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This thesis is a series of experiments performed on how ribbon-like bands of material can be folded to generate special volumes that can accommodate the functional aspects of a building program. / Master of Architecture

Muitos problemas de otimização multi-objetivo utilizam os algoritmos evolutivos para encontrar as melhores soluções. Muitos desses algoritmos empregam as fronteiras de Pareto como estratégia para obter tais soluções. Entretando, conforme relatado na literatura, há a limitação da fronteira para problemas com até três objetivos, podendo tornar seu emprego insatisfatório para os problemas com quatro ou mais objetivos. Além disso, as propostas apresentadas muitas vezes eliminam o emprego dos algoritmos evolutivos, os quais utilizam tais fronteiras. Entretanto, as características dos algoritmos evolutivos os qualificam para ser empregados em problemas de otimização, como já vem sendo difundido pela literatura, evitando eliminá-lo por causa da limitação das fronteiras de Pareto. Assim sendo, neste trabalho se buscou eliminar as fronteiras de Pareto e para isso utilizou a lógica Fuzzy, mantendo-se assim o emprego dos algoritmos evolutivos. O problema escolhido para investigar essa substituição foi o problema de predição de estrutura terciária de proteínas, pois além de se encontrar em aberto é de suma relevância para a área de bioinformática. / Several multi-objective optimization problems utilize evolutionary algorithms to find the best solution. Some of these algoritms make use of the Pareto front as a strategy to find these solutions. However, according to the literature, the Pareto front limitation for problems with up to three objectives can make its employment unsatisfactory in problems with four or more objectives. Moreover, many authors, in most cases, propose to remove the evolutionay algorithms because of Pareto front limitation. Nevertheless, characteristics of evolutionay algorithms qualify them to be employed in optimization problems, as it has being spread out by literature, preventing to eliminate it because the Pareto front elimination. Thus being, this work investigated to remove the Pareto front and for this utilized the Fuzzy logic, remaining itself thus the employ of evolutionary algorithms. The choice problem to investigate this remove was the protein tertiary structure prediction, because it is a open problem and extremely relevance to bioinformatic area.

Proteins are chain molecules built from amino acids. The precise sequence of the 20 different types of amino acids in a protein chain defines into which structure a protein folds, and the three-dimensional structure in turn specifies the biological function of the protein. The reliable folding of proteins is a prerequisite for their robust function. Misfolding can lead to protein aggregates that cause severe diseases, such as Alzheimer's, Parkinson's, or the variant Creutzfeldt-Jakob disease. Small single-domain proteins often fold without experimentally detectable metastable intermediate states. The folding dynamics of these proteins is thought to be governed by a single transition-state barrier between the unfolded and the folded state. The transition state is highly instable and cannot be observed directly. However, mutations in which a single amino acid of the protein is substituted by another one can provide indirect access. The mutations slightly change the transition-state barrier and, thus, the folding and unfolding times of the protein. The central question is how to reconstruct the transition state from the observed changes in folding times. In this habilitation thesis, a novel method to extract structural information on transition states from mutational data is presented. The method is based on (i) the cooperativity of structural elements such as alpha-helices and beta-hairpins, and (ii) on splitting up mutation-induced free-energy changes into components for these elements. By fitting few parameters, the method reveals the degree of structure formation of alpha-helices and beta-hairpins in the transition state. In addition, it is shown in this thesis that the folding routes of small single-domain proteins are dominated by loop-closure dependencies between the structural elements. / Proteine sind Kettenmoleküle, die aus einzelnen Aminosäuren aufgebaut sind. Die genaue Sequenz der 20 verschiedenartigen Aminosäuren innerhalb der Proteinkette bestimmt dabei, in welche spezielle Struktur sich ein Protein faltet. Die dreidimensionale Struktur bestimmt wiederum die Funktion der Proteine. Doch nur korrekt gefaltet kann ein Protein seine Funktion erfüllen. Fehler bei der Faltung können zu Proteinaggregaten führen, die schwere Krankheiten wie Alzheimer, Parkinson oder das Creutzfeldt-Jakob-Syndrom hervorrufen. Viele kleine Proteine falten ohne experimentell beobachtbare metastabile Zwischenzustände. Entscheidend für die Faltungsdynamik dieser Proteine ist der Übergangszustand zwischen dem ungefalteten und gefalteten Zustand. Der Übergangszustand ist instabil und kann nicht direkt beobachtet werden. Einen indirekten Zugang ermöglichen jedoch Mutationen eines Proteins, bei denen einzelne Aminosäuren ausgetauscht werden. Die Mutationen verändern geringfügig die Übergangszustandsbarriere, und damit die Faltungs- und Entfaltungszeiten des Proteins. Die zentrale Frage ist, wie sich der Übergangszustand aus den beobachteten Änderungen der Faltungszeit rekonstruieren lässt. In dieser Habilitationsschrift wird eine neuartige Methode zur Rekonstruktion von Übergangszuständen aus Mutationsdaten vorgestellt. Die Methode beruht auf (i) der Kooperativität von Strukturelementen wie alpha-Helizes und beta-Haarnadeln, und (ii) der Aufspaltung von mutationsinduzierten Veränderungen der freien Energie in Komponenten für diese Strukturelemente. Die Modellierung der experimentellen Daten verrät, in welchem Grad alpha-Helizes and beta-Haarnadeln im Übergangszustand strukturiert sind. Zudem wird in dieser Habilitationsschrift gezeigt, dass die Faltungswege vieler kleiner Proteine durch Schleifenschließungsbeziehungen zwischen den Strukturelementen dominiert werden.

