Boolean Networks are emerging as a simple yet powerful for- malism to model and study Gene Regulatory Networks. Nevertheless, the most widely used Boolean Network-based models do not include any post-transcriptional regulation mechanism. In this paper we discuss how the post-transcriptional regulation mechanism mediated by miRNAs can be included in a Boolean Network based model to have a more realistic representation of a Gene Regulatory Networks. This contribution con- stitutes a critical preparatory step in the study of the topological and structural role of miRNAs in complex regulatory network

Benedettini, S.

Benso, Alfredo

Di Carlo, Stefano

Politano, Gianfranco Michele Maria

Rehman, H.U.

Savino, Alessandro

Squillero, Giovanni

Vasciaveo, Alessandro

PORTO Publications Open Repository TOrino

Accounting for Post-Transcriptional Regulation in Boolean Networks Based Regulatory Models

Boolean Networks are emerging as a simple yet powerful for- malism to model and study Gene Regulatory Networks. Nevertheless, the most widely used Boolean Network-based models do not include any post-transcriptional regulation mechanism. In this paper we discuss how the post-transcriptional regulation mechanism mediated by miRNAs can be included in a Boolean Network based model to have a more realistic representation of a Gene Regulatory Networks. This contribution con- stitutes a critical preparatory step in the study of the topological and structural role of miRNAs in complex regulatory networks

BENSO, ALFREDO

DI CARLO, STEFANO

POLITANO, GIANFRANCO MICHELE MARIA

SAVINO, ALESSANDRO

SQUILLERO, Giovanni

VASCIAVEO, ALESSANDRO

Rehman, H. U.

