The objective of this research was to investigate the behavioural, physiological and immunological effects of routine surgical procedures in neonatal swine in order to provide producers with science-based recommendations. In the first experiment, low- or average-birth-weight piglets that were tail docked and ear notched at 1 or 3 days of age showed subtle differences resulting from age at processing. However, low-birth-weight male piglets had the lowest attendance during nursing bouts and spent the greatest amount of time lying alone. Vocalization data suggests that ABW piglets may be less reactive to the procedures on d 1. Overall, the decreased vitality and reduced survivability of low-birth-weight piglets suggests that delaying processing until day 3 for these piglets may be preferable. In the second experiment, the effects of docked tail length and nursery stocking density on tail-biting behaviour, skin lesions and rectal prolapses were investigated. Long-tailed pigs (docked to 4.5 cm at birth) were most vulnerable to tail-biting, and housing at a moderate versus high nursery stocking density was not sufficient to reduce tail-biting. High nursery stocking density negatively impacted skin lesion scoring and growth performance for the majority of the grower-finisher period. Pigs from either nursery stocking density and docked tail length groups were equally likely to be affected by prolapsed rectal mucosa. Given the decreased survivability and significantly lighter weaning weight for low-birth-weight piglets compared to those of average-birth-weight, delaying processing of low-birth-weight piglets may be the most humane option. Further, until tail-biting is better understood and a more effective solution found, the routine docking of tails remains the optimal method for balancing a situation with enormous welfare-reducing potential. / Agriculture and Agri-Food Canada

The role of odorant binding proteins in the olfaction of mosquitoes, the primary mechanism of human host recognition, has been an important focus of biological research in the field of infectious disease transmission by these insects. This thesis provides an in depth knowledge of these proteins in three mosquito species Anopheles gambiae, Aedes aegypti and Culex quinquefasciatus. A large scale analysis on these genomes has been carried out towards the identification of the odorant binding proteins in the mosquito genomes. Identification of many new OBP members, in particular in the Aedes aegypti and Culex quinquefasciatus species, and an extensive phylogenetic analysis presenting a novel classification of the OBP subfamilies of these mosquito species has been proposed. This results further demonstrates the extraordinary multiplicity and diversity of the OBP gene repertoire in these three mosquito genomes and highlights the striking sequence features that are nevertheless highly conserved across all mosquito OBPs. Owing to the availability of homologous structures from mosquitoes or related species, the 3D structure modelling of all the Classic OBPs from the three genomes (representing in total 137 structures) has been performed. This was completed by large scale docking studies on these structures by screening a large set of compounds that are known to be mosquito attractants or repellents. These provide many exciting new insights into the structural and functional aspects towards understanding the efficacy of some repellents and of some attractants from human emanations. Through molecular dynamics simulation, the structural changes observed in an OBP bounded to an odorant when pH conditions are modified were characterized and the probable mechanism of ligand binding and release is presented. This work provides the first insights to many of the long awaited questions on the genomic, structural and functional characterization of mosquito OBPs and can be viewed as a reliable starting point for further experimental research focussed on these aspects.

In the distribution network of a large retailer, shipments can either be transported by the retailer's own trucks or outsourced to third-party logistics (3PL) companies. In the former case, shipments are consolidated and transported from their origins through an intermediate facility, namely a crossdock. At a crossdock, shipments are unloaded, sorted, re-consolidated, loaded and transported to their destinations. The consolidation process offers economies of scale that reduce the transportation costs. At the same time, it increases travel distances and incurs handling costs at a crossdock. For this reason, consolidation is uneconomic for a shipment in which origin and destination are located close to one other, especially through a distant crossdock. It is cheaper to outsource transportation of such a shipment to 3PL companies. This shipping decision raises a series of questions. Should a shipment be consolidated through a crossdock or outsourced to 3PL companies? How do facility locations, the operational cost of a crossdock and mode of shipments influence the shipping decision? Can the robustness and potential growth of a crossdock be measured? How does outsourcing affect the robustness and potential growth of a crossdock? We formulate a strategic model of a retailer's distribution network as an economic trade-off between consolidated shipments through a crossdock and outsourced shipments to 3PL companies. We study the locus of facility locations where the costs of a consolidated shipment and an outsourced shipment are equal and discover that the trade-off can be modeled by classical geometric curves, particularly an ellipse, a hyperbola, a limacon and a Cartesian oval. These curves can be developed into a preliminary routing and locating tool. We also observe interesting connections between the single hub crossdocking network and other fields of geometric study, such as Voronoi diagrams and geometric inversion. In addition, the area bounded by these curves represents the likelihood in which a particular shipment is consolidated through a crossdock. We expand this concept to multiple vendor-store pairs and suggest an index that measures robustness and potential growth of a particular crossdock. This asymptotic-probability index explains economic driving factors of consolidation and outsourcing. Although the derivation of the index is limited by the dimension and spatial distribution of facilities, its numerical value can be determined by a computer simulation. Therefore, we use Monte Carlo simulation to compute the proposed index to explain the outsourcing and the interaction between TL threshold0.1 and mode of shipments. The analysis and computer simulation suggest that outsourcing may cause an adverse effect in a single hub crossdocking network, resulting in the abrupt reduction of consolidated shipments in the network. Furthermore, we propose transportation planning to alleviate this effect and compare them to the optimal allocation. The routing and locating application of the model is illustrated using the Home Depot distribution network. Our model predicts 5.5% and additional 1.0% savings in transportation cost by re-allocation of shipments and re-location of crossdocks, respectively. The empirical study shows that the adverse effect of outsourcing can be eliminated by limiting the number of crossdocks used by each store.

