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PubMed2006

Multi-layered network structure of amino acid (AA) metabolism characterized by each essential AA-deficient condition.

The concentrations of free amino acids in plasma change coordinately and their profiles show distinctive features in various physiological conditions; however, their behavior can not always be explained by the conventional flow-based metabolic pathway network. In this study, we have revealed the interrelatedness of the plasma amino acids and inferred their network structure with threshold-test analysis and multilevel-digraph analysis methods using the plasma samples of rats which are fed diet deficient in single essential amino acid. In the inferred network, we could draw some interesting interrelations between plasma amino acids as follows: 1) Lysine is located at the top control level and has effects on almost all of the other plasma amino acids. 2) Threonine plays a role in a hub in the network, which has direct links to the most number of other amino acids. 3) Threonine and methionine are interrelated to each other and form a loop structure.

Amino Acids, Essential↗

PubMed2004

GeneNetwork: an interactive tool for reconstruction of genetic networks using microarray data.

UNLABELLED: Inferring genetic network architecture from time series data generated from high-throughput experimental technologies, such as cDNA microarray, can help us to understand the system behavior of living organisms. We have developed an interactive tool, GeneNetwork, which provides four reverse engineering models and three data interpolation approaches to infer relationships between genes. GeneNetwork enables a user to readily reconstruct genetic networks based on microarray data without having intimate knowledge of the mathematical models. A simple graphical user interface enables rapid, intuitive mapping and analysis of the reconstructed network allowing biologists to explore gene relationships at the system level. AVAILABILITY: Download from http://genenetwork.sbl.bc.sinica.edu.tw/. SUPPLEMENTARY INFORMATION: Supplement documentation of algorithms for the four approaches is downloadable at the above location.

Algorithms↗

PubMed2001

Development of a system for the inference of large scale genetic networks.

We propose a system named AIGNET (Algorithms for Inference of Genetic Networks), and introduce two top-down approaches for the inference of interrelated mechanism among genes in genetic network that is based on the steady state and temporal analyses of gene expression patterns against some kinds of gene perturbations such as disruption or overexpression. The former analysis is performed by a static Boolean network model based on multi-level digraph, and the latter one is by S-system model. By integrating these two analyses, we show our strategy is flexible and rich in structure to treat gene expression patterns; we applied our strategy to the inference of a genetic network that is composed of 30 genes as a case study. Given the gene expression time-course data set under the conditions of wild-type and the deletion of one gene, our system enabled us to reconstruct the same network architecture as original one.

Algorithms↗

PubMed2006

Using complexity for the estimation of Bayesian networks.

Statistical inference of graphical models has become an important tool in the reconstruction of biological networks of the type which model, for example, gene regulatory interactions. In particular, the construction of a score-based Bayesian posterior density over the space of models provides an intuitive and computationally feasible method of assessing model uncertainty and of assigning statistical confidence to structural features. One problem which frequently occurs with this approach is the tendency to overestimate the degree of model complexity. Spurious graphical features obtained in this way may affect the inference in unpredictable ways, even when using scoring techniques, such as the Bayesian Information Criterion (BIC), that are specifically designed to compensate for overfitting. In this article we propose a simple adjustment to a BIC-based scoring procedure. The method proceeds in two steps. In the first step we derive an independent estimate of the parametric complexity of the model. In the second we modify the BIC score so that the mean parametric complexity of the posterior density is equal to the estimated value. The method is applied to a set of test networks, and to a collection of genes from the yeast genome known to possess regulatory relationships. A Bayesian network model with binary responses is employed. In the examples considered, we find that the number of spurious graph edges inferred is reduced, while the effect on the identification of true edges is minimal.

Algorithms↗

PubMed2006

Inference of gene regulatory networks and compound mode of action from time course gene expression profiles.

MOTIVATION: Time series expression experiments are an increasingly popular method for studying a wide range of biological systems. Here we developed an algorithm that can infer the local network of gene-gene interactions surrounding a gene of interest. This is achieved by a perturbation of the gene of interest and subsequently measuring the gene expression profiles at multiple time points. We applied this algorithm to computer simulated data and to experimental data on a nine gene network in Escherichia coli. RESULTS: In this paper we show that it is possible to recover the gene regulatory network from a time series data of gene expression following a perturbation to the cell. We show this both on simulated data and on a nine gene subnetwork part of the DNA-damage response pathway (SOS pathway) in the bacteria E. coli. CONTACT: dibernardo@tigem.it SUPLEMENTARY INFORMATION: Supplementary data are available at http://dibernado.tigem.it

Algorithms↗

PubMedDate not supplied

Constructing and analyzing a large-scale gene-to-gene regulatory network--lasso-constrained inference and biological validation.

