour décrire les résolutions et les déformations de ces singularités à l'aide de la théorie de Lie. En 1998 P. Slodowy et H. Cassens ont construit les déformations semiuniverselles des ℂ2/Γ à l'aide de la théorie des carquois ainsi que des travaux de P.B. Kronheimer en géométrie symplectique datant de 1989. En théorie de Lie, la classification des algèbres de Lie simples divisent ces dernières en deux classes: les algèbres de Lie de types Ar, Dr et Er qui sont simplement lacées, et celles de types Br, Cr, F4 et G2 appelées non-homogènes. A l'aide d'un second sous-groupe fini Γ' de SU2(ℂ) tel que Γ ⊲ Γ', P. Slodowy a étendu en 1978 la notion de singularité de Klein aux algèbres de Lie non-homogènes en ajoutant à ℂ2/Γ le groupe d'automorphismes Ω= Γ'/Γ du diagramme de Dynkin associé à la singularité. L'objectif de cette thèse est de généraliser la construction de H. Cassens et P. Slodowy à ces singularités de types Br, Cr, F4 et G2. Il en résultera des constructions explicites des déformations semiuniverselles de types inhomogènes sur les fibres desquelles le groupe Ω agit. Le passage au quotient d'une telle application révèle alors une déformation d'une singularité de type ℂ2/Γ'
Let Γ be a finite subgroup of SU2(ℂ). Then the quotient ℂ2/Γ can be embedded in ℂ3 as a surface with an isolated singularity. The quotient ℂ2/Γ is called a Kleinian singularity, after F. Klein who studied them first in 1884. Through their minimal resolutions, these singularities have a deep connection with simply-laced Dynkin diagrams of types Ar, Dr and Er. In the 1970's E. Brieskorn and P. Slodowy took advantage of this connection to describe the resolutions and deformations of these singularities in terms of Lie theory. In 1998 P. Slodowy and H. Cassens constructed the semiuniversal deformations of the Kleinian singularities using quiver theory and work from 1989 by P.B. Kronheimer on symplectic geometry. In Lie theory, the classification of simple Lie algebras allows for a separation in two classes: those simply-laced of types Ar, Dr and Er, and those of types Br, Cr, F4 and G2 called inhomogeneous. With the use of a second finite subgroup Γ’ of SU2(ℂ) such that Γ ⊲ Γ’, P. Slodowy extended in 1978 the definition of a Kleinian singularity to the inhomogeneous types by adding to ℂ2/Γ the group of automorphisms Ω= Γ’/Γ of the Dynkin diagram associated to the singularity. The purpose of this thesis is to generalize H. Cassens' and P. Slodowy's construction to the singularities of types Br, Cr, F4 and G2. It will lead to explicit semiuniversal deformations of inhomogeneous types on the fibers of which the group Ω acts. By quotienting such a map we obtain a deformation of a singularity ℂ2/Γ’

A contribuição deste trabalho foi orientada principalmente ao desenvolvimento de alternativas de hardware para a execução nativa de bytecodes Java em sistemas embarcados que naturalmente possuem restrições quanto à potência consumida, ao desempenho e à área ocupada. Primeiramente, o desenvolvimento do Femtojava Low- Power demonstra que a utilização de um pipeline e de um banco de registradores interno em arquiteturas de pilha resultam em uma redução significativa no consumo de potência. Após, a técnica de folding, que basicamente transforma várias operações de pilha em uma operação tipo RISC, é avaliada. A análise de uma segunda solução arquitetural, baseada em VLIW (Very Long Instruction Word), também traz resultados satisfatórios na redução do consumo de potência, sendo que a paralelização do código, feita por um analisador desenvolvido, é facilitada devido à utilização de uma arquitetura de pilha. O desempenho e a potência consumida de todas as arquiteturas propostas neste trabalho foram validadas utilizando-se o simulador CACO-PS, também desenvolvido no contexto desta dissertação. Os estudos de caso adotados para a validação das alternativas arquiteturais compreenderam algoritmos matemáticos, de ordenação, busca e processamento de sinais, bastante utilizados no domínio de sistemas embarcados. Resultados promissores principalmente em termos de energia consumida são alcançados, assim como na disponibilização de diferentes arquiteturas para a execução nativa de Java, principal proposta deste trabalho.
The main contribution of this work was the development of hardware alternatives for native execution of Java bytecodes for embedded systems that have power, performance and area constraints. Firstly, the development of the Femtojava Low- Power shows that the use of a pipeline and an internal register bank in stack architectures brings a significant reduction in the power consumption. After that, the folding technique, that basically changes a set of stack operations into a simple RISC one, is evaluated. Then, the analysis of a second architectural solution, based on VLIW (Very Long Instruction Word), demonstrates also good results concerning power consumption. Moreover, it is shown that the parallelization of the code is facilitated due to the specific stack architecture. The power consumption and performance of all architectures here proposed were evaluated using the CACO-PS simulator, which was also developed in this work. The case studies adopted for the validation of the architectures were mathematic, sort, search and DSP algorithms, widely used in the embedded system domain. Promising results mainly in energy consumption were achieved, as well as the disponibilization of different architectures for native execution of Java, the main objective of this work.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado.
