User Manual
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1. null and visited 7 repeat 8 set position s count count count 1 9 set visited visited U s and s F s 10 if s visited then 11 current Attractor s 12 else 13 if attractor s 4 null then 14 currentAttractor attractor s 15 end if 16 end if 17 if currentAttractor null then 18 for all s visited do 19 attractor s lt current Attractor 20 end for 21 else 22 sts 23 end if 24 until currentAttractor NULL 25 end loop Algorithm 3 Compute the ATM matrix 1 initialize an empty matrix m A A lt 0 2 for alla Ado 3 for all s ado 4 for 1 0 s do a s mutation s i 6 mlattractor s attractor s lt mlattractor s attractor s 1 T end for 8 end for 9 end for 10 perform normalization of m 142. the generative algorithm can accept one further restriction for each node besides the root the number of its input or output edges can be fixed Basic generative algorithms to obtain the desired topologies are implemented in GESTODIFFERENT Networks of type i are fully random and are created by Erd s R nyi algorithm top panel of Algorithm 1 where U 1 v is a uniform number generated in 1 v and the algorithm returns V and E Networks of type ii are scale free and generated with a preferential attachment approach 2 A Barabasi Albert procedure is shown in bottom panel of Algorithm 1 In there U a b b a is a choice between either a b or b a with uniform probability i e 0 5 whereas R V is a random choice of an element from set V with non uniform probability i e node z is picked with probability p As for the other case the algorithm returns V and E The input parameters of these algorithms are set in the next Wizard step GeStoDifferent task editor 1 Input and Output Genetic functions in RBNs are modeled as boolean functions PROGNAME supports basic logical functions e g and or as well as canalizing and completely random functions 2 Topology A canalizing function is a function in which at least one of its inputs determines the function output You should select the percentage of boolean functions used 3 Network Settings in each RBN Also you can specify for some boolean functions a bias i
3. in the colonic crypts i e stem Paneth Goblet enterocytes and enteroendocrine in 8 In turn the matched networks have been used to define a multiscale model of crypt development 2 The model Noisy Random Boolean Networks Noisy Random Boolean Networks NRBNs 25 are a generalization of classical RBNs 17 19 a highly abstract and general model of GRN which was proven to reproduce several biological properties of real networks 27 28 26 Classical RBNs are directed graphs in which nodes represent genes and their Boolean value stands for the corresponding activation i e production of a specific protein or RNA or inactivation while the edges symbolize the paths of regulation A Boolean updating function is associated to each node and the update occurs synchronously at discrete time step for each node of the network according to the value of the inputs nodes at the previous time step Formally a RBN is determined by the two sets o i E 0 1 i 1 n Tf 0 1 S404 lis len where the former are n boolean variables and the latter n boolean functions For any node o the set J jk determines the topology of the network for that node and consequently for the overall RBN An execution of an RBN is a series of steps a 0 o 1 gt where o t is n dimensional boolean vector termed state of the network Given that the RBN has a finite state space i e there exist at most 2 vectors
4. networks As such the number of initial configurations an upper bound to the number of attractors and the number of flips i e mutations should be chosen as a compromise between accuracy and time of computing We remark that the real number of visited configurations is always greater than the starting configurations proportionally at the length of transient paths that leads to the attractor Algorithms to evaluate the transient to the attractor are defined in Appendix A Also in the computation of the approximated ATM algorithm in Ap pendix new attractors can be found when the mutation leads to a state that was not visited before The number of start configurations must be less or equal than 2 if n is the number of genes considered also and the number or mutations must be less or equal than n Finally we remark that for small networks exhaustive approaches are likely possible however the plugin is not optimized for this purpose so no support is provided by GESTODIFFERENT 4 5 Final panel output Each computational task is tracked by a progress bar in a task dialog Once the task is finished two tables are shown in Cytoscape Data Panel as shown in Figure 8 Top table summarizes the data of networks matching the differential tree Bottom table those discarded By clicking on some row the corresponding network is visualize within Cytoscape so its features can be exploited to perform other analysis on the network Also
