Modeling Bottom-Up Visual Attention Using Dihedral Group D4

Published version. Source at http://dx.doi.org/10.3390/sym8080079 In this paper, first, we briefly describe the dihedral group D4 that serves as the basis for calculating saliency in our proposed model. Second, our saliency model makes two major changes in a latest state-of-the-art model known as group-based asymmetry. First, based on the properties of the dihedral group D4, we simplify the asymmetry calculations associated with the measurement of saliency. This results is an algorithm that reduces the number of calculations by at least half that makes it the fastest among the six best algorithms used in this research article. Second, in order to maximize the information across different chromatic and multi-resolution features, the color image space is de-correlated. We evaluate our algorithm against 10 state-of-the-art saliency models. Our results show that by using optimal parameters for a given dataset, our proposed model can outperform the best saliency algorithm in the literature. However, as the differences among the (few) best saliency models are small, we would like to suggest that our proposed model is among the best and the fastest among the best. Finally, as a part of future work, we suggest that our proposed approach on saliency can be extended to include three-dimensional image data

Computational Modeling and Simulations of Protein-Drug and Protein-Protein Complexes: as potential target for therapeutics development

The main objective of my thesis is to illustrate the potential of computational modeling techniques in determining decisive protein-protein interactions and protein-ligand interactions of two relevant macromolecular biological systems associated to human diseases. Computational tools such as homology modeling, molecular docking, molecular dynamics simulations and the developed protocols implemented for the preparation, simulation and analysis of each biological system are presented. The first contribution is the simulation of modeling of protein-peptide-protein complexes related to adaptive immune system and multiple sclerosis disease. Investigation of molecular similarity between self-peptide and two microbial peptides for the complexes with respect to molecular recognition mechanism is presented. The second contribution is the investigation of protein-ligand interactions of biological systems associated to Alzheimer’s disease. Computational results are compared with experiments to evidence the origin and degree of selective inhibition displayed by 2-Phenylbenzofurans ligands against butyrylcholinesterase (BChE) protein. The final contribution is on the application of a priori knowledge gathered on protein-ligand interactions in designing ligands with specific structural modifications that display an improved inhibitory activity against BChE protein. In conclusion, therapeutical perspectives and application of hybrid computational approaches to design and develop of potential drugs are discussed

