Collective dynamics of flexible active particles on substrates : from cells to tissues

We study the effects of disorder in epithelial confluent tissues through the Voronoi model for dense tissues. The modeling of epithelial tissues relies on three different mechanisms: cell-cell and cell-medium interactions, and propulsion or activity. First, we focus on the role of cell-cell interaction in this model by exploring, in the athermal limit, its anomalous jamming behavior. We introduce a new metric that allows us to find a hierarchical structure in its energy landscape similar to colloidal particle systems. We then introduce a cell-medium interaction by explicitly considering an interaction between the cells and their underlying substrate. We consider that the targeted geometry of the cells changes according to their spatial position and in turn affects the cells motility. We show that when the characteristic length scale of the disorder is smaller than the cell size, the cell motility increases when compared to its homogeneous counterpart. This result is in sharp contrast to what has been reported for tissues with heterogeneity in the mechanical properties of the individual cells, where the disorder favors rigidity. Due to the internal biological complexity of the cells, changes to the cell-substrate interaction should trigger a hierarchy of biochemical responses in the cell that lead to its adaptation to the new substrate region. As such, the process of cell adaptation to its underlying structure is not instantaneous but requires a finite time that in many cases competes with other relevant timescales for the dynamics such as, for example, the diffusion timescale. With this in mind, we then introduce a characteristic adaptation time of the cells to the cell-substrate interaction changes. We study how the competition between the adaptation of the cells and their mobility can compromise the fidelity of the substrate and by relating this with the previous disordered substrate propose a typical time scale for the adaptation of cells that is relevant for experiments. Lastly, we consider non-confluent tissues by allowing the cells to break from one another and create empty spaces. This change opens the door to the study of the surface properties of cell colonies and it is a first step towards the study of the transition from a single cell to confluent tissue. Implications of our findings in the field of Soft Condensed Matter Physics are discussed

