complete manual
Contents
1. 0 2 for all a Ado 3 4 5 6 7 8 for all s a do for i 0 gt s do s mutation s i m attractor s attractor s m attractor s attractor s 1 end for end for 9 end for 10 perform normalization of m 22 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 H H Chang M Hemberg M Barahona D E Ingber and S Huang Transcriptome wide noise controls lineage choice in mammalian protenitor cells Nature 453 544 548 2008 C Furusawa and K Kaneko Chaotic expression dynamics implies pluripotency when theory and experiment meet Biol Direct 4 17 2009 A Graudenzi G Caravagna G De Matteis and M Antoniotti Investigating the relation between stochastic differentiation homeostasis and clonal expansion in intestinal crypts via multiscale model ing PLoS ONE 9 5 e97272 2014 K Hayashi S M Lopes and M A Surani Dynamic equilibrium and heterogeneity of mouse pluripo tent stem cells with distinct functional and epigenetic states Cell Stem Cell 3 391 440 2008 M Hoffman H H Chang S Huang D E Ingber M Loeffler and J Galle Noise driven stem cell and progenitor population dynamics PLoS ONE 3 e2922 2008 M Hu D Krause M Greaves S Sharkis M Dexter C Heyworth and T Enver Multilineage gene expression precedes commi2. 14 Function table Gene name gene_37 Function type OR Bias value 0 9999847412109375 Used inputs gene_9 gene_11 gene_14 gene_18 gene_19 gene_21 aene 23 Figure 12 Functions Exploration 4 2 Functions Exploration This function allows the user to analyze the details of a specific updating function by se lecting a node of the chosen network and in the right click menu selecting Apps Explore node function CABERNET The same function is accessible from Apps CABERNET Functions Explore node function function The explores function view is composed by two tabs in the first Function summary some general information about the selected function likes the type and the inputs is provided In the second tab Function table there is the explicit representation of the function Figure 12 Note that the order of the genes in the input sequence represented in the truth table is the same defined in the summary tab 4 3 ATM view This function allows the user to display the Attractor Transition Matrix ATM of the se lected network The ATM describes all the possible transitions among attractors that are induced by user defined perturbations In order to show the ATM view it is necessary to choose a network view and select the Apps Show ATM CABERNET right click menu command The same functionality can be accessed from Apps CABERNET Functions Show attractor stability analysis Show Attractor Transition Matrix In the A
3. ew Attractor_graph_netw12 12 A a eoo TES_graph_7_threshold_0 0 0 035 S t eta network_6 A Pa es network_6 10 29 es Y f get Attractor_graph_netw39 0 39 0 a saa Network_7 network_7 10 29 N 001 os K Attractor_graph_netw8 0 8 0 P ee ATM network_7 ne N Al A2 A3 0 98 0 01 0 01 0 04 0 96 0 0 0 035 0 0 0 965 0 0 0 0 0 03 n lela Edge Table Network Table Threshold _ Collapsed view TES network Memory OK 6 Figure 13 ATM view view and TES graphs not collapsed on the left and collapsed on the right D A ea d aaa E tas fg Network Style Select Dynamic Network network_7 View i Gade iiaii em Uee A Big Labels BioPAX BioPAX_SIF o CABERNET Attractors CABERNET Collapsed TES SE VET o E CABERNET TES default default black Directed Minimal Nested Network Style o 9 z oo Wy f z eles Edge Table Network Table Figure 14 Styles each node is proportional to its degree The edges are oriented e CABERNET Attractors this style has been thought for the attractors graph The nodes are the network states that belong to a specific attractor and the edges corre spond to transitions among states e CABERNET TES complete graph e CABERNET TES collapsed graph 16 4 5 TES number chart This function allows the user to visualize the variation of the number of TESs with respect to different values
4. 17 17 17 18 20 21 Figure 1 Example RBN and attractors landscape In left the RBN Boolean nodes rep resent genes either active or inactive and the edges regulatory pathways A specific Boolean function not shown here is associated to each node In right each node rep resent 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 1 Introduction the theoretical framework CABERNET is a Cytoscape 3 2 0 17 app for the generation the simulation and the anal ysis of dynamical models of gene regulatory networks GRN In this current version GRNs are represented as Noisy Random Boolean Networks NRBNs 15 16 18 Classical RBNs 13 are conceived to represent the complex processes of gene regula tion in the simplest possible way GRNs are represented as directed graphs in which Boolean nodes represent genes either synthesizing their specific protein RNA or not and regulating the activation of other genes in complex combinations The value of the Boolean nodes is defined according to specific Boolean functions associated to each node which depend on the value of input genes In the original formulation the system is syn chronous and deterministic and each node of the network is updated simultaneously at each discrete time step Hence after a certain transient the dynamical trajectory of the system will neces
