A study on the impact of the distance types involved in protein structure determination by NMR

International audienceThe Distance Geometry Problem (DGP) consists of finding the coordinates of a given set of points where the distances between some pairs of points are known. The DGP has several applications and one of the most relevant ones arises in the context of structural biology, where NMR experiments are performed to estimate distances between some atom pairs in a given molecule, and the possible conformations for the molecule are calculated through the formulation and the solution of a DGP. We focus our attention on DGP instances for which some special assumptions allow us to discretize the DGP search space and to potentially perform the complete enumeration of the solution set. We refer to the subclass of DGP instances satisfying such discretizability assumptions as the Discretizable DGP (DDGP). In this context, we propose a new procedure for the generation of DDGP instances where real data and simulated data (from known molecular models) can coexist. Our procedure can give rise to peculiar DDGP instances that we use for studying the impact of every distance type, involved in NMR protein structure determination, on the quality of the found solutions. Surprisingly, our experiments suggest that the distance types implying a larger effect on the solution quality are not the ones related to NMR data, but rather the more abundant, but much less informative, van der Waals distance type

Operations research: from computational biology to sensor network

In this dissertation we discuss the deployment of combinatorial optimization methods for modeling and solve real life problemS, with a particular emphasis to two biological problems arising from a common scenario: the reconstruction of the three-dimensional shape of a biological molecule from Nuclear Magnetic Resonance (NMR) data. The fi rst topic is the 3D assignment pathway problem (APP) for a RNA molecule. We prove that APP is NP-hard, and show a formulation of it based on edge-colored graphs. Taking into account that interactions between consecutive nuclei in the NMR spectrum are diff erent according to the type of residue along the RNA chain, each color in the graph represents a type of interaction. Thus, we can represent the sequence of interactions as the problem of fi nding a longest (hamiltonian) path whose edges follow a given order of colors (i.e., the orderly colored longest path). We introduce three alternative IP formulations of APP obtained with a max flow problem on a directed graph with packing constraints over the partitions, which have been compared among themselves. Since the last two models work on cyclic graphs, for them we proposed an algorithm based on the solution of their relaxation combined with the separation of cycle inequalities in a Branch & Cut scheme. The second topic is the discretizable distance geometry problem (DDGP), which is a formulation on discrete search space of the well-known distance geometry problem (DGP). The DGP consists in seeking the embedding in the space of a undirected graph, given a set of Euclidean distances between certain pairs of vertices. DGP has two important applications: (i) fi nding the three dimensional conformation of a molecule from a subset of interatomic distances, called Molecular Distance Geometry Problem, and (ii) the Sensor Network Localization Problem. We describe a Branch & Prune (BP) algorithm tailored for this problem, and two versions of it solving the DDGP both in protein modeling and in sensor networks localization frameworks. BP is an exact and exhaustive combinatorial algorithm that examines all the valid embeddings of a given weighted graph G=(V,E,d), under the hypothesis of existence of a given order on V. By comparing the two version of BP to well-known algorithms we are able to prove the e fficiency of BP in both contexts, provided that the order imposed on V is maintained

A distance geometry procedure using the Levenberg-Marquardt algorithm and with applications in biology but not only

International audienceWe revisit a simple, yet capable to provide good solutions, procedure for solving the Distance Geometry Problem (DGP). This procedure combines two main components: the first one identifying an initial approximated solution via semidefinite programming, which is thereafter projected to the target dimension via PCA; and another component where this initial solution is refined by locally minimizing the Smooth STRESS function. In this work, we propose the use of the projected Levenberg-Marquart algorithm for this second step. In spite of the simplicity, as well as of its heuristic character, our experiments show that this procedure is able to exhibit good performances in terms of quality of the solutions for most of the instances we have selected for our experiments. Moreover, it seems to be promising not only for the DGP application arising in structural biology, which we considered in our computational experiments, but also in other ongoing studies related to the DGP and its applications: we finally provide a general discussion on how extending the presented ideas to other applications

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Scattering Processes via Tensor Network Simulations

Scattering processes are a crucial ingredient for the investigation of fundamental interactions. The ever-increasing amount of data produced at particle colliders has fuelled recent progresses in the field of scattering amplitudes computation. To date, on the numerical side, the results achieved are mainly based on Monte-Carlo simulations. In this Thesis the problem is attacked with a different approach: a real-time simulation of the dynamics of a 1+1 dimensional quantum field theory is performed, exploiting the powerful tensor network methods from many-body theory. A matrix product state representation of the asymptotic input states is identified, allowing for the preparation of the initial momentum wave packets. This initial state is then evolved and we aim to compute the S-matrix elements from the knowledge of the final state. We focus on a specific fermionic U(1)-gauge model, developing a set of tools which are relevant for a broader class of 1+1 dimensional quantum field theories with global or local symmetries