FCModeler User`s Manual
Contents
1. lt nodeFigure node a coord 145 0 102 0 gt lt nodeFigure node b coord 154 0 182 0 gt lt edgeFigure edge el coords 46 30384824371398 39 255371240230595 39 0 86 0 36 0 182 0 40 983984375000006 248 45312500000006 gt lt edgeFigure edge e3 coords 55 74 65254934210526 88 453125 gt lt edgeFigure edge e7 coords 64 121 59381461183149 82 19148 7053735959 gt lt edgeFigure edge e2 coords 43 50 07136821892032 39 35616514650896 gt lt edgeFigure edge e4 coords 76 45 26993534482756 248 453125 gt lt edgeFigure edge e5 94 67187900213835 158 14967821435278 gt 6932 766600647095 30 0331 91L666CGl 74 61 0 52 0 65 0 64 0 F0080770148686 34 984392638123198 84 0 51 0 109 0 72 0 935261853 1 14286 248 453125 5120 199 0 54 0 103 0 148 5 115 546875 68 0 152 0 56 0 204 0 coords 81 693359375 115 546875 84 0 134 0 89 0 148 0 lt edgeFigure edge e6 coords 105 97348484848486 168 625 103 0 149 0 99 0 135 0 93 78728924749427 125 94634448249002 gt lt edgeFigure edge e8 coords 146 3546875 115 546875 148 0 132 0 149 0 142 0 150 5711534974295 154 569227979436 gt lt edgeFigure edge e9 coords 141 21599264705884 197 5234375 140 0 199 0 137 0 202 0 134 0 204 0 115 0 218 0 83 0 237 0 65 60492910952841 247 60675054297047 gt lt coordinates gt lt mappings gt lt mapping type node gt lt atom property type value dna gt lt attributeValue attribute2. connective atom composite gt lt ELEMENT connective EMPTY gt lt ATTLIST connective type and or REQUIRED gt gt lt layout gt lt rank label rank1 gt lt atom property type value typel gt lt rank gt lt rank label rank2 gt lt atom property type value type2 gt lt rank gt lt rank label rank3 gt lt atom property type value type3 gt lt rank gt lt cluster label AandB gt lt composite gt lt atom property label value a gt lt connective type or gt lt atom property label value b gt lt composite gt lt cluster gt lt cluster label BandF gt lt composite gt lt atom property label value e gt lt connective type or gt lt atom property label value f gt lt composite gt lt cluster label OnlyG gt lt atom property label value g gt lt cluster gt lt eluster gt lt layout gt The lt ranx gt tag is used to specify the nodes that should be placed in a certain horizontal rank Each rank has a label specified by the 1abe1 attribute which is shown on the left hand side of the graph view Nodes are selected using the same type of XML as in the property to visual attr bute mappings see the Mappings section above Similarly the lt ciuster gt tag 1s used to specify nodes to place in a cluster Each cluster is surrounded by a rectangle and has a label specified by the 1abe1 attribute which is shown
3. node shape value ellipse gt lt mapping gt lt mapping type edge gt lt atom property type value regulate gt lt attributeValue attribute connector end value filled rectangle head gt lt mapping gt lt mappings gt lt graph gt lt nodeProperties gt type location lt nodeProperties gt lt node id u 1 gt dna loci lt node gt lt node id v gt rna locl lt node gt lt node id w gt molecule loc2 lt node gt lt node id z gt molecule loci lt node gt lt node id a gt enzyme loc2 lt node gt lt node id b gt enzyme locl lt node gt lt edgeProperties gt type strength lt edgeProperties gt lt edge id el tail u 1 head v directed true gt regulate 1 0 lt edge gt lt edge id e3 tail u 1 head w directed true gt regulate 1 0 lt edge gt lt edge id e7 tail u 1 head a directed true gt convert 1 0 lt edge gt lt edge id e2 tail v head u 1 directed true gt regulate 1 0 lt edge gt lt edge id e4 tail w head v directed true gt regulate 1 0 lt edge gt lt edge id e5 tail w head z directed true gt catalyze 1 0 lt edge gt lt edge id e6 tail z head w directed true gt convert 1 0 lt edge gt lt edge id e8 tail a head b directed true gt convert 1 0 lt edge gt lt edge id e9 tail b head v directed true gt convert 1 0 lt e
4. 3 below shows a graph layout done using the simple dot layout IA FCModeler cycleTest xml a 0 x file view layout graph properties Sal AIAS Bo Figure 3 Simple dot layout 4 2 Rank Cluster Dot Layout Dot can also be used to compute a more customized layout Based on their values of certain node properties the node figures can be placed on horizontal ranks or into clusters When a graph is open in FCModeler select the dot rank cluster layout menu item from the layout menu An open file dialog box is then shown and a layout XML file must be selected see below Figure 4 below shows the same graph as in Figure 3 using the rank cluster layout O x VA FCModeler rankClusterTest xml file view layout graph properties 198 4849 BO 1ANAD rankl rank2 ranks Figure 4 Rank cluster dot layout 4 2 1 Layout XML File The ranks and clusters for the rank cluster layout are specified in a layout XML file The XML file used n the layout for Figure 4 1s shown below lt xml versione 1 0 lt DOCTYPE lt ELEMENT lt ELEMENT lt ATTLIST standalone yes gt rank cluster gt atom composite gt label CDATA FREQUIRED gt lt ELEMENT cluster atom composite cluster gt lt ATTLIST cluster label CDATA FREQUIRED gt lt ELEMENT atom EMPTY gt lt ATTLIST atom property CDATA REQUIRED value CDATA REQUIRED gt lt ELEMENT composite atom composite
5. B see the Selecting Node and Edge Figures section above To create a subgraph when some nodes and or edges are selected either select the create subgraph menu item from the graph menu or click the l toolbar button The subgraph creation dialog box is then shown as in Figure 11 below This dialog allows the user to select one of the subgraph creation algorithms described above Making a selection and clicking the ok button opens a new FCModeler window showing the subgraph ENTE Algorithm Selection E x algorithms 8 all edges connecting selected vertices gt closed p th neighborhood of selected vertices O all vertices incident with a selected edge gt all selected vertices amp all selected edges with both end vertices selected Co em Figure 11 The subgraph creation dialog box 8 1 2 Strongly Connected Components A digraph D is strongly connected if every vertex of D is reachable from every other vertex of D The strongly connected components SCC s of a digraph D are the maximal strongly connected subdigraphs of D The SCC s are useful to analyze because every node in an SCC is reachable from every other node in the same SCC 22 The algorithm for finding the SCC s of a digraph D is extremely simple and 1s based on two modifications of depth first search DFS 1 Compute an acyclic ordering of the nodes using DFS 2 Compute the converse D of D 3 Perform DFS on D usi