5. 19 a An avalanche is defined as the number of nodes whose activation pattern in the at tractor of the wild type network is different if compared to the pattern in the attractor of the perturbed one in a specific perturbation experiment b The sensitivity of a node is the number of times calculated for all the experiments where the status of that node in the original attractor is different if compared to its sta tus in the attractor reached through the perturbation This view is shown only if the avalanches and the sensitivity have been computed see Robustness analysis on section 4 8 The view is composed by two tabs one for the avalanches distribution and one for the sensitivity For the avalanches chart it is possible to choose the number of bins and to up date the chart by pressing the Update chart button It is possible to choose if compute the chart for only one network or for all the generated networks Note that this second fea ture is possible only if the robustness analysis has been performed for all the networks In the rightmost panel in both the tabs some statistics and indexes such as e g mean standard deviation are listed Also in this case it is possible to export the distributions data as csv files 20 Appendix main algorithms Algorithm 1 Erdos R nyi and Barabasi Albert network generation algorithms Erd s R nyi Algorithm 2 Input number of nodes v number of edges e 15 17 set V e
6. of threshold It can be accessed from the right click network menu se lecting Apps Show threshold dependent TES variation chart command or from Apps CABERNET Functions Show attractor stability analysis Show threshold dependent TES variation chart It is possible to choose the thresh old step and update the chart pressing the Update chart button Figure 15 4 6 Representative tree This functionality allows the user to visualize the representative tree with a defined depth derivable from the selected network figure 16 The representative tree of a network is the most frequently tree with the required depth obtained from the network The algorithm computes all the TES trees selecting all the possible ordered combinations of thresholds and at the end returns the most frequently emergent tree There are three different ways to define the required depth for the tree e Absolute in this case the inserted value is the real depth of the representative tree the value must be between 1 and the number of the attractors e Ratio of attractors in this case the inserted value is a ratio of the number of the attractors discovered for the selected network the value must be between 0 and 1 The real depth of the representative tree depends on the number of the attractors of the analyzed network e log2 n in this case the representative tree depth is obtained as lg n where n is the number of attractors discovered in the selected network
7. perturbation experiment for the same state this value must be greater than 0 If the selected perturbations type is flip it is necessary to set the number of nodes to flip at the same time in the same experiment It is also necessary to set the duration of the perturbations for each experiment the duration is determined ac cording to a uniform probability distribution between the minimum and maximum values If the selected perturbations type is knock in knock out it is necessary to set separately the number of knocked in and knocked out nodes at the same time and their relative durations 11 CABERNET task editor e gIMIB bioinformatics milano bicocca Tree from file Tree from Cytoscape M Select only the networks in which the emergent differentiation tree matches with an input tree Differentiation tree input file any format Network generation mode Match type Perfect match Topology and Functions Distance based selection Min distance Histogram distance Matching threshold 0 Sampling V Compute representative tree Experiment settings Tree depth Absolute Ratio of attractors Differentiation tree comparison log2 n Outputs Next Cancel Figure 9 Wizard E Differentiation tree comparison 3 5 Wizard E Differentiation tree comparison The tree matching input form is used in order to define all the parameters for the com parison of an input differentiation tree with the emerging tree as defined on
8. the basis of the stability of the attractors of the networks figure 9 This task is not mandatory and it is possible to select two different input methods for the tree either a from file or from b the selected Cytoscape view Once the tree has been defined it is important to choose the comparison distance to use e Perfect matching the original and the built trees must be identical and in the worst case all the possible trees from the same network are tested This method is ex tremely hard to perform NP Complete problem 19 e Threshold distance given a certain threshold and a distance type between a edit distance and b histogram distance only those networks in which the distance between the emerging and the input tree is below the threshold are selected Note if the threshold value has been set to 0 this is equivalent to the perfect match In this section is also possible to select the compute representative tree features If the function is selected the representative tree of each network will be computed For a more detailed description of this functionality see section 4 6 Tree file format The file format for the tree input is a simple blank separated values file defined as follows lt Differentiation tree description file gt level lt blank gt node_id lt blank gt parent Example lt Differentiation tree description file gt 0O 0 0 M N e he Aa Ww N e e e OoOO 12 CABERNET task editor 000 gIMIB O
