Algorithms for Big Data: Graphs and PageRank

This work consists of a study of a set of techniques and strategies related with algorithm's design, whose purpose is the resolution of problems on massive data sets, in an efficient way. This field is known as Algorithms for Big Data. In particular, this work has studied the Streaming Algorithms, which represents the basis of the data structures of sublinear order $o(n)$ in space, known as Sketches. In addition, it has deepened in the study of problems applied to Graphs on the Semi-Streaming model. Next, the PageRank algorithm was analyzed as a concrete case study. Finally, the development of a library for the resolution of graph problems, implemented on the top of the intensive mathematical computation platform known as TensorFlow has been started.Comment: in Spanish, 143 pages, final degree project (bachelor's thesis

Studying Focal Adhesions on Nanometric Platforms by Single-Molecule Localisation Microscopy

Focal adhesions are integrin-based protein complexes that form at the interface between cells and the extracellular matrix (ECM). These adhesion structures connect the cell to the adhesive ligands presented on the ECM and serve as signalling hubs to help cells to sense and respond to signals from the ECM. It has been shown that cells require an average 50-70 nm spacing of adhesive ligands for the formation of stable adhesion structures. However, the molecular organisation of ligands and adhesion proteins is less documented. The aim of this project was to produce surfaces with varying spacing of fluorescently-labelled adhesive ligand nano-domains and obtain single-molecule images of both the adhesive ligands and the adhesion proteins to better understand how adhesive ligand distribution influences adhesion organisation.First, the di-block copolymer phase separation method was optimised to produce surfaces with nano-domains with different average inter-domain spacing ranging from 18 to 93 nm (Chapter 3). Next, the nano-domains were functionalised with fluorescently-tagged adhesive ligands to facilitate cell attachment to the surfaces and formation of focal adhesions. Direct stochastic optical reconstruction microscopy (dSTORM) and quantitative analysis of the fluorescently-labelled adhesive ligands, based on density-based spatial clustering of application with noise (DBSCAN), were successfully combined in order to map the molecular organisation of adhesive ligands on the fabricated surfaces. Then, mouse embryonic Fibroblasts (MEF) were cultured on the surfaces for various time points. Cell attachment was found to be independent of the adhesive ligand nano-domain spacing while cells exhibited different patterns for spreading and adhesion formation on the different surfaces over time. Finally, two-colour single-molecule localisation microscopy (SMLM) was combined with DBSCAN and colocalisation analysis to produce colocalisation maps of adhesion proteins and adhesive ligands on surfaces with different spacings of adhesive ligand nano-domains, and to evaluate the degree of co-localisation between them (Chapter 5).In conclusion, the results presented in this thesis provide new insights on how the nanoscale distribution of adhesive ligand nano-domains influences cell attachment and spreading as well as the formation and organisation of focal adhesions at the molecular level

Super-resolving botulinum neurotoxin type A molecules: from surface landing to internalization in synaptic vesicles

Botulinum neurotoxin type-A (BoNT/A) is internalized into motor nerve terminals as part of its intoxication strategy to incapacitate nerve-muscle communication. The “dual receptor” model explained how BoNT/A initially interacts with GT1b gangliosides, thereby concentrating the toxin on the presynaptic membrane to foster the subsequent interaction with a proteinaceous co-receptor SV2 which triggers receptor-mediated endocytosis. I will revisit the “dual receptor” concept using two single-molecule imaging strategies,1-3 allowing tracking of single Atto647N-labeled BoNT/A molecules upon (i) landing on the plasma membrane (by uPAINT) and (ii) internalization in synaptic vesicles (by sdTIM) of living mature hippocampal neurons. With 30 to 40 nm localization precision, we revealed that once internalized in synaptic vesicles, Atto647N-tagged BoNT/A exhibits a markedly lower mobility than on the plasma membrane. I will discuss how individual genetic inactivation of the GT1b and SV2 binding sites of the neurotoxin affects the diffusion states of BoNT/A mutants on the plasma membrane and axonal trafficking. Single neurotoxin super-resolution imaging uncovers an updated dual receptor model taking into consideration the diffusive patterns generated by each of the co-receptors and leading to defined nanoscale dynamic organizations at key steps of the intoxication journey

DBSCAN and NND analysis of simulated nanodomain surface.

