320 research outputs found

    Machine Learning for Exploring State Space Structure in Genetic Regulatory Networks

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    Genetic regulatory networks (GRN) offer a useful model for clinical biology. Specifically, such networks capture interactions among genes, proteins, and other metabolic factors. Unfortunately, it is difficult to understand and predict the behavior of networks that are of realistic size and complexity. In this dissertation, behavior refers to the trajectory of a state, through a series of state transitions over time, to an attractor in the network. This project assumes asynchronous Boolean networks, implying that a state may transition to more than one attractor. The goal of this project is to efficiently identify a network\u27s set of attractors and to predict the likelihood with which an arbitrary state leads to each of the network’s attractors. These probabilities will be represented using a fuzzy membership vector. Predicting fuzzy membership vectors using machine learning techniques may address the intractability posed by networks of realistic size and complexity. Modeling and simulation can be used to provide the necessary training sets for machine learning methods to predict fuzzy membership vectors. The experiments comprise several GRNs, each represented by a set of output classes. These classes consist of thresholds τ and ¬τ, where τ = [τlaw,τhigh]; state s belongs to class τ if the probability of its transitioning to attractor belongs to the range [τlaw,τhigh]; otherwise it belongs to class ¬τ. Finally, each machine learning classifier was trained with the training sets that was previously collected. The objective is to explore methods to discover patterns for meaningful classification of states in realistically complex regulatory networks. The research design took a GRN and a machine learning method as input and produced output class \u3c Ατ \u3e and its negation ¬ \u3c Ατ \u3e. For each GRN, attractors were identified, data was collected by sampling each state to create fuzzy membership vectors, and machine learning methods were trained to predict whether a state is in a healthy attractor or not. For T-LGL, SVMs had the highest accuracy in predictions (between 93.6% and 96.9%) and precision (between 94.59% and 97.87%). However, naive Bayesian classifiers had the highest recall (between 94.71% and 97.78%). This study showed that all experiments have extreme significance with pvalue \u3c 0.0001. The contribution this research offers helps clinical biologist to submit genetic states to get an initial result on their outcomes. For future work, this implementation could use other machine learning classifiers such as xgboost or deep learning methods. Other suggestions offered are developing methods that improves the performance of state transition that allow for larger training sets to be sampled

    Online adaptation in Boolean network robots

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    Questa tesi si concentra su molteplici processi di adattamento online utilizzati su un robot autonomo, che è controllato da una rete booleana; l’obiettivo è adattare il suo comportamento ad un ambiente e ad un compito specifici. I risultati mostrano che il robot può adattarsi per navigare l’ambiente ed evitare le collisioni, seguendo inoltre un altro robot in movimento; riesce anche a generalizzare, quando posizionato in un’arena diversa rispetto a quella usata in allenamento. Con due dei processi di adattamento testati, il robot può esprimere più fenotipi (comportamenti) dallo stesso genotipo (nodi e connessioni della rete booleana), ottenendo così la plasticità fenotipica. Ciò si ottiene modificando l’accoppiamento tra i sensori o gli attuatori del robot con la rete

    Boolean Networks as Predictive Models of Emergent Biological Behaviors

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    Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory networks to species in ecological networks) and the often-incomplete state of system knowledge (e.g., the unknown values of kinetic parameters for biochemical reactions). Boolean networks have emerged as a powerful tool for modeling these systems. We provide a methodological overview of Boolean network models of biological systems. After a brief introduction, we describe the process of building, analyzing, and validating a Boolean model. We then present the use of the model to make predictions about the system's response to perturbations and about how to control (or at least influence) its behavior. We emphasize the interplay between structural and dynamical properties of Boolean networks and illustrate them in three case studies from disparate levels of biological organization.Comment: Review, to appear in the Cambridge Elements serie

    Boolean Delay Equations: A simple way of looking at complex systems

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    Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time. They represent therewith metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil's staircases and ``fractal sunbursts``. All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid earth problems. The former have used small systems of BDEs, while the latter have used large networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (``partial BDEs``) and discuss connections with other types of dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular the discussion on partial BDEs is updated and enlarge

    Qualitative networks: a symbolic approach to analyze biological signaling networks

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    BACKGROUND: A central goal of Systems Biology is to model and analyze biological signaling pathways that interact with one another to form complex networks. Here we introduce Qualitative networks, an extension of Boolean networks. With this framework, we use formal verification methods to check whether a model is consistent with the laboratory experimental observations on which it is based. If the model does not conform to the data, we suggest a revised model and the new hypotheses are tested in-silico. RESULTS: We consider networks in which elements range over a small finite domain allowing more flexibility than Boolean values, and add target functions that allow to model a rich set of behaviors. We propose a symbolic algorithm for analyzing the steady state of these networks, allowing us to scale up to a system consisting of 144 elements and state spaces of approximately 10(86 )states. We illustrate the usefulness of this approach through a model of the interaction between the Notch and the Wnt signaling pathways in mammalian skin, and its extensive analysis. CONCLUSION: We introduce an approach for constructing computational models of biological systems that extends the framework of Boolean networks and uses formal verification methods for the analysis of the model. This approach can scale to multicellular models of complex pathways, and is therefore a useful tool for the analysis of complex biological systems. The hypotheses formulated during in-silico testing suggest new avenues to explore experimentally. Hence, this approach has the potential to efficiently complement experimental studies in biology

    Boolean models for genetic regulatory networks

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    This dissertation attempts to answer some of the vital questions involved in the genetic regulatory networks: inference, optimization and robustness of the mathe- matical models. Network inference constitutes one of the central goals of genomic signal processing. When inferring rule-based Boolean models of genetic regulations, the same values of predictor genes can correspond to di®erent values of the target gene because of inconsistencies in the data set. To resolve this issue, a consistency-based inference method is developed to model a probabilistic genetic regulatory network, which consists of a family of Boolean networks, each governed by a set of regulatory functions. The existence of alternative function outputs can be interpreted as the result of random switches between the constituent networks. This model focuses on the global behavior of genetic networks and re°ects the biological determinism and stochasticity. When inferring a network from microarray data, it is often the case that the sample size is not su±ciently large to infer the network fully, such that it is neces- sary to perform model selection through an optimization procedure. To this end, the network connectivity and the physical realization of the regulatory rules should be taken into consideration. Two algorithms are developed for the purpose. One algo- rithm ¯nds the minimal realization of the network constrained by the connectivity, and the other algorithm is mathematically proven to provide the minimally connected network constrained by the minimal realization. Genetic regulatory networks are subject to modeling uncertainties and perturba- tions, which brings the issue of robustness. From the perspective of network stability, robustness is desirable; however, from the perspective of intervention to exert in- °uence on network behavior, it is undesirable. A theory is developed to study the impact of function perturbations in Boolean networks: It ¯nds the exact number of a®ected state transitions and attractors, and predicts the new state transitions and robust/fragile attractors given a speci¯c perturbation. Based on the theory, one algorithm is proposed to structurally alter the network to achieve a more favorable steady-state distribution, and the other is designed to identify function perturbations that have caused changes in the network behavior, respectively
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