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1. ATALIA Software for Binary Network Analysis User s Manual Version 1 English version Alvaro Chaos Cador Index Introduction The screen 1 The main window 2 Atalia s tabs 3 The status bar Tabs 1 About 2 Start 3 Network 4 Graphic 5 Omega 6 Monitoring 7 Neighborhoods 8 Derrida 9 Landscapes 10 Sensibility 11 Morphospace Glossary References Introduction Monod and Jacob 1961 proposed that complex networks of gene interactions regulate cell differentiation Kauffman 1969 introduced the Boolean network approach to study these systems This approach starts idealizing the behavior of each component genes in this case as a binary variable that can have one of two states on 1 or off 0 A logical rule is assigned to each gene according ideally to experimental data The logical rule represents the behavior of the gene which depends on the states of its neighbors genes that are connected directly to it The network configuration at certain moment is expressed with vector 81 2 gv Where N is the total number of genes of the network and g is the particularly state of expression of n th gene If the gene is active g 1 otherwise g 0 The state of each gene changes in time according to the next equation En t 1 fn En1 t 8n2 t o amp nk 1 where 2 1 2n2 gt nk are the states of the k genes that regulate the activity of gene n and fais the logical fu
2. Available languages are Spanish and English The Start Tab Here is where you read the topology of the network and the rules of each node If the actualization of your network is asynchronic you must read the file with the order of actualization of the nodes otherwise the topology and the rules files are enough You can generate an output file checking what kind of data you want to save in it The default name is atalia sal txt yes with double extension You may change this name by typing the desire name in the text box The file will be saved as a text file In the Atalia s website you may find some topology and rules files to work with You can generate your own files networks and rules with any text processor or editor these files must be saved in text format In order to do that you must know the syntax of the input files topology rules and asynchrony optional After reading the input files clicking on its corresponding icon and checking what information you want to save in the output file press the magic button w to start the analysis If you already know the syntax of the input files skip this section and go directly to section the network tab Syntax of topology file The topology of a network is represented by a square matrix each entry of the matrix represents a connection between two nodes or a node to itself the diagonal Suppose you want to work with the network showed in Figure 1 Figure 1
3. Mutation of LFY will change the destiny of the configuration The Derrida Tab According to Kauffman 1991 the chaotic behavior of a Boolean network persists until approximately K 3 number of inputs per node Below this connectivity the properties of random Boolean networks change abruptly now the networks exhibit unexpected and collective order Derrida curve is a way to determine this transition phase between chaos and order Slopes greater than implies that two very similar initial conditions diverge exponentially in time characteristic of a chaotic phase in contrast with an ordered regime which has a slope lower than 1 The Derrida curve can be calculated with all possible configurations of the network but for some sizes this can be very time consuming In order to explore this time it is possible to perform the analysis with a sample of configurations The Total box performs the complete analysis just press the corresponding magic button S If you want to explore times of calculation use the sample box Type the size of the sample in the Sample size box and press the corresponding magic button The printer button will print the graph The graph button M will save the graphic into a file Available formats are jpg and bmp Example Curva de Derrida 7 H t 1 6 H t Figure 8 Derrida curve obtained for the A thaliana floral network with a sample size of 100 The Landscapes Tab The omega s
4. research The screen The main window This is the work space You can select different routines by choosing the appropriate tab the general display of the window will change In the bottom will be located the status bar which has some basic and general information about the ridden network The status bar The status bar located below the main screen displays some general information of the network and its dynamical properties Read the input files and perform the analysis see the section Atalias s Tabs Start tab and it will appear in this bar the number of nodes of the network the size of the omega space the network type lt K gt p the absolute and proportional numbers of Edens Atalia s Tabs Atalia is organized in several tabs each one has specific routines to perform different analysis read input files draw network topology display results etc TABS The About Tab The About tab serves as a presentation of the program it has the e mail of the author to establish contact and from this tab you can access Atalia s homepage http www ecologia unam mx achaos Atalia atalia htm where you can find and download the latest version of the program and some files network files to work with a gallery with the graphic representation of some networks and basins of attraction etc In this tab you can change the language clicking on the corresponding am e E F a flag or the default language is Spanish