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEAccounting for Post-Transcriptional Regulation in Boolean Networks Based Regulatory Models. / Benso, A.; Di Carlo, S.;Rehman, H. U.; Politano, G.; Savino, A.; Squillero, G.; Vasciaveo, A.; Benedettini, S.. - STAMPA. - (2013), pp. 397-404.((Intervento presentato al convegno International Work-Conference on Bioinformatics and Biomedical Engineering,IWBBIO 2013 tenutosi a Granada, ES nel 18-20 March , 2013.OriginalAccounting for Post-Transcriptional Regulation in Boolean Networks Based Regulatory Models.Publisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2518695 since: 2016-09-16T17:53:30ZCopicentro EditorialAccounting for Post-Transcriptional Regulationin Boolean Networks Based Regulatory ModelsAlfredo Benso1, Stefano Di Carlo1, Hafeez Ur Rehman1, Gianfranco Politano1,Alessandro Savino1, Giovanni Squillero1, Alessandro Vasciaveo1, and StefanoBenedettini21 Politecnico di Torino, Control and Comp. Engineering Department, Torino (Italy)E-mail: <firstname>.<lastname>@polito.it,Home page: http://www.testgroup.polito.it/index.php/bio-menu-home2 European Centre for Living Technology, Venice, ItalyE-mail: s.benedettini@unive.itAbstract. Boolean Networks are emerging as a simple yet powerful for-malism to model and study Gene Regulatory Networks. Nevertheless,the most widely used Boolean Network-based models do not include anypost-transcriptional regulation mechanism. In this paper we discuss howthe post-transcriptional regulation mechanism mediated by miRNAs canbe included in a Boolean Network based model. This contribution consti-tutes a key preparatory step in the study of the topological and structuralrole of miRNAs in complex regulatory networks.Keywords: miRNA, Gene Regulatory Networks, post-transcriptionalregulation, Boolean Networks, Complex Systems, Network Analysis1 IntroductionRemarkable advances in molecular biology enabled in the recent years to se-quence the complete genome of several living organisms [18], and to identifyand functionally annotate several of the thousand of proteins these genomesencode [4, 15]. Unfortunately the identification of the genome is only the firststep in understanding how it works. Researchers are now switching to the nextmajor challenge consisting in the determination of all interactions among genes,proteins and other cellular components [2]. Complex Systems Biology aims atsystematically studying complex interactions among components of biologicalsystems, by means of theoretical instruments provided by the science of com-plex systems [10]. In this context, the definition of models and computationalmethods to understand gene regulatory networks (GRN) is a primary objective.In biological systems, decisions are reached and actions are taken by methodsthat are exceedingly parallel and extraordinarily integrated [12]. To understandthe nature of cellular functions, it is necessary to study the behavior of genesin a holistic rather than in an individual manner because the expressions andactivities of genes are not isolated or independent of each other [16]. Therehave been a number of attempts to model GRN, including linear models [17]IWBBIO 2013. Proceedings Granada, 18-20 March, 2013 3972 Benso et al.and Bayesian Networks [14]. However the model that probably received mostattention is the Boolean Network (BN) model originally introduced by Kauffmanabout 30 years ago [11]. A Boolean network consists of a set of Boolean variableswhose state is determined by other variables in the network. When used to modelGRNs, gene expression is quantized into a Boolean value and the expression ofeach gene is constructed as a Boolean function of the expression of other genes.This approach is obviously a strong simplification, since in reality the expressionof a gene is a continuous value and not a boolean (on/off) one. Nevertheless,Boolean Networks allow us to study high-level properties of a network like itsrobustness to noise, or its behavior under different initial conditions.Recent researches suggest that several realistic biological questions may bestudied by looking at this simple Boolean formalism and in particular com-puting and analyzing the related network attractors (i.e., a state or a set ofstates towards which a system, that is moving according to its dynamic, evolvesover time) [13] [9]. However, most published models focus on a very high-levelgene/gene or gene/protein interaction, neglecting post-transcriptional regulatoryactivities carried out by small non-coding RNA sequences such as micro RNA(miRNA). miRNA and non-coding RNA have demonstrated to play a centralrole in how the genome is regulated and how traits are passed on or eliminatedby environmental and genetic factors.In this paper we discuss how post-transcriptional regulatory interaction me-diated by miRNA can be modeled by means of Boolean Networks, and howattractors of a network can be identified taking into account the peculiarity ofthis regulatory activity. The main contribution of the paper is therefore a morerealistic representation of the cell regulatory activity that will in turn improvethe exploratory power provided by the BN formalism.2 Materials and MethodsAt the molecular scale, the DNA of a specific organism encodes all the necessaryinformation to synthesize RNAs and proteins. The interactions among genes andtheir products are at the basis of all vital cellular processes, like, for instance,cell metabolism, signal transduction, cell differentiation, cell fates and so on.Figure 1 shows a simple example of cellular regulatory