9. 1 2 v and E for i 1 e do let a U 1 v and b U 1 v if a b E then E EUf a b end if end for Barabasi Albert Algorithm Input number of initial total n n nodes average connectivity m requires m lt nj lt nf set V lt l n and E lt for all a b V do E E U U a b b a end for fora n 1 nf do for i 1 m do repeat let p k kj where k is the number of connections for node 1 set b R V p and e U a b a until e E E lt Evfe end for VeVuU i end for 21 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 NULL 6 setcurrentAttractor null and visited 7 repeat 8 set position s count count count 1 9 set visited visited U s and s lt F s 10 if s visited then 11 currentAttractor lt s 1 else 13 if attractor s null then 14 currentAttractor lt attractor s 15 end if 16 end if 17 if currentAttractor null then 18 for all s visited do 19 attractor s currentAttractor 20 end for 2i else 22 ses 23 end if 24 until currentAttractor NULL 25 end loop Algorithm 3 Compute the ATM matrix 1 initialize an empty matrix m A A
10. CABERNET a Cytoscape app for Augmented Boolean modEls of gene Regulatory NETworks USER MANUAL Andrea Paroni Alex Graudenzi Giulio Caravagna Giancarlo Mauri and Marco Antoniotti Dept of Informatics Systems and Communication University of Milan Bicocca March 23 2015 Contents 1 Introduction the theoretical framework 2 CABERNET installation and settings 3 CABERNET Wizard 3 1 Wizard A Network Generation Mode 3 2 Wizard B Topology and Functions Jr Wizard C oamp 4 but aoe bee Save we Oe Sue So 3 4 Wizard D Experiment settings 3 5 Wizard E Differentiation tree comparison S30 Wizard Pe OUDS oa amp amp aio att amp dyed Se e s Gi Se 4 CABERNET functions in Cytoscape Active Window 4 1 Cytoscape Network Panel 4 2 Functions Exploration 644 4 846 Soe 7 25k 4 SA So Be GeV NTCWN enmar 1h a ih Geek San ee i de Bo dh Bn ee Pe Se Bee SOU VMS ct Mou a eran by ye ss Ot sete ob deci oe Bagh ieee epee Gres A gt ES numer Chat 4 40 5 5 ye data 6 uy a es Me 4 6 REPresemldlive ree moar goi pede Sree a bk Se SG 4 7 Dynamical properties analysis 4 8 Robustness analysis 02 0 0000 4 8 1 Robustness analysis report avalanches and sensitivity Appendix main algorithms to whom the correspondence should be addressed a paroni campus unimib it 10 11 12 13 14 14 15 15 15
11. GRNML is the CABERNET and GRNSim i e the stand alone terminal version of CABERNET output format This format stores all the network structure features such as the network nodes edges and functions GRNML network definition file format An example of the file format for the spec ification of the network complete or partial structure and functions is the following lt graph topology ScaleFree nodes_number 10 gt lt node id 0 name gene_O gt lt function type canalizing inputenumber 2 gt lt input_node gt 5 lt input_node gt lt input_node gt 8 lt input_node gt lt input_node gt 3 lt input_node gt lt canalizing_input gt 5 lt canalizing_input gt lt canalizing_input gt 8 lt canalizing_input gt lt bias gt 0 5 lt bias gt lt entry input 11 output 1 gt lt entry gt lt entry input 00 output 0 gt lt entry gt lt entry input 01 output 1 gt lt entry gt lt entry input 10 output 1 gt lt entry gt lt f uncti n gt lt node gt Other node definitions lt edge source 0 destination 6 gt lt edge gt lt edge source 0 destination 7 gt lt edge gt lt edge source 1 destination 4 gt lt edge gt Other edge definitions lt graph gt PANEL 2 When required the user will be asked to insert the structural parameters to generate the networks in two possible ways e From input form option In this c
12. TM view the ATM shows the network with all the transition probabilities This view offers also the possibility to create a Threshold Ergodic Set graph TES graph and a corresponding view with a specific threshold value given a certain threshold all the transitions that are characterized by a frequency below the threshold are removed and a pruned transition network is shown Note that the threshold value must be between 0 and 1 There are two different types of TES graphs a the complete and b the collapsed one In the complete graph all the states of each attractor are displayed as nodes and there are two types of edges the state to state transition and the attractor to attractor transition In the latter type the edges show the transition probabilities and the edge width is pro portional to that probability The collapsed view shows each attractor as a unique node and only the transitions edges are displayed Figure 13 4 4 Styles CABERNET allows to use several ad hoc network styles selectable from the style tab in the control panel Figure 14 e CABERNET Network this style has been thought for the representation of NRBNs The color of the nodes is defined on the basis of the functions type and the size of 15 ee se 2 et mw Qqag amp tas t GC sve Network No Ed network_3 10 29 Attractor_graph_netw25 0 25 0 sea Network_4 network_4 10 ee Attractor_graph_netw19 kai cea Nnetwork_5 fs y network_5 10
13. The number of networks to generate and simulate with common structural features will be included at this step 3 2 Wizard B Topology and Functions If required in the following section the topological properties of the networks and those relative to the updating functions will be defined Figure 5 In particular the input form includes the following parameters PANEL 1 Number of nodes This property is used in order to define the total number of nodes of the network If the network is partially defined this number includes both the added and the original nodes PANEL 2 Network topology This property is used in order to define the topology of the network The topology defines the arrangement of the various elements of a network such as nodes and edges CABERNET allows to use all the following topologies Erd s R nyi random ingoing topology Erd s R nyi random outgoing topology If this topology has been selected the succeeding required parameter is the number of edges to add The implemented model uses directly the number of edges and not the edge probability Fixed number of inputs Erd s R nyi random outgoing topology If this topology has been selected the succeeding required parameter are the number of inputs for every node The actual number of added edges will be nodes inputs Barabasi Albert s preferential attachment Scale free If this topology has been se lected the succeeding required parameters are
