Understanding microRNA-mediated gene regulatory networks through mathematical modelling.pdf

Published online 17 June 2016Nucleic Acids Research,2016,Vol.44,No.1360196035doi:10.1093/nar/gkw550SURVEY AND SUMMARYUnderstanding microRNA-mediated gene regulatorynetworks through mathematical modellingXin Lai1,*,Olaf Wolkenhauer2,3and Julio Vera1,*1Laboratory of Systems Tumour Immunology,Department of Dermatology,Erlangen University Hospital andFriedrich-Alexander University Erlangen-Nuremberg,Erlangen,91054,Germany,2Department of Systems Biology&Bioinformatics,University of Rostock,Rostock,18051,Germany and3Stellenbosch Institute for Advanced Study,Wallenberg Research Centre at Stellenbosch University,7600,South AfricaReceived December 29,2015;Revised June 2,2016;Accepted June 6,2016ABSTRACTThe discovery of microRNAs(miRNAs)has addeda new player to the regulation of gene expression.With the increasing number of molecular species in-volved in gene regulatory networks,it is hard to ob-tain an intuitive understanding of network dynam-ics.Mathematical modelling can help dissecting therole of miRNAs in gene regulatory networks,and weshall here review the most recent developments thatutilise different mathematical modelling approachesto provide quantitative insights into the function ofmiRNAs in the regulation of gene expression.KeymiRNA regulation features that have been elucidatedvia modelling include:(i)the role of miRNA-mediatedfeedback and feedforward loops in fine-tuning ofgene expression;(ii)the miRNAtarget interactionproperties determining the effectiveness of miRNA-mediated gene repression;and(iii)the competitionfor shared miRNAs leading to the cross-regulationof genes.However,there is still lack of mechanisticunderstanding of many other properties of miRNAregulation like unconventional miRNAtarget inter-actions,miRNA regulation at different sub-cellularlocations and functional miRNA variant,which willneed future modelling efforts to deal with.This re-view provides an overview of recent developmentsand challenges in this field.INTRODUCTIONMicroRNAs(miRNAs)are a class of small endogenousnon-coding RNAs(ncRNAs)with a length of 22 nt(1,2).MiRNAs function as evolutionarily conserved post-transcriptional gene regulators that,in most cases,decreasethestabilityorinhibittranslationofmessengerRNAs(mR-NAs)through binding to complementary sequences.Thesesequences are found in different regions of mRNAs,mainlyin their three prime untranslated regions(3?-UTRs;(3),and also in their 5-UTRs(4)and coding sequences(5).In addition to their well-studied repressive function,miR-NAs can act in a context-dependent fashion to increasetranslation of targets by both transcriptional and post-transcriptional mechanisms(6).So far,2588 mature miR-NAs have been identified in humans,and the genome loca-tion,sequence and annotation of these transcripts can befound in the public data repository miRBase v21(7).Esti-mates based on computational and experimental analysessuggest that more than half of protein-coding genes are tar-gets of miRNAs in Homo sapiens(8).In addition,recentexperimental studies have shown that miRNAs can also in-teractwithlongncRNAs(9).ThebroadinteractionofmiR-NAs with other molecular species indicates their pervasiveroles in the regulation of key cellular processes,includingproliferation,differentiation and apoptosis(10,11).In ad-dition to exerting critical function during normal develop-ment and cellular homeostasis,miRNAs have been foundderegulatedinmanymultifactorialandhighlyprevalenthu-man diseases such as cancer(1215).Computational methods that utilise the canonical seed-match model,evolutionary conservation,miRNAtargetbinding energy as well as miRNA and mRNA expressiondata have been developed to identify putative miRNA tar-gets.This has fostered the discovery and experimental vali-dationofmiRNAtargets.Theimplementationandapplica-tion of these methods have already been reviewed and dis-cussed elsewhere(1618).Despite the relative ease in identi-fication of putative miRNAtarget interactions using com-*To whom correspondence should be addressed.Tel:+49 913 1854 5888;Fax:+49 913 1853 3874;Email:xin.laiuk-erlangen.deCorrespondence may also be addressed to Julio Vera.Tel:+49 913 1854 5876;Fax:+49 913 1853 2780;Email:julio.vera-gonzalezuk-erlangen.deC?The Author(s)2016.Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License(http:/creativecommons.org/licenses/by-nc/4.0/),whichpermits non-commercial re-use,distribution,and reproduction in any medium,provided the original work is properly cited.For commercial re-use,please 6020 Nucleic Acids Research,2016,Vol.44,No.13putational algorithms,experimentation is essential to iden-tify bona fide miRNA targets.Analyses using sequencingtechnologies,such as high-throughput sequencing of RNAisolated by crosslinking immunoprecipitation(HITSCLIPalso known as CLIP-seq),can provide a transcriptome-wideviewofmiRNAtargetinteractions(19).ThedatabasestarBase is established for identifying miRNA targets fromlarge scale CLIP-seq data(20).On the other hand,under the systems biology paradigmthe integration of quantitative experimental data withmathematical modelling has been used to investigate theregulationofgeneexpressionbymiRNAsasdynamicalsys-tems.The key idea is that miRNA regulation embedded ingene regulatory networks can be represented with mathe-matical models that encode molecular species and interac-tions that make up these networks.The general procedurefor creating mathematical models accounting for miRNA-mediated gene regulatory networks includes four key steps(21).Firstly,a miRNA-mediated gene regulatory networkcanbereconstructedbyestablishingmolecularinteractions,suchasmiRNAtargetinteractionsandtheinteractionsbe-tweenmiRNAsandtheirtranscriptionalfactors(TFs).Sec-ondly,the network can be translated into a mathematicalmodel using a particular framework,such as ordinary dif-ferential equations(ODEs)that can be used to describebiochemical reactions that make up the network.Thirdly,model parameter values can be characterised using infor-mation from the literature,databases and/or estimated byfitting model simulations to experimental data.Finally,themodel can be used to study properties and behaviours ofthe dynamic system represented by the regulatory network.The available tools for constructing and simulating suchkind of models have been reviewed and summarised byAlves et al.(22).Data-driven modelling provides the meansfor integrating quantitative data into the model equations,thereby making the model a tool for predicting the featuresof miRNA regulation in these networks(2325).Mathe-matical modelling has proven to be useful at elucidating thefine-tuning of biological processes underlying cell and tis-sue function both at temporal and spatial resolution(26).It has also been used to develop hypothesis on the structureand regulation of biochemical networks,to integrate mul-tiple sources of quantitative data into a coherent analysisframework,or to pave the way towards biomarker discov-ery,a new drug or a novel therapy(24,25,2729).Weshallherefocusonareviewofthosestudiesthatmakeuse of mathematical modelling to describe the molecularactivity and biological function of miRNAs in the contextof gene regulatory networks.These studies illustrate howmathematical modelling can advance our understanding ofmiRNA function at both cellular and disease levels.Thisreview article includes four sections.In the first section,weshow mathematical modelling helps to unravel the role ofmiRNA-mediated network motifs,such as feedback loops(FBLs),feedforward loops(FFLs)and target hubs,in fine-tuninggeneexpression.Inthesecondsection,wediscussthequantitative description of molecular mechanisms underly-ing miRNA-mediated gene regulation through mathemati-cal modelling.In the third section,we demonstrate the util-ity of mathematical modelling in elaborating the role thatmiRNA played in determining the cross-regulation of com-peting endogenous RNAs(ceRNAs).In the last section,weenumeratemodellingstudiesthatcharacterisetherolemiR-NAs in orchestrating gene regulatory networks that are es-sential to the initiation,progression and treatment of can-cer.MiRNA-mediated network motifs fine-tune gene expressionNetwork motifs are small recurring regulatory circuits em-bedded in complex gene regulatory networks(30).Thesmall network motif composed by two interacting compo-nents can induce complex regulatory patterns,which arecritical for the emergence of given phenotypes(30).Intra-cellular networks are specially enriched by network motifsintegrating TFs and their targets,and these motifs are wellknown to enable regulatory features like homeostasis,oscil-latorybehaviourandall-or-nothinggeneexpressionpattern(31).In recent times,it has been found that miRNAs canplayaroleinthesecircuits,andtheyacteitherasatargetsorrepressors of TFs(32).The involvement of miRNAs in TFnetwork motifs adds an additional layer of complexity byprovidingtarget-specificrepressionmechanismsatthepost-transcriptionallevel,thusallowinguniquefeaturesfortheseTF-miRNA motifs.For example,in comparison to TFs,miRNAs can quickly turn off or resume protein translationby binding to or disassociating from an already transcribedmRNA,thus leading to rapid and adaptive changes in geneexpression(33).The evolutionary advantage of combiningTF and miRNA target regulation in gene circuits is stillan open debate,but one promising hypothesis is that thecombination of miRNA-and TF-mediated gene regulationallows for defining tightly controlled gene expression pro-grams at both temporal and spatial scales(33).In addition,these circuits are crucial for controlling cell fate,includingcell proliferation and apoptosis(34).For example,cell dif-ferentiationcanbeassociatedwiththeexistenceofmiRNA-mediated positive FBLs governing the occurrence of bista-bility,asophisticatedregulatoryconditioninwhichthenet-work switches to a new state upon a transient perturbation(Figure 1).These