Structure Identification And Parameter Estimation Of Dynamic Biological Networks

Our study focused on developing methods to recognize the biological network and estimate its parameters. Identification of the dynamic biological networks is a tough but vital work. Without the estimated parameters in the identification of dynamic biological networks, any quantitative analysis of the biological process could not be implemented. Up to date, little related work has been reported in the literature, except of the existing methods used in simple applications. The methods have not been developed corresponding to biological networks identification and parameter estimation. State-space approach to modelling biological networks is presented in this report. We are mainly devoted to the following eight aspects on structure identification and parameters estimation:(1) We put forward and develop extended kalman filter with structural constraints. Structural constraints are the main distinctive characteristics during applying extended kalman filter algorithm in genetic networks area and in engineering technology area. The latter usually has not been taken into account in structural information. However, genetic networks have structural information. For example, there are mutual interactions between some genes, but they may be not between others. Structural constraints can help trim the number of parameters that need estimate and alleviate over-fitting, which are especially acute given the limited amount of data we have.(2) Hao Xiong and we cooperatively and independently develop a second-order dynamics model in genetic networks and present the extended kalman filter to estimate the parameters in the second-order linear state-space model for gene regulation networks. The Gene regulation networks based on microarray gene expression profile data are usually adopted one-order linear state-space model. Hao and Yoonsuck used expectation maximization (EM) to estimate the parameters in the second-order linear state-space model for gene regulation networks, while we implement the extended kalman filter to estimate the parameters in second-order linear state-space model for gene regulation networks.(3) This is the first study to use the iterated extended kalman filter to estimate the parameters in nonlinear state-space model for biological networks and to develop extended kalman filter to estimate the parameter in general nonlinear state-space model for biological networks.(4) We are the first one to propose rao-blackwellised particle filter algorithm to estimate the parameters in nonlinear state-space model for biological networks, and also the first one to adopt rao-blackwellised particle filter algorithm to estimate the parameter in general nonlinear dynamic system.(5) This is the first time to implement continuous-time extended kalman filter for linear and nonlinear continuous-time dynamics with continuous-time measurements in the biological networks. We program the Hybrid extended kalman filter for linear and nonlinear continuous-time dynamics with discrete-time measurements in biology networks.(6) We deal with panel data in our parameter estimation algorithm. Multiple samples in the time-course data are seldom appeared in engineer application but it is common in biology data. So, we incorporate multiple samples into the state-space equation. Since mathematical model becomes more complex, the derived process of EKF and RBPF algorithm were more difficult. We finished all programs and had the absolute patent right.(7) This is the first study to use EM algorithm to estimate system noise covariance Q and measurement noise covariance R during adopting extend kalman filter to estimate the parameter in nonlinear dynamical state-space models for gene regulation and signal transduction networks. Since the state and state error covariance in the EKF depend on the initial values of parameters system noise covariance Q and the measurement noise covariance R. Thus, we consider a simple recursive procedure for estimation of the parameters Q and R. the precision of the algorithm is greatly improved.(8) We use the estimation of distribution algorithm for the first time to search the networks of epidemic disease data and compare it with genetic algorithm. Experiment results showed that the estimation of distribution algorithm has the following advantages: fast convergence speed, consume little time, easy to obtain the optimal solution and do not destroy the relationships between the variables.