COMPUTATIONAL TECHNIQUES TO EVALUATE AT ATOMIC LEVEL THE MECHANISM OF MOLECULAR BINDING

Integrins are an important class of transmembrane receptors that relay signals bidirectionally across the plasma membrane, regulating several cell functions and playing a key role in diverse pathological processes. Specifically, integrin subtype \u3b1IIb\u3b23 is involved in thrombosis and stroke, while subtypes \u3b1v\u3b23 and \u3b15\u3b21 play an important role in angiogenesis and tumor progression. They therefore emerged as attractive pharmacological targets. In the past decades several peptides and peptidomimetics targeting these proteins and based on the integrin recognition motif RGD (Arg-Gly-Asp) have been developed, whereby their affinity and selectivity for a specific integrin subtype have been fine-tuned by modulation of RGD flanking residues, by cyclization or by introduction of chemical modifications. Thus far, the design and development of RGD-based cyclopeptides have been mainly based on empirical approaches, requiring expensive and time-consuming synthesis campaigns. In this field, the employment of computational tools, that could be valuable to accelerate the drug design and optimization process, has been limited by the inherent difficulties to predict in silico the three-dimensional structure and the inhibitory activity of cyclopeptides. However, recent improvements in both computational resources and in docking and modeling techniques are expected to open new perspectives in the development of cyclopeptides as modulators of protein-protein interactions and, particularly, as integrin inhibitors. Within this PhD project, I have investigated the applicability of computational techniques in predicting and rationalizing how the environment of the recognition-motif in cyclopeptides (i.e. flanking residues and introduction of chemical modification) could influence their integrin affinity and selectivity. These features can regulate integrin affinity both by favoring direct interactions with the receptor and/or by modulating the three-dimensional conformation properties of the recognition motif. To take into account both these aspects, I have proposed and optimized a multi-stage computational protocol in which an exhaustive conformational sampling of the investigated cyclopeptides is followed by docking calculations and re-scoring techniques. Specifically: i) the exhaustive sampling could be achieved by using Metadynamics in its Bias Exchange variant (BE-META), an enhanced sampling technique which represents a valuable methodology for the acceleration of rare events, allowing to cross the high free energy barriers characteristic of cyclopeptides and providing reliable estimations of the populations of the accessible conformers. ii) The docking calculations, complemented with the re-scoring technique MM-GB/SA (Molecular Mechanics Generalized Born Surface Area) and the cluster analysis of the decoy poses, allow to evaluate the ability of each peptide to engage interactions with the receptors and to rank the docking poses according to their binding ability; iii) a joint analysis of the previous outcomes results in a reliable ranking of cyclopeptides based on their binding affinity and in the rationalization of their structure-activity relationship. This computational protocol has been exploited in two different applications, illustrated within the thesis. In the first application the protocol has been applied to rationalize how the introduction of chemical modifications, specifically backbone N-methylation, impacts on the equilibrium conformation and consequently on the integrin affinity of five RGD containing cyclic hexapeptides, which were previously generated by the group of professor Kessler to modulate their selectivity for \u3b1IIb\u3b23 integrin. The study revealed that backbone N-methylation affects the preferences of the \u3c6 dihedral angle of the methylated residue, specifically favoring the adoption of additional conformations, characterized by a 180\ub0 twist of the peptide bond plane preceding the methylated residue. These twists of dihedral angles were found to have relevant consequences on the cyclopeptides conformation, influencing the formation of intra-molecular hydrogen bonds as well as some structural features which are known to be fundamental in integrin binding. Both structural analysis and docking calculations allowed to identify the \u201cbioactive\u201d conformation (i.e. an extended RGD conformation able to recapitulate the canonical electrostatic and the additional stabilizing hydrophobic interactions). Of note, the cyclopeptides that are pre-organized, already in their free state, in this bioactive conformation are the ones displaying the best \u3b1IIb\u3b23 binding affinity in terms of IC50 values, confirming that pre-organization of cyclopeptides in solution can strongly affect their binding strength to the receptor and demonstrating that the knowledge of their conformational equilibrium is fundamental to provide reliable affinity predictions. In the second application, I have focused my attention on cyclopeptides harboring a recently discovered integrin recognition motif: isoDGR (isoAsp-Gly-Arg), deriving from the spontaneous deamidation of NGR (Asp-Gly-Arg) sequence present in integrin natural ligands. As a preliminary step, I have systematically tested the accuracy of eight Molecular Mechanics force fields in reproducing the equilibrium properties of isoDGR-based cyclopeptides, for which NMR experiments have been acquired. The comparison between simulated and NMR-derived data (i.e. chemical shifts and J scalar couplings) revealed that, while most of the investigated force fields can properly reproduce the equilibrium conformational properties of cyclic peptides, only two of them (i.e. the AMBER force fields ff99sb-ildn and ff99sb*-ildn) are able to recover the NMR observables characteristics of the non-standard residue isoAspartate with an accuracy close to the systematic uncertainty. Overall, these results suggest that the transferability of force field parameters to non standard amino acids is not straightforward. However, two force fields allowed to obtain a satisfactory accuracy and have been therefore employed for the subsequent investigation. I thus applied the computational protocol to rationalize the diverse selectivity and affinity profiles for integrins \u3b1v\u3b23 and \u3b15\u3b21, both related to cancer, displayed by three isoDGR-based cyclic hexapeptides. These molecules differ in the residues flanking the isoDGR motif and show appealing tumor-homing properties; specifically it has been shown that one of these, c(CGisoDGRG), can be coupled with human serum albumin through a chemical linker to be used as a drug delivery agent for functionalized gold nanoparticles. Herein, I investigated the role of the chemical linker in improving affinity and selectivity of c(CGisoDGRG) for \u3b1v\u3b23. The application of the multi-stage protocol allowed to propose an explanation for the different selectivity profiles displayed by these molecules, where the direct interactions engaged by the flanking residues and/or their steric hindrance seem to be largely responsible for the observed different affinities. As a last result, through the combination of MD and NMR techniques, I demonstrated that the chemical linker improved the \u3b1v\u3b23 affinity of c(CGisoDGRG) by engaging direct interactions with the receptor and I proposed two possible complex models, which well-reproduce data from Saturation Transfer Difference experiments. Overall, in this PhD work I have shown that the combination of different computational techniques, BE-META, docking and MM-GB/SA re-scoring, could be a reliable approach to perform structure-activity relationship studies in cyclopeptides. Specifically, the proposed protocol is able to predict the influence of the recognition motif environment (i.e. chemical modification and flanking residues) on integrin affinities. These two features regulate integrin affinity differently: the first one by conformational modulation of the recognition motif, the second by engaging direct interactions with the receptor. Of note, the approach can deal with both these mechanisms of affinity modulation. We expect that the protocol herein described could be used in future to screen novel peptides library or to complement biochemical experiments during the drug optimization stages, assisting organic chemists in the design of more effective integrin-targeting peptides

