Plato's Cave Algorithm: Inferring Functional Signaling Networks from Early Gene Expression Shadows

Improving the ability to reverse engineer biochemical networks is a major goal of systems biology. Lesions in signaling networks lead to alterations in gene expression, which in principle should allow network reconstruction. However, the information about the activity levels of signaling proteins conveyed in overall gene expression is limited by the complexity of gene expression dynamics and of regulatory network topology. Two observations provide the basis for overcoming this limitation: a. genes induced without de-novo protein synthesis (early genes) show a linear accumulation of product in the first hour after the change in the cell''s state; b. The signaling components in the network largely function in the linear range of their stimulus-response curves. Therefore, unlike most genes or most time points, expression profiles of early genes at an early time point provide direct biochemical assays that represent the activity levels of upstream signaling components. Such expression data provide the basis for an efficient algorithm (Plato''s Cave algorithm; PLACA) to reverse engineer functional signaling networks. Unlike conventional reverse engineering algorithms that use steady state values, PLACA uses stimulated early gene expression measurements associated with systematic perturbations of signaling components, without measuring the signaling components themselves. Besides the reverse engineered network, PLACA also identifies the genes detecting the functional interaction, thereby facilitating validation of the predicted functional network. Using simulated datasets, the algorithm is shown to be robust to experimental noise. Using experimental data obtained from gonadotropes, PLACA reverse engineered the interaction network of six perturbed signaling components. The network recapitulated many known interactions and identified novel functional interactions that were validated by further experiment. PLACA uses the results of experiments that are feasible for any signaling network to predict the functional topology of the network and to identify novel relationships.     

Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analysis.

MOTIVATION: A large number of molecular mechanisms at the basis of gene regulation have been described during the last few decades. It is now becoming possible to address questions dealing with both the structure and the dynamics of genetic regulatory networks, at least in the case of some of the best-characterized organisms. Most recent attempts to address these questions deal with microbial or animal model systems. In contrast, we analyze here a gene network involved in the control of the morphogenesis of flowers in a model plant, Arabidopsis thaliana. RESULTS: The genetic control of flower morphogenesis in Arabidopsis involves a large number of genes, of which 10 are considered here. The network topology has been derived from published genetic and molecular data, mainly relying on mRNA expression patterns under wild-type and mutant backgrounds. Using a 'generalized logical formalism', we provide a qualitative model and derive the parameter constraints accounting for the different patterns of gene expression found in the four floral organs of Arabidopsis (sepals, petals, stamens and carpels), plus a 'non-floral' state. This model also allows the simulation or the prediction of various mutant phenotypes. On the basis of our model analysis, we predict the existence of a sixth stable pattern of gene expression, yet to be characterized experimentally. Moreover, our dynamical analysis leads to the prediction of at least one more regulator of the gene LFY, likely to be involved in the transition from the non-flowering state to the flowering pathways. Finally, this work, together with other theoretical and experimental considerations, leads us to propose some general conclusions about the structure of gene networks controlling development.     

Inferring adaptive regulation thresholds and association rules from gene expression data through combinatorial optimization learning

There is a need to design computational methods to support the prediction of gene regulatory networks. Such models should offer both biologically-meaningful and computationally-accurate predictions, which in combination with other techniques may improve large-scale, integrative studies. This paper presents a new machine learning method for the prediction of putative regulatory associations from expression data, which exhibit properties never or only partially addressed by other techniques recently published. The method was tested on a Saccharomyces cerevisiae gene expression dataset. The results were statistically validated and compared with the relationships inferred by two machine learning approaches to gene regulatory network prediction. Furthermore, the resulting predictions were assessed using domain knowledge. The proposed algorithm may be able to accurately predict relevant biological associations between genes. One of the most relevant features of this new method is the prediction of adaptive regulation thresholds for the discretization of gene expression values, which is required prior to the rule association learning process. Moreover, an important advantage consists of its low computational cost to infer association rules. The proposed system may significantly support exploratory, large-scale studies of automated identification of potentially-relevant gene expression associations.     

