User Manual for GNLab - The University of Sydney
Contents
1. ll K X Ga K 35 X G KE j l rj syn G V I 14 1 The rate mRNA degradation is assumed to only depend linearly on the current ex pression level Therefore the rate law of mRNA breakdown can be formulated as break G bi X G 2 Overall the change of gene expression level for a gene G can be modeled by the following ordinary differential equation syn G break G 3 This is a deterministic approach to simulate a GRN This ODE approach however ignores the inherent stochasticity in the a real gene network Moreover solving a large set of ODEs analytically is computationally intensive which often requires the use of approximation methods In this study Euler s method is used to simulate the GRN due to its simplicity With the use of a small time step e g 0 1 Euler s method is sufficient to simulate the gene system To incorporate stochasticity into the simulation the deterministic model is extended into a stochastic model using an approach recently described by Tian and Burrage 2006 The key is to replace each state variable x in equation 3 by a Poisson random variate with mean x The expression of a gene G measured in mRNA molecular number is simulated as X G t 7 X Gi P syn G P break G 4 The variable X G t denotes the molecular number of mRNA of G and 7 denotes the time elapsed P x generates a Poisson random variate with mean x Using this2. technique the level of mRNA of a gene is affected by Poisson noise which is consistent with the chance event in transcription and translation Thattai and van Oudenaarden 2001 3 1 Microarray Dataset Synthesis There are three main types of microarray datasets available namely time series gene perturbation and condition specific datasets A summary of how each type of dataset is generated is shown as follows 3 1 1 Time series Microarray Dataset 1 Initialize the gene system and simulate 10007 rounds to bring the system to a steady state 2 Knockout one gene i e set concentration 0 and V 0 3 Simulate the system and repeatedly take the expression level at certain intervals 4 3 1 2 Gene Perturbation Microarray Dataset 1 Initialize the gene system and simulate 1 000x7 rounds 2 Knockout one gene i e set concentration 0 and V 0 3 Repeatedly simulate the system for 1 000x7 rounds 4 Obtain gene expression level after each iteration 3 1 3 Condition specific Microarray Dataset 1 Initialize the gene system and simulate 1 000x7 rounds 2 randomly select a set of n genes each gene is randomly assigned to undertake one of the following actions e conc 0 V 0 i e down regulate e conc conc 2 and V V 4 i e up regulate 3 Repeatedly simulate the system 1 000x7 rounds 4 Obtain the gene expression level after each iteration 3 2 Experimental Noise Model Microarray is an inherently noisy te
3. directed graph ae EN Topological Distance undirected graph ere Sensitivity Recall te Specificity TE Precision TEF Table 4 Summary of reliability metrics of network inference methods TP true positive TN true negative FP false positive FN false negative n number of nodes 9 GNLab Options Summary Parameter Description e seeding the random number generator seed an integer to seed the random number generator g generating random network based on the CH model n number of genes ptrans Ptrans prob of horizontal gene transfer pdup Pdup prob of gene duplication pig Pig prob of ineteraction gain pil pa prob of interaction loss pgl Pg prob of gene loss mst mts maximum size of subgraph transferable pdr Par probability of duplication of regulator mc mc Maximum arc weight change pr Pr probability of retaining a duplicate interaction fileBase base name of the input file r generating random network based on the ER model fileBase base name of the input file numNodes number of nodes numArcs number of arcs f generating random network based on the SF model fileBase base name of the input file numNodes number of nodes pAdd probability of adding an arc between existing nodes u random perturbation of arcs fileBase base name of the input file add number of arcs to be added del number of arcs to be deleted outBase base name of the output file w produce random nu
4. similarity measures can be found at Table 4 Sensitivity specificity and precision are the commonly used criteria for assessing network inference reliability The topological distance is essentially a ratio of number of non matching edges false positive and false negative over all possible edge positions For example let s assume we are comparing the original graph A with an inferred graph B both having n nodes If there are two false positive arcs two arcs appeared in B but not in A and one false negative arc one arc appeared in A but not in B the number of non matching arcs is three The total number of all possible arc is n Therefore the topological distance is 3 The total number of 8 arcs for an undirect graph is different from an directed graph However it is expected that two randomly generated networks would have a non zero topological distance Therefore the theoretical topological distance for any two random networks are calculated and used as a base line for meaningful comparisons of network differences detailed calculation omitted for simplicity If a topological distance is larger than this expected distance it implies that the existence of systematic bias in the inference algorithm Two networks in gnl txt format can be compared through the command option c in GNLab A one line summary of network difference are printed onto the standard output Reliability Measure Description Topological Distance