14. There are two distinct strategies for the attractor search a the Brute force and b the Partial sampling With the Brute force sampling method all the possible initial states of the system are simulated on the other hand with the Partial sampling method only a random subset of the possible initial states are tested The first choice is advised only for small networks note that in a Boolean network all the possible initial states are 2 4 s For both the CABERNET task editor gIMIB Sampling bioinformatics milano bicocca Sampling of the initial configurations Partial Initial configuratons to simulate 10000 Network generation mode Maximum number of simulation steps simulation cutoff 1 means unrestricted search Topology and Functions Sampling Experiment settings Differentiation tree comparison Outputs Cancel Figure 7 Wizard C Sampling 10 CABERNET task editor gIMIB Sampling b 10 l nfor m atics M Compute the stability matrix of the attractors Attractor Transition Matrix ATM milano bicocca Perturbation type Node Flip 1 gt 0 0 gt 1 Network generation mode Number of random nodes to flip in each perturbation experiment 1 Mininum duration of the perturbation 1 Topology and Functions pollosy Maximum duration of the perturbation 1 Sampling Experiment settings Differentiation tree comparison Number of randomly selected single multiple node perturbations for each
15. This functionality can be accessed from the right click network menu selecting Apps Compute representative treeor from Apps CABERNET Functions Compute representative cree 4 7 Dynamical properties analysis This functionality allows the user to visualize several statistics regarding the dynami cal behaviour of the networks a the attractor length distribution b the distribution Step 0 0001 Update chart 3 Ww tt Ww _ ui 2 o 2 2 3 2 0 4 0 5 0 6 Threshold Figure 15 TES number chart 17 ose Session New Session Control Panel Network Style Select Dynamic Network Network Nodes Edges sea Network_1_file_1 network_1_file_1 40 0 58 0 Attractor_graph_network_1 file_1 14 0 14 0 Tree_d3_n0 14 0 13 0 gaa Network_2_file_1 network_2_file_1 40 0 58 0 Attractor_graph_network_2_file_1 14 0 14 0 gaa Network_3_file_1 network_3_file_1 40 0 58 0 Attractor_graph_network_3_file_1 14 0 14 0 Tree_d3_n0 17 3 16 2 Tree_d3_n1 17 0 16 0 Tree_d3_n2 20 0 19 0 gaa Network_4_file_1 network_4_file_1 40 0 58 0 Attractor_graph_network_4_file_1 14 0 14 0 gaa Network_5_file_1 network_5S_file_1 40 0 58 0 Attractor_graph_network_5S_file_1 14 0 14 0 Network network_3_file_1 Tree depth _ Absolute e Ratio of the attractors Log2 n Dutco Degree Norma State name 0 Compute telelsumeis Edge Table Network Table Attractors Lengt
16. ape Network Panel network view creation e Networks Cytoscape views Creates a Cytoscape network object for every matching network e Attractors network Cytoscape views Creates a Cytoscape network object for every attractors network An attractors network is a graph where the nodes are N RBN states and the edges connected two reachable states This network shows the at tractors and their states e All trees Cytoscape views Creates a view for all the representative tree that can be obtained from each network This feature is visible only if the compute represen tative tree property is set in the Wizard E Differentiation tree comparison panel see section 3 5 4 CABERNET functions in Cytoscape Active Window Once the networks have been created and the simulation is completed several impor tant functions implemented in CABERNET are available directly in the Cytoscape active window 4 1 Cytoscape Network Panel In the network panel all the generated networks are listed namely 1 the simulated NRBNs 2 the relative Attractor networks i e the representation of all the network config urations belonging to the attractors that have been found during the simulation Each node in this network is a network configuration i e a state vector and each edge represents a transition between states In order to create the Cytoscape view it is necessary to right click the selected network and choose the Create View command Figure 11
17. ase the user will be asked to insert the structural properties of the networks step by step with an interactive form e From txt text file option The features file is a blank separated text file in each row a property with its relative value are defined txt network features file format An example of the file format for the specification of the structural features of the networks is the following lt simulation features file gt topology ScaleFree nodes 100 algorithm BarabasiAlbert k 3 ni 4 in gul probability 045 completely defined functions no CABERNET task editor g M B Features bioinformatics milano bicocca Power law exponent Average connectivity Network generation mode Add feature Topology and Functions Feature Value 100 topology Erd s R nyi random ingoing topology Power law based Sampling Experiment settings Differentiation tree comparison Outputs Cancel Figure 5 Wizard B Topology and Functions panel 2 Function type Boolean bias type 0 4 bias value 0 6 or type 0 2 and type 0 2 canalized type 0 2 sampling method Partial Initial conditions 10000 max Simulation times 1 how many nodes to perturb 1 ratio of states to perturb 0 9 mutation type Flip min duratlion of perturb 1 max duration of perturb 1 max net to test 10000 atm computation yes tree matching no avalanches sensitivity computation no unmatching store no PANEL 3