5. progenies of different types through a stochastic differentiation process 72 Instead of focusing on a few master genes that would drive the systems as in one of the commons views in our model the differentiation properties are Email marco antoniotti disco unimib it strictly correlated with the dynamical properties of the underlying GRNs and in particolar with the stability of their steady states in presence of biological noise The general idea is that more differentiated cells would wander in a smaller portion of the phase space because of more refined control mechanism against possible perturbations and fluctuations 9 5 Furthermore the model in allows to relate lineage commitment trees with steady states hence allowing to match the stable states of a GRN against know differentiation trees e g hematopoietic cells 6 In this regard given an input differentiation tree the plugin allows to search for GRNs in terms of their Boolean network representation whose emergent behaviour is in accordance with the input tree in terms of the expected stability and dynamical trajectory The plugin is based on a generative approach i e GRNs are randomly created according to user defined features such as statis tical properties and topologies and a batch process accepts discard the GRNs matching the input lineage commitment tree The plugin has been used to find GRWNs describing the lineage commitment tree of cell populations
6. GESTODIFFERENT a Cytoscape plugin for the identification of Boolean gene regulatory networks describing the stochastic differentiation process Reference manual for version 1 0 Giulio Caravagna Silvia Crippa Alex Graudenzi Giancarlo Mauri Marco Antoniotti Department of Informatics Systems and Communication University of Milan Bicocca Viale Sarca 336 I 20126 Milan Italy 1 Introduction Describing the systems based characterization of cell differentiation i e the pro cess according to which the progeny of stem cells becomes progressively more specialized by developing in different cell types is one key goal of both systems and computational biology By using the dynamical model of cell differentia tion described in 30 i e a random Boolean network model we developed a Cytoscape plugin that address this theme In this approach was proven to reproduce several key properties of the main phenomena The model is general and is not referred to any specific organism or cell types and is mainly centred on the key concept of emergent dynamical behaviour of Gene Regulatory Networks GRNs The model can reproduce among other important properties i different degree of differentiation i e from totipotent multipotent stem cells to transit amplifying stages up to to fully differentiated cells 1 ii the important phenomenon of stochastic differentiation according to which a population of multipotent cells can generate
7. TN For a formal definition of how these sets are determined we refer the reader to 30 8 The biological metaphor In it is assumed that each TES of a NRBN represents a specific cell type characterized by a peculiar noise resistance as indicated by the relative threshold The degree of differentiation i e highly differentiated against less differentiated is related to the particular threshold or in other words to the possibility for the cell in its attractor to roam in a wider or smaller portion of the phase space i e the size of the TESs which decreases as the threshold increases At the best of our knowledge in fact less differentiated cells e g stem cells show fewer control mechanisms against noise e g copy errors and thus we characterize them by a smaller threshold allowing them for roaming in a wider portion of the phase space On the opposite cells in a more differentiated state present more refined control mechanisms and consequently are associated to higher thresholds which actually prevent random fluctuations 21 As an example in totipotent stem cells are associated with TESs at threshold 0 cells in a pluripotent or multipotent state i e transit amplifying stage or intermediate state with TESs with a larger threshold composed by one or more attractors while completely differentiate cells correspond to TESs with the highest threshold A generative approach for NRBNs An apriori choice of a specific NRBN d