We construct a gene-to-gene regulatory network from time-series data of expression levels for the whole genome of the yeast Saccharomyces cerevisae, in a case where the number of measurements is much smaller than the number of genes in the network. This network is analyzed with respect to present biological knowledge of all genes (according to the Gene Ontology database), and we find some of its large-scale properties to be in accordance with known facts about the organism. The linear modeling employed here has been explored several times, but due to lack of any validation beyond investigating individual genes, it has been seriously questioned with respect to its applicability to biological systems. Our results show the adequacy of the approach and make further investigations of the model meaningful.

Algorithms↗

PubMed2004

Temporal aggregation bias and inference of causal regulatory networks.

Time course experiments with microarrays have begun to provide a glimpse into the dynamic behavior of gene expression. In a typical experiment, scientists use microarrays to measure the abundance of mRNA at discrete time points after the onset of a stimulus. Recently, there has been much work on using these data to infer causal regulatory networks that model how genes influence each other. However, microarray studies typically have slow sampling rates that can lead to temporal aggregation of the signal. That is, each successive sampling point represents the sum of all signal changes since the previous sample. In this paper, we show that temporal aggregation can bias algorithms for causal inference and lead them to discover spurious relations that would not be found if the signal were sampled at a much faster rate. We discuss the implications of temporal aggregation on inference, the problems it creates, and potential directions for solutions.

Computational Biology↗

PubMed2004

A mixed integer linear programming (MILP) framework for inferring time delay in gene regulatory networks.

In this paper, an optimization based modeling and solution framework for inferring gene regulatory networks while accounting for time delay is described. The proposed framework uses the basic linear model of gene regulation. Boolean variables are used to capture the existence of discrete time delays between the various regulatory relationships. Subsequently, the time delay that best fits the expression profiles is inferred by minimizing the error between the predicted and experimental expression values. Computational experiments are conducted for both in numero and real expression data sets. The former reveal that if time delay is neglected in a system a priori known to be characterized with time delay then a significantly larger number of parameters are needed to describe the system dynamics. The real microarray data example reveals a considerable number of time delayed interactions suggesting that time delay is ubiquitous in gene regulation. Incorporation of time delay leads to inferred networks that are sparser. Analysis of the amount of variance in the data explained by the model and comparison with randomized data reveals that accounting for time delay explains more variance in real rather than randomized data.

Computational Biology↗

PubMed2006

Inferring rules of Escherichia coli translational efficiency using an artificial neural network.

Although the machinery for translation initiation in Escherichia coli is very complicated, the translational efficiency has been reported to be predictable from upstream oligonucleotide sequences. Conventional models have difficulties in their generalization ability and prediction nonlinearity and in their ability to deal with a variety of input attributions. To address these issues, we employed structural learning by artificial neural networks to infer general rules for translational efficiency. The correlation between translational activities measured by biological experiments and those predicted by our method in the test data was significant (r=0.78), and our method uncovered underlying rules of translational activities and sequence patterns from the obtained skeleton structure. The significant rules for predicting translational efficiency were (1) G- and A-rich oligonucleotide sequences, resembling the Shine-Dalgarno sequence, at positions -10 to -7; (2) first base A in the initiation codon; (3) transport/binding or amino acid metabolism gene function; (4) high binding energy between mRNA and 16S rRNA at positions -15 to -5. An additional inferred novel rule was that C at position -1 increases translational efficiency. When our model was applied to the entire genomic sequence of E. coli, translational activities of genes for metabolism and translational were significantly high.

Base Sequence↗

PubMed2006

Inference in multiply sectioned Bayesian networks: methods and performance comparison.

This paper extends lazy propagation for inference in single-agent Bayesian networks (BNs) to multiagent lazy inference in multiply sectioned BNs (MSBNs). Two methods are proposed using distinct runtime structures. It was proved that the new methods are exact and efficient when the domain structure is sparse. Both improve space and time complexity more than the existing method, which allows multiagent probabilistic reasoning to be performed in much larger domains given the computational resource. The relative performances of the three methods are compared analytically and experimentally.

Algorithms↗

PubMed2005

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy.

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.

Algorithms↗

PubMed2003

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks.

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements

Bayes Theorem↗

PubMed2000

Algorithms for inferring qualitative models of biological networks.

Modeling genetic networks and metabolic networks is an important topic in bioinformatics. We propose a qualitative network model which is a combination of the Boolean network and qualitative reasoning, where qualitative reasoning is a kind of reasoning method well-studied in Artificial Intelligence. We also present algorithms for inferring qualitative networks from time series data and an algorithm for inferring S-systems (synergistic and saturable systems) from time series data, where S-systems are based on a particular kind of nonlinear differential equation and have been applied to the analysis of various biological systems.

Algorithms↗

PubMed2003

Dynamic modeling of genetic networks using genetic algorithm and S-system.

