Using Graph Theory to Analyze Gene Network Coherence Francisco A. Gómez-Vela fgomez@upo.es Norberto Díaz-Díaz ndiaz@upo.es José A. Lagares José A. Sánchez Jesús S. Aguilar Hello Good Morning everybody. My name is Francisco Gómez and I ‘m going to present the work: “Using Graph Theory to Analyze Gene Network Coherence”. This work has been performed in collaborations with Norberto Díaz, Jose Antonio Lagares, Jose A. Sanchez and Jesús Aguilar.

Outlines Introduction Proposed Methodology Experiments Conclusions In this work we propose a novel methodology to assess a gene network reability based on a weel-known Graph theory algorithm. The outline of this presentation is: A short Introduction, where I will present the framework of our work. In the Methodology section, We will see our approach in detail. Next, in the Experiments section, I’m going to show the performed experiments. And the most representative obtained results. And finally, The most important conclusions and future works, will be presented.

Outlines Introduction Proposed Methodology Experiments Conclusions In this work we propose a novel clustering algorithm based on the idea of grouping pairs of genes that present similar interactions. The outline of this presentation is: A short Introduction, where I present the framework of our work. In the Method section, I’m going to explain in detail our approach. Next, in the section Experiments, I’m going to show the experiments carried out. And finally, I will summarize the conclusions of our work and future research directions.

Introduction Gene Network There is a need to generate patterns of expression, and behavioral influences between genes from microarray. GNs arise as a visual and intuitive solution for gene-gene interaction. They are presented as a graph: Nodes: are made up of genes. Edges: relationships among these genes. Currently, many biological studies try to model the processes ocurring in living organinms. In this regard, Gene networks have become as a visual, powerful and intuitive tools to represent the behaviour of genes into these processes. The are presented as a graph, where the genes represents the nodes and the relationships between them are the edges.

Introduction Gene Network Many GN inference algorithms have been developed as techniques for extracting biological knowledge Ponzoni et al., 2007. Gallo et al., 2011. They can be broadly classified as (Hecker M, 2009): Boolean Network Information Theory Model Bayesian Networks There are many algorithm to modeling Gene networks. Depending of the model architecture used they can be broadly classified as: Boolean networks, where there are only two possible states fot hte genes (expressed and no-expressed), Information theory networks (like correlation networks) and bayesian networks (Where the bayes theory is used to generate the models).

Introduction Gene Network Validation in Bioinformatics Once the network has been generated, it is very important to assure network reliability in order to illustrate the quality of the generated model. Synthetic data based validation This approach is normally used to validate new methodologies or algorithms. Well-Known data based validation The literature prior knowledge is used to validate gene networks. Once the model is generated a very important task is to asses the predicted relationships in order to prove the quality of the generated network . Typically, we can found two different tecniquesin the literature to validate the model: -synthetic data validation, that use artificial data to compare the results by different techniques. -well-known data based validation, in this way, the obtained results are compared with contrast biological data in order to prove the reliability of the obtained network. Our approach belongs to this technique.

Introduction Well-Known Biological data based Validation The quality of a GN can be measured by a direct comparison between the obtained GN and prior biological knowledge (Wei and Li, 2007; Zhou and Wong, 2011). However, these approaches are not entirely accurate as they only take direct gene–gene interactions into account for the validation task, leaving aside the weak (indirect) relationships (Poyatos, 2011). Normally, The quality of a GN can be measured by a direct comparison between the obtained GN and prior biological knowledge (Wei and Li, 2007; Zhou and Wong, 2011). However this approaches have the lack as they only take direct gene relationships into account leaving aside indirect ones. Our approach not only takes into account direct but also the indrect ones to make a biological validation. This is posible through the inclusion of graph Theory, as we will see in the methodology section.

Outlines Introduction Proposed Methodology Experiments Conclusions

Introduction Proposed methodology The main features of our method: Evaluate the similarities and differences between gene networks and biological database. Take into account the indirect gene-gene relationships for the validation process. Using Graph Theory to evaluate with gene networks and obtain different measures. As we mentioned before, In this work we use graph theory to make a biological validation of a Gene Network. The main idea is to find similarities and differences between gene networks and prior biological knowledge. With this goal, a well-known graph algorithm is used, concretly the floyd-Warshall algorithm, that is able to find the shortest path between a pair of nodes in a graph, or in our case, between a pair of genes. Finally we will be able to obtain several measures to rate the network quality.