5. 05 Cytoscape Shannon et al 2003 and pajek Batagelj and Mrvar 1998 respectively 7 Network Inference Although GNLab does not contain network inference functionality it provides util ity command option d to convert a ma txt file into an input file of other infer ence programs currently only available for ARACNe Margolin et al 2006 and Banjo http www cs duke edu amink software banjo 8 Network Comparison A network comparison method is implemented in GNLab to measure GRN inference reliability The objective of this network comparison step is to quantify how different two networks are e g the original and the inferred network The two networks are assumed to contain the same set of nodes Sharan and Ideker 2006 A set of machine learning performance metrics can be used to quantify how well a GRN is inferred from the data Four quantities are essentials in these metrics true positive count TP number of edges that are correctly inferred true negative edges count TN number of non interacting relationships inferred false positive count FP number of inferred edges that are not present in the original network and false negative count FN number of true edges that are not inferred A combination of some machine learning metrics sensitivity specificity and precision and the topological distance the one similar to Trusina et al 2005 is used to measure network similarity in GNLab A brief description of the four
6. User Manual for GNLab Joshua W K Ho and Michael A Charleston 3 School of Biological Sciences and School of Information Technologies University of Sydney Sydney Australia 3Sydney University Biological Informatics and Technologies Centre Sydney Australia January 17 2007 Correspondent author M A Charleston mcharleston it usyd edu au 1 Contents 1 Introduction 2 Network Generation 2 1 Modeling evolution of GRNs 2 oe ab oe wate eG se EPA G48 2 2 Generating Networks with GNLab 04 3 Simulation of Gene Expression Dynamics 3 1 Microarray Dataset Synthesis 0 22 0200204 ee 3 1 1 Time series Microarray Dataset 2 3 1 2 Gene Perturbation Microarray Dataset 3 1 3 Condition specific Microarray Dataset 3 2 Experimental Noise Model 4 2 soo Ae Aes 2 ea Se eee bs 3 3 Invoking Microarray Simulation in GNLab 4 Network Analysis Ast Topological Feat res i apna ts paas fa sat aa es iat a a aia een ea te og 5 Robustness Score 6 Network Visualization 7 Network Inference 8 Network Comparison 9 GNLab Options Summary 11 1 Introduction GNLab stand for Gene Network virtual Laboratory implements a computational pipeline for large scale analysis of gene networks The pipeline allows iterative experi ments on GRNs to be designed and carried out in a simple and flexible manner This framework consists of distin
7. a for normal ization by array t simulate time series of gene expression fileBase base name of the input file type type of microarray data d for deterministic or s for stochastic iter number of iteration tau T time step interval in the Euler s method perturbTime time of gene perturbation c simulate time series of gene expression fileBasel base name of the input file 1 fileBase2 base name of the input file 2 direct direct or indirect edges direct or undirect d microarray data file conversion fileBase base name of the input file type inference method aracne or banjo 11 References Ahmed A Dwyer T Foster M Fu X Ho J Hong S Koschutzki D Murray C Nikolov N Taib R Tarassov A and Xu K 2005 GEOMI GEOmetry for Maximum Insight In Proc 13t Intl Symp Graph Drawing pp 468 479 Albert R and Barabasi A L 2000 Topology of evolving networks local events and universality Phys Rev Lett 85 5234 5237 Barabasi A L and Albert R 1999 Emergence of scaling in random networks Science 286 509 512 Basso K Margolin A A Stolovitzky G Klein U Dalla Favera R and Califano A 2005 Reverse engineering of regulatory net works in human B cells Nature Genet 37 382 390 Batagelj V and Mrvar A 1998 Pajekprogram for large network analysis Connections 21 47 57 Erd s P and R nyi A 1959 On random graphs Publ Math Debrecen 6 290 297 Gansner E R and No
8. chnology Being able to incorporate a realistic amount of noise into the simulated microarray data is essential for a range of microarray analysis experiments By studying the structure of microarray noise at the DNA hybridization and the preparation level the noise in an oligonucleotide microarray has been shown to be signal intensity dependent Tu et al 2002 In general the stronger the signal the less the signal is affected by noise In this work a normal distribution of noise with standard deviation of Be I6 is applied to each signal with log intensity 6 The term is the noise coefficient which can be varied The higher the 8 the more noisy the data becomes 3 3 Invoking Microarray Simulation in GNLab In GNLab network simulation can be carried out using option t which generates a time series of gene expression Simulation results are written into a data file Time series gene perturbation and condition specific microarray datasets can be simulated from a network using the option s The number of technical and biological replicates can be specified as arguments The resulting data resemble the microarray data generated by a one channel oligonucleotide array The microarray data can optionally be log transformed and mean normalized per array The microarray data is stored in a ma txt file 4 Network Analysis 4 1 Topological Features A set of 11 commonly used topological features are calculated to characterize a GRN