This research shows optimization approaches to protein folding. The protein folding problem is to predict the compact three dimensional structure of a protein based on its amino acid sequence. This research focuses on ab-initio mathematical models to find provably optimal solutions to the 2D HP-lattice protein folding model. We built two integer programming (IP) models and five constraint programming (CP) models. All the models give provably optimal solutions. We also developed some CP techniques to solve the problem faster and then compared their computational times. We tested the models with several protein instances. My models, while they are probably too slow to use in practice, are significantly faster than the alternatives, and thus are mathematically relevant. We also provided reasons why protein folding is hard using complexity analysis. This research will contribute to showing whether CP can be an alternative to or a complement of IP in the future. Moreover, figuring out techniques combining CP and IP is a prominent research issue and our work will contribute to that literature. It also shows which IP/CP strategies can speed up the running time for this type of problem. Finally, it shows why a mathematical approach to protein folding is especially hard not only mathematically, i.e. NP-hard, but also practically.

The thesis entitled “Folding studies on Peanut Agglutinin: A lectin with an unusual quaternary structure” deals with the several aspects of the folding of the tetrameric legume lectin Peanut Agglutinin (PNA). PNA is a well studied legume lectin and several interesting observations regarding its unfolding have been published from our laboratory. The present thesis is an extension of the same work to enrich our knowledge about the folding behaviour of PNA. The thesis describes both experimental as well as theoretical insight on unfolding of PNA. Chapter 1 is a general discussion on lectins. Lectins are carbohydrate binding proteins of non immune source. Lectins are generally found in all type of organisms- plants, animals as well as micro-organisms. Among the plant lectins “legume lectin” is a very well studied system. Legume lectins share a general tertiary structural fold; “jelly roll fold” while they vary in their quaternary structure. Thus they can be considered as “natural mutants” in the context of quaternary structure. The origin of the lectins, structure and sugar specificity have been discussed with emphasis on legume lectin family. Chapter 2 describes the thermodynamics related to the urea induced denaturation of PNA. PNA shows a very interesting unfolding profile, populating one molten globule like intermediate during thermal as well as chaotrope induced denaturation. The molten globule like intermediate loses most of its tertiary structure but retains sufficient secondary structure. Surprisingly, the molten globule like state retains its carbohydrate binding specificity like the native PNA. A model has been developed to fit the chaotrope induced three state denaturation profile of PNA. The model considers the tetramer to dissociate to monomeric intermediate, which in turn dissociates to complete denatured state. All the relevant thermodynamic parameters (∆G, ∆Cp, Tg) associated in the denaturation process have been extracted. The tetramer is found to be ~30 kcal/Mole more stable compared to the intermediate and the intermediate is ~8 kcal/Mole more stable compared to the denatured. The denaturation process has been followed by the changes in hydrodynamic radii by dynamic light scattering (DLS). The profile of change in hydrodynamic radius and the % intensity clearly identify the generation of two species simultaneously. The analysis shows that the intermediate is ~40 % unfolded in nature. Thus this chapter deals with the detailed study of thermodynamics and dynamic light scattering study of the urea induced denaturation of PNA. Chapter 3 deals with the effect of 2, 2, 2 - trifluoroethanol (TFE) on the structure of PNA at two different pH. TFE is a well known co-solvent and is widely used to induce α- helical structure in a protein. The secondary structures induced by TFE are assumed to reflect conformations that prevail during early stages of protein folding. Thus it was quite interesting to notice the structural changes induced by TFE. The effect of TFE has been studied at two different pH- neutral pH of 7.4 and acidic pH 2.5. The  