5. 0 Sumideros Figure 4 Basins of attraction relative sizes of A thaliana floral network The Omega Tab In this tab you will find on the left upper corner a box with the list of all the attractors The attractors are numbered consecutively starting from 1 By clicking with the mouse on any of them the basin of attraction will be represented graphically The colors are chosen at random each time you modify the graph colors will change The attractor will be positioned at the center of the graphic if it is a point attractor it will be represented by a point if it is a cyclic attractor it will be represented by a circle Configurations box If you want to see the configurations in the graph you should mark any of the two boxes in the Configuration box Selecting binary checkbox will display configurations as strings of zeros and ones selecting decimal checkbox will convert the string in a 10 base number Both are unchecked as default values Effects box The fan button turn back arrow icon changes the angle in which all the configurations will be arranged Its default value is 90 degrees This is useful when the basin of attraction is very large or complicated If you diminish the angle the graph will be clearer Try 0 degrees This button affects the opening of all the fans but the center circle The magnifier button AL zooms in and out the graph For example this is useful when the basin is too large to see a particular co
6. Four node network The first thing to specify in the topology file is the number of the nodes In this case the first line of the file must contain a 4 On the next line it must be the name of the node followed by its connections The name of the node cannot be larger than 5 letters Connections are represented by the number 1 The columns represent the outputs of the nodes and the rows represent de inputs of the nodes In the previous example must be 4 columns and 4 rows because there are 4 nodes For the first row we will proceed as follows if the node A receives information input from node A first column a 1 is placed otherwise a 0 The same logic applies for the following three columns At the end the first row which indicates all the inputs of node A must contain the name of the node 5 spaces followed by a combination of 0 or 1 separated by a space The same syntax must be followed for the three other rows When you are done with all the rows your topology file is ready It is very useful to write some commentaries in the file to remember what kind of network is the references from whom it was obtained and other important data You can add all the data that you want after the last line of the topology the program will ignore any information beyond the last connection of the last node Examples of commentaries will be shown from now on in green color The topology file of the network from Figure 1 will be as follows Node A has 2 inpu
7. d with the combinations this imply that the maximum number of inputs of a particular node is 11 You must respect this situation the combinations must be right justified The output must be always in the 13 column and the separator the vertical bar between inputs and output in the 12 column Immediately after the logical rule of node A comes the logical rule of node B and so on In our example all nodes have the same logical rule Or exclusive Ox In real genetic examples this is very rare and the normal condition is that each node has its own different logical rule You can write any comments at the end of the file as in the topology file texts in green are comments It is recommended that you save the rules files with the double extension reg txt because it is the default extension for searching files in the open file dialog window of Atalia It allows you to open those files with the default text editor and Atalia will recognize them as its rules files without changing any default extensions in your computer Syntax of the asynchrony file optional The asynchrony file specifies the order of actualization of the nodes Each row specifies the order of actualization of a particular node In our previous example we have a 4 node network each row will represent the order of actualization of a node so you will have 4 rows Row number 1 refers to the order of actualization of the first node node A the row number 2 represents t
8. e type of the mutation with a particular color After the analysis four graphs will be shown with different information about the mutations and the attractors recovered The printer button ES will print the corresponding graph The graph button EE will save the corresponding graphic into a file Available formats are Jpg and bmp Example Regimen IRON a E E Figure 10 Mutation types percentage Sensibilidad 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 Salida Figure 11 Number of attractors recovered according to the mutated output The Morphospace Tab This is a complement to the sensibility analysis It shows in a mosaic whose squares represent a particular configuration which configurations are attractors after performing the sensibility analysis There are 3 possible outcomes The first one is configurations that are originally attractors they are colored in blue The configurations that are new attractors under the mutations are colored in red The third and last possibility is configurations that never are attractors under any of the possible mutations they are presented in white The cactus icon FE will save the landscape showed Available formats are jpg and bmp Example Figure 12 Original attractors blue and new attractors red after mutating each one of the outputs Glossary Attractor Certain configuration or group of them once attained the sy
9. he order of actualization of the second node and so on Again remember that the order of nodes depends of the topology file By default all nodes will be actualized at the same time if you want to specify a different order of actualization the file will be like this Node A will be actualized in 4 place Node B will be actualized in 3 place Node C will be actualized in 2 place Node D will be actualized in 1 place My first asynchrony file Order of actualization D C B A These file tells the program the order of actualization of the nodes The first node to be actualized is D then C then B and finally A You can write comments at the end of the file Texts in green are comments It is recommended that you save the asynchrony files with the double extension asi txt because that one is the default extension for searching files in the open file dialog window of Atalia It allows you to open those files with the default text editor and Atalia will recognize them as its asynchrony files without changing any default extensions in your computer The Network Tab This section draws the topology of the input network You can see the network after reading a topology file in the Start tab You can modify some of its attributes as the labels and the size of the nodes as well their fill and edge color The size of the network and the width of the connections can be changed too To restore default values press the undo bu