Protein fold recognition is an important task in the biological area. Different machine learning methods such as multiclass classifiers, one-vs-all and ensemble nested dichotomies were applied to this task and, in most of the cases, multiclass approaches were used. In this paper, we compare classifiers organized in tree structures to classify folds. We used a benchmark dataset containing 125 features to predict folds, comparing different supervised methods and achieving 54% of accuracy. An approach related to tree-structure of classifiers obtained better results in comparison with a hierarchical approach.
Revisión por pares

The Protein Data Bank (PDB) is the definitive electronic repository for experimentally-derived protein structures, composed mainly of those determined by X-ray crystallography. Approximately 200 new structures are added weekly to the PDB, and at the time of writing, it contains approximately 97,000 structures. This represents an expanding wealth of high-quality information but there seem to be few bioinformatics tools that consider and analyse these data as an ensemble. This thesis explores the development of three efficient, fast algorithms and software implementations to study protein structure using the entire PDB. The first project is a crystal-form matching tool that takes a unit cell and quickly (< 1 second) retrieves the most related matches from the PDB. The unit cell matches are combined with sequence alignments using a novel Family Clustering Algorithm to display the results in a user-friendly way. The software tool, Nearest-cell, has been incorporated into the X-ray data collection pipeline at the Diamond Light Source, and is also available as a public web service. The bulk of the thesis is devoted to the study and prediction of protein disorder. Initially, trying to update and extend an existing predictor, RONN, the limitations of the method were exposed and a novel predictor (called MoreRONN) was developed that incorporates a novel sequence-based clustering approach to disorder data inferred from the PDB and DisProt. MoreRONN is now clearly the best-in-class disorder predictor and will soon be offered as a public web service. The third project explores the development of a clustering algorithm for protein structural fragments that can work on the scale of the whole PDB. While protein structures have long been clustered into loose families, there has to date been no comprehensive analytical clustering of short (~6 residue) fragments. A novel fragment clustering tool was built that is now leading to a public database of fragment families and representative structural fragments that should prove extremely helpful for both basic understanding and experimentation. Together, these three projects exemplify how cutting-edge computational approaches applied to extensive protein structure libraries can provide user-friendly tools that address critical everyday issues for structural biologists.

碩士
國立雲林科技大學
電子與光電工程研究所碩士班
100
For many people, origami is not only an art of paper folding, but also a fun memory of childhood. Compared with straightedge and compass, origami is a more powerful geometry construction tool. In this study, a paper folding system for Android phones has been developed. Some of the Huzita axioms and Hatori Axiom are implemented. Foldings are accomplished with these axioms. Furthermore, the process of paper folding is visualized. Users also can also observe the 3D animation of folding steps from different viewpoints.

碩士
國立臺灣大學
生醫電子與資訊學研究所
101
In the field of Computational Biology research, predicting protein structure and function after folding is a significant issue. Protein Structures are composed of different sequences of amino acid. Since interactions between atoms and molecules exist, attractive and repulsive forces are generated, and this results in folding. There is an affinity between protein structure and protein function. If the folding process fails, abnormal protein structures form, and the function and characteristics of protein are spent, which can lead to severe disease. Alzheimer’s disease and Parkinson’s disease are examples of the physiological changes caused by protein misfolding. This thesis offers a system-calculated process of protein folding prediction. In our calculated system, we first apply the Hydrophobic-Hydrophilic Lattice Model to classify amino acids into two types, characterized by hydrophobic and hydrophilic molecules. We then fold the protein sequence in perpendicular direction, or not fold, and apply the Genetic Algorithm to obtain the preliminary three-dimensional structure of the protein. Second, we apply the Hydrophobic-Hydrophilic Off-Lattice Model, and input the result of the first step into the system, considering the continuous bending angles and torsional angles in specific range, and then we apply the Genetic Algorithms and Tabu Search to get the stable protein structure and general minimum energy. Based on our calculated system, we propose that the Hybrid Model is composed of a Lattice Model and an Off-Lattice Model. We intercept the advantages of these two models, and not only reduce the computation time, but also retain good accuracy on energy calculation. Finally, we propose the Branch Model, which is the new model used in the protein folding simulation. In the Branch Model, we regard the peptide as the big polar molecules in the protein sequence, and take the side chains of each amino acid into account. Indeed, the characteristics of hydrophobic and hydrophilic amino acids, and the structure of protein after folding, even the protein-protein interaction, are related, in that the side chains of each amino acid have interactions with each other. This is the primary reason we propose the use of the Branch Model; we want to consider the influence of side chain interaction in protein folding calculation. The protein folding simulation results using the Branch Model that this thesis advances are more precise than either the Lattice Model or Off-Lattice Model. Moreover, we can reduce the computation time and retain good accuracy simultaneously. There is no doubt that we provide highly reliable information for drug design simulation after the step of predicting the protein folding structure.