activity in which thedifferent actors that will be considered in our BN-based post-transcriptionalmodel are introduced.In the example, two genes, G1 and G2 are responsible for the biosyntheses oftwo mRNA molecules (mRNA1 and mRNA2) that convey the genetic informa-tion required to be translated into proteins P1 and P2. P1 represents an outcomeof this specific sample regulatory activity whereas P2 works as an upstream pro-moter of gene G3 (i.e., G2 is a transcription factor of gene G3) thus giving shapeto a simple GRN. RNAs are not the only molecules produced during gene tran-scription. miRNAs are often produced during transcription as reported in oursample GRN where G1 also produces a microRNA molecule named miRNA1.miRNAs are short non-coding RNA sequences that act as post-transcriptionalIWBBIO 2013. Proceedings Granada, 18-20 March, 2013 398Post-Transcriptional Regulation in BN-GRNs 3DNAG1 G2 G3mRNA1P1miRNA1mRNA2P2TranscriptionTranslationTranscriptionPost-transcriptional reg.TranscriptionUpstream gene regulationFig. 1: Modeling of post-transcriptional mechanisms.regulators. They bind to complementary sequences on target mRNAs, usuallyresulting in translational repression or target degradation. In our specific exam-ple miRNA1 acts as a post-transcriptional repressor of mRNA1 which results ina translation repression of P2 and therefore in an inhibition effect on gene G3.Even if simple, the proposed example allows us to visualize all the actorsrequired to introduce post-transcriptional regulation into GNR models. Figure 2shows an extended BN representing the proposed regulatory example.G1 G2G3mRNA1_P1miRNA1mRNA2_P2mRNA1 P1 = G1miRNA1 = G1mRNA2 P2 = G2 ·miRNA1G3 = mRNA2 P2C1 = mRNA1 P1 ·G1C2 = miRNA1 ·G1C3 = mRNA P2 ·G2Fig. 2: Boolean network model.For simplicity, the translation process that leads to the protein produc-tion starting from the related mRNA molecule has not been explicitly mod-eled. Three types of nodes are therefore used to model the GRN: (1) genes, (2)IWBBIO 2013. Proceedings Granada, 18-20 March, 2013 3994 Benso et al.mRNA Protein pairs, and (3) miRNA. This is not a limitation, since, if neces-sary, the proposed approach could be easily extended to explicit the translationprocess.The post-transcriptional regulation model is obtained by carefully designingthe state function of each transcriptional product targeted by a miRNA (i.e.,the mRNA2 P1 node in the previous example). Post-transcriptional regulationacts at mRNA level, hence considering the final protein production it has higherpriority compared to gene expression activity. In terms of boolean network, itcan be modeled by placing the miRNA expression status in Boolean AND withthe mRNA expression function.Modeling the miRNA activity into the mRNA node update function of theBN is however not enough to properly model post-transcriptional activity, es-pecially when the simulation of the dynamics of the BN is used to search fornetwork attractors. If we define the state of the system as the value each nodeof the BN assumes at a given time, the search algorithm of network attractorstraces a trajectory in the state space starting from an initial state and flowingthrough a set of intermediate states until an attractor is identified. This is doneby simulating the dynamics of the system.However, in gene regulatory networks not all states are biologically accept-able. While the dynamics of the network, if well designed, avoid to move thesystem into an illegal state, if such a state is selected as an initial condition inthe attractor search process, biological meaningless results could be inferred. Asan example, let us consider G1 and the related protein mRNA1 P1. A protein canbe expressed only if the related gene has been expressed thus triggering the tran-scription/translation process. In this example, any state in which mRNA1 P1is equal to 1 (expressed) while G1 is equal to 0 (not expressed) is actually anillegal state and should be discarded.We therefore propose to complement the description of the BN with a set ofconditions identifying illegal states of the networks. In Figure 2 these conditionsare represented by the three Boolean equations C1, C2, and C3. Every time astate of the network is considered, the three conditions must be evaluated. Thestate is considered legal if all conditions return zero, illegal otherwise.There are a number of software applications for experimenting with BNs[5, 1, 8]. Some of them are too narrow in scope, inefficient or difficult to inte-grate. Since our primary need was to integrate the BN representation, we foundthe Boolean Network Toolkit (BNT), presented in [3], very easy to customizebecause of the C++ open implementation of its core engine. Resorting to theBTN, we implemented an attractor search procedure based on the extended BNrepresentation proposed in Figure 1. In the BNT core, a boolean network is adirect graph implemented using adjacent lists supported by the BOOST C++Library, [7]. Each node in this structure contains different data such as the nodename, type (e.g., gene, protein or miRNA), and other parameters useful to char-acterize the node, also from a graphical point of view. The graphical frameworkchosen to represent the network is Cytoscape [6]. Algorithm 1 shows the overallattractor search process.IWBBIO 2013. Proceedings Granada, 18-20 March, 2013 400Post-Transcriptional Regulation in BN-GRNs 5Given the high number of states a complex BN may assume, attractors aresearched by selecting a limited number of candidate initial conditions, whosenumber is identified by the