A recent shift towards proteomics has seen many structural genomics initiatives set up for high-throughput structure determination using traditional methods of x-ray crystallography and NMR. The next step in the proteomic revolution focuses on the interplay of multi-protein complexes and transient protein-protein interactions, which are involved in many cellular functions. Greater understanding of protein-protein interactions will inevitably lead to better comprehension of the regulation of cellular process, which has implications in biomedical sciences and biotechnology. Even though many high-resolution initiatives focus on proteins and protein complexes, their structure-determination success rates are still low. An emerging approach uses chemical cross-linking and mass spectrometry to derive a set of sparse distance constrains, which can be used for building models of proteins and to map out residues in protein interaction interface based on partial structural information. This technique allows low-resolution identification of protein structures and their interactions in cases where traditional structure determination techniques did not produce results. Chemical cross-linkers have been successfully used for many years in identifying interacting proteins. However, recent advances in mass spectrometry have allowed the identification of exact insertion points of low-abundance cross-links and hence has opened up a new perspective on the use of cross-linkers in combination with computational structure prediction. For protein interaction studies, the approach uses chemical cross-linking information with molecular docking, so that the cross-links are treated as explicit constraints in the calculations. This study focuses on a low-cost and rapid approach to structure prediction, where partial structural information and distance constraints can be used to obtain the relative orientation of interacting proteins and domains, specifically as a rescue strategy where traditional high resolution structure determination methods were unsuccessful. This hybrid biochemical/bioinformatics approach was applied in the determination of structure of the latexin:carboxypeptidase A complex, and succeeded in achieving 4 Å rmsd compared to the crystal structure determined subsequently (Mouradov et al., 2006). Application of the bioinformatics/biochemical approach to multi-domain proteins was carried out on murine acyl-CoA thioesterase 7 (Acot7). X-ray crystallography provided structures of the two separate domains of Acot7, however the full length protein did not crystalise. Combining chemical cross-linking, mass spectrometry, molecular docking and homology modeling we were able to reconstruct how the two domains are arranged in the full length protein (Forwood et al., 2007). Limitations of this technique caused by the enormous complexity of the cross-linking reaction mixtures were identified and emphasized by analysing a large (four protein) complex of DNA polymerase III, where only one inter-protein cross-link was identified. A rapid and cost-effective method for identification of cross-linked peptides using a commercially available cross-linker was developed as part of the overall aim of streamlining the hybrid biochemical/bioinformatics in order for it to become a generally applicable technique for rapid protein structure characterisation (King et al., 2008). Finally an in-house software package was developed for assignment of cross-linked peptides based on m/z values.