6. a directed graph This approach is implemented in FCModeler a bioinformatics tool and uses the JSOMap package for self organizing maps An example with real world data is used to show the effectiveness of the SOM in finding clusters of similar cycles Once the SOM algorithm is finished the results are viewed n another window This map view window shows a grid of small graphs one for each unit of the map Each graph represents the model for that particular map unit The models are just the generalized median of the set of cycles assigned to that map unit as presented earlier Figure 14 below shows an example of a 4 by 4 SOM applied to a larger graph Node color and edge thickness are used to show the weights of the nodes and edges of the models Brighter red corresponds to higher weights of the nodes while thicker lines correspond to higher weights of the edges As Figure 14 shows it can be a bit difficult to fully examine the model graphs in the map view Clicking on one of the graphs in the map view puts it in an additional FCModeler window for easier analysis A good cluster of cycles can be seen in Figure 15 below which 1s a view of the model graph in the bottom left map unit of Figure 14 This model represents ten individual cycles All cycles contain the nodes ACC synthase ACC ethylene CTR1 EIN2 EIN3 senescence NIT2 and IAA Note the dark red color of these nodes and the edges between them showing the maximum weight value Also note
7. graph or on head node Modify the tail or head node of an edge Left click to select the edge then left click and drag the blue rectangle on either end of the edge snap blue rectangle to new tail or head node Delete an edge Ctrl right click on an edge Moving To be written 13 5 3 1 Adding To add a new edge to the graph hold down Ctrl and left click on the tail node of the edge Then release the mouse button on either an empty portion of the graph or on the head node of the edge If the button 1s released on an empty portion of the graph the head end of the edge can be placed on the head node as described in the next section 5 3 2 Modifying To move the tail or head end of an edge to a new tail or head node first select the edge by left clicking on it Then left click and drag the blue rectangle at the desired end of the edge until it snaps to the new tail or head node 5 3 3 Deleting To delete an existing edge hold down Ctrl and right click on the edge The edge will then be removed from the graph 5 3 4 Moving Nodes and edges can be moved in the graph by first selecting the element In the figure below the highlighted node has been selected and moved The edges move along with the node unfortunately the result is often very strange looking The edges can be moved by selecting the edge then manipulating the control points which are shown as blue boxes Once an acceptable view has been created the coordinates
8. lt time n n4 gt lt mapping type node gt lt atom property label value w gt lt attributeValue attribute fill value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e5 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n5 gt lt mapping type node gt lt atom property label value z gt lt attributeValue attribute fi11 value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e6 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n6 gt lt mapping type node gt lt atom property label value w gt lt attributeValue attribute fill value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e4 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n7 gt lt mapping type node gt lt atom property label value v gt lt attributeValue attribute fill value 1 0 0 0 1 0 gt lt mapping gt lt time gt lt animation gt The mapping rules are specified at individual time points A lt time gt tag represents each time point and the n attribute defines which point in time the tag represents The lt mapping gt tags within the l
9. of the nodes and edges can be saved LA FCModeler cycle Test12 xml file view layout graph properties Fl FCModeler cycle Testi 2 xml fle view layout graph properties en ANAL Bo aa aa Ag Be i I f Figure 6 shows the manipulation of node and edge objects in FCModeler 14 __ JF2s xj Lookin grape ANO BS 5 animationTestxml werte to file 3 eyeleTest umi ri coordinates 5 cycleTest1 0 Ci mappings Py cvyeleTestt 1 xml l rl topology 5 cuclelestl xrl 5 cyctleTest2 xml cycleTests xml A eset Tet ae File name icycleTestl 2coord xml Save Files of type FCModeler Graph xml z Cancel Figure 7 shows how to save graph coordinates using the save function under the File menu 9 4 Zooming FCModeler supports zooming of the graph view to examine the graph in varying levels of detail To zoom in either select the zoom in menu item from the view menu or click the amp toolbar button To zoom out either select the zoom out menu item from the view menu or click the toolbar button 9 9 Panning For large graphs the FCModeler window may not be large enough to view the entire graph Thus FCModeler supports panning to view different areas of a large graph The scrollbars on the bottom and left side of the FCModeler window control panning in the horizontal and vertical directions respectively 5 6 Finding a Particular Node To find a particular no
10. on the upper left of the cluster The lt ciuster gt tag uses the same node selection mechanism as the lt ranx gt tag lt cluster gt tags can be nested inside each other creating nested clusters as shown in clusters EandF and OnlyG above 4 3 GEM Layout s Additional layout options are also featured GEM AGEM FastGEM These algorithms are modeled off code developed by the Tulip project www tulip org 10 GEM This is the standard layout as detailed in A Fast Adaptive Layout Algorithm for Undirected Graphs by Frick Ludwig and Mehldau This code s a Java translation of the Frick s implementation in C code GEM turns every node into an electron and every edge into a stretched spring and places a gravitational force at the barycenter of the layout A node is attracted to all nodes adjacent to it and is repelled by every node whether or not it is connected by an edge In addition there is an attractive gravitational force between each node and the barycenter of the graph GEM has three main loops the insertion loop the arrangement loop and the optimization loop The insertion loop is where the nodes are initially placed The closer a placement is to the final layout the faster the arrangement loop runs The arrangement loop does most of the work getting the nodes to their final positions Following the example of Tulip we did not implement the optimization loop Figure 5 Example of a GEM layout 11 AGEM This is the new s
