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

Inferring cellular networks – a review

In this review we give an overview of computational and statistical methods to reconstruct cellular networks. Although this area of research is vast and fast developing, we show that most currently used methods can be organized by a few key concepts. The first part of the review deals with conditional independence models including Gaussian graphical models and Bayesian networks. The second part discusses probabilistic and graph-based methods for data from experimental interventions and perturbations

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

Inference of Cancer-specific Gene Regulatory Networks Using Soft Computing Rules

Perturbations of gene regulatory networks are essentially responsible for oncogenesis. Therefore, inferring the gene regulatory networks is a key step to overcoming cancer. In this work, we propose a method for inferring directed gene regulatory networks based on soft computing rules, which can identify important cause-effect regulatory relations of gene expression. First, we identify important genes associated with a specific cancer (colon cancer) using a supervised learning approach. Next, we reconstruct the gene regulatory networks by inferring the regulatory relations among the identified genes, and their regulated relations by other genes within the genome. We obtain two meaningful findings. One is that upregulated genes are regulated by more genes than downregulated ones, while downregulated genes regulate more genes than upregulated ones. The other one is that tumor suppressors suppress tumor activators and activate other tumor suppressors strongly, while tumor activators activate other tumor activators and suppress tumor suppressors weakly, indicating the robustness of biological systems. These findings provide valuable insights into the pathogenesis of cancer

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

<p>Abstract</p> <p>Background</p> <p>A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data.</p> <p>Results</p> <p>The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (<it>l</it>₁-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the I<smcaps>N</smcaps>S<smcaps>ILICO</smcaps>1, I<smcaps>N</smcaps>S<smcaps>ILICO</smcaps>2 and I<smcaps>N</smcaps>S<smcaps>ILICO</smcaps>3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published <it>Saccharomyces cerevisae </it>cell cycle transcript profiling data sets capture known regulatory associations. In each <it>S. cerevisiae </it>LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification.</p> <p>Conclusion</p> <p>A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.</p

Redescription Mining and Applications in Bioinformatics

Our ability to interrogate the cell and computationally assimilate its answers is improving at a dramatic pace. For instance, the study of even a focused aspect of cellular activity, such as gene action, now benefits from multiple high-throughput data acquisition technologies such as microarrays, genome-wide deletion screens, and RNAi assays. A critical need is the development of algorithms that can bridge, relate, and unify diverse categories of data descriptors. Redescription mining is such an approach. Given a set of biological objects (e.g., genes, proteins) and a collection of descriptors defined over this set, the goal of redescription mining is to use the given descriptors as a vocabulary and find subsets of data that afford multiple definitions. The premise of redescription mining is that subsets that afford multiple definitions are likely to exhibit concerted behavior and are, hence, interesting. We present algorithms for redescription mining based on formal concept analysis and applications of redescription mining to multiple biological datasets. We demonstrate how redescriptions identify conceptual clusters of data using mutually reinforcing features, without explicit training information.

Effective Identification of Conserved Pathways in Biological Networks Using Hidden Markov Models

The advent of various high-throughput experimental techniques for measuring molecular interactions has enabled the systematic study of biological interactions on a global scale. Since biological processes are carried out by elaborate collaborations of numerous molecules that give rise to a complex network of molecular interactions, comparative analysis of these biological networks can bring important insights into the functional organization and regulatory mechanisms of biological systems.In this paper, we present an effective framework for identifying common interaction patterns in the biological networks of different organisms based on hidden Markov models (HMMs). Given two or more networks, our method efficiently finds the top matching paths in the respective networks, where the matching paths may contain a flexible number of consecutive insertions and deletions.Based on several protein-protein interaction (PPI) networks obtained from the Database of Interacting Proteins (DIP) and other public databases, we demonstrate that our method is able to detect biologically significant pathways that are conserved across different organisms. Our algorithm has a polynomial complexity that grows linearly with the size of the aligned paths. This enables the search for very long paths with more than 10 nodes within a few minutes on a desktop computer. The software program that implements this algorithm is available upon request from the authors