E(2)-Equivariant Graph Planning for Navigation

Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D navigation, which originates from Euclidean transformations between reference frames and enables parameter sharing. To address the challenges of unstructured environments, we formulate the navigation problem as planning on a geometric graph and develop an equivariant message passing network to perform value iteration. Furthermore, to handle multi-camera input, we propose a learnable equivariant layer to lift features to a desired space. We conduct comprehensive evaluations across five diverse tasks encompassing structured and unstructured environments, along with maps of known and unknown, given point goals or semantic goals. Our experiments confirm the substantial benefits on training efficiency, stability, and generalization

Structural elucidation and quantification of novel toxins in marine microalgae by NMR- and molecular modelling-based techniques

Marine biotoxins produced by dinoflagellates exhibit a remarkable structural diversity. During the course of this thesis, I present the elucidation of six novel compounds in total, two for each of the toxin groups of azaspiracids, gymnodimines, and spirolides. The LC-MS based quantification, as used in shellfish surveillance, of the novel azaspiracids was compared with NMR based quantification. Further, four cyclic imine toxins had their full relative stereochemistry elucidated. The simulated chemical shifts revealed a systematic effect between the chirality at C 4 and neighboring nuclei. Based on this systematic effect, reasonable doubts arise towards determination of R configuration at C-4 in 13,19-didesmethyl SPX C. The configuration of C-4 was assigned with simulated and measured NMR spectra, suggesting that all tested GYMs and SPXs have the S configuration at that position. This assignment supports the hypothesis of a common biosynthetic pathway for both compound groups

A computational study of cyclic peptides with vibrational circular dichroism

Cyclic peptides are a class of molecules that has shown antimicrobial potential. These are complex compounds to investigate with their large conformational space and multiple chiral centers. A technique that can be used to investigate both conformational preferences and absolute configuration (AC) is vibrational circular dichroism (VCD). To extract information from the experimental VCD spectra a comparison with calculated spectra is often needed and this is the focus of this thesis: the calculation of VCD spectra. The VCD spectra are very sensitive to small structural changes, and to accurately calculate the spectra, all important conformers need to be identified. The first part of this thesis has been to establish a reliable computational protocol using meta-dynamics to sample the conformational space and ab initio methods to calculate the spectra for cyclic peptides. Using our protocol, we have investigated if VCD alone can determine the AC of cyclic tetra- and hexapeptides. We show that it is possible to determine the AC of the cyclic peptides with two chiral centers while for the peptides with three and four chiral centers, VCD is at best able to reduce the number of possible ACs and further investigation with other techniques is needed. Further, we investigated four cyclic hexapeptides with antimicrobial potential. These peptides, in contrast to the ones used for validating the protocol, consist of several amino acids with long and positively charged side chains. For these peptides, a molecular dynamics based approach provided VCD spectra in better agreement with experiment than our protocol. Reasons for this may be the lack of atomistic detail in the solvent model used during the conformational search and insufficient description of dispersion interactions during the meta-dynamics simulation