A recent shift towards proteomics has seen many structural genomics initiatives set up for high-throughput structure determination using traditional methods of x-ray crystallography and NMR. The next step in the proteomic revolution focuses on the interplay of multi-protein complexes and transient protein-protein interactions, which are involved in many cellular functions. Greater understanding of protein-protein interactions will inevitably lead to better comprehension of the regulation of cellular process, which has implications in biomedical sciences and biotechnology. Even though many high-resolution initiatives focus on proteins and protein complexes, their structure-determination success rates are still low. An emerging approach uses chemical cross-linking and mass spectrometry to derive a set of sparse distance constrains, which can be used for building models of proteins and to map out residues in protein interaction interface based on partial structural information. This technique allows low-resolution identification of protein structures and their interactions in cases where traditional structure determination techniques did not produce results. Chemical cross-linkers have been successfully used for many years in identifying interacting proteins. However, recent advances in mass spectrometry have allowed the identification of exact insertion points of low-abundance cross-links and hence has opened up a new perspective on the use of cross-linkers in combination with computational structure prediction. For protein interaction studies, the approach uses chemical cross-linking information with molecular docking, so that the cross-links are treated as explicit constraints in the calculations. This study focuses on a low-cost and rapid approach to structure prediction, where partial structural information and distance constraints can be used to obtain the relative orientation of interacting proteins and domains, specifically as a rescue strategy where traditional high resolution structure determination methods were unsuccessful. This hybrid biochemical/bioinformatics approach was applied in the determination of structure of the latexin:carboxypeptidase A complex, and succeeded in achieving 4 Å rmsd compared to the crystal structure determined subsequently (Mouradov et al., 2006). Application of the bioinformatics/biochemical approach to multi-domain proteins was carried out on murine acyl-CoA thioesterase 7 (Acot7). X-ray crystallography provided structures of the two separate domains of Acot7, however the full length protein did not crystalise. Combining chemical cross-linking, mass spectrometry, molecular docking and homology modeling we were able to reconstruct how the two domains are arranged in the full length protein (Forwood et al., 2007). Limitations of this technique caused by the enormous complexity of the cross-linking reaction mixtures were identified and emphasized by analysing a large (four protein) complex of DNA polymerase III, where only one inter-protein cross-link was identified. A rapid and cost-effective method for identification of cross-linked peptides using a commercially available cross-linker was developed as part of the overall aim of streamlining the hybrid biochemical/bioinformatics in order for it to become a generally applicable technique for rapid protein structure characterisation (King et al., 2008). Finally an in-house software package was developed for assignment of cross-linked peptides based on m/z values.

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Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-10-11T22:26:01Z No. of bitstreams: 1 ValeskaSantanaDeSenaPereira_TESE.pdf: 4424545 bytes, checksum: 27d11137997bb962be78ddc99763e2fe (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-10-17T22:34:42Z (GMT) No. of bitstreams: 1 ValeskaSantanaDeSenaPereira_TESE.pdf: 4424545 bytes, checksum: 27d11137997bb962be78ddc99763e2fe (MD5) / Made available in DSpace on 2016-10-17T22:34:42Z (GMT). No. of bitstreams: 1 ValeskaSantanaDeSenaPereira_TESE.pdf: 4424545 bytes, checksum: 27d11137997bb962be78ddc99763e2fe (MD5) Previous issue date: 2016-05-18 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq) / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / A resist?ncia aos antimal?ricos dispon?veis no mercado leva ? necessidade do desenvolvimento de novos compostos com novos alvos farmacol?gicos. Os derivados de naftoquinonas s?o descritos como compostos l?deres promissores para o desenvolvimento de f?rmacos antimal?ricos. Em vista disso, n?s avaliamos a atividade antiplasmodial in vitro de tr?s derivados de hidroxinaftoquinonas contra o est?gio intraeritroc?tico assexuado de Plasmodium falciparum, assim como par?metros toxicol?gicos in vitro e in vivo e investigamos um prov?vel mecanismo de a??o relacionado ? via dos isopren?ides atrav?s de marca??es metab?licas de precursores da via com tr?tio radioativo, complementado com estudos de docking com um template da octaprenil pirofosfato sintase. Os derivados de hidroxinaftoquinonas analisados tiveram boa atividade antiplasmodial, com IC50 menor que 20 ?M para a cepa 3D7 e menor