9. ct functional components for network generation simulation analysis visualization inference and comparison By piping different components together in different ways many types of systems biology analyses can be carried out effectively Although the development of such a computational pipeline was inspired to assess limita tions of GRN inference methods this pipeline is designed for the general analysis of GRN structures and dynamics Analogous to running various experiments in a laboratory using a range of equipments GNLab provides a collection of computational tools that can be used for constructing various repeatable experiments The design principle of GNLab is that each functional component is invoked and controlled separately in a coherent manner Instead of gen erating analyzing and simulating a gene network in a single run GNLab is invoked several times and piped together by a simple user defined script e g using any scripting language such as Perl or Python Simple tab delimited text files are used for commu nication between each component GNLab is implemented in ASCII C and has a command line interface Individual components of GNLab are invoked by command line options For example the command GNLab a net1 reads in a text file net1 gnl txt and outputs a detailed summary of topological features in a file called net1 ana txt The command line option a specifies the action and any parameters following this option are the argume
10. ggle switch Proc Natl Acad Sci U S A 103 8372 8377 Trusina A Sneppen K Dodd I B Shearwin K E and Egan J B 2005 Functional alignment of regulatory networks a study of temperate phages PLoS Comput Biol 1 0599 0603 Tu Y Stolovitzky G and Klein U 2002 Quantitative noise analysis for gene expression microarray experiments Proc Natl Acad Sci U S A 99 14031 14036 Van den Bulcke T Van Leemput K Naudts B van Remortel P Ma H Verschoren A De Moor B and Marchal K 2006 SynTReN a generator of synthetic gene expression data for design and analysis of structure learning algorithms BMC Bioin formatics 7 43 Watts D J and Strogatz S H 1998 Collective dynamics of small world networks Nature 393 440 442 12 Index Charleston Ho model 3 Erdos R nyi model 3 Scale free model 3 ARACNe 9 Banjo 9 computational pipeline 1 gene duplication 3 GNLab 1 hub dominance 7 microarray condition specific 6 gene perturbation 6 noise 6 simulation 5 time series 5 network analysis 1 7 comparison 1 9 evolution 3 generation 1 growth model 3 inference 9 robustness 9 simulation 1 4 deterministic 4 stochastic 5 visualization 1 9 ODE 4 Perl 1 precision 9 preferential attachment 1 Python 1 recall 9 scale free network 1 sensitivity 9 small world network 1 specificity 9 topological distance 9 topological feature 7 13
11. in GNLab see Table 3 These features are used to describe the global and local network properties For global network statistics one can extract the number of gene n number of interactions per genes inter proportion of genes with self loops loop proportion of regulator genes reg number of disjoint network components comp proportion of the maximum component size mcs longest path length lpl longest directed path between a regulator and any other gene proportion of activation amongst all interactions act and hub dominance hubDom defined as the proportion of arcs connected to the top 5 of most connected genes compared to the total number of arcs For local properties they can be characterized by the average clustering coefficient cc and the number of feed forward loops per gene ff In particular hub dominance is a new topological feature used in GNLab Normally the importance of hub genes is characterized by the slope of a power law curve However fitting a power law curve to the out degree of a GRN may not be appropriate thus a new method of measuring hub usage is needed The idea of measuring the proportion of arcs connected to the top 5 of hub genes compared to the total number of arcs was used by Basso et al 2005 This work formally adopts this measurement as a topological feature for network analysis Topological features can be calculated using option a which calculates a range of topological features such a
