The Application Of Stochastic Differential Equation System In Models With Noise Of Signaling Transduction Pathway And Metabolic Network

Bioinformatics has been developing from structural bioinformatics to functional bioinformatics and bioinformatics of so-called post genome era. Syetems biology can help us to study oejects in a systematic view.Models with noise are used to built more accurate mathematical models fitting the observed data. They also can help us to get the information of influence of noise in model and study the robustness property.From the study cases about stochastic modeling of the pathway of GPCR, RKIP regulated ERK pathway of signaling transduction network and the metabolic networks of Red Blood Cell, Purple Non-sulfur Bacteria or Escherichia coli repectively, this dissertation illustrate the application of stochastic differential equation system in models of signaling transduction pathway and metabolic network with noise.The researches of this paper accomplish five aspect works as follows:1. We first use stochastic differential equations system to model the pathway of GPCR and RKIP regulated ERK pathway of signaling transduction network repectively. And we use Monte Carlo (MC)> Markov Chain Monte Carlo (MCMC), combinational optimization strategy, i.e. particle swarm algorithm combined with down-hill simplex method and Maximun Likelihood (ML) estimation method to learn optimization parameters. Finally, we use learning parameters to do model simulatons.2. We do stochastic sensitivity analysis to models of the pathway of GPCR and RKIP regulated ERK pathway of signaling transduction network repectively. We mainly syudy the influence of trajectory number and the diffusion coefficient items of stochastic differential equations for simulation.3. We utilize stochastic differential equations system to model the metabolic networks of Red Blood Cell, Purple Non-sulfur Bacteria or Escherichia coli respectively. We get the model parameters from the metabolic flux analysis and also do simulation for these models.4. We use stochastic differential equations system to study the influence and transmission of signal noise source in Red Blood Cell, Purple Non-sulfur Bacteria and Escherichia coli repectively.5. According to the robust feature of biological metabolic networks, we utilize time-variable diffusion items of differential equation systems from two class of functions to model mechanism of noise suppression in metabolic netowrks. We also do numerical simulations and compare the results.Some primary conclusions can be drawn from the studies mentioned above.1. ML can get better results for fully observed data in learning for parameters of models. MC-. MCMC and combinational optimization strategy method can be used to get optimal model parameters for not completely observed data. But MCMC depends on priori probability distribution of parameters.2. Above methods of parameters learning for stochastic differential equation system are utilized repeatedly. The results show three classifications of variables in model, i.e., big noise, small noise and intermediate noise. In GPCR model, a-GDP bind G Protein and cAMP have big noise, while Active Adenylate Cyclase (AC) have small noise. In RKIP regulated ERK model, Raf-1* and MEK-PP have big noise, while Raf-1*/RKIP, Raf-1*/RKIP/ERK-PP, ERK, RKIP-P, MEK-PP/ERK and RKIP-P/RP have small noise. The methods can be used to predict noise producted by variables of new models.3. From the results of sensitivity analysis of stochastic conditions, we can find that a-GTP bind G Protein, Active Adenylate Cyclase (AC) and a-GDP bind G Protein are more easily affected by trajectory number, meanhile, a-GTP bind G Protein, a-GDP bind G Protein, Active Adenylate Cyclase (AC) and cAMP are more easily affected by coefficients diffusion items of stochastic differential equation system. It can also be found that ERK, RKIP-P, MEK-PP/ERK, Raf-1*/RKIP and Raf-1 */RKIP/ERK-PP are more easily affected by trajectory number and coefficients diffusion items in RKIP regulated ERK model.4. Stochastic noise fluctuation is more larger in metabolic networks of Purple Non-sulfur Bacteria or Escherichia coli than in Red Blood Cell according to the results of numerical simulation.5. We do noise transmission analysis by single noise source of 10,15 or 18 metabolites respectively in metabolic networks of Red Blood Cell, Purple Non-sulfur Bacteria or Escherichia coli. From existing data of network, it suggest that metabolic pathway and noise transmission rule of stochastic model are more similar in Purple Non-sulfur Bacteria and Escherichia coli.6. Numerical simulations are done for stichastic differential equation model with noise suppression. The results show that model noise can be confined to a small scope of variation of value. It reach the expectation to build model.Stochastic differential equation system can be used in modeling signaling transduction network and the metabolic networks with noise. It is a fine mathematical tools to study noise and its transmission in systems biology.