que 50 ?M para a cepa Dd2. A janela terap?utica ? segura, com ?ndice de seletividade variando entre 36,7 e 143,0. Os compostos n?o causaram hem?lise nas doses testadas (10 e 50 vezes maiores que as respectivas IC50), e n?o desencadearam sinais de toxicidade no teste de toxicidade aguda in vivo apesar de o composto 4a ter promovido esteatose hep?tica e hemorragia no tecido renal. Considerando um prov?vel mecanismo de a??o, os derivados de hidroxinaftoquinonas parecem inibir a s?ntese dos precursores isopr?nicos, principalmente a menaquinona e o tocoferol e os estudos de docking revelaram nove poss?veis intera??es com alta energia em quatro s?tios de liga??o diferentes com um template da octaprenil pirofosfato sintase. Em nossos resultados, o composto 4c foi o mais promissor, visto que possuiu o menor IC50 no teste antiplasmodial in vitro, menor citotoxicidade in vitro e toxicidade aguda in vivo, al?m de ter inibido os tr?s produtos da via dos isopren?ides testados, podendo ser considerado um candidato padr?o para o processo de ?hit-to-lead. / The resistance to antimalarial drugs available on the market leads to the need for the development of new compounds with novel pharmacological targets. The naphthoquinone derivatives are described as promising compounds leading to the development of antimalarial drugs. That said, we evaluated the antiplasmodial in vitro activity of three derivatives of hydroxy-naphthoquinones against asexual intraeritrocitic stage of Plasmodium falciparum, as well as toxicological in vitro and in vivo parameters and investigate a possible mechanism of action related to the isoprenoid pathway through metabolic markers via the precursors of radioactive tritium, complete with docking studies with a template of octaprenil pyrophosphate synthase. Hydroxy-naphthoquinones derivatives analyzed had good antiplasmodial activity with IC50 less than 20 ?M for 3D7 strain and less than 50 ?M for Dd2 strain. The therapeutic window is safe with selectivity index ranging between 36.7 and 143.0. The compounds did not cause hemolysis at the doses tested (10 and 50 times greater than their IC50), and not triggered signs of toxicity in acute toxicity test in vivo even though the compound 4a have promoted hepatic steatosis and haemorrhage in kidney tissue. Whereas a likely mechanism of action, the hydroxy-naphthoquinones derivatives appear to inhibit the synthesis of isoprenic precursors, especially menaquinone and tocopherol and docking studies revealed nine possible interactions with high energy in four different binding sites with a template of octaprenil pyrophosphate synthase. In our results, the compound 4c was the most promising, since it possessed the lowest IC50 in antiplasmodial test in vitro, lower cytotoxicity in vitro and in vivo acute toxicity, and has inhibited the three via the tested isoprenoid products, might be considered a standard candidate for the process "hit-to-lead.

Computational tools play an important role in the description of biological systems. Scientists describe and study structure, conformational changes and interactions between molecules in silico, often as a cheaper and faster alternative for biosynthesis. The simulated dynamic behavior in time of a molecular system is a straight forward source of information about substrate-enzyme interactions at the atomic level, and a powerful tool for the identification of molecular properties important in enzymatic reactions. Our study is focused on the computational investigation of structure and substrate specificity of hydrolases important in biotransformation. The computational work was performed in close collaboration with biochemists-experimentalists from Charles University and the Microbiological Institute of the Academy of Sciences of the Czech Republic. Hydrolases have great a potential in the chemoenzymatic synthesis of modified carbohydrates with regulated properties. Carbohydrates, as substrates of hydrolases, are important in normal functionality of many organisms. They have a dual role in immune response regulation: some carbohydrates (like GlcNAc and ManNAc) participate in activation and some (like GalNAc) in suppressing immunity; glycosidase deficiency is associated with a number of lysosomal disorders. We used homology modeling, computational docking and molecular dynamics simulation (MD) methods for the complex study of fungal hydrolases: alpha-galactosidase/alpha-N-acetylgalactosaminidase from Aspergillus niger; beta-N-acetylhexosaminidases (HEX) (from Aspergillus oryzae and Penicillium oxalicum); nitrilase from Aspergillus niger. Our structural study unambigously demonstrates that the enzyme encoded by genes variant A (aglA) from A. niger is able to accept alpha-N-acetylgalactosamine as its substrate and explains structural features responsible for its specificity. Homology models of HEXs from P. oxalicum and A. oryzae were built and compared. Homology models were used to study the role of protein glycosylation, disulfide bonds, dimer formation and interaction with natural and modified substrates. Model of nitrilase from Aspergillus niger helped to analyze multimer formation.

