Direct regulation estimation of cellular networks with time series and steady state data

One of the main aims in systems biology is to gain knowledge about direct regulation effects among numerous cellular components. In this paper, two algorithms are proposed to estimate direct causal regulations from noisy time series experimental data. Through incorporating a so-called power law which is an important network structural characteristic of most large scale cellular networks, a likelihood function is developed and minimized by three steps. One essential step is determining which chemical elements have direct regulation effects on a prescribed element, when the number of direct regulations is known. To avoid the inherent combinatorial computation problem, two procedures are proposed you give analytical solutions about the positions of these elements. In addition, the possibility of integrating information of time series and steady state data into network inferences is also investigated in this paper, and finally two improved algorithms are developed based on these two kinds of data. These algorithms have been applied to many artificially constructed networks with 101 elements. Compared with total least squares (TLS) method, which is widely used in noisy measurement data case, numerical simulations show that, the false positive errors can be significantly reduced and estimation accuracy can be extremely increased. Moreover, the performances of improved algorithms are greatly better than the time series data based algorithms.