MOTIVATION: The modeling of system dynamics of genetic networks, metabolic networks or signal transduction cascades from time-course data is formulated as a reverse-problem. Previous studies focused on the estimation of only network structures, and they were ineffective in inferring a network structure with feedback loops. We previously proposed a method to predict not only the network structure but also its dynamics using a Genetic Algorithm (GA) and an S-system formalism. However, it could predict only a small number of parameters and could rarely obtain essential structures. In this work, we propose a unified extension of the basic method. Notable improvements are as follows: (1) an additional term in its evaluation function that aims at eliminating futile parameters; (2) a crossover method called Simplex Crossover (SPX) to improve its optimization ability; and (3) a gradual optimization strategy to increase the number of predictable parameters. RESULTS: The proposed method is implemented as a C program called PEACE1 (Predictor by Evolutionary Algorithms and Canonical Equations 1). Its performance was compared with the basic method. The comparison showed that: (1) the convergence rate increased about 5-fold; (2) the optimization speed was raised about 1.5-fold; and (3) the number of predictable parameters was increased about 5-fold. Moreover, we successfully inferred the dynamics of a small genetic network constructed with 60 parameters for 5 network variables and feedback loops using only time-course data of gene expression.

Algorithms↗

PubMed2004

A model-based optimization framework for the inference on gene regulatory networks from DNA array data.

MOTIVATION: Identification of the regulatory structures in genetic networks and the formulation of mechanistic models in the form of wiring diagrams is one of the significant objectives of expression profiling using DNA microarray technologies and it requires the development and application of identification frameworks. RESULTS: We have developed a novel optimization framework for identifying regulation in a genetic network using the S-system modeling formalism. We show that balance equations on both mRNA and protein species led to a formulation suitable for analyzing DNA-microarray data whereby protein concentrations have been eliminated and only mRNA relative concentrations are retained. Using this formulation, we examined if it is possible to infer a set of possible genetic regulatory networks consistent with observed mRNA expression patterns. Two origins of changes in mRNA expression patterns were considered. One derives from changes in the biophysical properties of the system that alter the molecular-interaction kinetics and/or message stability. The second is due to gene knock-outs. We reduced the identification problem to an optimization problem (of the so-called mixed-integer non-linear programming class) and we developed an algorithmic procedure for solving this optimization problem. Using simulated data generated by our mathematical model, we show that our method can actually find the regulatory network from which the data were generated. We also show that the number of possible alternate genetic regulatory networks depends on the size of the dataset (i.e. number of experiments), but this dependence is different for each of the two types of problems considered, and that a unique solution requires fewer datasets than previously estimated in the literature. This is the first method that also allows the identification of every possible regulatory network that could explain the data, when the number of experiments does not allow identification of unique regulatory structure.

Algorithms↗

PubMed1999

Identification of genetic networks from a small number of gene expression patterns under the Boolean network model.

Liang, Fuhrman and Somogyi (PSB98, 18-29, 1998) have described an algorithm for inferring genetic network architectures from state transition tables which correspond to time series of gene expression patterns, using the Boolean network model. Their results of computational experiments suggested that a small number of state transition (INPUT/OUTPUT) pairs are sufficient in order to infer the original Boolean network correctly. This paper gives a mathematical proof for their observation. Precisely, this paper devises a much simpler algorithm for the same problem and proves that, if the indegree of each node (i.e., the number of input nodes to each node) is bounded by a constant, only O(log n) state transition pairs (from 2n pairs) are necessary and sufficient to identify the original Boolean network of n nodes correctly with high probability. We made computational experiments in order to expose the constant factor involved in O(log n) notation. The computational results show that the Boolean network of size 100,000 can be identified by our algorithm from about 100 INPUT/OUTPUT pairs if the maximum indegree is bounded by 2. It is also a merit of our algorithm that the algorithm is conceptually so simple that it is extensible for more realistic network models.

Algorithms↗

PubMed2002

Genetic network modeling.

The inference of genetic interactions from measured expression data is one of the most challenging tasks of modern functional genomics. When successful, the learned network of regulatory interactions yields a wealth of useful information. An inferred genetic network contains information about the pathway to which a gene belongs and which genes it interacts with. Furthermore, it explains the function of the gene in terms of how it influences other genes and indicates which genes are pathway initiators and therefore potential drug targets. Obviously, such wealth comes at a price and that of genetic network modeling is that it is an extremely complex task. Therefore, it is necessary to develop sophisticated computational tools that are able to extract relevant information from a limited set of microarray measurements and integrate this with different information sources, to come up with reliable hypotheses of a genetic regulatory network. Thus far, a multitude of modeling approaches have been proposed for discovering genetic networks. However, it is unclear what the advantages and disadvantages of each of the different approaches are and how their results can be compared. In this review, genetic network models are put in a historical perspective that explains why certain models were introduced. Various modeling assumptions and their consequences are also highlighted. In addition, an overview of the principal differences and similarities between the approaches is given by considering the qualitative properties of the chosen models and their learning strategies.

Gene Expression Regulation↗

PubMed2006

Bayesian sequential inference for stochastic kinetic biochemical network models.

As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discrete-time (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters on-line in several data-poor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic auto-regulatory gene network.

Kinetics↗