10. ing the corresponding box Finally press the monitoring button 1 An image consisting of red and blue squares at the right of the screen will be displayed Each square represents a node and its color the state of that node blue signifies inactive and red active Each row of squares represents a particular configuration The uppermost row is the input configuration below this one a set of configurations will be showed each one represents the next configuration at time f and eventually when color do not changes or changes in a cyclic form an attractor will be reached The cactus icon e will save this set of colored configurations Available formats are jpg and bmp Example Figure 6 Scanning of configuration 0000000000000 until it reaches an attractor 1100110101100 The Neighborhoods Tab In this section you can perform an analysis of small perturbations to any configuration and calculate the stability of an attractor or any other configuration The input configuration can be read in binary or decimal formats After giving it press the Neighbors button to start de analysis On the left panel the results will appear in text format The analysis consists in change the state of each node one by one and recon its destiny attractor On the right you will find the results in a graphic form The graph shows a central node which represents the original configuration painted with the color of its attractor The surrounding nodes represe
11. ld Spring Harb Symp Quant Biol 26 389 401 Kauffman SA 1969 Metabolic stability and epigenesis in randomly constructed genetic nets J Theor Biol 22 437 467 Kauffman SA 1991 Antichaos and adaptation Sci Amer 265 2 64 70 Kauffman SA 1993 The origins of order self organization and selection in evolution Oxford University Press Raup D M 1966 Geometric analysis of shell coiling general problems Journal of Paleontology 40 1178 1190 Waddington C H 1940 Organisers and Genes Cambridge University Press Wuensche A 2002 Basins of Attraction in Network Dynamics A Conceptual Framework for Biomolecular Networks in Modularity in Development and Evolution eds G Schlosser and G P Wagner Chicago University Press 2004 chapter 13 288 311 Santa Fe Institute working paper 02 02 004 2002
12. nction i e logical rule associated to gene n A particular set of the states of all the genes is called a configuration According to the logical rules of the genes this configuration can or cannot change at time If it does not change it is called an attractor An attractor is certain configuration or group of them once attained the system will stay there forever An attractor conformed by just one configuration is called a point attractor otherwise it is a cyclic attractor and the number of configurations that conforms it are its period The long term behavior of the system leads to these few in comparison to total number under certain connectivity configurations This particularly set of gene activity in equilibrium with certain stability can be interpreted as a cell type Kauffman 1991 Recently works grounded on experimental data have proved the strength of this approach by recovering the genetic profiles of gene activation of those characterizing different cell types Espinosa Soto et al 2004 Chaos et al 2006 Such profiles correspond to the attractors of the gene networks being interpreted as cell fates This model has been used to explore the importance of stochastic perturbations over genetic systems which contrasts with a classical view of a programmed development Alvarez Buylla et al 2008 Atalia is designed to analyze the dynamics of binary or Boolean networks and to perform a variety of analysis useful in this kind of
13. nfiguration Default value is 1 Movement box The x control moves the graph on the x axis The y control moves the graph on the y axis upside down Keep in mind this for the y button a negative value will move the graph higher and a positive value will move it lower Default values of both controls are 0 Ratios box Nodes control modifies the size of the nodes Default value is 2 Fan control modifies the radio length of all the fans except the central circle Default value is 50 Central control modifies the radio length of the central circle Default value is 50 The undo button will redraw the graph with default values The cactus button will save the current graph in a file Available extensions are bmp and jpg You can keep any modified graph in RAM memory without saving it in a file by clicking on the Keep it on the list button Bil The image will be stored in memory and it will appear an identifier name and number on the left lower box list You can delete any of these graphs by typing its number in the box at the right of the row button E and press it Example Figure 5 Basin of attraction of one of the stamens attractors of A thaliana floral network The Monitoring Tab This section allows following a particular configuration to its attractor The configuration may be in decimal or in binary format You must select what type of configuration will be typed in the Configuration box by check