11. the table represent the different values that are present in the graph Note that there s not an entry for each individual node or edge in the table only for the different property values that the nodes and edges possess The visual attributes are shown in a list on the right side of the window To create a mapping first select a property value from the table Then double click on the desired visual attribute Another window will open allowing you to select the value of that visual attribute Clicking ok creates the mapping applies it to the graph view and adds it to the list of mappings on the left side of the Mapping Editor To delete a mapping rule simply left click on the rule in the list and press the Delete key on the keyboard Mapping rules can be created with multiple property values For instance nodes with a value of molecule for the property type and a value of loc1 for the property location can be assigned to the value of ellipse for the visual attribute node shape Thus only nodes with both property values will be shown as ellipses Nodes with only one property value but not the other will be unaffected by the mapping rule To create this type of mapping select multiple property values from the table by holding down Ctrl and left clicking The and and or radio buttons determine how the property values are combined in the example given n this paragraph the and button wo
12. 168 625 103 0 149 0 99 0 135 0 93 78728924749427 125 94634448249005 gt lt edgeFigure edge e8 coords 148 0 42 546875 148 0 132 0 149 0 142 0 150 57115349742952 154 56922797943605 gt lt edgeFigure edge e9 coords 141 21599264705884 197 5234375 140 0 199 0 137 0 202 0 134 0 204 0 115 0 218 0 83 0 237 0 119 41225756327451 250 72921186812 gt lt coordinates gt The lt noderigure gt tag provides the coordinate of the center of the node figure for the node given by the node attribute Similarly the lt eagerigure gt tag provides the bezier control point coordinates of the edge figure for the edge given by the edge attribute Coordinates are specified as XVii A2Ya ves Mao Vn gt The DTD for the topology XML is given by lt ELEMENT coordinates nodeFigure edgeFigure gt lt ELEMENT nodeFigure EMPTY gt lt ATTLIST nodeFigure node CDATA REQUIRED coord CDATA REQUIRED gt lt ELEMENT edgeFigure EMPTY lt ATTLIST edgeFigure edge CDATA REQUIRED coords CDATA REQUIRED gt gt This DTD must be included at the beginning of the XML file 1f the file contains coordinate information 3 1 2 Example of a Complete XML File The following shows a complete graph XML file containing topology mapping and coordinate information lt xml version 1 0 standalone yes gt lt DOCTYPE graphFile lt ELEMENT graphFile graph mappings coordinates gt lt ELEMENT coordinates n
13. FCModeler User s Manual Version 1 0 September 2002 Written by Zach Cox Julie Dickerson Adam Tomjack Copyright Julie Dickerson lowa State University 2002 Table of Contents l 2 3 4 5 8 IntoauelHon to RE MOI een nk l Sone Up POMOC CIS orrein a aa aio l 2 1 petting up the FE Modeler Conna Bil aa ae ees l Zo RUNM RONDAS id l DOULCES Ole MPU Euer l 3 1 E E a a A l 3 1 1 AMI POMO l 31 2 Example or a Complete XML Files i aa e 5 3 1 3 Openine a Graph AML Fie ai a aio 6 3 1 4 Savino 2 Gra DONE Pla ee een 7 3 1 5 paving a JPEG mais OF the Graph nee 8 32 NMOL Database 8 A A A ee 8 4 1 Simple DOLL o ad ieee ai but 8 AD Rank Cluster Dot LaySul eu ae ek 9 4 2 1 EXAMEN aa 9 4 3 CEM Layon S nio 10 Interactino with the Graph VIW ua u 12 5 1 Seleelins Node and Bdge PIU ana 12 52 Node PAUSA ie 13 Sl IN as antes E E Bee 13 32 2 DO ee ikea 13 5 2 3 MOVIDO et re 13 5 3 Bdse Rinteln 13 5 3 1 A Raia ot arena grace ctv Rae Reni dt are OE 14 3 3 2 MOI een 14 5 3 3 Delta rasen 14 5 3 4 AN PE ae cet nen 14 A ee ena eee Monee rn 15 3 5 Panne se neigt 15 3 6 Finding a Particular Node alli ada 15 A a N 15 6 1 Node and Edge Properties me Nie 15 6 1 1 Property VIC WEE ae 16 6 2 Visual Attributes of Node and Edge Figures cccccccccnnnnnnnnnnnnonnnnnncnnnnnnnnnnnnnnnnnonononanannos I7 6 3 Using Visual Attributes to Visualize Properties o oooooooooooooccccncconnnonnnnnnnnnononononananon 17 6 4 Creating Mappin
14. Map view showing results of the SOM algorithm Each graph shows the model of the corresponding map unit which 1s the generalized median of the cycles assigned to that MAN UI nea 26 Figure 15 Full view of the bottom left map unit showing ten cycles clustered together 27 111 1 Introduction to FCModeler FCModeler models and visualizes metabolic networks as graphs Nodes of the graph represent specific biochemicals such as proteins RNA and small molecules or stimuli such as light heat or nutrients Edges of the graph capture regulatory and metabolic relationships found in biological systems FCModeler can dynamically display user specified graphs and animate the results of different modeling algorithms on the graph The fuzzy cognitive map modeling software is currently written in Matlab and interfaces with FCModeler via xml graph files We plan to translate this software at a later date 2 Setting Up FCModeler The FCModeler distribution 1s compatible with Windows 2000 XP and Linux machines Download the file and unzip into your directory This version 1s already compiled and the Java source code 1s included If you make any improvements to the code please send the updated modules back for inclusion n the next distribution FCModeler requires the installation of Java 1 3 x It does not currently work with Java 1 4 2 1 Setting up the FCModelerConfig File This file contains the path information for finding the dot layout p
15. T 2001 Durham North Carolina Dickerson J A Z Cox et al 2001 Creating Metabolic and Regulatory Network Models using Fuzzy Cognitive Maps North American Fuzzy Information Processing Conference NAFIPS Vancouver B C 10 2 Open Source Code Used in FCModeler Dot graph layout routine from the Graphviz package of AT amp T http www research att comsw tools graphviz Diva framework graph nodes and edges http www gigascale org diva Java SDK 1 3 x http Java sun com j2se 1 3 Tulip GEM Routine for graph layout http www tulip software org 28
