Reverse engineering of dynamic networks

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

A regulatory network modeled from wild-type gene expression data guides functional predictions in Caenorhabditis elegans development

BACKGROUND

Complex gene regulatory networks underlie many cellular and developmental processes. While a variety of experimental approaches can be used to discover how genes interact, few biological systems have been systematically evaluated to the extent required for an experimental definition of the underlying network. Therefore, the development of computational methods that can use limited experimental data to define and model a gene regulatory network would provide a useful tool to evaluate many important but incompletely understood biological processes. Such methods can assist in extracting all relevant information from data that are available, identify unexpected regulatory relationships and prioritize future experiments.

RESULTS

To facilitate the analysis of gene regulatory networks, we have developed a computational modeling pipeline method that complements traditional evaluation of experimental data. For a proof-of-concept example, we have focused on the gene regulatory network in the nematode C. elegans that mediates the developmental choice between mesodermal (muscle) and ectodermal (skin) cell fates in the embryonic C lineage. We have used gene expression data to build two models: a knowledge-driven model based on gene expression changes following gene perturbation experiments, and a data-driven mathematical model derived from time-course gene expression data recovered from wild-type animals. We show that both models can identify a rich set of network gene interactions. Importantly, the mathematical model built only from wild-type data can predict interactions demonstrated by the perturbation experiments better than chance, and better than an existing knowledge-driven model built from the same data set. The mathematical model also provides new biological insight, including a dissection of zygotic from maternal functions of a key transcriptional regulator, PAL-1, and identification of non-redundant activities of the T-box genes tbx-8 and tbx-9.

CONCLUSIONS

This work provides a strong example for a mathematical modeling approach that solely uses wild-type data to predict an underlying gene regulatory network. The modeling approach complements traditional methods of data analysis, suggesting non-intuitive network relationships and guiding future experiments.

What can causal networks tell us about metabolic pathways?

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies.

High-throughput profiling data are pervasive in modern genetic studies. The large-scale nature of the data can make interpretation challenging. Methods that estimate networks or graphs have become popular tools for proposing causal relationships among traits. However, it is not obvious that these methods are able to capture causal biological mechanisms. Here we address the power and limitations of causal inference methods in biological systems. We examine metabolic data from simulation and from a well-characterized metabolic pathway in plants. We show that variation has to propagate through the pathway for reliable network inference. While it is possible for causal inference methods to recover the ordering of the biological pathway, it should not be expected. Causal relationships create subtle patterns in correlation, which may be dominated by other biological factors that do not reflect the ordering of the underlying pathway. Our results shape expectations about these methods and explain some of the successes and failures of causal graphical models for network inference.

NETGEM: Network Embedded Temporal GEnerative Model for gene expression data

Background

Temporal analysis of gene expression data has been limited to identifying genes whose expression varies with time and/or correlation between genes that have similar temporal profiles. Often, the methods do not consider the underlying network constraints that connect the genes. It is becoming increasingly evident that interactions change substantially with time. Thus far, there is no systematic method to relate the temporal changes in gene expression to the dynamics of interactions between them. Information on interaction dynamics would open up possibilities for discovering new mechanisms of regulation by providing valuable insight into identifying time-sensitive interactions as well as permit studies on the effect of a genetic perturbation.

Results

We present NETGEM, a tractable model rooted in Markov dynamics, for analyzing the dynamics of the interactions between proteins based on the dynamics of the expression changes of the genes that encode them. The model treats the interaction strengths as random variables which are modulated by suitable priors. This approach is necessitated by the extremely small sample size of the datasets, relative to the number of interactions. The model is amenable to a linear time algorithm for efficient inference. Using temporal gene expression data, NETGEM was successful in identifying (i) temporal interactions and determining their strength, (ii) functional categories of the actively interacting partners and (iii) dynamics of interactions in perturbed networks.

Conclusions

NETGEM represents an optimal trade-off between model complexity and data requirement. It was able to deduce actively interacting genes and functional categories from temporal gene expression data. It permits inference by incorporating the information available in perturbed networks. Given that the inputs to NETGEM are only the network and the temporal variation of the nodes, this algorithm promises to have widespread applications, beyond biological systems.

The source code for NETGEM is available from https://github.com/vjethava/NETGEM

Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks

Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic polynomial dynamical systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic polynomial dynamical system. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Background

A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it.

Results

We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered.

Conclusions

The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.

Computational methods for discovering gene networks from expression data

Designing and conducting experiments are routine practices for modern biologists. The real challenge, especially in the post-genome era, usually comes not from acquiring data, but from subsequent activities such as data processing, analysis, knowledge generation and gaining insight into the research question of interest. The approach of inferring gene regulatory networks (GRNs) has been flourishing for many years, and new methods from mathematics, information science, engineering and social sciences have been applied. We review different kinds of computational methods biologists use to infer networks of varying levels of accuracy and complexity. The primary concern of biologists is how to translate the inferred network into hypotheses that can be tested with real-life experiments. Taking the biologists' viewpoint, we scrutinized several methods for predicting GRNs in mammalian cells, and more importantly show how the power of different knowledge databases of different types can be used to identify modules and subnetworks, thereby reducing complexity and facilitating the generation of testable hypotheses.

Reverse engineering and verification of gene networks: principles, assumptions, and limitations of present methods and future perspectives

Reverse engineering of gene networks aims at revealing the structure of the gene regulation network in a biological system by reasoning backward directly from experimental data. Many methods have recently been proposed for reverse engineering of gene networks by using gene transcript expression data measured by microarray. Whereas the potentials of the methods have been well demonstrated, the assumptions and limitations behind them are often not clearly stated or not well understood. In this review, we first briefly explain the principles of the major methods, identify the assumptions behind them and pinpoint the limitations and possible pitfalls in applying them to real biological questions. With regard to applications, we then discuss challenges in the experimental verification of gene networks generated from reverse engineering methods. We further propose an optimal experimental design for allocating sampling schedule and possible strategies for reducing the limitations of some of the current reverse engineering methods. Finally, we examine the perspectives for the development of reverse engineering and urge the need to move from revealing network structure to the dynamics of biological systems.