8. all the information are exported to textual 10 4664 6027 5797 9379 4996 Network match click on row for view Network Gen Explored Space Attractors Se Attractors Nu ATM Generati Tree Generation Tree Deep Tree Leaf Comparison a 0030 0 0 0 0 0 0 0 0010 0 0 Network Gen Explored Space Attractors Se Attractors Nu ATM Generati Tree Generati Tree Deep Tree Leaf Comparison 0 0020 5395 0 0020 4180 0 67 1 0 0 0 0 0 0 0 633 0 0010 2 4 0 0 Network Gen Explored Space Attractors Se Attractors Nu ATM Generati Tree Generation Tree Deep Tree Leaf Comparison 0 0080 0 0020 0 0020 0 0010 4664 0 714 2 0 266 6027 0 691 2 0 271 2 0 0 5797 0 975 4 0 472 0 0010 4 0 0 5556 0 821 T a CET 2 0 0 F Node Attribute Browser Edge Attribute Browser Network Attribute Browser _ GeStoDifferent Figure 8 Screenshot version 1 0 Final panel output files if selected in first panel so that matched GRNs can be used in simulation environments external to Cytoscape References 1 B Alberts A Johnson J Lewis M Raff K Roberts and P Walter Molecular Biology of the Cell Garland Science fifth edition edition 2007 2 A L Barabasi and R Albert Emergence of scaling in random networks Science 286 509 512 1999 3 W Blake and et al Noise in eukaryotic gene expression Nature 422 633 637 2003 4 H Chang and
9. e dynamics of random boolean networks subject to noise attractors ergodic sets and cell types J Theor Biol 265 185 193 2010 26 R Serra M Villani A Graudenzi and S Kauffman Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data J Theor Biol 249 449 460 2007 27 R Serra M Villani and A Semeria Genetic network models and statisti cal properties of gene expression data in knock out experiments J Theor Biol 227 149 157 2004 28 I Shmulevich S Kauffman and M Aldana Eukaryotic cells are dy namically ordered or critical but not chaotic Proc Natl Acad Sci USA 102 13439 44 2005 29 P Swains and et al Intrinsic and extrinsic contributions to stochasticity in gene expression Proc Natl Acad Sci USA 99 12795 12800 2002 30 M Villani A Barbieri and R Serra A dynamical model of genetic networks for cell differentiation PLoS ONE 6 3 e17703 doi 10 1371 journal pone 0017703 2011 A Appendix Here follow the algorithms implemented in GESTODIFFERENT to e efficiently search for NRBN attractors Algorithm 2 e compute the ATN matrix Algorithm 3 13 Algorithm 2 Search of attractor 1 build a empty 2 1 dimensional vector attractor 0 2 1 2 loop 3 repeat 4 let s random 0 1 be a n dimensional Boolean random vector 5 until attractor s A NULL 6 set currentAttractor
10. e the desired ration between number of ones and zeros 4 Update Functions Functions Type Vi AND 5 Run Option Vor V CANALIZING _ ALL RANDOM Functions Bias Bias 0 5 Cancel Prev Figure 6 Screenshot version 1 0 Wizard step 4 update functions 3 shown in Figure 5 right panel In this panel the number of genes constitut ing each generated NRBN is to be given Also the average connectivity of each NRBN node can be set Since the NRBN is a directed graph the average is con sidering both incoming and outgoing connections If a fixed incoming outgoing number of connections has been selected then this is the number of connection here specified 4 3 Wizard step 4 update functions NRBN dynamics depend both on connections and on the update Boolean func tions that define the time evolution of the network configuration We remark that to each node a single Boolean function is associated as shown in Figure There are different types of Boolean function available in GESTODIFFERENT e AND OR functions are the standard A V Boolean operators on the input connection of the specific node e canalizing functions which use a specific input as canalizing input i e the nodes is active 1 as soon as the canalizing input does so a value of this input controls the whole output e all random functions which include all the possible randomly generated Boolean functions i e if n ge