This dissertation proposes new optimization algorithms targeting protein-protein docking which is an important class of problems in computational structural biology. The ultimate goal of docking methods is to predict the 3-dimensional structure of a stable protein-protein complex. We study two specific problems encountered in predictive docking of proteins. The first problem is Side-Chain Positioning (SCP), a central component of homology modeling and computational protein docking methods. We formulate SCP as a Maximum Weighted Independent Set (MWIS) problem on an appropriately constructed graph. Our formulation also considers the significant special structure of proteins that SCP exhibits for docking. We develop an approximate algorithm that solves a relaxation of MWIS and employ randomized estimation heuristics to obtain high-quality feasible solutions to the problem. The algorithm is fully distributed and can be implemented on multi-processor architectures. Our computational results on a benchmark set of protein complexes show that the accuracy of our approximate MWIS-based algorithm predictions is comparable with the results achieved by a state-of-the-art method that finds an exact solution to SCP. The second problem we target in this work is protein docking refinement. We propose two different methods to solve the refinement problem. The first approach is based on a Monte Carlo-Minimization (MCM) search to optimize rigid-body and side-chain conformations for binding. In particular, we study the impact of optimally positioning the side-chains in the interface region between two proteins in the process of binding. We report computational results showing that incorporating side-chain flexibility in docking provides substantial improvement in the quality of docked predictions compared to the rigid-body approaches. Further, we demonstrate that the inclusion of unbound side-chain conformers in the side-chain search introduces significant improvement in the performance of the docking refinement protocols. In the second approach, we propose a novel stochastic optimization algorithm based on Subspace Semi-Definite programming-based Underestimation (SSDU), which aims to solve protein docking and protein structure prediction. SSDU is based on underestimating the binding energy function in a permissive subspace of the space of rigid-body motions. We apply Principal Component Analysis (PCA) to determine the permissive subspace and reduce the dimensionality of the conformational search space. We consider the general class of convex polynomial underestimators, and formulate the problem of finding such underestimators as a Semi-Definite Programming (SDP) problem. Using these underestimators, we perform a biased sampling in the vicinity of the conformational regions where the energy function is at its global minimum. Moreover, we develop an exploration procedure based on density-based clustering to detect the near-native regions even when there are many local minima residing far from each other. We also incorporate a Model Selection procedure into SSDU to pick a predictive conformation. Testing our algorithm over a benchmark of protein complexes indicates that SSDU substantially improves the quality of docking refinement compared with existing methods.

La biologie structurale est la branche de la biologie qui étudie la structure et l'organisation spatiale des macromolécules.La biologie structurale concerne en particulier la détermination à l'échelle atomiquede la structure 3D, aux changement de conformation des macromolécules, et à la dynamique de ces structures.De nos jours, les techniques expérimentales modernes telles que la résonance magnétique nucléaire, la cristallographie aux rayons X et plus récemmentla microscopie cryoélectronique peuvent produire des cartes de densité à haute résolution, qui combinées aux informations sur la séquence d'une moléculepermettent aux biologistes de résoudre les structures 3D de la molécule à l'étude.Cependant, dans certains cas, la résolution des cartes de densité n'est pas suffisante.Dans un tel cas, on alignegénéralement des sous-unités individuelles, obtenues à haute résolution, dans la carte de densité de base résolution.Mentionnons qu'il est également également possible de déterminer la structure 3D d'un assemblage biologique en ancrant plusieurs sous-unités ensemble.C'est cependant un problème beaucoup plus difficile.Ces problèmes d'amarrage et d'alignement peuvent être formulés comme un problème d'optimisation dont la fonction de coût est écrite comme la corrélation croisée de deux autres fonctions.Les algorithmes d'ancrage originaux ont été formulés comme des problèmes de "clé et verrou", dans lesquels les protéines étaient considérées comme des corps rigides.Il est cependant naïf de considérer les macromolécules comme des corps rigides. Les protéines sont flexibles et peuventsubir de grands changements conformationnels lors de la liaison à d'autres molécules. Considérer les problèmes d'ancrage comme des problèmes de"clé et verrou" n'est donc pas suffisant.Une méthode d'ancrage flexible standard utilise donc l'approche "aligner puis affiner", qui, dans certains cas, peut omettre de bonnes conformations.Cette thèse se concentre sur deux axes principaux.Le premier axe est le développement d'une nouvelle méthode qui échantillonne de manière exhaustive les mouvements de corps rigides et les mouvements collectifs, calculés par analyse en modes propres (AMP).Nous présentons d'abord