12. ll network model by re wiring fileBase base name of the input file numRewire number of rewiring steps outBase base name of the output file a calculate network topological features fileBase base name of the input file n calculate network topological features for command line fileBase base name of the input file b calculate robustness score fileBase base name of the input file nKnock number of genes to be knocked out 10 Parameter Description v produce files for visualization fileBase base name of the input file format type of visualization file format dot for GraphViz xwg for GEOMI sif for Cytoscape and net for Pajek analysisOpt type of network analysis options inD for in degree and outD for out degree p decomposing a network fileBase base name of the input file type type of decomposition pos for positive arcs only neg for negative arcs only and undir for undirected graph s simulate microarray dataset from a GRN fileBase base name of the input file type type of microarray data numRep number of technical replicates numSample number of samples gapTime time gap between each time point tau T time step interval in the Euler s method noise microarray noise coefficient deter deterministic or stochastic simulation d for deterministic and s for stochastic analysisOpt preprocessing options combination of 1 for log transformation and n
13. nts of the call A list of GNLab command options can be found in Table 1 The first few sections of this manual explains the theoretical background of most of tools and the detailed usage of each option is explained in section 9 2 Network Generation A number of procedures have been suggested to generate networks that are topologically similar to real GRNs Current algorithms for generating GRNs are mostly mathematically motivated Since most biological networks exhibit both small world Watts and Strogatz 1998 and scale free Barab si and Albert 1999 Albert and Barabasi 2000 topology a preferential attachment growth model has been used to generate artificial GRNs Mendes et al 2003 An alternative approach is to generate a GRN by sampling a subset of genes and interactions from experimentally validated gene networks Van den Bulcke et al 2006 Despite being able to generate GRNs of the desired topology the success of this method depends on the validity of the source network None of these can effectively produce network structures that are topologically consistent with real GRNs 2 1 Modeling evolution of GRNs To overcome the shortcomings of the existing approaches a biologically motivated GRN evolution model comprising horizontal gene transfer gene duplication and gene muta tion is proposed The model is referred to as the Charleston Ho CH model Ho and Charleston in prep The CH model is probabilistic in nature Star
14. one line summary of topological features b Calculate robustness score V Generate input files for GraphViz GEOMI Cytoscape or Pajek p Process a network e g remove activation or repression Network Simulation S Simulate microarray data t Generate time series expression data Network Comparison C Calculate network topological differences Others d Convert microarray data into ARACNe and Banjo input files e Provide a seed number for the random number generator Table 1 Summary of command line options of GNLab Parameter Description n number of genes Ptrans probability of horizontal gene transfer Pdup probability of gene duplication Pig probability of interaction gain Pi probability of interaction loss Pg probability of gene loss mts maximum size of subgraph transferable Par probability of duplication of regulator mc maximum arc weight change Pr probability of retaining a duplicate interaction Table 2 Description of parameters for the Charleston Ho model a node insertion event the new node is inserted and linked preferentially to a highly connected node In an edge addition event an edge is randomly added between a pair of nodes which are preferentially highly connected In GNLab command line options r f and g are used to invoke the generation of random networks using the ER SF and CH model respectively The randomly generated network is written into a simple text file with extension gn1 txt This te
15. op e g A gt A proportion of regulator genes i e nodes with out degree gt 1 number of disjoint network components proportion of the maximum component size longest path length It represents the longest directed path between a regulator and any other gene An lpl of one means any regulator in the network can at most influence the expression of one other gene average clustering coefficient A high clustering coefficient signifies a high local edge density and therefore a dense local gene regulation proportion of activation amongst all interactions E g if act is greater than 0 5 than activation is a more important type of regulation compared to repression hub dominance which is defined as the proportion of arcs connected to the top 5 of most connected genes compared to the total number of arcs The higher the hub dominance the more important the hub genes are number of feed forward loops per gene Table 3 Descriptions of the 11 topological features used in GNLab robustness scores can be calculated by b The robustness scores are then summarized in a file with an rob txt extension 6 Network Visualization Network visualization is not explicitly performed in GNLab GNLab generates data files for other visual analysis programs Using GNLab command option v a network can be converted into a dot xwg sif and net file which can then be parsed into GraphViz Gansner and North 1999 GEOMI Ahmed et al 20