14. nt what happens if that node changes its state if the destiny is the same the color of the node will be the same as the central node and otherwise the color will be different The stability of the node will be calculated on the basis of small mutations at a Manhattan distance equals to 1 A node with 10090 of stability at that range of perturbation will show all the nodes with the same color as the central node The sizes box controls the graphic style Names checkbox allows showing or hiding the labels of the nodes Its default value is checked Network control modifies the size of the entire graph Its default value is 250 Nodes control changes the size of all the nodes of the graph Its default value is 50 Lines control modifies the width of the connecting lines of the network Its default value is 1 As in the Omega tab section you can keep any modified graph in RAM memory without saving it in a file by clicking on the Keep it on the list button Maa The image will be stored in memory and it will appear an identifier name and number on the left lower box list You can delete any of these graphs by typing its number in the box at the right of the row button E and press it Fox button saves the graph into a file Available formats are jpg and bmp Example Atalia Figure 7 Stability of sepal attractor of A thaliana floral network Mutations on AP1 TFL1 AG WUS AP2 genes will lead to the same attractor
15. pace is difficult to analyze unless for very small networks due to its huge set of configurations There are no methods to do this because it is not clear what to analyze either Atalia has some visual analysis to explore the Omega space In this section it is possible to represent the Omega space in three different ways the destinies mosaic the Manhattan distances mosaic and the topological distances mosaic In all of these mosaics each configuration is represented by a square The color of each square represents respectively the destiny configuration its corresponding attractor of that particular configuration the topological and the Manhattan distances to its attractor It is possible to compare two landscapes and to obtain a final landscape showing the differences between them This is useful in order to observe the effects of certain mutation or alteration in the logical rules of the network The mosaic represents in biological terms the morphospace over the genetic configurations the space FOGC space of Forms Over Genetic Configurations Landscapes box Point attractors By clicking on it the mosaic will mark in blue those configurations squares that are point attractors Cyclic attractors Clicking this option the mosaic will mark with different colors those configurations squares that are cyclic attractors Topologic distance This option colors each configuration square according to its topological distance to its corres
16. ponding attractor Manhattan distance Selecting this option will color each configuration square according its Manhattan distance to its corresponding attractor Destiny Epigenetic landscape Clicking on this option each configuration square will be colored according to its final destiny attractor Save file box This selection will save the data of the landscape showed on a file It will not save the image Load files box This section permits to load two landscapes saved previously to make a comparison between them Compare carpets box After loading the two files press the magic button to make the comparison between them If you select the first magic button 4 the result will show just the configurations with different destiny red The second magic button 4 makes the comparison more subtle Its results will show how many configurations have attained a new attractor red but it will show which configurations attained an attractor that already exists purple but it was not its original destiny The configurations that end on the same attractor will be displayed in yellow Figure 9 Destinies landscape of all configurations of A thaliana floral network The uppermost left square represents the first configuration 0000000000000 the one at its right is the next one 0000000000001 The lower right square represents the last configuration 1111111111111 The Sensibility Tab One of the characteri
17. s file must contain the rules of each of the nodes from the topology file You have to be very careful when you make this file The nodes must have the same number of entries as were specified in the topology file For example if the node A in the topology file has two input connections from B and D the rules file for the node A must have two columns each one representing an input node The order of the inputs is established as mentioned before in the topology file In our example all nodes will have two columns The rules file must be as follows remember comments are on green Columns input nodes B D Columns input nodes A C Columns input nodes B D Columns input nodes A C Here a rules of my first network All nodes have the same logical rule OR exclusive Ox The first row must contain the name of the node remember just 5 spaces are allowed After this you can write anything you want a commentary the program will not read it For example you can add a line and the names of the input nodes for clarity when you create the file In the previous example appears a line never mind is Just design The next rows must be filled with all the combinations of the input nodes As in our example all nodes have two inputs the total number of combinations are four 22 4 Each input combination must have associated an output which is the logical rule of the node A There are 11 spaces to be fille
18. stem will stay there forever An attractor conformed by just one configuration is called a point attractor otherwise it is a cyclic attractor and the number of configurations that conforms it are its period Basin of attraction Set of all configurations with the same destiny attractor Configuration A particular set of states from all the nodes of the network Eden Configuration with no previous configuration at time 1 7 Without any perturbation the only possible way to attain an Eden is to start in one Wuensche 2002 Epigenetic landscape Metaphor proposed by C Waddington 1940 in which the fate and the routes of differentiation of a cell are represented by a downhill landscape The cell is a ball that travels through this rugged surface and finally attains a stable place on it its final cellular type Genetic regulatory network GRN Abstraction of a genetic system with a network model Hamming distance The number of bits which differ two binary strings Hamming distance can be seen as Manhattan distance between bit vectors Manhattan distance The distance between two points measured along axes at right angles Morphospace The set of all possible forms or varieties of a structure or character can have either real or in theory Word proposed by D Raup 1966 Omega space The set of all possible configurations of a network For example a 5 node binary network has an omega space equal to 23 32 configurations State Nat