Molecular chaperones and proteases help maintain protein homeostasis in the cell. While chaperones assist in the folding of polypeptide chains to their native state, proteases degrade misfolded or unfolded proteins and also help regulate protein levels. While mapping chaperone interaction networks, we found that tig (trigger factor chaperone gene), clpP and clpX genes co-localize next to each other on the genome of most examined bacteria. This led us to hypothesize that trigger factor (TF) chaperone and ClpXP protease might interact functionally. TF is a ribosome-associated chaperone that co-translationally folds polypeptide chains. ClpXP is a proteolytic complex that degrades a wide range of substrate proteins. We observed that TF enhanced the rate of the ClpXP degradation of the λO phage protein in vitro and in vivo. TF was also found to enhance the degradation of ribosome-stalled λO thus suggesting the existence of co-translational protein degradation in E. coli.

博士
國立臺灣科技大學
高分子系
94
Control of the carriage steady at a speed is crucial when one wants to advance the state of the art with higher productivity and efficiency to fabric folding machine systems. Three steps are necessary. First, a good design based model of the plant needs to be developed. Second, a good realizable actuator, sensor, and controller must exist. Third, the system output should be modified using the knowledge of the system dynamic response. This dissertation presents a complete control strategy for a fabric folding machine system, and the system mathematical modeling, dynamic analysis, linearization, and controller design are illustrated. A very realizable actuator and a sensor, which uses a motor and an encoder, are applied to design the control system. The computer simulation results for linear and nonlinear system models indicate that the system steady-state errors for this designed controller can be eliminated and good tracking property can be achieved as well. Traditional folding machine system is a stable but sluggish with large steady state errors according to the carriage unit step velocity input. Therefore, it is valuable to develop a realizable controller which can not only make the closed-loop system efficient for good tracking property but also can achieve the meaningful design objectives. In this dissertation, the modeling, stability, model reduction, dynamic analysis and controller design for a folding machine system are presented. The control system performance can be effectively seen from the computer simulation. Proportional plus Integral control (PI) scheme was presented to show the control strategy and design effort of the folding machine system. Although the PI controller not only can eliminate the steady-state error, but also can get the specified damping ratio and undamped natural frequency for a pair of dominant closed loop poles, the response still exist overshoot. Due to a pair of dominant closed loop poles can be designed for a folding machine system, in this dissertation, corresponding with the regulated input command to obliterate the overshoot for achieving precise trajectory tracking and settling-time optimal control will be demonstrated. At the same time, the folding machine system drives frequently use microprocessors, developing a mathematical and computational tool that will ultimately lead to the design of real-time controllers for this system can be visible through this dissertation.

碩士
國立勤益科技大學
工業工程與管理系
107
This study explores the innovative design of the innovative system approach to the rapid assembly and deployment of folding chairs. The research methods used in this study include literature analysis, TRIZ methods, human factors engineering and general design applications. Firstly, the folding chair design and the layout of the chair related literature are analyzed. The contradiction matrix in the TRIZ method is used to find out the relative invention principles for analysis, and as a reference for the innovative design of the folding chair, the rapid assembly and deployment are designed. Folding chair, the innovative design of the universal design folding chair makes the product more popular. Finally, the human-computer interaction of human factors makes the design of the quick assembly and the folding design of the folding chair faster and safer. The drawing software is drawn, and the research results are as follows. 1. Quick expansion function: Pull the chair foot up with the pull ring, and deploy it naturally downwards by gravity to achieve the speed expansion function. 2. Quick folding function: use the pedaling method, stepping on the seat cushion with one foot, and buckle The fasteners on the back of the chair are used to achieve the quick folding function. 3. Quick handling and deployment function: The chair back can be connected with the chair back extension, and can be transported at the same time, and then combined with quick assembly and The rapid expansion and quick folding function of the folding folding chair achieves the effect of rapid deployment and exhibition.