Geometric algorithms for cavity detection on protein surfaces

Macromolecular structures such as proteins heavily empower cellular processes or functions. These biological functions result from interactions between proteins and peptides, catalytic substrates, nucleotides or even human-made chemicals. Thus, several interactions can be distinguished: protein-ligand, protein-protein, protein-DNA, and so on. Furthermore, those interactions only happen under chemical- and shapecomplementarity conditions, and usually take place in regions known as binding sites. Typically, a protein consists of four structural levels. The primary structure of a protein is made up of its amino acid sequences (or chains). Its secondary structure essentially comprises -helices and -sheets, which are sub-sequences (or sub-domains) of amino acids of the primary structure. Its tertiary structure results from the composition of sub-domains into domains, which represent the geometric shape of the protein. Finally, the quaternary structure of a protein results from the aggregate of two or more tertiary structures, usually known as a protein complex. This thesis fits in the scope of structure-based drug design and protein docking. Specifically, one addresses the fundamental problem of detecting and identifying protein cavities, which are often seen as tentative binding sites for ligands in protein-ligand interactions. In general, cavity prediction algorithms split into three main categories: energy-based, geometry-based, and evolution-based. Evolutionary methods build upon evolutionary sequence conservation estimates; that is, these methods allow us to detect functional sites through the computation of the evolutionary conservation of the positions of amino acids in proteins. Energy-based methods build upon the computation of interaction energies between protein and ligand atoms. In turn, geometry-based algorithms build upon the analysis of the geometric shape of the protein (i.e., its tertiary structure) to identify cavities. This thesis focuses on geometric methods. We introduce here three new geometric-based algorithms for protein cavity detection. The main contribution of this thesis lies in the use of computer graphics techniques in the analysis and recognition of cavities in proteins, much in the spirit of molecular graphics and modeling. As seen further ahead, these techniques include field-of-view (FoV), voxel ray casting, back-face culling, shape diameter functions, Morse theory, and critical points. The leading idea is to come up with protein shape segmentation, much like we commonly do in mesh segmentation in computer graphics. In practice, protein cavity algorithms are nothing more than segmentation algorithms designed for proteins.Estruturas macromoleculares tais como as proteínas potencializam processos ou funções celulares. Estas funções resultam das interações entre proteínas e peptídeos, substratos catalíticos, nucleótideos, ou até mesmo substâncias químicas produzidas pelo homem. Assim, há vários tipos de interacções: proteína-ligante, proteína-proteína, proteína-DNA e assim por diante. Além disso, estas interações geralmente ocorrem em regiões conhecidas como locais de ligação (binding sites, do inglês) e só acontecem sob condições de complementaridade química e de forma. É também importante referir que uma proteína pode ser estruturada em quatro níveis. A estrutura primária que consiste em sequências de aminoácidos (ou cadeias), a estrutura secundária que compreende essencialmente por hélices e folhas , que são subsequências (ou subdomínios) dos aminoácidos da estrutura primária, a estrutura terciária que resulta da composição de subdomínios em domínios, que por sua vez representa a forma geométrica da proteína, e por fim a estrutura quaternária que é o resultado da agregação de duas ou mais estruturas terciárias. Este último nível estrutural é frequentemente conhecido por um complexo proteico. Esta tese enquadra-se no âmbito da conceção de fármacos baseados em estrutura e no acoplamento de proteínas. Mais especificamente, aborda-se o problema fundamental da deteção e identificação de cavidades que são frequentemente vistos como possíveis locais de ligação (putative binding sites, do inglês) para os seus ligantes (ligands, do inglês). De forma geral, os algoritmos de identificação de cavidades dividem-se em três categorias principais: baseados em energia, geometria ou evolução. Os métodos evolutivos baseiam-se em estimativas de conservação das sequências evolucionárias. Isto é, estes métodos permitem detectar locais funcionais através do cálculo da conservação evolutiva das posições dos aminoácidos das proteínas. Em relação aos métodos baseados em energia estes baseiam-se no cálculo das energias de interação entre átomos da proteína e do ligante. Por fim, os algoritmos geométricos baseiam-se na análise da forma geométrica da proteína para identificar cavidades. Esta tese foca-se nos métodos geométricos. Apresentamos nesta tese três novos algoritmos geométricos para detecção de cavidades em proteínas. A principal contribuição desta tese está no uso de técnicas de computação gráfica na análise e reconhecimento de cavidades em proteínas, muito no espírito da modelação e visualização molecular. Como pode ser visto mais à frente, estas técnicas incluem o field-of-view (FoV), voxel ray casting, back-face culling, funções de diâmetro de forma, a teoria de Morse, e os pontos críticos. A ideia principal é segmentar a proteína, à semelhança do que acontece na segmentação de malhas em computação gráfica. Na prática, os algoritmos de detecção de cavidades não são nada mais que algoritmos de segmentação de proteínas