structure of the protein is accentuated in the presence of TFE at low concentration at both the pH. TFE induces α-helical structure from 40 % (v/v) concentration onwards at both the pH. TFE at 15 % concentration induces a molten globule like structure at low pH. The quenching of acrylamide suggests that the protein at low pH and 15 % TFE concentration has a more compact structure compared to the protein at low pH in absence of TFE as well as 6M guanidine hydrochloride (GdnHCl). Further studies of hydrodynamic radii by dynamic light scattering (DLS) also reveal that the protein undergoes some kind of compaction in presence of 15 % TFE at low pH. The induction of this type of molten globule like state at neutral pH has not been observed. Chapter 4 describes the molecular dynamics simulation of deoligomerization of PNA. The native PNA (PDB code 2PEL), excluding any ligand and metal ions has been simulated at 300 K, 400 K, 500 K and 600 K for 500 ps. The overall destabilisation has been followed by root mean square deviation (RMSD), the radius of gyration (Rg) and the solvent accessible surface area (ASA), while the atomistic details are revealed by residue wise RMSD (RRMS), hydrogen bonds and cluster analysis. The protein shows a quite a dramatic change in RMSD and radius of gyration profile at 600 K. RRMS shows that the residues belonging to the loops, mainly in the metal binding site show quite high flexibility. The relative change in average accessible surface area reveals that the primary core of the protein is exposed at 600 K while it is well buried till 500 K. The hydrogen bond analysis clearly shows that with increase in temperature number of hydrogen bonds starts decreasing. Mainly the hydrogen bonds involving side chain interactions are broken. Surprisingly, not all the monomers behave similarly. Monomers C and D are more perturbed compared to monomers A and B. The asymmetry in the interfaces of the monomers may be the key reason for it. The change in the interfaces has been probed by hydrogen bond analysis and cluster analysis. The GSIV type interfaces (A-D and B-C) have been found out to be the most dynamic in nature compared to the other two interfaces. Thus, this chapter reveals the early stage of unfolding of PNA, where perturbation in secondary and tertiary structural level is quite prominent but the interfaces are still holding weakly and are not completely dissociated. Chapter 5 is the continuation of the molecular dynamics simulation on unfolding of PNA, where the effect of metal ions has been illustrated. The monomeric PNA has been simulated to compare its dynamics with the tetramer. The metal binding loop (125-135) becomes unstable and opens up for the monomer even at 300 K after 800 ps. The monomer at 600 K is completely disorganized. The instability of the metal binding loop of the monomer triggers the urge to study the simulation in presence of metal ions (Ca2+ and Mn2+). The monomer bound with metal ions shows steady fluctuation at 300 K. Binding of metal ions seems to bring stability even at 600 K. Surprisingly binding of metal ions to the metal binding site not only stabilises the metal binding loop but also stabilises residues at back beta sheet which are involved in oligomerization. Hence, another simulation of the tetramer at 600 K bound with metal ions has been done. It has been shown that binding of metal ions increases the stability of the protein without altering the denaturation pathway. Appendix A describes a completely different study from PNA. The initial spectral and kinetic characterization of 7, 8- Diaminopelargonic acid Synthase (DAPA Synthase) has been done from Mycobacterium tuberculosis. The DAPA Synthase gene has been cloned earlier in our laboratory and the same has been used for further studies. This is a well known pyridoxal-5′ phosphate (PLP) dependent enzyme, which converts 8- Amino-7-oxopelargonic Acid (KAPA) to 7, 8-Diaminopelargonic Acid (DAPA) in the second step of biotin biosynthesis. DAPA Synthase uses S-adenosylmethionine (SAM) and KAPA as substrate. The first half of the enzymatic reaction has been followed spectroscopically, both by steady state and stopped flow. The enzyme seems to undergo change in conformation as evident from fluorescence and circular dichroism study. The Km value has been determined using bioassay technique. The detailed characterization of the enzyme has been described in this chapter.