This dissertation explores the aeroelastic stability of a folding wing using both theoretical and experimental methods. The theoretical model is based on the existing clamped-wing aeroelastic model that uses beam theory structural dynamics and strip theory aerodynamics. A higher-fidelity theoretical model was created by adding several improvements to the existing model, namely a structural model that uses ANSYS for individual wing segment modes and an unsteady vortex lattice aerodynamic model. The comparison with the lower-fidelity model shows that the higher-fidelity model typical provides better agreement between theory and experiment, but the predicted system behavior in general does not change, reinforcing the effectiveness of the low-fidelity model for preliminary design of folding wings. The present work also conducted more detailed aeroelastic analyses of three-segment folding wings, and in particular considers the Lockheed-type configurations to understand the existence of sudden changes in predicted aeroelastic behavior with varying fold angle for certain configurations. These phenomena were observed in carefully conducted experiments, and nonlinearities - structural and geometry - were shown to suppress the phenomena. Next, new experimental models with better manufacturing tolerances are designed to be tested in the Duke University Wind Tunnel. The testing focused on various configurations of three-segment folding wings in order to obtain higher quality data. Next, the theoretical model was further improved by adding aircraft longitudinal degrees of freedom such that the aeroelastic model may predict the instabilities for the entire aircraft and not just a clamped wing. The theoretical results show that the flutter instabilities typically occur at a higher air speed due to greater frequency separation between modes for the aircraft system than a clamped wing system, but the divergence instabilities occur at a lower air speed. Lastly, additional experimental models were designed such that the wing segments may be rotated while the system is in the wind tunnel. The fold angles were changed during wind tunnel testing, and new test data on wing response during those transients were collected during these experiments.

Dissertation

Indiana University-Purdue University Indianapolis (IUPUI)
This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as the complex scaling of the plane followed by folding the plane once. Most of the time, scaling by a complex number will \twist" the plane, hence the name. The "folding" both breaks analyticity (and even smoothness) and leads to interesting dynamics ranging from easily understood and highly geometric behavior to chaotic behavior and fractals.

Water plays a critical role in the function and structure of biological systems. Current techniques to study biologically relevant events that span many length and time scales are limited by the prohibitive computational cost of including accurate effects from the aqueous environment. The aim of this work is to expand the reach of current molecular dynamics techniques by reducing the computational cost for achieving an accurate description of water and its effects on biomolecular systems. This work builds from the assumption that the “local” effect of water (e.g. the local orientational preferences and hydrogen bonding) can be effectively modelled considering only the atomistic detail in a very limited region. A recent adaptive resolution simulation technique (AdResS) has been developed to practically apply this idea; in this work it will be extended to systems of simple hydrophobic solutes to determine a characteristic length for which thermodynamic, structural, and dynamic properties are preserved near the solute. This characteristic length can then be used for simulation of biomolecular systems, specifically those involving protein dynamics in water. Before this can be done, current coarse grain models must be adapted to couple with a coarse grain model of water. This thesis is organized in to five chapters. The first will give an overview of water, and the current methodologies used to simulate water in biological systems. The second chapter will describe the AdResS technique and its application to simple test systems. The third chapter will show that this method can be used to accurately describe hydrophobic solutes in water. The fourth chapter describes the use of coarse grain models as a starting point for targeted search with all-atom models. The final chapter will describe attempts to couple a coarse grain model of a protein with a single-site model for water, and it’s implications for future multi-resolution studies.

To get a comprehensive understanding of protein folding, the structural complexity of many proteins as well as the properties of the cellular milieu must be considered. For oligomeric proteins, not only is there polypeptide folding, but protein-protein interactions are also involved. For all proteins, but perhaps most important for aspherical ones, steric effects due to macromolecular crowding may modulate structure, stability, and folding. This is important as 5--40% of the available volume is occupied by various macromolecules in cells. To address these issues, I have used two model systems. Human mitochondrial co-chaperonin protein 10 (cpn10) is used for folding and assembly studies where the number of monomers is large (i.e., 7) and the fold of each monomer contains mostly beta-structure. In contrast, Borrelia burgdorferi VlsE is a football-shaped, monomeric protein with mostly alpha-helical structure that is employed in studies of how protein biophysical properties are affected by the surroundings in terms of membranes and crowding. Using in vitro biophysical and computational methods, my studies have identified the folding and assembly mechanism of cpn10: whereas heptamer unfolding precedes disassembly, a fraction of unfolded monomers assemble before folding while in the other fraction folding of monomers takes place before assembly. Furthermore, in crowded solutions, the helical structure of VlsE first increases and then, at more extreme conditions, a compact, non-native state with beta-sheet content can be populated that exposes an antigenic region. My results have implications for protein folding in general and for the function of these two proteins in particular ( i.e., chaperonin activity for cpn10 and Lyme disease for VlsE).