18. attractor state Outputs Ratio of randomly selected attractor states in which performing the perturbations 0 5 Next Cancel Figure 8 Wizard D Experiment settings panel 1 strategies a cutoff value number of iterations for a single initial state is required but it can be ignored if set equal to 1 If the Partial sampling method is selected it is necessary to set the number of initial states to test it must be between 0 and 2 4 5 3 4 Wizard D Experiment settings The next input frame is needed to define the perturbation parameters and the types of experiments to perform Figure 8 PANEL 1 First the user is asked to choose whether compute the Attractor Transition Matrix ATM which represent the stability matrix describing the transitions among the attractors as a consequence of perturbations of various types e Type of perturbations Two types of perturbations are possible Flips a flip is the negation of the value of a node e g if the value of the is 0 the flip sets it to 1 Knock in and Knock out regardless of the real value of the perturbed node this perturbation sets it to 1 i e knock in or to 0 i e knock out The ratio of attractors states to perturb value expresses the number in ratio of states of each attractor to use for the perturbations experiments this value must be be tween 0 and 1 e The Number of experiments for the same node value expresses the number of times to repeat a
19. d the analysis settings In what follows we explain all the possible parameters for a CABERNET session 3 CABERNET Wizard The wizard is divided in six different sections representing the main simulation and analysis stages namely e Network Generation Mode e Topology and Functions e Sampling e Experimental Settings e Differentiation Tree Comparison e Outputs CABERNET task editor gIMIB bioinformatics milano bicocca Select the generation mode of the Gene Regulatory Network GRN model Generate random networks NRBNs by explicitly specifying the structural features either via file or form Generate networks completely defined via grnml file s Network generation mode Augment the topology and functions of networks partially defined via gnrml files by explicitly specifying the structural features either via file or form Augment the topology and functions of partially defined networks retrieved from the Cytoscape network Topology and Functions a Sampling Experiment settings Differentiation tree comparison Outputs Next Cancel Figure 4 Wizard A Network Generation Mode 3 1 Wizard A Network Generation Mode The first section of the Wizard named Network Generation Mode consists of different panels as shown in Figure 4 PANEL 1 In the first panel of the section the user is asked to define the network generation mode among the following e Generate random networks NRBNs by
20. esent less differentiated cells e g toti and multi potent stem cells and which by increasing the threshold breaks into some disjoint and smaller TESs i e intermediate stages until at the highest levels of the threshold all the attractors are also TESs standing for fully differentiated cells In this way it is pos sible to define a hierarchy among cell types which identify a specific differentiation tree see Figure 3 The model can reproduce among other key properties i different degree of differ entiation i e from totipotent multipotent stem cells to transit amplifying stages up to to fully differentiated cells 1 iz the phenomenon of stochastic differentiation accord ing to which a population of multipotent cells can generate progenies of different types through a stochastic differentiation process 9 2 8 For a more detailed description of the RBN and NRBN models please refer to the wide relative literature as e g 14 Oo 0 15 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 tran sitions 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 6 0 15 and 6 1 TESs i e strongly connected components in the thres
21. etwork diameter number of attractors in the network average attractors lengths the tree distance and the thresholds sequence if the tree comparison is performed e The attractors lengths in a CSV file Each row contains all the lengths of the found attractors e The basins of attraction sizes in a CSV file Each row contains all the sizes of the basins of attraction The exporting frame can be reached from the right click network menu selecting Apps Export CABERNET command or from Apps CABERNET Export option It is possible to export only the selected network or all the networks at the same time It is also possible to visualise in the Cytoscape active window 13 Session New Session meaaqag t Create View Destroy Views Attractor_graPh Destroy Network ir saa Network_3 network_3 Rename Network Attractor_graph Apply Style si network_4 Show Hide Graphics Details network_4 TOOT 290 Attractor_graph_network_4 193 193 sia Network_ network_S 100 297 Attractor_graph_network_5 123 123 saa Network_6 network_6 100 294 Attractor_graph_network_6 39 0 39 0 saa network_7 network_7 100 296 Attractor_graph_network_7 8 0 8 0 saa network_8 Table Panel D gz o D m f z shared name Gene n Function Incomi Outco Degree Norma ene 0 aene 0 Rando 14 16 30 1 0 SESA Edge Table Network Table Figure 11 Cytosc
