International Symposium on Integrative Bioinformatics 2011
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英文:
Wageningen, Netherlands
アブストラクト
In the analysis of gene regulatory networks, we have to consider possible behaviours depending on initial conditions, scenarios of external inputs, and settings of parameters. Quantitative methods, such as numerical simulations based on ordinary differential equations, are not suitable to analyze all of possible behaviours. Therefore, we developed a qualitative method for analyzing all of possible behaviours of gene regulatory networks, by focusing on essential qualitative features of the behaviours.
In our method, behaviors are captured in transition systems using propositions for genes state (ON or OFF), and those related to threshold values for genes activation/inhibition. We characterized possible behaviors of networks by specifying changes of concentration levels of products of genes and changes of genes states in Linear Temporal Logic. The constraints are intended to cover all possible behaviors of networks. Then, expected biological properties such as reachability, stability and oscillation etc. are also described in Linear Temporal Logic. We check satisfiability of those formulae and know whether some/all of behaviours satisfy the expected biological property. We can test any hypothesis and predict behaviours of networks in silico by using our method.
Our method depends on satisfiability checking of Linear Temporal Logic. The complexity of the checking is PSPACE-complete in the length of a formula. Therefore, the algorithm is exponential time to check the satisfiability. The length of a formula specifying possible behaviours of a network is proportional to the size of the network. Therefore, analyses of large networks are generally intractable in this method. We applied the technique of modular satisfiability checking to analyze larger networks. A network is divided into a few subnetworks and we integrate possible behaviours of the subnetworks to obtain behaviours of the whole network. We ignore local propositions in subnetworks from its behaviours. Thus this method may improve the cost of checking process.
Moreover, we propose an approximated analysis method using network motifs. In this method, we specify constraints of behaviours of subnetworks using less propositions. Such specification is simpler than the original one but generally not equivalent. Therefore, the behaviours characterized by the specification are in a sense approximated. We give an approximated specification so as to be stronger than the original one in the sense that its satisfiability implies the original one’s satisfiability. If an approximated specification is satisfiable, also is the original specification. As an application of this method, we give approximated specifications for network motifs. Network motifs occur in many gene regulatory networks. Thus these approximated specifications can be used in analyses of many gene regulatory networks. We give approximated specification for negative auto-regulation, coherent type 1 feed-forward loops, single-input modules and multi-output feed-forward loops. The approximated specifications are given by hand considering their functions. For demonstration, we applied this method for networks of E. coli involving MalT gene expression. The checking process becomes drastically faster by approximated analysis.
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