Floyd Warshall Algorithm Proposed Methodology Biological Database Input Network DMIN B A D C DMDB B A E C F CM=|DMi – DMj| Floyd Warshall Algorithm DMIN DMDB Distance Matrices Coherence Matrix CM Measures Firstly i’m going to present a general vision of our proposal. As we mentioned before our method makes an asseasment of an input network through a comparison with prior knowledge. In the first step, the Floyd and warshall algorithm is used to obtain disctance matrices for both networks. These Distance matrices will be used to generate a new one, that we call Coherence Matrix. Using this Coherence Matriz several measures are obtained to stablish the queality of the input network. CM = |DMIN – DMDB|

Proposed Methodology Floyd-Warshall Algorithm This approach is a graph analysis method that solves the shortest path between nodes. Network Distance Matrix B F E A C A B C E F 2 1 Now, i’m going to explain the hole process in detail. The fist step is the generation of the distance matrix for the input network and biological database. With this goal,we use the floy-Warshall Algorithm.This is a graph analysis method that is able to find the shortest path between a pair of nodes, or in our case between a pair of genes. Obviously, the greater the distance, the lower the significance of the relationship between the genes. And to solve this problem,we use a treshol, the distance treshold

Proposed Methodology Distance Threshold It is used to exclude relationships that lack biological meaning. This threshold denotes the maximum distance to be considered as relevant in the Distance Matrix generation process. If the minimum distance between two genes is greater than δ, then no path between the genes will be assumed. Obviously, the greater the distance, the lower the relevance of the relationship. Depending of the performed study, it is possible to choose a threshold to stablish the minimun significance of the relationship With this threshold: -It is used to remove the relationships without relevance. - When the distance between a pair of genes ir greater than the Distance Trhre, we assume that don’t exist a path between them.

Proposed Methodology Distance Threshold Network Distance Matrix δ = 1 B F E A C A B C E F 2 1 A B C E F 2 1 A B C E F ∞ 1 For example, in this case, for a Threshold value of 1. Lets see the gene A, the relations with the genes C and E exxeccd the threshols, so we assume that the relation is no relevant for this case and an infinite value are stored for them.

Proposed Methodology DMDB DMIN A B C E F 2 1 A B C E F 2 1 A B C D 1 ∞ 2 1 A B C E F 2 1 A B C D 1 ∞ 2 A B C D 1 3 2 CM=|DMi – DMj| Coherence Matrix (CM) A B C 1 ∞ Once, the Distance matrices are obtained it is time to generate, the Coherence matrix. This matrix contains the existing gaps amongthe distances of the common genes between the two distance matrices. We have to use the common genes because we have no information to rate the quality of the rest of interactions from the genes that are no present into the database. Each element of the matrix is obtained by the absolute value for the subtraction of the distances previously obtained. For example, in the slide

Proposed Methodology Obtaining Measures Coherence Level threshold (θ) This threshold denotes the maximum coherence level to be considered as relevant in the Coherence Matrix generation process. It is used to obtain well-Known indices by using the elements of the coherence matrix: |v-y|<=θ TP 0< v,y <∞ |v-y|>θ FP Esta diapositiva no explica lo que es el CT CMi,j |∞-y| (α) FN |∞-∞|(β) TN

Proposed Methodology θ = 3 α β α β α β α β α β α β β β A B C D E - TP θ = 3 Coherence Matrix A B C D E - TP α FP β A B C D E - TP FN FP TN A B C D E - TP α FP β A B C D E - TP α 4 7 β 5 8 A B C D E - 1 α 4 7 β 2 5 8 A B C D E - TP α 4 7 β 5 8 A B C D E - 1 α 4 7 β 2 5 8 A B C D E - TP FN FP β A B C D E - TP FN FP β Esto esta mal

Outlines Introduction Proposed Methodology Experiments Conclusions In this work we propose a novel clustering algorithm based on the idea of grouping pairs of genes that present similar interactions. The outline of this presentation is: A short Introduction, where I present the framework of our work. In the Method section, I’m going to explain in detail our approach. Next, in the section Experiments, I’m going to show the experiments carried out. And finally, I will summarize the conclusions of our work and future research directions.

Results Real data experiment Input networks were obtained by applying four inference network techniques on the well-known yeast cell cycle expression data set (Spellman et al., 1998). Soinov et al., 2003. Bulashevska et al., 2005. Ponzoni (GRNCOP) et al., 2007 Comparison with Well-Known data: BioGrid KEGG SGD YeastNet Produced no Obtained. For the experiments we have used 3 yeast networks obtained with different techniques from the well-known yeast dataset (Spellman et al. 1998). The techniques are published by Soinov et al, bulashevka and Ponzoni. For the comparison, we also used 4 well-known gene-gene interaction databases: BioGrid,KEGG, SGD and YeastNet.