11. ecting all the noise induced transitions between attractors This allows to draw the so called Attractor Transition Network ATN In this sense the ATN resembles a stability matrix of the system where its entries determine the prob ability of switching from one attract to another NRBNs rely on the assumption that the level of noise is sufficiently low to allow the system to reach its new or old attractor before another flip occurs Noise resistance a concept which determines the differentiation level of a cell driven by a NRBN is implemented by introducing the notion of threshold dependent ATNs A threshold is used to remove from the ATN those transitions that are considered too rare to occur i e some jumps are too rare to happen with a significant probability within the lifetime of the cell Accordingly a Threshold Ergodic Set TES in brief or TESs when 6 0 1 is the threshold is a set of attractors in which the dynamics of the system continue to transit in the 0 1650 p 0967 p 0207 Figure 2 Example ATN Each node represents a specific NRBN attractor inscribed number is the attractor s length The edges depict the transitions between attractors that occur after single flip perturbations of nodes with the corresponding frequency of occurrence long run due to random flips i e noise or using the graph theory terminology a strongly connected component SCC in the threshold dependent A
12. editor GeStoDifferent task editor 1 Input and Output 1 Input and Output Despite being all different and independently generated you can assign an Each RBN represents a Genetic Network with an arbitrary number of genes and a underlying topology to all the RBNs certain degree of connectivity resembling genetic interactions GeStoDifferent supports both random and scale free networks generation Also 2 Topology ingoing and outgoing connections can be arbitrarily fixed so to obtain hybrid 2 Topology You can here select how many genes you want to consider and the average RBN topologies connectivity In next panel you will decide the kind of interaction among genes 3 Network Settings Topology 3 Network Settings Option ow Jas Number of genes 4 Update Functions ir A yong j 4 Update Functions Average connectivity 5 Run Option T LT aea z 5 Run Option O Scale Free Random Generative algorithm Algorithm Erdos with Fix incoming connection Figure 5 Screenshot version 1 0 Wizard step 2 topology and 3 network settings e non root nodes must have at least one incoming edges e there must not be unconnected nodes i e the tree can not be partitioned To check out your tree you can use Cytoscape Tree Layout and watch if it is correctly rendered Output GESTODIFFERENT output consists on information and statistics concerning the NRBNS matching the input differentiation tree Outpu
13. et al Transcriptome wide noise controls lineage choice in mammalian protenitor cells Nature 453 544 548 2008 5 A Eldar and M Elowitz Functional roles for noise in genetic circuits Nature 467 167 173 2010 11 6 7 N Felli and et al Hematopoietic differentiation a coordinated dynamical process towards attractor stable states BMC Systems Biology 4 85 2010 C Furusawa and K Kaneko Chaotic expression dynamics implies pluripo tency when theory and experiment meet Biol Direct 4 17 2009 A Graudenzi G Caravagna G De Matteis G Mauri and M Antoniotti A multiscale model of intestinal crypts dynamics In Proc of the Ital ian Workshop on Artificial Life and Evolutionary Computation WIVACE 2012 number ISBN 978 88 903581 2 8 2012 K Hayashi and et al Dynamic equilibrium and heterogeneity of mouse pluripotent stem cells with distinct functional and epigenetic states Cell Stem Cell 3 391 440 2008 M Hoffman and et al Noise driven stem cell and progenitor population dynamics PLoS ONE 3 e2922 2008 M Hu and et al Multilineage gene expression precedes commitment in the hemopoietic system Genes Dev 11 774 785 1997 S Huang Reprogramming cell fates reconciling rarity with robustness Bioessays 31 546 560 2009 S Huang and et al Bifurcation dynamics in lineage commitment in bipo tent progenitor cells Dev Biol 305 695 713 2007 D Hume Probability in tra