The study of synthetic peptides aid in improving our current understanding of the fundamental principles for the de novo design of functional proteins. The investigation of designed peptides has been instrumental in providing answers to many questions ranging from the conformational preferences of amino acids to the compact folded structures and also in developing tools for understanding the growth and formation of the protein secondary structures (helices, sheets and turns). In addition, the self-assembly of peptides through non-covalent interactions is also an emerging area of growing interest. The design of peptides which can mimic the protein secondary structures relies on the use of stereochemically constrained amino acid residues at select positions in the linear peptide sequences, leading to the construction of protein secondary structural modules like helices, hairpins and turns. The use of non-coded amino acid residues with strict preferences for adopting particular conformations in the conformational space becomes the most crucial step in peptide design strategies. In addition the crystallographic characterization and analysis of the sequences provides the necessary optimization of the design strategies. The crystallographic characterization of designed peptides provides a definitive and conclusive proof of the success of a design strategy. Furthermore, the X-ray structures provide an atomic view of the interactions, both strong and weak, which govern the growth of the crystal. The information on the geometric parameters and stereochemical properties of a series of peptides, through a systematic study, provides the necessary basis for further scientific investigation, like the molecular dynamics and can also aid in improving the force field parameters meant for carrying out molecular simulations. This can be further complemented by constructing biologically active peptide sequences. The focus of this thesis is to characterize crystallographically the conformational and structural aspects of peptide nanotubes and encapsulated water wires and the β-hairpin peptide models of β-sheets. The systematic study of a series of pentapeptide and octapeptide sequences, containing Aib and D-amino acid residues incorporated at strategic positions, establish the conformation and structural properties of designed peptides as mimics of protein secondary structures and hydrophobic tubular peptide channels and close-packed forms. The structures reported in this thesis are given below: 1 Boc-DPro-Aib-Leu-Aib-Val-OMe (DPUL5) C30H53N5O8 2 Boc-DPro-Aib-Val-Aib-Val-OMe (DPUV5a) C29H51N5O8 .(0.5) H2O 3 Boc-DPro-Aib-Val-Aib-Val-OMe (DPUV5b) C27H51N5O8 .(0.17) H2O 4 Boc-DPro-Aib-Ala-Aib-Val-OMe (DPUA5) C27H47N5O8 5 Boc-DPro-Aib-Phe-Aib-Val-OMe (DPUF5) C33H48N5O8 6 Boc-Pro-Aib-DLeu-Aib-DVal-OMe (PUDL5) C30H53N5O8 7 Boc-Pro-Aib-DVal-Aib-DVal-OMe (PUDV5a) C27H51N5O8 .(0.17) H2O 8 Boc-Pro-Aib-DVal-Aib-DVal-OMe (PUDV5b) C27H51N5O8 . 2H2O 9 Boc-Pro-Aib-DAla-Aib-DVal-OMe (PUDA5) C27H47N5O8 10 Boc-Pro-Aib-DPhe-Aib-DVal-OMe (PUDF5) C33H48N5O8 11 Ac-Phe-Pro-Trp-OMe (FPW) C28H32N4O5.(0.33)H2O 12 Boc-Leu-Phe-Val-DPro-Pro-Leu-Phe-Val-OMe (DPLP8) C56H84N8O1 1 .(0.5) H2O 13 Boc-Leu-Phe-Val-DPro-Pro-Leu-Phe-Val-OMe (YDPP8) C56H83N8O12 .(1.5) H2O 14 Boc-Leu-Val-Val-DPro-ψPro-Leu-Val-Val-OMe (PSIP8) C56H84N8O11S1 .(1.5) H2O 15 Boc-Leu-Phe-Val-DPro-Pro-Leu-Phe-Val-OMe (DPPV8) C48H84N8O11 16 Boc-Leu-Phe-Val-DPro-Aib-Leu-Phe-Val-OMe (DPUF8) C57H88N8O11.(1.5) H2O 17 Piv-Pro-ψH,CH3Pro-NHMe (PSPL3) C22H37N3O5S1 18 Boc-Leu-Val-Val-Aib-DPro-Leu-Val-Val-OMe (UDPV8) C47H84N8O11.2(C3H7NO) 19 Boc-Leu-Phe-Val-DPro-Ala-Leu-Phe-Val-OMe (BH1P8) C54H78N8O11.H2O 20 Boc-Leu-Phe-Val-DPro-Aib-Leu-Phe-Val-OMe (DPUFP8) C55H84N8O11. (0.5) H2O 21 Boc-Leu-Phe-Val-DPro-Pro-Leu-Phe-Val-OMe (YDPPP8) C56H83N8O12. (1.5) H2O The crystal structure determination of the peptides presented in this thesis provides a wealth of information on the folding patterns of the sequences, in addition to the characterization of many structural and geometric properties. In particular, the study sheds light on the growth and formation of peptide nanotubes and the structure of encapsulated water wires, and also the structural details of Type I′ and Type II′β-turn nucleated hairpins. The study provides the backbone and side chain conformational parameters of the sequences, highlighting the varied conformational excursions possible in the peptide molecules. The thesis is divided into 6 chapters and one appendix. Chapter 1 gives a general introduction to the stereochemistry of the