<p>(A) Simulated dSTORM image with nanodomain of 10 nm in diameter and spaced 100 nm apart. Background was added to the simulated nanodomains by randomly choosing image regions of the experimental data of non-specific absorption data (Figure D (B-D) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.s001" target="_blank">S1 File</a>) and with 75% of missing domains. (B) Individual clusters, represented by different colors and black contour lines, identified by DBSCAN (parameters; ε = 20 nm and minPts = 3) of the simulated data set shown in (A). (C). Distribution curves of nearest neighbor distances (NDD) of simulated data shown in (A-B) for various DBSCAN search parameters, ε.</p

Effect of the domain spacing, presence of background, percentage of missing nanodomains and localization precision on NND between detected nanodomains by DBSCAN in simulated data.

<p>Simulation conditions were identical to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.g003" target="_blank">Fig 3</a>. From the NND distributions, the highest occurrence for the NND was extracted and plotted. (A-F) Modal NNDs for different search radii (ε = 10–50 nm) and minPts values of 3 (A, C, E) and 5 (B, D F), with 0% (blue), 50% (orange) and 75% (purple) of undetected domains and with (striped) or without (solid) included background. In (A-B), domain spacing was set to 100 nm. In (C-F), domain spacing was set to 50 nm. In (A-D), the log-normal distribution of the localization precision centered at 16 nm (μ = 2.8 and σ = 0.28; matching the experimental data, Figure B (D) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.s001" target="_blank">S1 File</a>); in (E-F), the log-normal distribution of the localization precision centered at 11 nm (μ = 2.4 and σ = 0.28; Figure B (D) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.s001" target="_blank">S1 File</a></p

Effect of the domain spacing, presence of background, percentage of missing nanodomains and localization precision on nanodomain detection in simulated data by DBSCAN.

<p>Each simulated nanodomain was constructed around a central point, which corresponds to its true center. After identification of clusters by DBSCAN, the contour of each identified cluster was tested against the true center of the simulated domain. A cluster was counted as correctly detected if its contour contained one and only one true center. (A-F). Percentage of correctly detected clusters for different search radii (ε = 10 to 50 nm) and values of minPts = 3 (A, C, E) and minPts = 5 (B, D F) with 0% (blue), 50% (orange) and 75% (purple) of missing domains with (striped) or without (solid) included background. In a-b, domain spacing was set to 100 nm. In (C-F), domain spacing was set to 50 nm. In (A-D), the log-normal distribution of the localization precision centered at 16 nm (μ = 2.8 and σ = 0.28; matching the experimental data, Figure B (D) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.s001" target="_blank">S1 File</a>); in (E-F), the log-normal distribution of the localization precision centered at 11 nm (μ = 2.4 and σ = 0.28, Figure B (D) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180871#pone.0180871.s001" target="_blank">S1 File</a>).</p

Visualizing endocytic recycling and trafficking in live neurons by subdiffractional tracking of internalized molecules

O ur understanding of endocytic pathway dynamics is restricted by the diffraction limit of light microscopy. Although super-resolution techniques can overcome this issue, highly crowded cellular environments, such as nerve terminals, can also dramatically limit the tracking of multiple endocytic vesicles such as synaptic vesicles (SVs), which in turn restricts the analytical dissection of their discrete diffusional and transport states. We recently introduced a pulsechase technique for subdiffractional tracking of internalized molecules (sdTIM) that allows the visualization of fluorescently tagged molecules trapped in individual signaling endosomes and SVs in presynapses or axons with 30- to 50-nm localization precision. We originally developed this approach for tracking single molecules of botulinum neurotoxin type A, which undergoes activity-dependent internalization and retrograde transport in autophagosomes. This method was then adapted to localize the signaling endosomes containing cholera toxin subunit-B that undergo retrograde transport in axons and to track SVs in the crowded environment of hippocampal presynapses. We describe (i) the construction of a custom-made microfluidic device that enables control over neuronal orientation; (ii) the 3D printing of a perfusion system for sdTIM experiments performed on glass-bottom dishes; (iii) the dissection, culturing and transfection of hippocampal neurons in microfluidic devices; and (iv) guidance on how to perform the pulsechase experiments and data analysis. In addition, we describe the use of single-molecule-tracking analytical tools to reveal the average and the heterogeneous single-molecule mobility behaviors. We also discuss alternative reagents and equipment that can, in principle, be used for sdTIM experiments and describe how to adapt sdTIM to image nanocluster formation and/or tubulation in early endosomes during sorting events. The procedures described in this protocol take 1 week