14. hat follows we explain all the possible parameters for a GESTODIFFERENT session 4 1 Wizard step 1 input and output The first step input form consists of two different panels called Input and Out put as shown in Figure 4 Input differentiation tree As explained in previous section a differentiation tree is required as main input for GESTODIFFERENT The input differentiation tree can be loaded as an input sif or cyt file these files are obtained by saving a tree from a window on focus Alternatively by selecting the checkbox the tree is obtained by the focused window in the Cytoscape workspace By clicking Next a consistency check over the tree is performed and er ror messages are prompted if any GESTODIFFERENT tree loader uses edges direction to infer which node is the root The consistency check requires that e the tree root does not have incoming edges GeStoDifferent task editor 1 Input and Output Select the input and the output of this task The input differentiation tree can be given as an input SIF file or by focusing a Cytoscape network window 2 Topology The output folder if any will contain textual informations on the RBNs matching the input tree 3 Network Settings Input differentiation tree vi Use window with focus 4 Update Functions 5 Run Option Output folder _ Save matching networks to disk Figure 4 Screenshot version 1 0 Wizard step 1 input and output GeStoDifferent task
15. in 0 1 and the dynamics is fully deterministic starting from any initial state a 0 o1 0 0n 0 in at most z lt 2 steps the RBN will encounter an Figure 1 Example NRBN and attractors landscape In left the NRBN Boolean nodes represent genes either active or inactive and the edges regula tory pathways A specific Boolean function not shown here is associated to each node In right each node represent a state of the system i e the vector of the activation values of the genes and the edges display the transitions between the states according to the deterministic dynamics already visited state o z entering a limit cycle We term attractor of the RBN the loop starting from o z and the sequence of steps from o 0 to o z the transient of the attractor The set of initial condition that end up in a specific attractor o z is its basin of attraction The Noisy Random Boolean Networks NRBNs 30 was developed because noise plays a major role in numerous cellular phenomena and is supposed to drive the differentiation process ZO Classical RBN are fully deterministic and hence they do not properly ac count for noise However NRBN are built on top of RBN by introducing noise as unexpected jumps between network states Jumps are determined by flip ping genes state i e from active to inactive and viceversa possibly in an exhaustive way i e flipping each node in each state of each attractor and by det
16. n undoubtedly costly operation this is the only possible approach Once the suitable NRBNs are collected they can be used to define and analyze more complex models as done in 8 Notice that this approach assumes a generic differentiation tree and then can be used for any model which should account for the stochastic differentiation phenomenon 3 Setting up GeStoDifferent GESTODIFFERENT is fully tested with Cytoscape version 2 8 We do not provide support for other versions of the application GESTODIFFERENT is distributed under the terms of a BSD like license included in file COPYING of the software package More information on GESTODIFFERENT can be found at the project website GESTODIFFERENT version 1 0 is released as a JAR archive GESTODifferent 1 0 jar Two downloads options are possible i download from GESTODIFFERENT website and ii download from the Cytoscape App Store at http apps cytoscape org Installation Place the downloaded file in the Cytoscape plugin folder typi cally folder plugin within Cytoscape installation directory reboot Cytoscape At next start you will find the GESTODIFFERENT item under Plugins menu 4 Running a GeStoDifferent session GESTODIFFERENT sessions are batch computations which depend on user defined parameters Parameters are given by a step by step Wizard procedure input parameters include for instance a differentiation tree the RBNs struc ture and the analysis accuracy In w
17. nes connect to the reference node a random n x n 1 binary random table defines the function The percentage of nodes that will have a specific type of function is user defined A full coverage is required so we remark that the percentage must sum to 1 If canalizing or random fuction are chosen is the bias coefficient must be defined i e the ratio of the number of output set to 1 over the total number of input combinations GeStoDifferent task editor 1 Input and Output If the number of genes i a RBN is big examining all its possible initial configurations and mutations is computationally unfeasible Here you can decide whether you want a brute force approach suggested for 2 Topology small RBNs or you want to sample from the state space and test at most a fixed number of mutations 3 Network Settings Method Search for all states 4 Update Functions Search with sampling 5 Run Option Sampling Number of initial configuration Number of Mutation Tries Number of Nets 4 Cancel J Nex Finish Figure 7 Screenshot version 1 0 Wizard step 5 run options 4 4 Wizard step 4 run options This plugin is designed to i search for RBN attractors with a certain degree of exploration of the state space and ii to create the ATM matrix by performing flips of gene states Since the size of each gene is determined by the user it is advised to assume longer computation tasks for bigger