22. explicitly specifying the structural fea tures either via file or form This option allows to specify all the network struc tural parameters for network generation Each simulated network will be randomly created before the successive tasks e Generate networks completely defined via grnml file s This option allows to load completely defined networks from GRNML files that will be successively sim ulated In this case the user can specify only the experiment and output features The user can select more than one network and the entire simulation process will be performed for each net e Augment the topology and functions of networks partially defined via gnrml files by explicitly specifying the structural features either via file or form This option allows to load a partially defined network which CABERNET will aug ment according to the specified structural features We remark that an incomplete network is a network with only a subset of nodes edges or functions defined The user can select more than one network and the entire simulation process will be performed for each of them e Augment the topology and functions of partially defined networks retrieved from the Cytoscape network view This option allows to load the network directly form the current selected view on Cytoscape As in the previous case the loaded network will be completed with other nodes or edges and functions as defined by the user in the succeeding steps
23. fficient control mechanism against possible genomic perturbations and random fluctuations 7 11 5 6 3 10 Formally consider a NRBN with m attractors and let A with 7 1 m be the i th 0 0975 0 0081 Figure 2 Example Attractor Transition Network Each node represents a specific NRBN attractor inscribed number is the attractor s length The edges depict the transitions be tween attractors that occur after single flip perturbations of nodes with the correspond ing frequency of occurrence attractor of the network and let A be the set of such attractors An attractor A is di rectly 6 reachable from another A i j 1 m i j if at least a fraction 6 of different flip perturbations on singles states of A leads the system when it is in attractor Aj to A A Threshold ergodic set TES is a set of attractors with the following properties 1 any attractor member of the TES is 6 reachable from any other attractor belonging to the set it is an ergodic set in the ATN 2 given that threshold value there are no outgoing connections from any member of the TES toward an attractor not belonging to it In the model TESs represent cell types characterized by a specific differentiation degree as that indicated by the threshold i e gene activation patterns in which the cell can wander due to random perturbations So at 6 0 one typically has a unique TES composed of many interconnected attractors which repr
24. g D Ramadge N Amin B Schwikowski and T Ideker Cytoscape a software environment for integrated models of biomolecular interaction networks Genome Res 13 11 2498 504 2003 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 Kaizhong Zhang Rick Statman and Dennis Shasha On the editing distance between unordered la beled trees Information Processing Letters 42 3 133 139 1992 23
25. hold dependent ATN are represented through dotted lines and the relative threshold is indicated in the subscripted index In the right dia gram it is shown the tree like representation of the TES landscape which determines the differentiation tree for this NRBN On the basis of this theoretical framework CABERNET presents a range of different simulation and analysis functions e Network generation a Random networks with specified structural properties Given the key pa rameters CABERNET can generate and simulate ensembles of random network with shared features b Augmentation of partial networks Given partially defined networks as in put e g from publicly available dataset or known GRNs CABERNET can augment the networks according to key structural and topological parameters e Network simulation The attractor landscape and the properties of the attractors of the networks can be extensively investigated e Network selection Given an input differentiation tree the app allows to search for NRBNs whose emergent behaviour is in accordance with the input tree in terms of the expected stability and dynamical trajectory The app is based on a generative approach i e NRBNs are randomly created according to user defined features such as statistical properties and topologies and a batch process accepts discard the GRNs matching the input lineage commitment tree e Robustness analysis Different kind of perturbations can be perfo
26. hs cESis oe s eteteces Oscillating Nodes Ratio Bins 10 M All networks Update Chart Export CSV file Basins of attraction distribution Mean 13742 0230 Std dev 17736 7279 Median 7826 0000 Geo Mean 4845 5782 N N w Min value 62 0 Frequency Max value 80561 0 Mid range 40249 5000 Ei Kurtosis index 5 1151 10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000 Basin of attraction dimension Observations 87 Figure 17 Dynamical properties analysis of the basins of attraction and c the ratio of oscillating nodes over fixed value nodes This function can be accessed from the right click network menu selecting Apps Show network dynamical properties or from Apps CABERNET Functions Show network dynamical properties The dynamical properties analysis is composed by three dif ferent tabs one for each measure For the attractor length distribution and for the dis tribution of the basins of attraction it is possible to choose the number of bins to use and the set of networks on which performing the analyses either the selected networks or all of them In the rightmost panel some further standard statistics and indexes such as e g mean standard deviation etc are listed It is also possible to export the data as a csv file using the Export CSV file button Figure 17 4 8 Robustness analysis With CABERNET it is possible to perform a robustness analysis over the simulated net w