16. These algorithms described below are also closely coupled with the graph view to visually present their results 8 1 1 Subgraph Creation For a digraph D V E a digraph H is a subdigraph of D if e V H CV D e E H c ED E H v u e E D v u V H In other words all of the nodes of H must be in D all of the edges of H must be in D and the edges of H must have both end nodes in H For a given digraph D V E a subdigraph H can be created in several ways e Given a set of nodes W lt V D o V H W o E H v u e E D v u eV H o H consists of some subset of nodes of D and all edges in D with both end nodes in that set e Given a set of nodes W c V D and an integer p 21 o V H NBlwW E H v u e E D v u e V H o N2 W is defined as the closed p th neighborhood of W Saving W and all nodes visited on directed paths of length p from each node in W forms the set o Nei Ne JUN WUN UUN W i 0 p o NyP W N 6 zed y LN 0 and N W is defined similarly l e Given a set of edges Bc E D o V H veV D v e v u E H o E H B o H consists of all end nodes of the edges in B and all of the edges in B e Given a set of nodes W c V D and a set of edges B c E D o V H W o E H v u e Blv u eV A o H consists of all nodes in W and all edges in B with both end nodes in W In FCModeler the selected node and edge figures in the graph view represent the node and edge sets W and
17. de in a graph select the find node menu item from the view menu A dialog box will appear asking for the label of the node After entering it and clicking ok the view will center on the node and it will be selected 6 Mappings 6 1 Node and Edge Properties The nodes and edges of the graph can have multiple properties associated with them For example node properties could be type or organelle while edge properties could be type or strength In this way the properties serve to provide information about what the nodes and edges of the graph represent 15 Each individual node and edge of the graph then has a specific value for each property For example values for the node property type could be gene RNA protein environmental factor etc Values for the edge property type could be conversion regulation catalyst etc FCModeler does not restrict the properties or values that a graph may possess They are determined from either the graph XML file or the MySQL database see the Graph XML Files and MySQL Database sections for more details 6 1 1 Property Viewer The Property Viewer can be used to observe the property values of specific nodes and edges in FCModeler To open the Property Viewer select the property viewer menu item from the properties menu The Property Viewer as seen in Figure will then be shown Sl E Es property viewer locat
18. dge gt lt graph gt lt graphFile gt 3 1 3 Opening a Graph XML File To open a graph XML file in FCModeler either select the open graph file menu item from the file menu or click the Figure 1 toolbar button The open graph dialog box will then be shown as in MH a on Om E Head from file o _ coordinates mappings 5 animationTestsml gt b024cyc1 cm 7 bigmap xml gt bigmapCycles xml 5 cycleTestxml gt cycleTesta xml topology File name Open Files of type FC Modeler Graph lt mb Cancel Figure 1 The open graph dialog box Since any graph XML can contain topology mappings or coordinates in any combination the dialog box allows the user to select which information is read from a specific file The checkboxes on the right side of the dialog configure the information to read from the XML file For instance if a graph is already open in FCModeler selecting only the mappings from an XML file that contains both mappings and topology will only read the mappings and apply them to the current graph Also reading a file of coordinates for an already open graph will reposition the node and edge figures appropriately 3 1 4 Saving a Graph XML File To save the current graph to an XML file either select the save graph menu item from the file menu or click the 4H toolbar button The save graph dialog box will then be shown as in Figure Ze Look in C
19. es can be mapped to the visual attributes of node and edge figures These mappings can be defined in an XML file An example with three different mappings 1s given below based on the graph specified in the Topology section above lt mappings gt lt mapping type node gt lt atom property location value loc2 gt lt attributeValue attribute fill value 0 2 1 0 0 4 gt lt mapping gt lt mapping type edge gt lt atom property strength value 1 0 gt lt attributeValue attribute color value 1 0 0 2 0 0 gt lt mapping gt lt mapping type node gt lt composite gt lt composite gt lt atom property location value loc1 gt lt connective type and gt lt atom property type value molecule gt lt composite gt lt connective type or gt lt atom property type value enzyme gt lt composite gt lt attributeValue attribute node shape value ellipse gt lt mapping gt lt mappings gt The lt mappings gt tag surrounds all of the mappings in the XML file Each individual mapping is specified by a lt mapping gt tag with the type attribute specifying if it is a node or an edge mapping Each mapping represents a statement of the form If location equals loc2 then fill equals the RGB color value 0 2 1 0 0 4 More complex statements like If either location equals loc and type equals molecule or type equals enzyme then shape equals ellipse can also be defined There
20. fore each mapping consists of two parts the specification of property value s and specification of a visual attribute The lt attributevalue gt tag specifies the visual attribute and value of the mapping The lt atom gt tag represents an individual property value the property and value attributes provide the details The first example in the preceding paragraph is shown above in XML as the first mapping The lt composite gt tag is used to join two property values together by an AND or an OR logical connective specified by the lt connective gt tag Composites can also be nested inside each other to create complex mapping statements The second example in the preceding paragraph is shown above in XML format in the third lt mapping gt tag The DTD for the topology XML 1s given by lt ELEMENT mappings mapping gt lt ELEMENT mapping atom composite attributeValue gt lt ATTLIST mapping type node edge REQUIRED gt lt ELEMENT atom EMPTY gt lt ATTLIST atom property CDATA REQUIRED value CDATA REQUIRED gt lt ELEMENT composite atom composite connective atom composite gt lt ELEMENT connective EMPTY gt lt ATTLIST connective type and or REQUIRED gt lt ELEMENT attributeValue EMPTY gt lt ATTLIST attributeValue attribute CDATA REQUIRED value CDATA REQUIRED gt This DTD must be included at the beginning of the XML file if the file contains mapping informatio