polypeptide chain, description of backbone torsion angles of α-amino acid residues and the major secondary structures of α-peptides, namely α-helix, β-sheet and β-turns. The basic structural features of helices and sheets are given. A brief introduction to polymorphism and weak interactions is also presented, followed by a discussion on X-ray diffraction and solution to the phase problem. Chapter 2 is divided into two parts. PART 1 describes the crystal structures of a series of eight related enantiomeric peptide sequences (Raghavender et al., 2009; Raghavender et al., 2010). The crystal structures of four sequences with the general formula Boc-DPro-Aib-Xxx-Aib-Val-OMe (Xxx = Ala/Val/Leu/Phe) and the enantiomeric sequences provided a set of crystal structures withdifferent packing arrangements. The structure of the peptide with Xxx = Leu revealed a nanotube formation with the Leu lining the inner walls of channel. The channels were found to be empty. The sequence with Xxx = Val revealed a solvent-filled water channel.Investigation of the water wire structures on the diffraction data collected on the same crystal over a period of time revealed the existence of two different kinds of water wires in thechannels. Comparison with the peptide tubular structures available in the literature and the water structure inside the aquaporin channels are contrasted. Close-packed structures are observed in the case of Xxx=Ala and Phe. The backbone conformations are essentially identical. Enantiomeric sequences also revealed similar structures. Polymorphic forms were observed in the case of DVal(3) containing sequence. One form is observed to have water-filled channels forming a nanotube, as opposed to the close-packed structure in the polymorphic form. Crystal parameters DPUL5: C30H53N5O8; P65; a = b = 24.3673 (9) Å, c = 10.6844 (13) Å; α = β = 90°, γ = 120°; Z = 6; R = 0.0671, wR2 = 0.1446. DPUV5a: C29H51N5O8 .(0.5) H2O; P65; a = b = 24.2920 (13) Å, c = 10.4838 (11) Å; α = β = 90°, γ = 120°; Z = 6; R = 0.0554, wR2 = 0.1546. DPUV5b: C29H51N5O8 .(0.17) H2O; P65; a = b = 24.3161 (3) Å, c = 10.1805 (1) Å; α = β = 90°, γ = 120°; Z = 6; R = 0.0617, wR2 = 0.1844. DPUA5: C27H47N5O8; P212121; a = 12.2403 (8), b = 15.7531 (11) Å, c = 16.6894 (11) Å; Z =4; R = 0.0439, wR2 = 0.1249. DPUF5: C33H48N5O8; P212121; a = 10.3268 (8), b = 18.7549 (15) Å, c = 18.9682 (16) Å; Z = 4; R = 0.0472, wR2 = 0.1325. PUDL5: C30H53N5O8; P61; a = b = 24.4102 (8) Å, c = 10.6627 (7) Å; α = β = 90°, γ = 120°; Z = 6; R = 0.0543, wR2 = 0.1495. PUDV5a: C29H51N5O8 .(0.17)H2O; P61; a = b = 24.3645 (14) Å, c = 10.4875 (14) Å; α = β = 90°, γ = 120°; Z = 6; R = 0.0745, wR2 = 0.1810. PUDV5b: C29H51N5O8. 2H2O; C2; a = 20.7278 (35), b = 9.1079 (15) Å, c = 19.5728 (33) Å; α = γ = 90°, β = 94.207°; Z = 6; R = 0.0659, wR2 = 0.1755. PUDA5: C27H47N5O8; P212121; a = 12.2528 (12), b = 15.7498 (16) Å, c = 16.6866 (16) Å; Z = 4; R = 0.0473, wR2 = 0.1278. PUDF5: C33H48N5O8; P212121; a = 10.3354 (8), b = 18.7733 (10) Å, c = 18.9820 (10) Å; Z = 4; R = 0.0510, wR2 = 0.1526. PART 2 describes the crystallographic characterization of the tubular structure in a tripeptide Ac-Phe-Pro-Trp-OMe (FPW) sequence. The arrangement of the single-file water moleculesin the peptide nanotubes of FPW could be established by X-ray diffraction. In addition, the energetically favoured arrangement of the water wire inside the peptide channels could be modeled by understanding the construction of the peptide nanotube. In particular, the helicalmacrodipole of the peptide nanotube and the water wire dipoles prefer an antiparallel arrangement inside the peptide channels as opposed to parallel arrangements, is established by the classical dipole-dipole interaction energy calculation. In addition, the growth of thenanotubes and the arrangement of the water wires inside the channels could be correlated to the macroscopic dimensions of the crystal by the indexing of the crystal faces and contrasted with the structure of DPUV5. Crystal parameters FPW: C28H32N4O5.