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Characterizing the Topology of Probabilistic Biological Networks
July-Aug. 2013 (vol. 10 no. 4)
pp. 970-983
Andrei Todor, Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL, USA
Alin Dobra, Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL, USA
Tamer Kahveci, Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL, USA
Biological interactions are often uncertain events, that may or may not take place with some probability. This uncertainty leads to a massive number of alternative interaction topologies for each such network. The existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. In this paper, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. Using our mathematical representation, we develop a method that can accurately describe the degree distribution of such networks. We also take one more step and extend our method to accurately compute the joint-degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. Our method works quickly even for entire protein-protein interaction (PPI) networks. It also helps us find an adequate mathematical model using MLE. We perform a comparative study of node-degree and joint-degree distributions in two types of biological networks: the classical deterministic networks and the more flexible probabilistic networks. Our results confirm that power-law and log-normal models best describe degree distributions for both probabilistic and deterministic networks. Moreover, the inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected. We also show that probabilistic networks are more robust for node-degree distribution computation than the deterministic ones. Availability: all the data sets used, the software implemented and the alignments found in this paper are available at >http://bioinformatics.cise.ufl.edu/projects/probNet/.
Index Terms:
topology,biochemistry,molecular biophysics,polynomials,probability,proteins,node-degree distribution computation,probabilistic biological network topology,biological interactions,alternative interaction topologies,joint-degree distributions,node pairs,mathematical model,polynomial time,protein-protein interaction networks,PPI networks,biological networks,classical deterministic networks,flexible probabilistic networks,power-law models,log-normal models,deterministic networks,Probabilistic logic,Random variables,Maximum likelihood estimation,Joints,Network topology,Mathematical model,random graphs,Probabilistic biological networks,network topology,degree distribution
Citation:
Andrei Todor, Alin Dobra, Tamer Kahveci, "Characterizing the Topology of Probabilistic Biological Networks," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 970-983, July-Aug. 2013, doi:10.1109/TCBB.2013.108
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