21. graphs x 5 El fe DD rite to file 7 _ coordinates _ mappings B animation estxrnil Ly bO 4cye g xml Y bigmap xm bigmapCycles xml cycleTestxml E cytleTest2 xml w topology File name Save Files of type FEModeler Graph lt ml od Cancel Figure 2 The save graph dialog box FCModeler can write the current topology mappings or coordinates in any combination to a graph XML file The checkboxes on the right side of the dialog control the information that is written to the file 3 1 5 Saving a JPEG Image of the Graph FCModeler can also save the current graph view in JPEG format This is useful for creating an image file of the entire graph which can then be viewed in a web browser or inserted into some other document To create a JPEG image of the graph view select the save as jpg menu item from the file menu 3 2 MySQL Database To be written 4 Graph Layout To view a graph a graph layout algorithm must compute positions of the node and edge figures Many different graph layout algorithms exist FCModeler currently uses Dot and GEM to compute its layout 4 1 Simple Dot Layout There are two types of layout that can be computed by Dot The first is a generic layout called the Simple Dot Layout When a graph is opened in FCModeler either select the dot layout menu item from the layout menu or click the e toolbar button to use the simple dot layout Figure
22. gs Using the Mapping EditoT o ooooooooooononccccncncnnnnnnnnnnnononononononanoos 18 AA ae 19 7 1 ANSE ACE OT a O E er 19 2 COR dol 21 Graph Theoreuc OP el 21 8 1 1 SUDSTaPh CTE AMON ani ae 21 8 1 2 Strongly Connected Components ais 22 11 8 1 3 Ecler 23 8 1 4 Cycle AMES e a 24 82 Alternate Paths between Nodes nta ae a a a 25 8 3 Cl sterine Cy CLES asustada did 25 WG IWIGGC ICE andino 28 10 PRC SINC 6 OOOO OPE race tsa E O EE A A 28 19 1 Publications relating to FEModeler esse ra E 28 192 Open Source Code Used 5 PC Model Ct wen aan 28 List of Figures Pigure The Open eraphrdialos Dr aaa a 7 Figure 2 The Save graph dialog Bora aan a ea A 7 Figure 3 Simple COU LAY OU na A A A A OT Ad 8 Figure 4 Rank cster dot layout eisrean I 9 Figure S Example ora GEM layout ti 11 Figure 6 shows the manipulation of node and edge objects in FCModeler 14 Figure 7 shows how to save graph coordinates using the save function under the File menu 15 Figure 8 Property viewer showing property values of selected nodes and edges 17 PUSO MAPAS lot ee paesitde ee 18 Figure 10 Animanon cr lamented A da 21 Figure 11 The subgraph creation dialog box ccccccccsssssesssssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 22 Figure 12 Example of selecting cycles and strongly connected components as subgraphs 23 Figure 13 Tne cycle search alalo o OOK un ner eu 24 Figure 14
23. id e3 gt lt cycle gt lt cycle gt lt node id v gt lt edge id e2 gt lt node id u 1 gt lt edge id e1 gt lt cycle gt lt cycles gt 24 This XML is extremely simple Each cycle is surrounded by a lt cycie gt tag and consists of alternating lt node gt and lt edge gt tags The nodes and edges are identified by the ia attributes in the lt node gt and lt edge gt tags These cycle XML files can also be re opened in FCModeler at a later time To do this select the open cycle file menu item from the graph menu The cycles in the XML file are then shown in a list Note that the cycles must be present in the current graph in FCModeler 8 2 Alternate Paths between Nodes One common problem is to find alternate paths between nodes This feature 1s being added into FCModeler and should be available with the next release 8 3 Clustering Cycles Cycles obtained from directed graphs may be similar to each other based on their node and edge content Thus clustering algorithms may be used to find natural groups of similar cycles Prior to clustering a distance metric and generalized set median must be defined for the objects to be clustered Several possible representations for the cycles are discussed including strings graphs and weighted sets Weighted sets are chosen because of the simplicity of the associated metric and median Self organizing maps are used to find the clusters of cycles obtained from
24. ion strength Figure 8 Empty property viewer The Property Viewer shows the property values of all selected nodes and edges Figure 8 shows an example of how it works When the Property Viewer is open simply select any nodes and edges as described in the Selecting Node and Edge Figures section above The property values for those nodes and edges are then shown in the Property Viewer The Property Viewer can be closed at any time 16 DS FCModeler cycleTest xml loj x file view layout graph properties 39988 4849 BY fe4 property viewer E 5 x location molecule enzyme dna strength convert regulate Figure 8 Property viewer showing property values of selected nodes and edges 6 2 Visual Attributes of Node and Edge Figures The node and edge figures in FCModeler have different visual attributes associated with them For instance node figures can have different shapes and edges can have different colors Table 4 lists the different visual attributes of the node and edge figures Table 4 The visual attributes of node and edge figures supported by FCModeler Visual Attributes of Node Figures Visual Attributes of Edge Figures Shape Line color Fill color po Arrowhead shape Each visual attribute then has specific values Node shapes can be ellipses rectangles round rectangles diamonds etc Colors for both nodes and edges can be specified by any RGB value 6 3 Using Visual Att
