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Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

ABSTRACT: Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the 'function' of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature.

SUBMITTER: Ahnert SE

PROVIDER: S-EPMC4971217 | biostudies-literature | 2016 Jul

REPOSITORIES: biostudies-literature

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Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

Ahnert S E SE Fink T M A TM

Journal of the Royal Society, Interface 20160701 120

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level de ...[more]

PMID: 27440255

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Project description:BACKGROUND: Qualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivotal role in dislypidemia and, ultimately, in cancer through intermediates such as mevalonate, farnesyl pyrophosphate and geranyl geranyl pyrophosphate, but no dynamic model of this pathway has been proposed until now. RESULTS: We set up a computational framework to dynamically analyze large biological networks. This framework associates a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous simulation. Based on this method, we present here the results of the analysis of the cholesterol biosynthesis pathway and its physiological regulation by the Sterol Response Element Binding Proteins (SREBPs), as well as the modeling of the action of statins, inhibitor drugs, on this pathway. The in silico experiments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway. CONCLUSION: We believe that the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models, thanks to the computational efficiency of synchronous simulation. Furthermore, to the best of our knowledge, we present here the first dynamic systems biology model of the human cholesterol pathway and several of its key regulatory control elements, hoping it would provide a good basis to perform in silico experiments and confront the resulting properties with published and experimental data. The model of the cholesterol pathway and its regulation, along with Boolean formulae used for simulation are available on our web site http://Bioinformaticsu613.free.fr. Graphical results of the simulation are also shown online. The SBML model is available in the BioModels database http://www.ebi.ac.uk/biomodels/ with submission ID: MODEL0568648427.

Project description:Comprehensive understanding of gene regulatory networks (GRNs) is a major challenge in the field of systems biology. Currently, there are two main approaches in GRN analysis using time-course observation data, namely an ordinary differential equation (ODE)-based approach and a statistical model-based approach. The ODE-based approach can generate complex dynamics of GRNs according to biologically validated nonlinear models. However, it cannot be applied to ten or more genes to simultaneously estimate system dynamics and regulatory relationships due to the computational difficulties. The statistical model-based approach uses highly abstract models to simply describe biological systems and to infer relationships among several hundreds of genes from the data. However, the high abstraction generates false regulations that are not permitted biologically. Thus, when dealing with several tens of genes of which the relationships are partially known, a method that can infer regulatory relationships based on a model with low abstraction and that can emulate the dynamics of ODE-based models while incorporating prior knowledge is urgently required. To accomplish this, we propose a method for inference of GRNs using a state space representation of a vector auto-regressive (VAR) model with L1 regularization. This method can estimate the dynamic behavior of genes based on linear time-series modeling constructed from an ODE-based model and can infer the regulatory structure among several tens of genes maximizing prediction ability for the observational data. Furthermore, the method is capable of incorporating various types of existing biological knowledge, e.g., drug kinetics and literature-recorded pathways. The effectiveness of the proposed method is shown through a comparison of simulation studies with several previous methods. For an application example, we evaluated mRNA expression profiles over time upon corticosteroid stimulation in rats, thus incorporating corticosteroid kinetics/dynamics, literature-recorded pathways and transcription factor (TF) information.

Project description:BackgroundIn the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded.MethodsWe propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood.ResultsFor the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib.ConclusionsFrom the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

Dataset Information

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

Publications

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

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