18. nscriptional regulation and its implications for leukocyte differentiation and inducible gene expression Blood 96 2323 2328 2000 T Kalmar and et al Regulated fluctuations in nanog expression mediate cell fate decisions in embryonic stem cells PLoS Biol 7 e1000149 2009 A Kashiwagi I Urabe K Kaneko and T Yomo Adaptive response of a gene network to environmental changes by fitness induced attractor selection PLoS ONE 1 e49 2006 S Kauffman Homeostasis and differentiation in random genetic control networks Nature 224 177 1969 S Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets J Theor Biol 22 437 467 1969 S Kauffman At home in the universe Oxford University Press 1995 J Kupiec A probabilist theory for cell differentiation embryonic mortality and dna c value paradox Speculations Sci Technol 6 471 478 1983 I Lestas and et al Noise in gene regulatory networks IEEE Trans Au tomat Contro 53 189 200 2008 12 22 H Mc Adams and A Arkin Stochastic mechanisms in gene expression Proc Natl Acad Sci USA 94 814 819 1997 23 T Peixoto and B Drossel Noise in random boolean networks Phys Rev E 79 036108 17 2009 24 A Raj and A van Oudenaarden Nature nurture or chance Stochastic gene expression and its consequences Cell 135 216 226 2008 25 R Serra M Villani A Barbieri S Kauffman and A Colacci On th
19. oes not guarantee the existence of the TES and thresholds corresponding to the ma s O 09 ex eee a ee o 08 oe A 0 0 15 i TES 15A 7 TES 15B i a3 TESo 15 B j ae on On aencacest a g eee lo bI J dae gt ne ma S 1 TESA TESC TESB t TES 15A NB T TEI parh SRG tte aca inde we ETTE poet Figure 3 Threshold dependent ATN and the tree like TES landscape The circle nodes are attractors of an example NRBN the edges represent the relative frequency of transitions from one attractor to another one after a 1 time step flip of a random node in a random state of the attractor performed an elevated number of times In this case we show three different values of threshold i e 6 0 0 15 and 6 1 TESs i e strongly connected components in the threshold dependent ATN are represented through dotted lines and the relative threshold is indicated in the subscripted index In the right diagram it is shown the tree like representation of the TES landscape which determines the differentiation tree for this NRBN desired differentiation tree i e Figure 2 In addition this would contradict our choice of not imposing specific detailed assumptions concerning the interaction which drive the modeled phenomena As a consequence in GESTODIFFERENT an acceptance rejection approach is used to determine which NRBNs match the input differentiation tree This is sometimes called model sweep and despite being a
20. t will be saved to numbered folders if a root folder is defined by the user We advise to use different paths for each GESTODIFFERENT task since matched networks are saved sequentially Every output file will contain structural information about the matched network number of nodes and network connectivity the list of thresholds the ATM matrix and the real bias Algorithm 1 Erdos R nyi and Barabasi Albert network generation algorithms 1 Erdos R nyt Algorithm 2 Input number of nodes v number of edges e 3 set V 1 2 v and E 4 for i 1 edo 5 let a U 1 v and b UJI v 6 if a b E then 7 E EU a b 8 end if 9 end for 1 Barabasi Albert Algorithm 2 Input number of initial total n n nodes average connectivity m 3 requires M lt n lt nF 4 set V 1 n and E 5 for all a b V do 6 amp E EUU a 6 4 5 a f 7 end for 8 fora njt 1 ny do 9 forz 1 4 m do 10 repeat 11 let p ki X_ k where k is the number of connections for node 7 12 set b R V and e U a b b a i3 until e E 14 E EU e 15 end for 1 VVU i 17 end for 4 2 Wizard step 2 topology and 3 network settings GESTODIFFERENT automatically generates NRBNs with shared structural prop erties In this version of the plugin two topologies are supported i Random and i Scale free as shown in Figure 5 left panel In addiction to the topol ogy
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