16. rth S C 1999 An open graph visualization system and its applications to software engineering Softw Pract Exper 00 S1 1 5 Hill A V 1910 The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves J Physiol Lond 40 iv vii Hofmeyr J H S and Cornish Bowden A 1997 The reversible hill equation how to incorporate cooperative enzymes into metabolic models Comput Appl Biosci 13 4 377 385 Ihaka R and Gentleman R 1996 R A language for data analysis and graphics J Comput Graph Stat 5 299314 Margolin A A Wang K Lim W K Kustagi M Nemenman I and Califano A 2006 Reverse engineering cellular networks Na ture Protocols 1 663 672 Mendes P Sha W and Ye K 2003 Artificial gene networks for objective comparison of analysis algorithms Bioinformatics 19 11122 11129 Shannon P Markiel A Ozier O Baliga N S Wang J T Ramage D Amin N Schwikowski B and Ideker T 2003 Cytoscape a software environment for integrated models of biomolecular interaction networks Genome Res 13 2498 2504 Sharan R and Ideker T 2006 Modeling cellular machinery through biological network comparison Nature Biotechnol 24 427 433 Thattai M and van Oudenaarden A 2001 Intrinsic noise in gene regulatory networks Proc Natl Acad Sci U S A 98 8614 8619 Tian T and Burrage K 2006 Stochastic models for regulatory networks of the genetic to
17. s degree distribution clustering coefficient distribution length of longest path The results are stored into a file with an ana txt extension The command line option n can be used to print a one line summary of the 11 topological features onto the console display The analysis results from the file can easily be parsed into statistical analysis packages such as R Ihaka and Gentleman 1996 5 Robustness Score The dynamic behaviour of a GRN can also be measured by a novel robustness score devised in this studied The network robustness can be estimated by the ability of a network to tolerate random gene perturbation using an in silico simulation procedure To calculate the robustness score a set of k genes is initially labeled as essential genes One thousand rounds of simulations are initially performed to bring the system to its steady state Then k mutant genomes are created by systematically knocking out one gene per mutant genome i e set X G 0 and V G 0 Each mutant genome is further simulated for 1 000 iterations If the expression of any essential gene in a mutant genome is dropped by more than 50 the mutant is non viable The robustness score is the proportion of viable mutant genomes over all possible single gene mutants In GNLab Feature Description n inter loop reg comp msc Ipl cc act hubDom number of nodes average number of interactions per node proportion of nodes with self lo
18. ting with a small seed network a network is grown by iteratively performing one of the evolutionary op erators according to their respective probability The growth process based on this CH model is governed by a set of ten parameters Table 2 2 2 Generating Networks with GNLab The two other commonly used network growth models are the Erd s R nyi ER model Erd s and R nyi 1959 and the Scale free SF model Barab si and Albert 1999 Networks generated by these two models have been used as benchmark datasets for evaluating per formance of GRN inference methods Mendes et al 2003 Along with the CH model these two growth models are also implemented in GNLab To construct a ER network with n nodes the model specifies that each of the e edges is randomly inserted between a pair of nodes The generation of a SF network relies on two parameters the number of nodes n and the probability of random edge addition paaa In the Scale free model either a node insertion or an edge addition event is performed in any one iteration In Option Description Network Generation g Generate a random Charleston Ho network r Generate a random Erd s R nyi network f Generate a random Scale free network u Add or remove a number of edges randomly W Produce a null model network with the same degree distribution Network Analysis and Visualization a Calculate network topological features n A produce a
19. xt file contains information about nodes edges and edge weights 3 Simulation of Gene Expression Dynamics The realistic simulation of the dynamic behaviour of an GRN is essential for simulation of microarray datasets Since microarray technology measures gene expression by the amount of mRNA present most modeling effect centred around the cellular mRNA level The level of mRNA molecules of a gene depends on two processes namely its synthesis from gene transcription and its natural breakdown The level of mRNA synthesis is in fluenced by the mRNA level of other genes as described by the Hill s kinetics Hill 1910 Hofmeyr and Cornish Bowden 1997 Hill s kinetics is a non linear model of gene to gene relationships It assumes the effect of all regulator genes to the target gene to be multi plicative Using the same model proposed by Mendes et al 2003 the dynamics of the GRN is modeled by a set of ordinary differential equations ODEs Assume that X G represents the level of mRNA of gene G and it is activated by genes Gy Ga Gam and repressed by genes Gr Gra lt Gra Constants Ka and K represent the expression levels of Ga and G respectively at which the effect on the target gene is half of its saturating value The Hill s constant n controls the sigmoidicity of the interaction curve V represents the basal transcriptional rate of gene G The rate law for mRNA synthesis can therefore be formulated as X Ga
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