Алгоритмы восстановления дискретных динамических систем с пороговыми функциями

Recovery of a dynamic system from its functioning is a problem of current interest in the theory of control systems. As a behavior model of gene network regulatory circuit, a discrete dynamic system has been proposed, where coordinates correspond to the concentration of substances, while special functions, which depend on the system value in the previous moment, account for their increase or decrease. Pseudo-polynomial discrete dynamic system recovery algorithms with additive and multiplicative functions have been obtained earlier. The generalized case of arbitrary threshold functions is considered in this article. Algorithms for significant variables recovery and threshold functions weight regulation, having pseudo-polynomial testing complexity, are given. These algorithms allow one either to recover the system completely, or to lower the threshold function dimension.Задача восстановления динамической системы по ее функционированию является актуальной в теории управляющих систем. Ранее были получены псевдополиномиальные алгоритмы восстановления дискретных динамических систем с аддитивными и мультипликативными функциями. Такие системы моделируют поведение регуляторного контура генной сети, а соответствующие функции отвечают за увеличение или уменьшения концентрации веществ. В настоящей статье рассматривается обобщение на случай произвольных пороговых функций. Приведены алгоритмы восстановления существенных переменных и алгоритм упорядочивания весов пороговых функций, имеющие псевдополиномиальную сложность тестирования. Эти алгоритмы позволяют либо полностью восстановить систему, либо уменьшить размерность пороговых функций

Scalable Steady State Analysis of Boolean Biological Regulatory Networks

Background: Computing the long term behavior of regulatory and signaling networks is critical in understanding how biological functions take place in organisms. Steady states of these networks determine the activity levels of individual entities in the long run. Identifying all the steady states of these networks is difficult due to the state space explosion problem. Methodology: In this paper, we propose a method for identifying all the steady states of Boolean regulatory and signaling networks accurately and efficiently. We build a mathematical model that allows pruning a large portion of the state space quickly without causing any false dismissals. For the remaining state space, which is typically very small compared to the whole state space, we develop a randomized traversal method that extracts the steady states. We estimate the number of steady states, and the expected behavior of individual genes and gene pairs in steady states in an online fashion. Also, we formulate a stopping criterion that terminates the traversal as soon as user supplied percentage of the results are returned with high confidence. Conclusions: This method identifies the observed steady states of boolean biological networks computationally. Our algorithm successfully reported the G1 phases of both budding and fission yeast cell cycles. Besides, the experiments suggest that this method is useful in identifying co-expressed genes as well. By analyzing the steady state profil

Reconstruction of large-scale regulatory networks based on perturbation graphs and transitive reduction: improved methods and their evaluation

BACKGROUND: The data-driven inference of intracellular networks is one of the key challenges of computational and systems biology. As suggested by recent works, a simple yet effective approach for reconstructing regulatory networks comprises the following two steps. First, the observed effects induced by directed perturbations are collected in a signed and directed perturbation graph (PG). In a second step, Transitive Reduction (TR) is used to identify and eliminate those edges in the PG that can be explained by paths and are therefore likely to reflect indirect effects. RESULTS: In this work we introduce novel variants for PG generation and TR, leading to significantly improved performances. The key modifications concern: (i) use of novel statistical criteria for deriving a high-quality PG from experimental data; (ii) the application of local TR which allows only short paths to explain (and remove) a given edge; and (iii) a novel strategy to rank the edges with respect to their confidence. To compare the new methods with existing ones we not only apply them to a recent DREAM network inference challenge but also to a novel and unprecedented synthetic compendium consisting of 30 5000-gene networks simulated with varying biological and measurement error variances resulting in a total of 270 datasets. The benchmarks clearly demonstrate the superior reconstruction performance of the novel PG and TR variants compared to existing approaches. Moreover, the benchmark enabled us to draw some general conclusions. For example, it turns out that local TR restricted to paths with a length of only two is often sufficient or even favorable. We also demonstrate that considering edge weights is highly beneficial for TR whereas consideration of edge signs is of minor importance. We explain these observations from a graph-theoretical perspective and discuss the consequences with respect to a greatly reduced computational demand to conduct TR. Finally, as a realistic application scenario, we use our framework for inferring gene interactions in yeast based on a library of gene expression data measured in mutants with single knockouts of transcription factors. The reconstructed network shows a significant enrichment of known interactions, especially within the 100 most confident (and for experimental validation most relevant) edges. CONCLUSIONS: This paper presents several major achievements. The novel methods introduced herein can be seen as state of the art for inference techniques relying on perturbation graphs and transitive reduction. Another key result of the study is the generation of a new and unprecedented large-scale in silico benchmark dataset accounting for different noise levels and providing a solid basis for unbiased testing of network inference methodologies. Finally, applying our approach to Saccharomyces cerevisiae suggested several new gene interactions with high confidence awaiting experimental validation

Identification of genetic networks by strategic gene disruptions and gene overexpressions under a boolean model

AbstractAnalysis of the interactions between genes by systematic gene disruptions and gene overexpressions is an important topic in molecular biology. This paper analyses the problem of identifying a genetic network from the data obtained by multiple gene disruptions and overexpressions in regard to the number of experiments and the complexity of experiments. An experiment consists of simultaneous gene disruptions and overexpressions and the complexity of an experiment is the number of genes disrupted or overexpressed. We define a genetic network as a boolean network and show a series of algorithms which describe methods for identifying the underlying genetic network by such experiments. Some lower bounds on the number of experiments required for the identification are also proved for some cases