25. n 3 1 1 3 Coordinates The coordinates of node and edge figures calculated by some graph layout algorithm can also be saved in XML format Currently the center coordinate of a node figure and bezier control point coordinates of an edge figure are specified in XML The following XML shows the coordinates of the node and edge figures of the graph defined in XML above lt coordinates gt lt nodeFigure node u 1 coord 49 0 22 0 gt lt nodeFigure node v coord 144 0 260 0 gt lt nodeFigure node w coord 80 0 102 0 gt lt nodeFigure node z coord 108 0 182 0 gt lt nodeFigure node a coord 148 0 29 0 gt lt nodeFigure node b coord 154 0 182 0 gt lt edgeFigure edge el coords 46 59765625000001 37 375 39 0 86 0 36 0 182 0 120 91247425920142 243 32567585386772 gt lt edgeFigure edge e3 coords 55 15 37 375 61 0 52 0 65 0 64 0 70 24655092527266 77 29126234402412 gt lt edgeFigure edge e7 coords 67 66964285714286 37 375 83 0 50 0 108 0 71 0 126 82235221674875 51 23653017241381 gt lt edgeFigure edge e2 coords 130 640625 251 23739919354838 51 0 199 0 54 0 103 0 50 688407577819234 49 35220276067163 gt lt edgeFigure edge e4 coords 76 74875 115 546875 68 0 152 0 56 0 204 0 120 5166871472147 245 05607363913657 gt lt edgeFigure edge e5 coords 81 693359375 115 546875 84 0 134 0 89 0 148 0 94 67187900213833 158 14967821435283 gt lt edgeFigure edge e6 coords 105 97348484848486
26. n 5 2 Node Figures FCModeler supports several different forms of interaction with nodes including adding new nodes deleting nodes and moving nodes These interactions are described in more detail below Table 2 Node interactions Behavior Add a new node Ctrl left click on an empty portion of graph Ctrl right click on a node Move a node s Left click and drag the node s 5 2 1 Adding To add a new node to the graph hold down the Ctrl key and left click with the mouse in an empty portion of the graph A dialog box will appear asking for a unique node name for the new node Enter the node name and click ok The new node will then appear in the graph view 9 2 2 Deleting To delete an existing node from the graph hold down the Ctrl key and right click with the mouse on a node in the graph view The node will be removed from the graph along with any edges going into or coming out from that node 5 2 3 Moving To re position a node figure in the graph view left click and drag the node figure The node figure along with all edges incident with that node will then move around the graph view 5 3 Edge Figures FCModeler supports several different forms of interaction with edges including adding new edges modifying edges deleting edges and moving edges These interactions are described in more detail below Table 3 Edge interactions Add a new edge Ctrl left click on tail node release mouse on empty portion of
27. ng the ordering from Step 1 Each DFS tree is a SCC of D To find the strongly connected components of a graph in FCModeler select the find strongly connected components menu item from the graph menu After performing the above algorithm FCModeler shows all of the SCC s to the user in a list Clicking on an SCC in the list selects all of the node figures in that SCC in the graph view A subgraph can then be created based on those nodes since their node figures are selected F DEJA fil vie gra propel y PEI u 998 lema lema file fiter 2 cycle le 29 c e3 el cycle d e6 b e2 c e4 d 3 cycle g es f e7 h 612 g Figure 12 Example of selecting cycles and strongly connected components as subgraphs 8 1 3 Cycle Search A path in a digraph is an alternating sequence of nodes and edges v e v e V3 V V such that tail e v head e v and all nodes are distinct A path can be viewed as starting at node v and following edges through the graph until node v is reached If v v the path is called a cycle Often it is useful to know all of the cycles of a digraph and finding all of the cycles in a digraph is a well studied problem in graph theory FCModeler implements a cycle search algorithm that finds all of the cycles in the graph To perform the cycle search either select the find cycles menu item from the graph menu or click the toolbar but
28. node gt lt atom property label value a gt lt attributeValue attribute fill value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e8 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n1 gt lt mapping type node gt lt atom property label value b gt lt attributeValue attribute fi11 yalue 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e9 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n2 gt lt mapping type node gt 19 lt atom property label value v gt lt attributeValue attribute fi11 value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt lt atom property label value e2 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt lt time n n3 gt lt mapping type node gt lt composite gt lt atom property label value u 1 gt lt connective type or gt lt atom property label val lt composite gt lt attributeValue attribute fi11 value 1 0 0 0 1 0 gt lt mapping gt lt mapping type edge gt wes Hh gt lt atom property label value e3 gt lt attributeValue attribute color value 1 0 0 0 0 0 gt lt mapping gt lt time gt
29. nodes and edges can also have multiple properties and each individual node and edge has a specific value for each property The following shows an example of the XML topology lt graph gt lt nodeProperties gt type location lt nodeProperties gt lt node id u 1 gt dna loc1 lt node gt lt node 1d w gt rna locl lt node gt lt node td w gt molecule loc2 lt node gt lt node id z gt molecule loc1 lt node gt lt node id a gt enzyme loc2 lt node gt lt node id b gt enzyme locl lt node gt lt edgeProperties gt type strength lt edgeProperties gt lt edge id el tail u 1 head v directed true gt regulate 1 0 lt edge gt lt edge id e3 tail u 1 head w directed true gt regulate 1 0 lt edge gt lt edge id e7 tail u 1 head a directed true gt convert 1 0 lt edge gt lt edge id e2 tail v head u 1 directed true gt regulate 1 0 lt edge gt lt edge id e4 tail w head v directed true gt regulate 1 0 lt edge gt lt edge id e5 tail w head z directed true gt catalyze 1 0 lt edge gt lt edge id e6 tail z head w directed true gt convert 1 0 lt edge gt lt edge id e8 tail a head b directed true gt convert 1 0 lt edge gt lt edge id e9 tail b head v directed true gt convert 1 0 lt edge gt lt graph gt The lt grapn gt tag surrounds the topology
30. odeFigure edgeFigure gt lt ELEMENT nodeFigure EMPTY gt lt ATTLIST nodeFigure node CDATA REQUIRED coord CDATA REQUIRED gt lt ELEMENT edgeFigure EMPTY gt lt ATTLIST edgeFigure edge CDATA REQUIRED coords CDATA REQUIRED gt lt ELEMENT mappings mapping gt lt ELEMENT mapping atom composite attributeValue gt lt ATTLIST mapping type node edge REQUIRED gt lt ELEMENT atom EMPTY gt lt ATTLIST atom property CDATA REQUIRED value CDATA REQUIRED gt lt ELEMENT composite atom composite connective atom composite gt lt ELEMENT lt ATTLIST type and lt ELEMENT lt ATTLIST attribute connective EMPTY gt connective or REQUIRED gt attributeValue EMPTY gt attributeValue CDATA REQUIRED value CDATA REQUIRED gt lt ELEMENT graph nodeProperties node compositeNode edgeProperties edge gt lt ELEMENT nodeProperties PCDATA gt lt ELEMENT node PCDATA gt lt ATTLIST node id ID REQUIRED gt lt ELEMENT edgeProperties PCDATA gt lt ELEMENT edge PCDATA gt lt ATTLIST edge id ID REQUIRED head IDREF REQUIRED tail IDREF REQUIRED directed truelfalse false gt gt lt graphFile gt lt coordinates gt lt nodeFigure node u 1 coord 49 0 22 0 gt lt nodeFigure node v coord 42 0 262 0 gt lt nodeFigure node w coord 80 0 102 0 gt lt nodeFigure node z coord 108 0 182 0 gt
