Causal relationship inference for a large scale genetic regulatory network

Inferring causal relationships of a genetic regulatory network is one of the fundamental problems in system biology. In this paper, an identification algorithm is developed that can be effectively applied to causal interaction identification of a large scale genetic regulatory network from noisy steady-state experiment data. A distinguished feature of the algorithm is that power law distribution has been quantitatively incorporated into estimations, which is one important structure property that most of large scale genetic regulatory networks have. Under the condition that parameters of the power law are known and measurement errors are Gaussian, an overall likelihood function is got by incorporating the power law distribution into a likelihood function of measurement noise. Then a maximum likelihood method is adopted, and the identification consists of 3 steps. At first, angle minimization between subspaces is utilized to identify nodes that have direct influences on a prescribed node, under the condition that the degree of the node is fixed. Secondly, interference strengths from prescribed nodes are estimated through likelihood maximization with respect to measurement errors. Finally, the degree of a node is identified through maximizing a lower bound of an overall likelihood function. To illustrate the effectiveness of the suggested algorithm, it has been applied to both an artificially constructed large scale linear system with 100 elements and a MAPK pathway model with 103 chemical elements. Compared with the widely adopted total least squares method, simulation results show that parametric estimation accuracy can be significantly increased and false-positive errors can be greatly reduced.