27. orks To this end it is necessary to use the dynamic perturbations form accessible from the right click network menu selecting the Apps Perform robustness analysis 18 9 Dynamic Statistics tions Permanent mutations Perturbations type Node Flip 1 gt 0 0 gt 1 Perturbation duration Min 1 Max 1 Number of nodes 1 M Use specific genes Specify the name of the nodes to perturb separated by a comma symbol gene_l gene_5 gene_7 Number of randomly selected single multiple node perturbations for each attractor state Ratio of randomly selected attractor states in which performing the perturbations M Repeat for all the networks Cancel Figure 18 Robustness analysis temporary perturbations tab avalanches and sensitivity command or from Apps CABERNET Functions Perform robustness analysis avalanches and sensitivity Figure 18 Two kinds of perturbation experiments are available a Temporary mutations and b Permanent mutations e Temporary perturbations Different parameters are required a type of perturbation 1 flips 2 knockin knockout b duration of the perturbation randomly defined at each experiment accord ing to an uniform distribution probability between the minimum and the maxi mum values c number of nodes perturbed at each perturbation d number of states of each attractor in which repeating the perturbation ex periment expressed as ratio of states e number different perturbation e
28. rmed on the net works and the relative stability can be subsequently assessed via robustness analy ses for instance by analyzing measures such as avalanches and sensitivity e Network analyses A wide range of statical and dynamical properties of the simu lated network can be analyzed with CABERNET e Visualization The powerful visualization capabilities of Cytoscape can be used to analyze the topological and dynamical properties of the simulated networks 2 CABERNET installation and settings CABERNET is fully tested with Cytoscape version 3 2 0 We do not provide support for other versions of the application CABERNET is distributed under the terms of a BSD like license included in file COPYING of the software package More information on CABERNET can be found at the project website http bimib disco unimib it index php CABERNET CABERNET version 1 0 is released as a JAR archive CLAPERNET 1 0 TAr Two downloads options are possible i download from CABERNET website and ii download from the Cytoscape App Store at Heit acps cylosceane ord Installation CABERNET can be installed using the App Manager service reachable at Apps App Manager Install from file Running a CABERNET session CABERNET sessions are batch computations which depend on user defined parameters Parameters are given by a step by step Wizard pro cedure input parameters include for instance a differentiation tree the NRBNs structure an
29. sary end up in a cycle at most of unitary length which represent an attractor of the network see Fig 1 Different initial conditions lead to the same attrac tors which represent different gene activation patterns that a cell with a unique genome is able to display possibly standing for different phenotypic functions 12 Since the model of RBNs is deterministic random perturbations representing biolog ical noise have been successively introduced in terms of temporary i e flips or per manent i e knockin knockout perturbations thus speaking of Noisy Random Boolean Networks Perturbations allow to identify noise induced transitions among the attrac tors thus defining a stability matrix also called Attractor Transition Network ATN see Fig 2 Following 18 4 NRBNs allow to define a dynamical model of cell differentia tion i e the process according to which the progeny of stem cells becomes progressively more specialized by developing in different cell types The model is general and is not referred to any specific organism or cell types and is grounded on the key concept of emergent dynamical behaviour In particular the differentiation properties are correlated with the dynamical properties of the underlying GRNs and in particular with the sta bility of their attractors 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 e
30. th high incoming degree nodes Five types of functions are available Bias based random functions e And e Or CABERNET task editor g M B Network augmentation provide the features of the network to be augmended bioinformatics milano bicocca Total number of nodes 0 Total number of edges 0 Fixed number of inputs 1 Note 1 not considered Network generation mode 9 Exclude the following nodes from source or destination node sets Each gene name must be separated by a comma Source genes Target genes Topology and Functions Sampling Replace the undefined functions with Experiment settings Function type Boolean Completely defined functions Differentiation tree comparison Random bias based 0 4 Logical AND 0 2 Logical OR 0 2 Random canalyzing 0 2 Bias value 0 5 Outputs Cancel Figure 6 Wizard B Topology and Functions for the network augmentation process e Canalizing functions In the wizard it is necessary to set the ratio of each function type to use Note that the sum of all the ratios must be equal to 1 Note for the augmentation process the Topology and Functions panel is lightly different from what presented above but the same information are required Figure 6 3 3 Wizard C Sampling Once the structure of the networks has been defined the next step is the sampling set tings figure 7 First of all it is necessary to set all the parameters for the attractor search