19. stics of a genetic regulatory network is its capacity to tackle a great quantity of mutations or perturbations without alter the normal behavior of the system Nevertheless is possible that certain mutations or perturbations change this behavior This property gives the opportunity to evolve Atalia allows performing a detailed analysis of all the possible single point mutations of the logical rules of the network and classify them according to the IRON Intrepid Reactionary Opportunistic Neutral mutations regime Each output of all the rules is changed and the dynamics is calculated There are four possible scenarios 1 If the mutation does not change the attractors or the number of them it is a neutral mutation 2 The mutation just reduces the number of attractors This is a reactionary mutation 3 The mutation keeps the original attractors and increases the number of attractors This is an opportunistic mutation 4 The mutation diminishes de original attractors but generates other new attractors This is an intrepid mutation Sensibility analysis box To start the analyses press the magic button Eq This test cans last very long depending on the number of nodes and the number of inputs of each one To see the effect of changing the output of a specific rule you can browse them by selecting the number of row of the output The row scanner will show what kind of effect will have changing a specific output with its corresponding node and th
20. ts from B and D 1 0 1 0 This is my first network It has 4 nodes and every node has two connections The first column of the matrix represents all the connections from the first node the outputs of A in this case The second column represents the B s outputs and so on The rows represent the input connections of each node You can read this file by row as follows A node has not an input from A the first column is O has an input from B the second column is1 has not an input from C the third column is O and has an input from node D the forth column is 1 Remember that O means no connection Similarly B node has an input from nodes A and C C node has an input from nodes A and C and D node has inputs from nodes A and C This is the topology of the network of Figure 1 You must keep in mind that the order of the nodes from now on depends of the order of the nodes in this file A node will be always the first node followed by B which is the second node and so on It is recommended that you save the topology files with the double extension top txt because that one is the default extension for searching files in the open file dialog window of Atalia It allows you to open those files with the default text editor and at the same time Atalia will recognize them as its topology files without changing any default extensions in your computer Syntax of the rules file The rules of each node must be in a separated file Thi
21. tton If you want to represent a particular configuration in the network s topology i e active nodes in one color inactive nodes in another fill the configuration box with a string of zeros and ones zeros represent inactive nodes and ones the active ones and press the brush buttonL You can choose the color of the nodes by pressing the active or inactive colored circles To restore default values press the undo button The topology can be saved with the cactus icon a Allowed formats are jpg and bmp Default values of this tab are Sizes box Labels On Network size 250 Node size 25 Lines 1 Colors box Node color Red Line color Black Edge color Black Configurations box Active color Inactive color The Graphic Tab This tab shows two histograms depicting the sizes of the basins of attraction The first histogram graphics their absolute sizes The second shows the percent of each basin of attraction i Ei You can print directly any of them by pressing its corresponding printer button a The histogram buttons B save the corresponding graphic Available formats are bmp emf and wmf Example Tama o de las cuencas de los sumideros 1 2 3 4 5 6 7 8 9 10 Sumideros Figure 3 Basins of attraction absolute sizes of A thaliana floral network Tama o de las cuencas de los sumideros 1 2 3 4 5 6 7 8 9 1
22. ure of a node at a particular moment For example a binary node can only have two states 0 or 1 Transient Configuration which has at least one previous configuration it is not an Eden and has at least one successor configuration it is not an attractor and does not conforms part of a cyclic attractor Stability The degree of resistance an attractor can suffer alterations in its configuration and return to itself A measure of how strong is an attractor to perturbations An attractor is an equilibrium point its stability depends on its capacity to return to itself after being modified References and bibliography Alvarez Buylla ER Chaos A Aldana M Benitez M Cortes Poza Y et al 2008 Floral Morphogenesis Stochastic Explorations of a Gene Network Epigenetic Landscape PLoS ONE 3 11 e3626 doi 10 1371 journal pone 0003626 Chaos A Aldana M Espinosa Soto C Garcia Ponce B Garay A and Alvarez Buylla E 2006 From Genes to Flower Patterns and Evolution Dynamic Models of Gene Regulatory Networks Journal of Plant Growth Regulation 25 278 289 Espinosa Soto C Padilla Longoria P Alvarez Buylla E 2004 A gene regulatory network model for cell fate differentiation during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles Plant Cell 16 2923 2939 Monod J and Jacob F 1961 General conclusions Telenomic mechanisms in cellular metabolism growth and differentiation Co

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