31. pring embedder algorithm that differs significantly from GEM It uses much of the framework of the GEM algorithm but the heart of it is different AGEM removes the repulsive force between pairs of nodes reverses the direction of the gravitational force to make it repulsive and retains the attractive spring forces between adjacent nodes AGEM gives a layout that is similar to the regular GEM but does it much faster Because of the lack of repulsion between nodes an unlucky initial random layout could leave many nodes bunched together Also the reversed gravity tends to push singletons and disconnected subgraphs away from the barycenter This increases the global temperature of the layout causing it to use 1ts maximum allowed number of iterations instead of stopping early due to settling of the graph FastGEM FastGEM is a compromise designed to give the more consistent quality of GEM while retaining some of the speed of AGEM FastGEM uses AGEM to do an initial layout and GEM to finish AGEM replaces Frick s insertion loop With a layout that is often near to the final layout the regular GEM algorithm runs significantly faster If there are disconnected pieces of the graph the AGEM algorithm will take a long time to complete so any speed advantages over GEM will be lost In summary GEM The standard GEM layout This one can handle disconnected graphs and takes the longest to run though the quality is good and consistent AGEM Runs much faste
32. r than GEM A disconnected graph will cause it to blow up and take a long time to complete This is visually close to GEM but the quality is fair at best and much more inconsistent FastGEM This uses AGEM to do the initial layout then GEM can polish it up AGEM gets the initial placement close making GEM much faster but GEM makes the quality much more consistent 5 Interacting with the Graph View FCModeler supports a great deal of interaction with the graph view This interaction is done using the mouse and keyboard keys 5 1 Selecting Node and Edge Figures One basic form of interaction with the graph view 1s selection Multiple nodes and or edges can be selected at any given time Node and edge figures can be selected in several ways as shown in Table 1 Table 1 Methods of selecting nodes and edges 5 1 1 1 1 User Action Individual node or edge Left click on a node or edge figure Multiple nodes and or edges Ctrl left click on multiple node and or edge figures Multiple nodes and or edges Left click amp drag around multiple node and or edge figures Selecting a node or edge highlights the figure in the graph view Highlighted nodes have a yellow border placed around them while a thick red line denotes the highlighted edges 12 Selecting not only visually highlights the node and edges figures but also creates a subset of the nodes and edges in the graph Thus selection is the starting point for other forms of interactio
33. ributes to Visualize Properties FCModeler allows the user to assign property values to visual attribute values For example the value gene of the node property type can be assigned to the value ellipse of the visual attribute node shape Then all nodes in the graph that are of type gene will be shown using an elliptical node shape Any property value can be assigned to any visual attribute value This mapping ability allows the user to visualize the property values of the nodes and edges in any 17 way they want These mappings can either be specified in a graph XML file see the Mappings section above or created by the user using the Mapping Editor 6 4 Creating Mappings Using the Mapping Editor The Mapping Editor is used to assign property values to visual attribute values so the property values can be seen in the graph view To open the Mapping Editor either select the mapping editor menu item from the view menu or click the toolbar button mapping editor A _ codes apping rules roperty values visual attribute location lact maps to ill 0 2 location type dna maps to node shape edges apping rules strength Figure 9 Mapping editor Figure 9 shows the Mapping Editor The property values of the nodes and edges are shown n the middle of the w ndow in a table the columns represent the different properties and the entries n
34. rogram and for selecting the directory of graph information These paths need to be set correctly to find the layout information and graphs If your version of FCModeler is stored on the C drive in a folder called FCModeler the file should contain the following lines pathToDot c femodeleruser dot pathToGraphs c femodeleruser graphs 2 2 Running FCModeler FCModeler can be run by double clicking on the run bat file in your directory or directly from the command l ne 3 Sources of Input FCModeler can currently obtain graphs from two different external sources XML files and a MySQL database 3 1 Graph XML Files FCModeler can read in graphs from specially formatted XML files 3 1 1 XML Format The XML files are standalone that means there 1s no separate DTD file needed The DTD information is given at the beginning of the XML file Additionally there are three types of information that can be stored in an XML file the topology of the graph the mappings between node and edge properties and node and edge figure visual attributes and coordinates of the node and edge figures Any combination of the three can be present in an XML file as long as the corresponding DTD is present FCModeler allows the user to choose which of the three is actually read from a given XML file 3 1 1 1 Topology The topology specifies the nodes and edges of the graph Each node and edge must have a unique id that is just some string of characters The