Reverse Engineering of Biological Systems

Gene regulatory network (GRN) consists of a set of genes and regulatory relationships between the genes. As outputs of the GRN, gene expression data contain important information that can be used to reconstruct the GRN to a certain degree. However, the reverse engineer of GRNs from gene expression data is a challenging problem in systems biology. Conventional methods fail in inferring GRNs from gene expression data because of the relative less number of observations compared with the large number of the genes. The inherent noises in the data make the inference accuracy relatively low and the combinatorial explosion nature of the problem makes the inference task extremely difficult. This study aims at reconstructing the GRNs from time-course gene expression data based on GRN models using system identification and parameter estimation methods. The main content consists of three parts: (1) a review of the methods for reverse engineering of GRNs, (2) reverse engineering of GRNs based on linear models and (3) reverse engineering of GRNs based on a nonlinear model, specifically S-systems. In the first part, after the necessary background and challenges of the problem are introduced, various methods for the inference of GRNs are comprehensively reviewed from two aspects: models and inference algorithms. The advantages and disadvantages of each method are discussed. The second part focus on inferring GRNs from time-course gene expression data based on linear models. First, the statistical properties of two sparse penalties, adaptive LASSO and SCAD, with an autoregressive model are studied. It shows that the proposed methods using these two penalties can asymptotically reconstruct the underlying networks. This provides a solid foundation for these methods and their extensions. Second, the integration of multiple datasets should be able to improve the accuracy of the GRN inference. A novel method, Huber group LASSO, is developed to infer GRNs from multiple time-course data, which is also robust to large noises and outliers that the data may contain. An efficient algorithm is also developed and its convergence analysis is provided. The third part can be further divided into two phases: estimating the parameters of S-systems with system structure known and inferring the S-systems without knowing the system structure. Two methods, alternating weighted least squares (AWLS) and auxiliary function guided coordinate descent (AFGCD), have been developed to estimate the parameters of S-systems from time-course data. AWLS takes advantage of the special structure of S-systems and significantly outperforms one existing method, alternating regression (AR). AFGCD uses the auxiliary function and coordinate descent techniques to get the smart and efficient iteration formula and its convergence is theoretically guaranteed. Without knowing the system structure, taking advantage of the special structure of the S-system model, a novel method, pruning separable parameter estimation algorithm (PSPEA) is developed to locally infer the S-systems. PSPEA is then combined with continuous genetic algorithm (CGA) to form a hybrid algorithm which can globally reconstruct the S-systems

Simulation and identification of gene regulatory networks

Gene regulatory networks are a well-established model to represent the functioning, at gene level, of utterly elaborated biological networks. Studying and understanding such models of gene communication might enable researchers to rightly address costly laboratory experiments, e.g. by selecting a small set of genes deemed to be responsible for a particular disease, or by indicating with confidence which molecule is supposed to be susceptible to certain drug treatments. This thesis explores two main aspects regarding gene regulatory networks: (i) the simulation of realistic perturbative and systems genetics experiments in gene networks, and (ii) the inference of gene networks from simulated and real data measurements. In detail, the following themes will be discussed: (i) SysGenSIM, an open source software to produce gene networks with realistic topology and simulate systems genetics or targeted perturbative experiments; (ii) two state of the arts algorithms for the structural identification of gene networks from single-gene knockout measurements; (iii) an approach to reverse-engineering gene networks from heterogeneous compendia; (iv) a methodology to infer gene interactions fromsystems genetics dataset. These works have been positively recognized by the scientific community. In particular, SysGenSIM has been used – in addition to providing valuable test benches for the development of the above inference algorithms – to generate benchmark datasets for international competitions as the DREAM5 Systems Genetics challenge and the StatSeq workshop. The identificationmethodologies earned their worth by accurately reverse-engineering gene networks at established contests, namely the DREAM Network Inference challenges. Results are explained and discussed thoroughly in the thesis

Simulation and identification of gene regulatory networks

Gene regulatory networks are a well-established model to represent the functioning, at gene level, of utterly elaborated biological networks. Studying and understanding such models of gene communication might enable researchers to rightly address costly laboratory experiments, e.g. by selecting a small set of genes deemed to be responsible for a particular disease, or by indicating with confidence which molecule is supposed to be susceptible to certain drug treatments. This thesis explores two main aspects regarding gene regulatory networks: (i) the simulation of realistic perturbative and systems genetics experiments in gene networks, and (ii) the inference of gene networks from simulated and real data measurements. In detail, the following themes will be discussed: (i) SysGenSIM, an open source software to produce gene networks with realistic topology and simulate systems genetics or targeted perturbative experiments; (ii) two state of the arts algorithms for the structural identification of gene networks from single-gene knockout measurements; (iii) an approach to reverse-engineering gene networks from heterogeneous compendia; (iv) a methodology to infer gene interactions fromsystems genetics dataset. These works have been positively recognized by the scientific community. In particular, SysGenSIM has been used – in addition to providing valuable test benches for the development of the above inference algorithms – to generate benchmark datasets for international competitions as the DREAM5 Systems Genetics challenge and the StatSeq workshop. The identificationmethodologies earned their worth by accurately reverse-engineering gene networks at established contests, namely the DREAM Network Inference challenges. Results are explained and discussed thoroughly in the thesis

Statistical model identification : dynamical processes and large-scale networks in systems biology

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2014von Robert Johann Flassi