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

Role of network topology based methods in discovering novel gene-phenotype associations

The cell is governed by the complex interactions among various types of biomolecules. Coupled with environmental factors, variations in DNA can cause alterations in normal gene function and lead to a disease condition. Often, such disease phenotypes involve coordinated dysregulation of multiple genes that implicate inter-connected pathways. Towards a better understanding and characterization of mechanisms underlying human diseases, here, I present GUILD, a network-based disease-gene prioritization framework. GUILD associates genes with diseases using the global topology of the protein-protein interaction network and an initial set of genes known to be implicated in the disease. Furthermore, I investigate the mechanistic relationships between disease-genes and explain the robustness emerging from these relationships. I also introduce GUILDify, an online and user-friendly tool which prioritizes genes for their association to any user-provided phenotype. Finally, I describe current state-of-the-art systems-biology approaches where network modeling has helped extending our view on diseases such as cancer.La cèl•lula es regeix per interaccions complexes entre diferents tipus de biomolècules. Juntament amb factors ambientals, variacions en el DNA poden causar alteracions en la funció normal dels gens i provocar malalties. Sovint, aquests fenotips de malaltia involucren una desregulació coordinada de múltiples gens implicats en vies interconnectades. Per tal de comprendre i caracteritzar millor els mecanismes subjacents en malalties humanes, en aquesta tesis presento el programa GUILD, una plataforma que prioritza gens relacionats amb una malaltia en concret fent us de la topologia de xarxe. A partir d’un conjunt conegut de gens implicats en una malaltia, GUILD associa altres gens amb la malaltia mitjancant la topologia global de la xarxa d’interaccions de proteïnes. A més a més, analitzo les relacions mecanístiques entre gens associats a malalties i explico la robustesa es desprèn d’aquesta anàlisi. També presento GUILDify, un servidor web de fácil ús per la priorització de gens i la seva associació a un determinat fenotip. Finalment, descric els mètodes més recents en què el model•latge de xarxes ha ajudat extendre el coneixement sobre malalties complexes, com per exemple a càncer

Proving the Turing Universality of Oritatami Co-Transcriptional Folding (Full Text)

We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerize the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable and checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalized to other discrete dynamical systems, where proofs involve large case enumerations as well

Visual analytics for relationships in scientific data

Domain scientists hope to address grand scientific challenges by exploring the abundance of data generated and made available through modern high-throughput techniques. Typical scientific investigations can make use of novel visualization tools that enable dynamic formulation and fine-tuning of hypotheses to aid the process of evaluating sensitivity of key parameters. These general tools should be applicable to many disciplines: allowing biologists to develop an intuitive understanding of the structure of coexpression networks and discover genes that reside in critical positions of biological pathways, intelligence analysts to decompose social networks, and climate scientists to model extrapolate future climate conditions. By using a graph as a universal data representation of correlation, our novel visualization tool employs several techniques that when used in an integrated manner provide innovative analytical capabilities. Our tool integrates techniques such as graph layout, qualitative subgraph extraction through a novel 2D user interface, quantitative subgraph extraction using graph-theoretic algorithms or by querying an optimized B-tree, dynamic level-of-detail graph abstraction, and template-based fuzzy classification using neural networks. We demonstrate our system using real-world workflows from several large-scale studies. Parallel coordinates has proven to be a scalable visualization and navigation framework for multivariate data. However, when data with thousands of variables are at hand, we do not have a comprehensive solution to select the right set of variables and order them to uncover important or potentially insightful patterns. We present algorithms to rank axes based upon the importance of bivariate relationships among the variables and showcase the efficacy of the proposed system by demonstrating autonomous detection of patterns in a modern large-scale dataset of time-varying climate simulation

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Inspired by biology’s most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems

Know When to Fold ’Em: Self-assembly of Shapes by Folding in Oritatami

International audienceAn oritatami system (OS) is a theoretical model of self-assembly via co-transcriptional folding. It consists of a growing chain of beads which can form bonds with each other as they are transcribed. During the transcription process, the δ most recently produced beads dynamically fold so as to maximize the number of bonds formed, self-assemblying into a shape incrementally. The parameter δ is called the delay and is related to the transcription rate in nature. This article initiates the study of shape self-assembly using oritatami. A shape is a connected set of points in the triangular lattice. We first show that oritatami systems differ fundamentally from tile-assembly systems by exhibiting a family of infinite shapes that can be tile-assembled but cannot be folded by any OS. As it is NP-hard in general to determine whether there is an OS that folds into (self-assembles) a given finite shape, we explore the folding of upscaled versions of finite shapes. We show that any shape can be folded from a constant size seed, at any scale n 3, by an OS with delay 1. We also show that any shape can be folded at the smaller scale 2 by an OS with unbounded delay. This leads us to investigate the influence of delay and to prove that, for all δ > 2, there are shapes that can be folded (at scale 1) with delay δ but not with delay δ < δ. These results serve as a foundation for the study of shape-building in this new model of self-assembly, and have the potential to provide better understanding of cotranscriptional folding in biology, as well as improved abilities of experimentalists to design artificial systems that self-assemble via this complex dynamical process.

Oritatami Systems Assemble Shapes No Less Complex Than Tile Assembly Model (ATAM)

Different models have been proposed to understand natural phenomena at the molecular scale from a computational point of view. Oritatami systems are a model of molecular co-transcriptional folding: the transcript (the "molecule") folds as it is synthesized according to a local energy optimisation process, in a similar way to how actual biomolecules such as RNA fold into complex shapes and functions. We introduce a new model, called turedo, which is a self-avoiding Turing machine on the plane that evolves by marking visited positions and that can only move to unmarked positions. Any oritatami can be seen as a particular turedo. We show that any turedo with lookup radius 1 can conversely be simulated by an oritatami, using a universal bead type set. Our notion of simulation is strong enough to preserve the geometrical and dynamical features of these models up to a constant spatio-temporal rescaling (as in intrinsic simulation). As a consequence, turedo can be used as a readable oritatami "higher-level" programming language to build readily oritatami "smart robots", using our explicit simulation result as a compiler. As an application of our simulation result, we prove two new complexity results on the (infinite) limit configurations of oritatami systems (and radius-1 turedos), assembled from a finite seed configuration. First, we show that such limit configurations can embed any recursively enumerable set, and are thus exactly as complex as aTAM limit configurations. Second, we characterize the possible densities of occupied positions in such limit configurations: they are exactly the ??-computable numbers between 0 and 1. We also show that all such limit densities can be produced by one single oritatami system, just by changing the finite seed configuration. None of these results is implied by previous constructions of oritatami embedding tag systems or 1D cellular automata, which produce only computable limit configurations with constrained density