3D-structure of synthetic peptides and molecular interactions in biomimetic media probed by NMR spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method to characterise the processes of biological macromolecules at an atomic level. The analysis of molecular structure properties enables the specific linkage of a structure with its associated activity. The study of such complex processes motivated the development of today’s biomolecular NMR. Bacteria have developed different strategies to survive in a host. One of these strategies is the continuous translation to advantageous habitats in the host organism. A well-known example is the protein PPEP-1, which initiates translational movement by selectively cleaving proline-proline bonds. So far, it was not known whether the addressed prolineproline bond has to adopt a preferred conformation for effective cleavage. Through detailed NMR spectroscopic investigations, a clearly preferred conformation of the bond could be identified. This finding contributes to a deeper understanding of the survival strategy. Thus, potentially new starting points for treatment options could emerge. The targeted treatment of carcinogenic cells is still of great research interest today. Cellpenetrating peptides could represent a solution for the selective addressing of these, whereby the exact uptake mechanism of the peptides has not yet been sufficiently analysed. In this work, NMR spectroscopic methods were used to show that the interaction between such peptides and membrane mimetics causes the peptide to undergo a conformational change. This represents a further approach in the elucidation of the uptake mechanism of these investigated peptides. Mechanism elucidation is of great importance in the process of protein folding as well. Misfolded proteins are often the cause of various diseases. The refolding of proteins into their functional form is the subject of current research. Small organic molecules can act as folding helpers. The spatial proximity of these molecules to small peptide-derived model systems could be proven with the help of NMR spectroscopy. Thus, in the context of this work, an approach was established with which the site of action of folding helpers on a protein could be localised in the future. Model systems are important in NMR spectroscopy to investigate, among other things,interaction mechanisms of small molecules to macromolecular systems. The investigation of spatial approximations of the interaction partners is one of the essential aspects. The use of micelles is particularly suitable for this purpose. Various molecules were investigated with regard to their positioning in micelles using a variety of NMR spectroscopic methods. The findings of these investigations were then transferred to a postulated reaction mechanism

Investigating Abstract Algebra Students' Representational Fluency and Example-Based Intuitions

The quotient group concept is a difficult for many students getting started in abstract algebra (Dubinsky et al., 1994; Melhuish, Lew, Hicks, and Kandasamy, 2020). The first study in this thesis explores an undergraduate, a first-year graduate, and second-year graduate students' representational fluency as they work on a "collapsing structure", quotient, task across multiple registers: Cayley tables, group presentations, Cayley digraphs to Schreier coset digraphs, and formal-symbolic mappings. The second study characterizes the (partial) make-up of two graduate learners' example-based intuitions related to orbit-stabilizer relationships induced by group actions. The (partial) make-up of a learner's intuition as a quantifiable object was defined in this thesis as a point viewed in R17, 12 variable values collected with a new prototype instrument, The Non-Creative versus Creative Forms of Intuition Survey (NCCFIS), 2 values for confidence in truth value, and 3 additional variables: error to non-error type, unique versus common, and network thinking. The revised Fuzzy C-Means Clustering Algorithm (FCM) by Bezdek et al. (1981) was used to classify the (partial) make-up of learners' reported intuitions into fuzzy sets based on attribute similarity

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table