Analysis of gene network robustness based on saturated fixed point attractors

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.     

Gene network inference from incomplete expression data: transcriptional control of hematopoietic commitment

MOTIVATION: The topology and function of gene regulation networks are commonly inferred from time series of gene expression levels in cell populations. This strategy is usually invalid if the gene expression in different cells of the population is not synchronous. A promising, though technically more demanding alternative is therefore to measure the gene expression levels in single cells individually. The inference of a gene regulation network requires knowledge of the gene expression levels at successive time points, at least before and after a network transition. However, owing to experimental limitations a complete determination of the precursor state is not possible. RESULTS: We investigate a strategy for the inference of gene regulatory networks from incomplete expression data based on dynamic Bayesian networks. This permits prediction of the number of experiments necessary for network inference depending on parameters including noise in the data, prior knowledge and limited attainability of initial states. Our strategy combines a gradual 'Partial Learning' approach based solely on true experimental observations for the network topology with expectation maximization for the network parameters. We illustrate our strategy by extensive computer simulations in a high-dimensional parameter space in a simulated single-cell-based example of hematopoietic stem cell commitment and in random networks of different sizes. We find that the feasibility of network inferences increases significantly with the experimental ability to force the system into different initial network states, with prior knowledge and with noise reduction. AVAILABILITY: Source code is available under: www.izbi.uni-leipzig.de/services/NetwPartLearn.html SUPPLEMENTARY INFORMATION: Supplementary Data are available at Bioinformatics online.     

Tissue-Specific Functional Networks for Prioritizing Phenotype and Disease Genes

Integrated analyses of functional genomics data have enormous potential for identifying phenotype-associated genes. Tissue-specificity is an important aspect of many genetic diseases, reflecting the potentially different roles of proteins and pathways in diverse cell lineages. Accounting for tissue specificity in global integration of functional genomics data is challenging, as “functionality” and “functional relationships” are often not resolved for specific tissue types. We address this challenge by generating tissue-specific functional networks, which can effectively represent the diversity of protein function for more accurate identification of phenotype-associated genes in the laboratory mouse. Specifically, we created 107 tissue-specific functional relationship networks through integration of genomic data utilizing knowledge of tissue-specific gene expression patterns. Cross-network comparison revealed significantly changed genes enriched for functions related to specific tissue development. We then utilized these tissue-specific networks to predict genes associated with different phenotypes. Our results demonstrate that prediction performance is significantly improved through using the tissue-specific networks as compared to the global functional network. We used a testis-specific functional relationship network to predict genes associated with male fertility and spermatogenesis phenotypes, and experimentally confirmed one top prediction, Mbyl1. We then focused on a less-common genetic disease, ataxia, and identified candidates uniquely predicted by the cerebellum network, which are supported by both literature and experimental evidence. Our systems-level, tissue-specific scheme advances over traditional global integration and analyses and establishes a prototype to address the tissue-specific effects of genetic perturbations, diseases and drugs.     

Probabilities of spurious connections in gene networks: application to expression time series

MOTIVATION: The reconstruction of gene networks from gene-expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance fluctuations rather than from a true biological relationship. RESULTS: Unlike the false discovery rate and positive false discovery rate, the decisive false discovery rate (dFDR) is exactly equal to a conditional probability without assuming independence or the randomness of hypothesis truth values. This property is useful not only in the common application to the detection of differential gene expression, but also in determining the probability of a spurious connection in a reconstructed gene network. Estimators of the dFDR can estimate each of three probabilities: (1) The probability that two genes that appear to be associated with each other lack such association. (2) The probability that a time ordering observed for two associated genes is misleading. (3) The probability that a time ordering observed for two genes is misleading, either because they are not associated or because they are associated without a lag in time. The first probability applies to both static and dynamic gene networks, and the other two only apply to dynamic gene networks.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.