(0.33)H2O; P65; a = b = 21.5674 (3) Å, c = 10.1035 (2) Å; α = β = 90°, γ = 120 °; Z = 6; R = 0.0786, wR2 = 0.1771 Chapter 3 provides the crystal structures of five octapeptide β-hairpin forming sequences and a tripeptide containing a modified amino acid, with modification in the side chain (pseudo-proline, ψH,CH3Pro). The parent peptide, Boc-Leu-Phe-Val-DPro-Pro-Leu-Phe-Val-OMe (DPLP8), was observed to form a strong Type II′β-turn at the DPro-Pro segment, and the strand segments adopting a β-sheet conformation. Two molecules were observed in the asymmetric unit, inclined to each other at approximately 70°. Modification in the strand sequence Phe(2) to Tyr(2) also resulted in a hairpin with identical conformation and similar packing arrangement. The difference was in the solvent content. In both the cases the molecules were packed orthogonal with respect to each other, resulting in the formation of ribbon-like structures in three dimensions. The replacement of Phe(2) and Phe(7) with Valine residues, with the retention of DPro-Pro β-turn segment, results in an entiely different packing arrangement (parallel). Modification of Pro(5) residue of the turn segment to Aib(5) and ψPro, also results in the molecules packing orthogonally to each other. The tripeptide with a modified form of ψPro, namely ψH,CH3Pro, resulted in a folded structure with a Type VIa β-turn, with the amide bond between the Pro-ψH,CH3Pro segment adopting a cis configuration (Kantharaju et al., 2009). Crystal parameters DPLP8: C56H84N8O11 .(0.5) H2O; P21; a = 14.4028 (8), b = 18.9623 (11) Å, c = 25.4903 (17) Å, β = 105.674 ° (4); Z = 4; R = 0.0959, wR2 = 0.2251. YDPP8: C56H84N8O12 .(1.5) H2O; P212121; a = 14.4028 (8), b = 18.9623 (11) Å, c = 25.4903 (17) Å, Z = 8; R = 0.0989, wR2 = 0.2064. PSIP8: C57H86N8O11S1.(1.5) H2O; C2; a = 34.6080 (2), b = 15.3179 (10) Å, c = 25.6025 (15) Å, β = 103.593 ° (3); Z = 4; R = 0.0931, wR2 = 0.2259. DPPV8: C48H84N8O11; P1; a = 9.922 (3), b = 11.229 (4) Å, c = 26.423 (9) Å, α = 87.146 (6), β = 89.440° (6), γ = 73.282 (7); Z = 2; R = 0.1058, wR2 = 0.2354. DPUF8: C57H88N8O11 .(1.5) H2O; P21; a = 18.410 (2), b = 23.220 (3) Å, c = 19.240 (3) Å, β = 118.036 ° (4); Z = 4; R = 0.1012, wR2 = 0.2061. PSPL3: C22H37N3O5S1; P31; a = b = 14.6323 (22), c = 10.4359 (22) Å, α = β = 90°, γ = 120°; Z = 3; R = 0.0597, wR2 = 0.1590. Chapter 4 describes the crystal structure and molecular conformation of Type I′β-turn nucleated hairpin. The incorporation of Aib-DPro segment in the middle of Leu-Val-Val strands in the peptide sequence Boc-Leu-Val-Val-Aib-DPro-Leu-Val-Val-OMe results in an obligatory Type I′ turn containing hairpin. The molecular conformation and the packing arrangement of the molecules in the crystal are contrasted with the only Type I′β-hairpin reported in the literature and with a sequence where the turn residues are flipped and strand residues replaced with Phe(2) and Phe(7). Crystal parameters UDPV8: C47H84N8O11.2(C3H7NO); P21; a = 11.0623 (53), b = 18.7635 (89) Å, c = 16.6426 (80) Å, β = 102.369 (8); Z = 2; R = 0.0947, wR2 = 0.1730. Chapter 5 provides the crystal structures of three polymorphic forms of β-hairpins. The structure of BH1P8 provides new insights into the packing of hairpins inclined orthogonally to each other. The two polymorphic forms differ not only in their modes of packing in crystals but also in the strong and weak interactions stabilizing the packing arrangements. The polymorphic forms of DPUFP8 differ only in the content of the solvent in the asymmetric unit and the role it plays in bridging the symmetry related pairs of molecules. The polymorphic form YDPPP8 crystallized in a completely different space group, revealing a completely different mode of packing and also the cocrystallized solvent participating in a different set of interactions. Crystal parameters BH1P8: C54H78N8O11.H2O; P212121; a = 18.7511 (9), b = 23.3396 (11) Å, c = 28.1926 (13)Å; Z = 8; R = 0.1208, wR2 = 0.2898. DPUFP8: C55H84N8O11. (0.5) H2O; P21; a = 18.0950 (4), b = 23.0316 (5) Å, c = 18.6368 (5) Å, β = 117.471 (2); Z = 4; R = 0.0915, wR2 = 0.2096. YDPPP8: C56H83N8O12. (1.5) H2O; P21; a = 14.3184 (8), b = 18.9924 (9) Å, c = 25.1569 (14) Å, β = 105.590 (4); Z = 4; R = 0.1249, wR2 = 0.2929. Chapter 6 provides a comprehensive overview of the β-hairpin peptide crystal structures published in the literature as well as those included in the thesis. The hairpins are classified based on the residues composing the β-strands and the mode of their packing in the crystals. In the crystal structures the hairpins are observed to adopt either a Type II′ or Type I′β-turns. The indexing of the crystal faces of a few representative hairpin peptides crystallographically characterized in this thesis, provides a rational explanation for the preferential growth of the crystals in certain directions, when correlated with the strong directional forces (hydrogen bonding) and weak interactions (van der Waals, aromatic-aromatic) observed in the crystal packing. The insights gained by these studies would be highly valuable in understanding the nucleation and growth of β-hairpin peptides