Results Real data experiment Several studies were carried out using different threshold value combinations: Distance threshold (δ) and Coherence level threshold (θ) have been modified from one to five, generating 25 different combinations. The results show that the higher δ and θ values, the greater is the noise introduced. The most representative result, was obtained for δ=4 and θ=1.

Soinov Bulashevska Ponzoni Results Soinov Bulashevska Ponzoni Accuracy F-measure Accuracy F-measure Accuracy F-measure Biogrid KEGG SGD YeastNet 0,27 0,58 0,31 0,29 0,42 0,48 0,47 0,45 0,65 0,34 0,53 0,50 0,79 0,50 0,69 0,66 0,82 0,28 1 0,90 0,43 1 Table 1 shows that inference method proposed by Gallo (GRNCOP2) generates the most reliable result, although Ponzoni technique (GRNCOP) provides the best result in three of the four data sets. Soinov approach obtains the worst values.   These results are consistent with the experiment carried out in (Ponzoni et al., 2007). And are cronologically sorted.

Results These results are consistent with the experiment carried out in Ponzoni et al., 2007. Ponzoni was successfully compared with Soinov and Bulashevska approaches. GRNCOP… es mejor poner ponzoni directamente.

Outlines Introduction Proposed Methodology Experiments Conclusions In this work we propose a novel clustering algorithm based on the idea of grouping pairs of genes that present similar interactions. The outline of this presentation is: A short Introduction, where I present the framework of our work. In the Method section, I’m going to explain in detail our approach. Next, in the section Experiments, I’m going to show the experiments carried out. And finally, I will summarize the conclusions of our work and future research directions.

Conclusions A new approach of a gene network validation framework is presented: The methodology not only takes into account the direct relationships, but also the indirect ones. Graph theory has been used to perform validation task.

Conclusions Experiments with Real Data. These results are consistent with the experiment carried out in Ponzoni et al., 2007. Ponzoni was successfully compared with Soinov and Bulashevska approaches. These behaviours are also found in the obtained results. Ponzoni presents better coherence values than Soinov and Bulashevska in BioGrid, SGD and YeastNet. GRNCOP… es mejor poner ponzoni directamente.

Future Works The methodology has been improved: The elements in coherence matrix will be weighted based on the gene-gene relationships distance. A new measure, based on different databases will be generated. Moreover, a Cytoscape plugin will be implemented. The methodology will be improved by weighting the elements of the coherence matrix based on the distance. Futhermore, the methodology will be implemented as a cytoscape plugin in a near future.

Thanks for your attention Using Graph Theory to Analyze Gene Network Coherence Thanks for your attention Thanks for your attention

Soinov Bulashevska Ponzoni Gallo Results - II Soinov Bulashevska Ponzoni Gallo Accuracy F-measure Accuracy F-measure Accuracy F-measure Accuracy F-measure Biogrid KEGG SGD YeastNet 0,27 0,58 0,31 0,29 0,42 0,48 0,47 0,45 0,65 0,34 0,53 0,50 0,79 0,50 0,69 0,66 0,82 0,28 1 0,90 0,43 1 0,75 0,47 0,58 0,62 0,86 0,61 0,73 0,77 Table 1 shows that inference method proposed by Gallo (GRNCOP2) generates the most reliable result, although Ponzoni technique (GRNCOP) provides the best result in three of the four data sets. Soinov approach obtains the worst values.   These results are consistent with the experiment carried out in (Ponzoni et al., 2007). And are cronologically sorted.

References Pavlopoulos GA, et al. (2011): Using graph theory to analyze biological networks. BioData Mining, 4:10. Asghar A, et al (2012) Speeding up the Floyd–Warshall algorithm for the cycled shortest path problem. AppliedMathematics Letters 25(1): 1 Bulashevska S and Eils R (2005) Inferring genetic regulatory logic from expression data. Bioinformatics 21(11):2706. Ponzoni I, et al (2007) Inferring adaptive regulationthresh-olds and association rules from gene expressiondata through combinatorial optimization learning.IEEE/ACM Transaction on Computation Biology andBioinformatics 4(4):624. Poyatos JF (2011). The balance of weak and strong interactions in genetic networks. PloS One 6(2):e14598.