complex,non-linear dynamical proper-ties such as bistability can only be fully understood by inte-gratingexperimentaldataintomathematicalmodellingandanalysing the properties of the network motifs using toolsand methods from theoretical biology.In the following,weshow some remarkable examples that integrate mathemati-calmodellingwithexperimentaldatatoadvanceourunder-standing of the dynamics and regulation of network motifsinvolving miRNAs(35,36).Nested TF-miRNA feedback loops govern cell cycle.In re-cent literature,an increasing number of TF-miRNA cir-cuits have been identified to have the structure of miRNA-mediated FBLs.In these circuits,a TF positively or nega-tively regulates the expression of a miRNA,which subse-quently suppresses the TF in a post-transcriptional manner(Table 1).These kinds of FBLs can give rise to bistability ingene expression(31),and they can also confer robustnessto biological processes by resisting intrinsic and extrinsicnoise(3739).Intrinsic noise stems from the stochasticityof transcription,translation and decay of molecular species(40),while extrinsic one refers to fluctuations propagatingNucleic Acids Research,2016,Vol.44,No.13 6021Figure 1.Bistability in miRNA-mediated feedback loops.Here,we used a model that accounts for a positive FBL composed of the TF p53 and miR-34ato explain bistability in p53 steady states.In the FBL,p53 upregulates the transcription of miR-34a,and in turn the miRNA indirectly upregulates p53expressionviarepressingSIRT1,anegativeregulatorofp53(36).Wealsoincludedupstreamsignals(S)suchasDNAdamagesignallingthatcanupregulatep53 expression.In Equation 1,the four terms correspond to the synthesis of p53,the upregulation of p53 by upstream signals,the upregulation of p53by miR-34a and the degradation of p53.In Equation 2,the Hill function represents the transcriptional activation of miR-34 by p53 and the second termcorresponds to the degradation of the miRNA.To identify bistability,we drew the trajectories of p53(the red line)and miR-34a(the blue line)at theirequilibrium states(i.e.dp53/dt=0 and dmiR34/dt=0).We obtained three intersections(the circles)of the trajectories that stand for three steady statesof p53.One of them is unstable(the black circle;Suns),and the other two are stable,corresponding to on(the red circle;Son)and off(the orange circle;Soff)steady states of p53,respectively.Biologically,the offsteady state of p53 can be associated with cell proliferation,and the onsteady state can beassociated with cell cycle arrest as a result of sudden upregulation of p53 expression by DNA damage signalling.The middle plot shows the evolution ofp53(the red line)and S(the green line)over time,and p53 can rest in Soffor Sondepending on the intensity of S.The bifurcation plot shows differentsteady states of p53(p53ss)against different intensities of S.The intersections of the stable steady states and unstable ones represent bifurcation points(BPland BPr).When the value of S crosses these points,the steady state of p53 switches between the two stable states(the solid lines)but cannot stay onthe unstable one(the dashed line).The numbers correspond to the steady states of p53 as shown in the middle plot.Similarly,bistability can also be foundin oscillatory behaviours:stable oscillation attracts neighbouring oscillations of a model variable,and unstable one drives them away.More examples ofbistability were reviewed by Tyson and Nov ak(31),and for fundamental mathematical explanation,the interested reader is referred to(35).from external factors(e.g.environment)to gene regulatorynetworks(41).AremarkablecaseofmultipleTF-miRNAFBLsappearsin the regulation of the E2F family,which is involved in theregulation of cancer-associated phenotypes like malignantproliferation,apoptosisevasion,angiogenesisandchemore-sistance(42).The E2F activity can be regulated by multiplemiRNAs adding a new layer to the regulation of the intri-cate E2F network(42).A well-known case is the regulationof E2F family by the miR-17-92 cluster.The cluster is en-coded within about 1 kilo base on chromosome 13 and con-tains six miRNAs.The transcription of the miRNA clustercan be induced by E2F while some members of the clusterinhibit E2F at the post-transcriptional level,thereby form-ing a negative FBL(43).In addition,E2F can promote itsown transcription forming a positive FBL.The two FBLscomposetheE2F/miR-17-92networkwhosecomplexregu-latorydynamicscanbestudiedthroughmathematicalmod-elling(Figure 2).ODE modelling of the network in the con-text of glioma showed that the miRNA cluster can functionalternatively as an oncogene or a tumour suppressor(44).Such a dual role of the miR-17-92 cluster could result fromthe bistable steady states that E2F possesses in the circuit.The switch between the two states is controlled by the val-ues of two key model parameters.The two parameters cor-respond to the intensity of growth factor signalling and theinhibitionofE2FtranslationbythemiRNAcluster,respec-tively.Model