and the formation of β-sheet structures. Appendix I describes the Cambridge Structural Database (CSD) analysis of the conformational preferences of the proline residues found in the peptide crystal structures. The frequency distributions of the backbone φ, ψ and ω and side chain χ1, χ2, χ3, χ4 and θ torsion angles of the proline residues are calculated, tabulated and represented as graphical plots. The correlation between the backbone and endocyclic torsion angles provides for a clear evidence of the role of a particular torsion variable χ2 in deciding the state of puckering. In addition, the endocyclic bond angles also appear to be correlated, relatively strongly, with the χ2 torsion. This provides a geometrical explanation of the factors governing the puckering of the proline ring.

This thesis examines so called folding neural networks as a mechanism for machine learning. Folding networks form a generalization of partial recurrent neural networks such that they are able to deal with tree structured inputs instead of simple linear lists. In particular, they can handle classical formulas - they were proposed originally for this purpose. After a short explanation of the neural architecture we show that folding networks are well suited as a learning mechanism in principle. This includes three parts: the proof of their universal approximation ability, the aspect of information theoretical learnability, and the examination of the complexity of training. Approximation ability: It is shown that any measurable function can be approximated in probability. Explicit bounds on the number of neurons result if only a finite number of points is dealt with. These bounds are new results in the case of simple recurrent networks, too. Several restrictions occur if a function is to be approximated in the maximum norm. Afterwards, we consider briefly the topic of computability. It is shown that a sigmoidal recurrent neural network can compute any mapping in exponential time. However, if the computation is subject to noise almost the capability of tree automata arises. Information theoretical learnability: This part contains several contributions to distribution dependent learnability: The notation of PAC and PUAC learnability, consistent PAC/ PUAC learnability, and scale sensitive versions are considered. We find equivalent characterizations of these terms and examine their respective relation answering in particular an open question posed by Vidyasagar. It is shown at which level learnability only because of an encoding trick is possible. Two approaches from the literature which can guarantee distribution dependent learnability if the VC dimension of the concept class is infinite are generalized to function classes: The function class is stratified according to the input space or according to a so-called luckiness function which depends on the output of the learning algorithm and the concrete training data. Afterwards, the VC, pseudo-, and fat shattering dimension of folding networks are estimated: We improve some lower bounds for recurrent networks and derive new lower bounds for the pseudodimension and lower and upper bounds for folding networks in general. As a consequence, folding architectures are not distribution independent learnable. Distribution dependent learnability can be guaranteed. Explicit bounds on the number of examples which guarantee valid generalization can be derived using the two approaches mentioned above. We examine in which cases these bounds are polynomial. Furthermore, we construct an explicit example for a learning scenario where an exponential number of examples is necessary. Complexity: It is shown that training a fixed folding architecture with perceptron activation function is polynomial. Afterwards, a decision problem, the so-called loading problem, which is correlated to neural network training is examined. For standard multilayer feed-forward networks the following situations turn out to be NP-hard: Concerning the perceptron activation function, a classical result from the literature, the NP-hardness for varying input dimension, is generalized to arbitrary multilayer architectures. Additionally, NP-hardness can be found if the input dimension is fixed but the number of neurons may vary in at least two hidden layers. Furthermore, the NP-hardness is examined if the number of patterns and number of hidden neurons are correlated. We finish with a generalization of the classical NP result as mentioned above to the sigmoidal activation function which is used in practical applications.