probes parameter. The attractor search procedureis an iterative process involving probes iteration. For each iteration, a randominitial state is selected, the validity of the state against the transcriptional andpost-transcriptional constraints is verified, and if the state is admissible, thenetwork dynamics are simulated to search for an attractor on the selected tra-jectory.Data: the Gene Regulatory NetworkResult: a Set which contains the attractorsinput : probes the number of initial condition to testforall the probes doσ ← generateRandomState;isV alid← isValidBooleanState(σ,C);if isV alid = true thenanAttractor ← findAttractor(σ);grnAttractorSet.add(anAttractor);elsecontinue;endendAlgorithm 1: Algorithm for searching for a GRN attractor.To check whether a state is valid or not, the isValidBooleanState function(see Algorithm 2) is used. This function receives in input the state to analyzeand the set of constraints established for the network. Each constraint representsa boolean function that is evaluated in the target state. If at least one of theconstraints is true, it means the state is not valid and the initial state is discarded.Otherwise, a true value is returned.3 Results and DiscussionFigure 3 shows the four attractors found for the simple network of Figure 2. Graynodes are active or expressed, while white nodes are silenced. It is easy to seethat all attractors fulfill the ”post-transcriptional” constraints. Therefore, theyare all valid network states. In this phase, besides adding the post-transcriptionalregulation mechanism to the GRN model, we concentrated in making the toolsetas flexible and computationally fast as possible. To better profile the scalabilityof the toolset we applied the attractors search algorithm on a set of artificiallygenerated GRNs that include post-transcriptional regulation. The challenge herewas also to considerably increase the manageable network size in order to be able,eventually, to analyze real regulatory networks of significant size. ExperimentsIWBBIO 2013. Proceedings Granada, 18-20 March, 2013 4016 Benso et al.Result: if the state is admissible or notinput : X the state to checkinput : stateConstraintSet the collection of constraints for the given networkoutput: true if the state being checked is admissibleoutput: false otherwisenotValid ← false;foreach anInvalidSchema in stateConstraintSet donotValid ← isValid OR anInvalidSchema (X) ;endif notValid = true thenreturn false ;elsereturn true ;endAlgorithm 2: Algorithm for checking the validity of an initial state.were performed on a 8-core workstation featuring multithreading programmingon three different network types:– dense networks: each node has an average in/out degree (number of in-put/output edges) equal to 25;– sparse networks: each node has an average in/out degree equal to 5;– scale-invariant networks: each node has an average in/out degree equal to5; a select number of nodes are hubs with in/out degree greater than 25;For each class we generated four networks with increasing number of nodes: 10,20, 50, and 100 nodes. For each network we applied the attractor search algorithmconsidering increasing number of initial probes (10K, 100K, 1M states), andeach experiment has been repeated 10 times to account for the casualty of theinitial state generation. The attractor search algorithm explores the networkstates exploiting all available cores. In this way, the search is 8-times fasterthen in a single-core implementation. The only actual limitation is the memoryconsumption since the search complexity considerably increases with the numberof nodes and edges of the network. With 8GB of available RAM we noticed aperformance breakdown when the GRN configuration reaches 100 nodes with anaverage number of incoming edges per node higher than 29.The results reported in Figure 4 show that it is possible to find the attractorsof networks up to 100 nodes in a reasonable time (Real Time is lower than CPUTime thanks to the multithreading approach).4 ConclusionsThe BNT presented in this paper is only a first step towards a more realisticanalysis of the high-level functional and topological characteristics of GRNs.Resorting to the tool facilities, such as multicore implementation and supportfor common input/output formats, dynamics of real networks of significant sizeIWBBIO 2013. Proceedings Granada, 18-20 March, 2013 402Post-Transcriptional Regulation in BN-GRNs 7Fig. 3: Set of attractors found for the Network of Figure 2can be analyzed. Moreover, thanks to the extended model that includes post-transcriptional regulation, not only the network simulation can be more reliable,but also it can offer new insights on the role of miRNAs from a functional aswell as structural point of view. To do this, the toolkit will be soon improvedwith several network analysis algorithms.References1. Albert, I., Thakar, J., Li, S., Zhang, R., Albert, R.: Boolean network simulationsfor life scientists. Source Code for Biology and Medicine 3(1), 16 (2008)2. Albert, R.: Boolean modelingof genetic regulatory networks. Complex Networkspp. 459–481 (2004)3. Benedettini, S., Roli, A.: An efficient simulator for boolean network models. In:European Conference on Complex Systems (2012)4. 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Accounting for Post-Transcriptional Regulation in Boolean Networks Based Regulatory Models.

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Accounting for Post-Transcriptional Regulation in Boolean Networks Based Regulatory Models

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