The atomic resolution structure of a low populated and transiently formed on-pathway folding intermediate of the FF domain from human HYPA/FBP11 has recently been reported[1]. The structure was determined on the basis of backbone chemical shift and bond vector orientation restraints measured on the ‘invisible’ intermediate state using relaxation dispersion nuclear magnetic resonance (NMR) spectroscopy that were subsequently input into the data-base structure determination program CS-Rosetta. This thesis focuses on the cross-validation of the structure so produced. We present here the solution NMR structure of a mimic of the folding intermediate that is highly populated in solution, obtained from the wild-type domain by protein mutagenesis. The ensemble of structures generated of the mimic are within 2Å of the relaxation dispersion/CS-Rosetta structures of the intermediate, with the non-native interactions in the intermediate also observed in the mimic. The results presented in this thesis strongly confirm the structure of the FF domain folding intermediate, in particular, and validate the use of relaxation dispersion derived restraints in structural studies of invisible excited states, in general.

The atomic resolution structure of a low populated and transiently formed on-pathway folding intermediate of the FF domain from human HYPA/FBP11 has recently been reported[1]. The structure was determined on the basis of backbone chemical shift and bond vector orientation restraints measured on the ‘invisible’ intermediate state using relaxation dispersion nuclear magnetic resonance (NMR) spectroscopy that were subsequently input into the data-base structure determination program CS-Rosetta. This thesis focuses on the cross-validation of the structure so produced. We present here the solution NMR structure of a mimic of the folding intermediate that is highly populated in solution, obtained from the wild-type domain by protein mutagenesis. The ensemble of structures generated of the mimic are within 2Å of the relaxation dispersion/CS-Rosetta structures of the intermediate, with the non-native interactions in the intermediate also observed in the mimic. The results presented in this thesis strongly confirm the structure of the FF domain folding intermediate, in particular, and validate the use of relaxation dispersion derived restraints in structural studies of invisible excited states, in general.

Muitos problemas de otimização multi-objetivo utilizam os algoritmos evolutivos para encontrar as melhores soluções. Muitos desses algoritmos empregam as fronteiras de Pareto como estratégia para obter tais soluções. Entretando, conforme relatado na literatura, há a limitação da fronteira para problemas com até três objetivos, podendo tornar seu emprego insatisfatório para os problemas com quatro ou mais objetivos. Além disso, as propostas apresentadas muitas vezes eliminam o emprego dos algoritmos evolutivos, os quais utilizam tais fronteiras. Entretanto, as características dos algoritmos evolutivos os qualificam para ser empregados em problemas de otimização, como já vem sendo difundido pela literatura, evitando eliminá-lo por causa da limitação das fronteiras de Pareto. Assim sendo, neste trabalho se buscou eliminar as fronteiras de Pareto e para isso utilizou a lógica Fuzzy, mantendo-se assim o emprego dos algoritmos evolutivos. O problema escolhido para investigar essa substituição foi o problema de predição de estrutura terciária de proteínas, pois além de se encontrar em aberto é de suma relevância para a área de bioinformática. / Several multi-objective optimization problems utilize evolutionary algorithms to find the best solution. Some of these algoritms make use of the Pareto front as a strategy to find these solutions. However, according to the literature, the Pareto front limitation for problems with up to three objectives can make its employment unsatisfactory in problems with four or more objectives. Moreover, many authors, in most cases, propose to remove the evolutionay algorithms because of Pareto front limitation. Nevertheless, characteristics of evolutionay algorithms qualify them to be employed in optimization problems, as it has being spread out by literature, preventing to eliminate it because the Pareto front elimination. Thus being, this work investigated to remove the Pareto front and for this utilized the Fuzzy logic, remaining itself thus the employ of evolutionary algorithms. The choice problem to investigate this remove was the protein tertiary structure prediction, because it is a open problem and extremely relevance to bioinformatic area.