Individual-based modeling and predictive simulation of fungal infection dynamics

The human-pathogenic fungus Aspergillus fumigatus causes life-threatening infections in immunocompromised patients and poses increasing challenges for the modern medicine. A. fumigatus is ubiquitously present and disseminates via small conidia over the air of the athmosphere. Each human inhales several hundreds to thousands of conidia every day. The small size of conidia allows them to pass into the alveoli of the lung, where primary infections with A. fumigatus are typically observed. In alveoli, the interaction between fungi and the innate immune system of the host takes place. This interaction is the core topic of this thesis and covered by mathematical modeling and computer simulations. Since in vivo laboratory studies of A. fumigatus infections under physiological conditions is hard to realize a modular software framework was developed and implemented, which allows for spatio-temporal agent-based modeling and simulation. A to-scale A. fumigatus infection model in a typical human alveolus was developed in order to simulate and analyze the infection scenario under physiological conditions. The process of conidial discovery by alveolar macrophages was modeled and simulated with different migration modes and different parameter configurations. It could be shown that chemotactic migration was required to find the pathogen before the onset of germination. A second model took advantage of evolutionary game theory on graphs. Here, the course of infection was modeled as a consecutive sequence of evolutionary games related to the complement system, alveolar macrophages and polymorphonuclear neutrophilic granulocytes. The results revealed a central immunoregulatory role of alveolar macrophages. In the case of high infectious doses it was found that the host required fully active phagocytes, but in particular a qualitative response of quantitatively sufficient polymorphonuclear neutrophilic granulocytes.Der human-pathogene Schimmelpilz Aspergillus fumigatus verursacht tödliche Infektionen und Erkrankungen vorrangig bei immunsupprimierten Patienten und stellt die moderne Medizin vor zunehmende Herausforderungen. A. fumigatus ist ubiquitär präsent und verbreitet sich über sehr kleine Konidien durch Luftströmungen in der Athmosphäre. Mehrere Hundert bis Tausende dieser Konidien werden täglich durch jeden Menschen eingeatmet. Die geringe Größe der infektiösen Konidien erlauben es dem Pilz bis in die Alveolen der Lunge des Wirtes vorzudringen,in denen eine Primärinfektionen mit A. fumigatus am häufigsten stattfindet. Die Alveolen sind der zentrale Schauplatz der Interaktion zwischen dem Pilz und dem angeborenen Immunsystem, welche Gegenstand dieser Arbeit ist. Diese Interaktion wird mit Hilfe von mathematischen Modellen und Computersimulationen nachgestellt und untersucht, da eine A. fumigatus Infektion im Nasslabor in vivo unter physiologischen Bedingungen nur sehr schwer realisiert werden kann. Als Grundlage für dieses Vorhaben wurde ein modulares Software-Paket entwickelt, welches agentenbasierte Modellierung und entsprechende Simulationen in Raum und Zeit ermöglicht. Ein maßstabsgetreues mathematisches Infektionsmodell in einer typischen menschlichen Alveole wurde entwickelt und die Suchstrategien von Alveolarmakrophagen unter der Berücksichtigung verschiedener Parameter wie Migrationsgeschwindigkeit, dem Vorhandensein von Chemokinen, dessen Diffusion und Chemotaxis untersucht. Es zeigte sich, dass Chemotaxis, notwendig ist, um die Konidie rechtzeitig finden zu können. In einem weiteren Modell, welches auf das Konzept evolutionärer Spieltheorie auf Graphen zurückgegriff, wurde der Infektionsverlauf als aufeinanderfolgende Serie evolutionärer Spiele mit dem Komplementsystem, Alveolarmakrophagen und Neutrophilen nachgestellt. Aus den Simulationsergebnissen konnte eine zentrale immunregulatorische Rolle von Alveolarmakrophagen entnommen werden

GPU parallel simulation algorithm of brownian particles with excluded volume using delaunay triangulations

A novel parallel simulation algorithm on the GPU, implemented in CUDA and C++, is presented for the simulation of Brownian particles that display excluded volume repulsion and interact with long and short range forces. When an explicit Euler-Maruyama integration step is performed to take into account the pairwise forces and Brownian motion, particle overlaps can appear. The excluded volume property brings up the need for correcting these overlaps as they happen, since predicting them is not feasible due to the random displacement of Brownian particles. The proposed solution handles, at each time step, a Delaunay triangulation of the particle positions because it allows us to efficiently solve overlaps between particles by checking just their neighborhood. The algorithm starts by generating a periodic Delaunay triangulation of the particle initial positions on CPU, but after that the triangulation is always kept on GPU memory. We used a parallel edge-flip implementation to keep the triangulation updated during each time step, checking previously that the triangulation was not rendered invalid due to the particle displacements. We designed and implemented an exact long range force simulation with an all-pairs N-body simulation, tiling the particle interaction computations based on the warp size of the target device architecture. The resulting implementation was validated with two models of active colloidal particles, also showing a speedup of up to two orders of magnitude when compared to a sequential implementation. A short range forces simulation using Verlet lists for neighborhood handling was also developed and validated, showing similar performance improvements. (C) 2018 Elsevier B.V. All rights reserved.FONDECYT 1140778 3160182 VID, Universidad de Chile ENL009/1

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described