35. section The lt nodeProperties gt and lt edgeProperties gt tags specify the node and edge properties respectively Each string surrounded by double quotes is defined as a single node or edge property A single lt node gt tag specifies each node The unique node ID is given by the ia element The text between the beginning and end node tags contains the values for the node properties Each string surrounded by double quotes is the value of a property in the order defined by the lt nodeProperties gt tag A single lt edge gt tag specifies each edge The unique edge ID is given by the ia element The tai and heaa elements specify the tail and head nodes of the edge respectively The airectea element indicates whether the edge is directed Like the node tags the text for the edge tags specifies the values of the edge properties for the particular edge The DTD for the topology XML is given by lt ELEMENT graph nodeProperties node compositeNode edgeProperties edge gt lt ELEMENT nodeProperties PCDATA gt lt ELEMENT node PCDATA gt lt ATTLIST node id ID REQUIRED gt lt ELEMENT edgeProperties PCDATA gt lt ELEMENT edge PCDATA gt lt ATTLIST edge id ID REQUIRED head IDREF REQUIRED tail IDREF REQUIRED directed true false false gt This DTD must be included at the beginning of the XML file 1f the file contains topology information 3 1 1 2 Mappings Node and edge properti
36. t time gt tags define the mapping rules in exactly the same way as in the graph XML files see the Mappings section above To open an animation XML file select the open animation file menu item from the file menu 20 7 2 Controls After FCModeler reads the XML file the animation control window in Figure 10 1s shown The controls work just like a cassette tape or CD player The user can play the animation pause it step forwards or backwards and adjust the time delay between steps E animation control E al x rcontrol frame 0 7 pka delay 7 1 0s delay 0 1 2 3 4 pause Figure 10 Animation control 8 Graph Theoretic Operations Graphs are well studied mathematical objects and an entire area of mathematics called graph theory exists to study their properties A graph consists of two parts a set of objects called nodes or vertices and a set of relations between nodes called edges Ifa graph is undirected its edges are unordered pairs of vertices e u v v u while a directed graph called a digraph has ordered pairs for edges e u v v u The first node of a directed edge is called the tail and the second node is called the head A graph is typically denoted G V E where V is the node set or vertex set and is the edge set FCModeler implements several graph theoretic algorithms that are useful for analyzing the properties of a specific graph
37. the five different paths between ethylene and CTR1 and the two different paths between CTR1 and EIN2 There are two cycles for each of the five different paths between ethylene and CTRI one path going from CTR1 directly to EIN2 and another going through MAPKK and MAPK This is where the ten cycles come from Obviously the SOM correctly grouped together these ten cycles into one cluster 25 Figure 14 Map view showing results of the SOM algorithm Each graph shows the model of the corresponding map unit which is the generalized median of the cycles assigned to that map unit 26 file wiew graph properties Oe LAS Be LASS protein 4 Figure 15 Full view of the bottom left map unit showing ten cycles clustered together ZA 9 FCModeler and R In work 10 References 10 1Publications relating to FCModeler Cox Z February 28 2002 JSOMap a Java based Self Organizing Map package http jsomap sourceforge net Date accessed June 18 2002 Dickerson J A D Berleant et al to be published in 2002 Creating and Modeling Metabolic and Regulatory Networks Using Text Mining and Fuzzy Expert Systems Computational Biology and Genome Informatics C H Wu P Wang and J T L Wang World Scientific Dickerson J A D Berleant et al 2001 Creating Metabolic Network Models using Text Mining and Expert Knowledge Atlantic Symposium on Molecular Biology and Genome Information Systems and Technology CBGIS
38. ton 23 save to file show results list _ max cycle length Co ct Figure 13 The cycle search dialog box Before performing the cycle search algorithm the user must select what to do with the results This is done through the dialog shown in Figure 13 The results can be shown in a list saved to a file or both If the list option is chosen when the algorithm finishes a list of cycles is shown Selecting a cycle from the list selects the nodes and edges of the cycle 8 1 4 Cycle XML Files The cycles can be saved to an XML file for later use The following XML shows an example of a cycle XML file lt xml version 1 0 standalone yes gt lt DOCTYPE cycles lt ELEMENT cycles cycle gt lt ELEMENT cycle node edge node edge node edge gt lt ELEMENT node EMPTY gt lt ATTLIST node id CDATA REQUIRED gt lt ELEMENT edge EMPTY gt lt ATTLIST edge id CDATA REQUIRED gt gt lt cycles gt lt cycle gt lt node id b gt lt edge id e9 gt lt node id v gt lt edge id e2 gt lt node id u 1 gt lt edge id e7 gt lt node id a gt lt edge id e8 gt lt cycle gt lt cycle gt lt node id z gt lt edge id e6 gt lt node id w gt lt edge id e5 gt lt cycle gt lt cycle gt lt node id w gt lt edge id e4 gt lt node id v gt lt edge id e2 gt lt node id u 1 gt lt edge
39. uld be selected Then configure the visual attribute the same way as before 18 7 Animation FCModeler has animation functionality allowing the visual attributes of the node and edge figures to change over time More specifically property value to visual attribute value mapping rules can be defined for discrete time steps FCModeler then steps through the sets of mappings and the user can see things changing in the graph view Animation can be used to show the progression of some modeling algorithm such as fuzzy cognitive maps among other things 7 1 XML File Format The mapping rules for the animation are specified in an XML file The following code segment shows an example of a complete animation XML file lt xml version 1 0 standalone yes gt lt DOCTYPE animation lt ELEMENT animation time gt lt ELEMENT time mapping gt lt ATTLIST time n ID REQUIRED gt lt ELEMENT mapping atom composite value gt lt ATTLIST mapping type node edge REQUIRED gt lt ELEMENT atom EMPTY gt lt ATTLIST atom property CDATA REQUIRED value CDATA REQUIRED gt lt ELEMENT composite atom composite connective atom composite gt lt ELEMENT connective EMPTY gt lt ATTLIST connective type and or REQUIRED gt lt ELEMENT value EMPTY gt lt ATTLIST value attribute CDATA REQUIRED value CDATA REQUIRED gt gt lt animation gt lt time n n0 gt lt mapping type
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