une méthode qui utilise la transformée de Fourier rapide pour échantillonner une approximation quadratique de la fonction coût. Ensuite, la méthode effectuela recherche flexible en maximisant l'approximation quadratique de la fonction de coût dans un certain domaine de recherche. Cette méthode garantit de trouver la meilleure conformation flexible.Nous présentons ensuite une version en itterative de notre algorithme, qui trouve les mouvements collectifs qui maximisent le score d'amarrage par rapport aux degrés de liberté (DDLs) du corps rigide.La méthode échantillonne de manière exhaustive à la fois les mouvements de corps rigides et les mouvements collectifs en maximisant le maximum lisse selon les DDls correspondant aux transformations rigides de la fonction coût.Les deux méthodes ont été appliquées à des problèmes d'alignement sur des exemples réels et artificiels.De plus, nous présentons un exemple dans lequel l'approche "aligner puis raffiner" n'est pas capable de trouver la bonne conformation tandis quenotre méthode peut trouver ladite conformation.Le deuxième axe est le développement d'une nouvelle extrapolation des mouvements calculés par l'AMP.Nous montrons qu'il est possible, avec des calculs minimaux, d'extrapoler les mouvements instantanés calculés par l'AMP dans le sous espaces des rotations-traslations des blocs (RTB) comme une rotationpresque pure autour d'un certain axe.Nous avons appliqué cette méthode appelée NOLB sur différents systèmes biologiques et avons pu, d'une part, récupérer des mouvements biologiquement pertinents et d'autre part démontrer que la méthode NOLB génère des structures avec une meilleure topologie qu'une méthode d'AMP linéaire. / Structural biology is a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of macromolecules, how they acquire the structures they have,and how alterations in their structures affect their function.These molecules are a topic of interest because they serve to keep the cellsalive and functioning.Nowadays, modern experimental techniques, such as nuclear magnetic resonance (NMR), X-ray crystallography and more recently cryo-electron microscopy (cryo-EM) canproduce high resolution density maps, which combined with the information about the sequence of a molecule allows biologists to solve thethree-dimensional (3D) structures of the molecule under study. However, when studding large biological assemblies, experimental techniques are notalways able to generate density maps with a high enough resolution. In such a case, one typically fits individual sub-units, which weresolved using at a higher resolution, into the lower-resolution density map.Let us also mention that it is also possible determine the 3D structure of a biological assembly by docking several sub-units together.This is a much more difficult problem though.These docking and fitting problems can be reformulated as an optimization problem whose cost function can be written as the cross-correlation of two functions.The first fitting and docking algorithms were formulated as "lock and key" problems, in which the proteins were considered as rigid body.However, considering macromolecules, especially proteins, as rigid bodies is not realistic.Proteins are indeed flexible and can undergo large conformational changesupon binding to other molecules.Considering docking and fitting problems as "lock and key" problems is therefore not sufficient.Therefore, a standard flexible docking/fitting method first uses a six-dimensional (6D) rigid body docking/fitting algorithm and then flexibly relaxes the top docking/fitting poses.This approach will be thus refereed to as to the fit then refine approach.However, in some cases, such an approach can miss good conformations.This thesis focuses on two main axes.The first axis is the development of a new method that exhaustively samples both rigid-body and collective motions computed via normal mode analysis (NMA).We first present a method that combines the advantages of the Fourier transform (FFT)-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique thatguarantees to find the nearest optimal off-grid and flexible conformation.The algorithm first samples a quadratic approximation of a scoring function on a 6D grid. Then, the method performs the flexible search by maximizing the quadratic approximation of the cost functionwithin a certain search space.We then present a multi-step version of our algorithm, which finds the collective motions that maximize the docking score with respect to the rigid-body degrees of freedom (DOFs).The method exhaustively samples both rigid-body and collective motions by maximizing the soft maximum over the rigid body DOFs of the docking/fitting cost function.Both methods were applied to docking problems on both real and artificial example and we were able to design a benchmark in which the fit then refine approach fails at finding the correct conformation whileour method succeeds.The second axis is the development of a new extrapolation of motions computed by NMA.We show that it is possible, with minimal computations, to extrapolate the instantaneous motions computed by NMA in the the rotations-translations of blocks (RTB) subspace as an almost pure rotation around a certain axis.We applied this non-linear block (NOLB) method on various biological systems and were able to, firstly, retrieve biologically relevant motions andsecondly, to demonstrate that the NOLB method generates structures with a better topology than a linear NMA method.