31. the number of initial nodes it must be between 0 and the number of nodes of the network the average connectivity and the ratio of incoming outcoming edges Erd s R nyi random ingoing topology Power law based outgoing topology Scale free If this topology has been selected the succeeding required parameters are the Power Law exponent and the average connectivity Note that in this case the scale free dis tribution will be obtained as outcoming degree distribution Fixed number of inputs Power law based outgoing topology Scale free If this topol ogy has been selected the succeeding required parameters are the average connec tivity the Power Law exponent and the number of inputs required for all the nodes Watts Strogatz small world topology If this topology has been selected the succeed ing parameters are the average connectivity and the edge switching probability this second parameter must be between 0 and 1 PANEL 3 Updating functions Once the topology of the network has been selected the next step is the definition of the updating functions First of all it is necessary to select the type of the functions in this version only boolean function are allowed Completely defined functions property means that each function will be completely de fined for all the possible input sequences the output value is produced during the net work creation process Note that it is dispirited to set this property on for networks wi
32. tment in the hemopoietic system Genes Dev 11 774 785 1997 S Huang Reprogramming cell fates reconciling rarity with robustness Bioessays 31 546 560 2009 D A Hume Probability in transcriptional regulation and its implications for leukocyte differentiation and inducible gene expression Blood 96 2323 2328 2000 T Kalmar C Lim P Hayward S Mun oz Descalzo J Nichols J Garcia Ojalvo and A Martinez Arias 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 A Kauffman Homeostasis and differentiation in random genetic control networks Nature 224 177 1969 S A Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets J Theor Biol 22 437 467 1969 T P Peixoto and B Drossel Noise in random boolean networks Phys Rev E 79 036108 17 2009 A S Ribeiro and S A Kauffman Noisy attractors and ergodic sets in models of gene regulatory net works J Theor Biol 247 743 755 2007 R Serra M Villani A Barbieri S A Kauffman and A Colacci On the dynamics of random boolean networks subject to noise attractors ergodic sets and cell types J Theor Biol 265 185 193 2010 P Shannon A Markiel O Ozier N S Baliga J T Wan
33. utputs bioinformatics cytoscape views milanobicocca M Attractors Network V All trees Network generation mode i Select the files to export Output directory Select directory Topology and Functions Networks grnml Networks sif ATM csv Sampling Attractors csv States in each attractor csv Synthesis file csv Experiment settings Attractor lenghts csv Basins of attraction csv F as Note that all the other CABERNET functions are acessibled from the Cytoscape application menu bar Differentiation tree comparison Outputs Next Cancel Figure 10 Wizard F Outputs 3 6 Wizard F Outputs The last input form concerns the outputs to export figure 10 In particular it is possible to export separate files for the following objects e The network in a GRNML file GRNML file is the standard input output format for CABERNET e The network in a SIF file e The ATM matrix in a CSV file e The attractors in a CSV file each row is an attractor and the comma separated sequences in each row are the attractor s states e States in each attractor in a CSV file in each row there are the states its attractor and its position in the basin of attraction The first row of this file can be Partial or BruteForce and defines the sampling type used in the simulation e The synthesis file It is a CSV file with some data and statistics network id clus tering coefficient average bias average path length n
34. xperiment For the knock in knock out type it is necessary to set all the parameters separately Also by selecting the Use specific genes flag it is possible to set the specific nodes to perturb in a comma separated names list e Permanent perturbations In this case the user can 1 set the nodes to knock in or knock out listing their names in a comma separated list in the correct box 2 choose a number of randomly chosen nodes to perturb Note that both the perturbation types temporary and permanent are performed at the same time in each experiment When the computation will be completed a the dynamic perturbation analysis view will be shown The robustness analysis can be performed for the selected network or for all the gener ated networks Repeat for all the networks checkbox selected 19 e0oe Dynamic Perturbations Statistics Dataset All ition Sensitivity Bins 15 Update chart Export CSV file Avalanches distribution Mean 39 4332 6 000 Std deviation 16 7900 5 000 Median 41 0000 Geo Mean 0 0000 Min Value 0 0000 Frequency Max Value 52 0000 Mid Range 26 0000 Kurtosis index 0 6503 5 20 25 30 35 40 45 50 Avalanches dimension Observations 30500 Figure 19 Robustness analysis report avalanches distribution tab 4 8 1 Robustness analysis report avalanches and sensitivity This view allows the user to visualize two types of distributions avalanches and sensi tivity Figure
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