T.Y. Liu

Global Sensitivity Analysis of Cell Signalling Transduction Networks Based on Latin Hypercube Sampling Method

The dynamic behavior of a cell model is affected by its structural complexity and parametric uncertainties. Two important issues in systems biology are how to quantitatively determine the relationship between system behaviors and parameter variations, and how to study the interactions between parameters. Using an NF-kB signaling pathway model as an example, and assuming that the parameters of this model are independent of each other and obey the identical uniform distribution in the range of variations, the global sensitivity analysis on the system output of NF-kB in the nucleus with respect to parameters is studied by means of the Latin hypercube sampling method. Simulation results demonstrate that the oscillation behavior of the concentration of NF-kB in the nucleus is sensitive to 6 key rate constants, which relates to reactions of IKKBa mRNA degradation, IkBa inducible mRNA synthesis, IKK adaption, constitutive IkBa mRNA translation, IKK-IkBa NF-kB association, and IkBbeta mRNA degradation, respectively.

Minimum Entropy Control Algorithm for General Dynamic Stochastic Systems

In order to measure the uncertainty of the stochastic systems subjected to arbitrary noise disturbance instead of Gaussian white noise, the minimum entropy control of tracking errors for dynamic stochastic systems is presented in this paper. Different from conventional hypothesis, it is assumed that the system output and noise obey multi-to-one mapping, which is more general in the practical application. A controller design was described based on minimizing system output error entropy and a recursive optimization algorithm was set up for dynamic, non-Gaussian and nonlinear system. This approach only used the formula of the probability density function of the tracking error to calculate the controller and it did not need to know the style of the system model and the probability density function of noise, which often is difficult to measure in fact. An illustrative example is utilized to demonstrate the efficiency of the minimum entropy control algorithm and the approving simulation results have been gained

Parameter Estimation of Signal Transduction Pathways Using Probability Density Function of Measurement

Parameter estimation of signal transduction pathway models is a challenging task as such models are normally nonlinear, high dimensional, and the measurement data is limited and corrupted by noise. In this paper, a novel method for parameter estimation is proposed, in which the distance between the probability density function (PDF) of the model output and the PDF of the measurement data is minimized. This method has been applied to estimate unknown parameters of a TNFalpha- mediated NF-kappaB signal transduction pathway model. The simulation results show the effectiveness of this new algorithm.