On stabilizability and exact observability of stochastic systems with their applications

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a necessary and sufficient condition is given for stabilizability and weak stabilizability of stochastic systems, respectively. Some new concepts called unremovable spectrums, strong solutions, and weakly feedback stabilizing solutions are introduced. An unremovable spectrum theorem is given, which generalizes the corresponding theorem of deterministic systems to stochastic systems. A stochastic Popov-Belevith-Hautus (PBH) criterion for exact observability is obtained. For applications, we give a comparison theorem for generalized algebraic Riccati equations (GAREs), and two results on Lyapunov-type equations are obtained, which improve the previous works. Finally, we also discuss robust quadratic stabilization of uncertain stochastic systems, and a necessary and sufficient condition is given for quadratic stabilization via a linear matrix inequality (LMI)

Construction of a cancer-perturbed protein-protein interaction network for discovery of apoptosis drug targets

<p>Abstract</p> <p>Background</p> <p>Cancer is caused by genetic abnormalities, such as mutations of oncogenes or tumor suppressor genes, which alter downstream signal transduction pathways and protein-protein interactions. Comparisons of the interactions of proteins in cancerous and normal cells can shed light on the mechanisms of carcinogenesis.</p> <p>Results</p> <p>We constructed initial networks of protein-protein interactions involved in the apoptosis of cancerous and normal cells by use of two human yeast two-hybrid data sets and four online databases. Next, we applied a nonlinear stochastic model, maximum likelihood parameter estimation, and Akaike Information Criteria (AIC) to eliminate false-positive protein-protein interactions in our initial protein interaction networks by use of microarray data. Comparisons of the networks of apoptosis in HeLa (human cervical carcinoma) cells and in normal primary lung fibroblasts provided insight into the mechanism of apoptosis and allowed identification of potential drug targets. The potential targets include BCL2, caspase-3 and TP53. Our comparison of cancerous and normal cells also allowed derivation of several party hubs and date hubs in the human protein-protein interaction networks involved in caspase activation.</p> <p>Conclusion</p> <p>Our method allows identification of cancer-perturbed protein-protein interactions involved in apoptosis and identification of potential molecular targets for development of anti-cancer drugs.</p

A network-based biomarker approach for molecular investigation and diagnosis of lung cancer

<p>Abstract</p> <p>Background</p> <p>Lung cancer is the leading cause of cancer deaths worldwide. Many studies have investigated the carcinogenic process and identified the biomarkers for signature classification. However, based on the research dedicated to this field, there is no highly sensitive network-based method for carcinogenesis characterization and diagnosis from the systems perspective.</p> <p>Methods</p> <p>In this study, a systems biology approach integrating microarray gene expression profiles and protein-protein interaction information was proposed to develop a network-based biomarker for molecular investigation into the network mechanism of lung carcinogenesis and diagnosis of lung cancer. The network-based biomarker consists of two protein association networks constructed for cancer samples and non-cancer samples.</p> <p>Results</p> <p>Based on the network-based biomarker, a total of 40 significant proteins in lung carcinogenesis were identified with carcinogenesis relevance values (CRVs). In addition, the network-based biomarker, acting as the screening test, proved to be effective in diagnosing smokers with signs of lung cancer.</p> <p>Conclusions</p> <p>A network-based biomarker using constructed protein association networks is a useful tool to highlight the pathways and mechanisms of the lung carcinogenic process and, more importantly, provides potential therapeutic targets to combat cancer.</p

Comparisons of Robustness and Sensitivity between Cancer and Normal Cells by Microarray Data

Robustness is defined as the ability to uphold performance in face of perturbations and uncertainties, and sensitivity is a measure of the system deviations generated by perturbations to the system. While cancer appears as a robust but fragile system, few computational and quantitative evidences demonstrate robustness tradeoffs in cancer. Microarrays have been widely applied to decipher gene expression signatures in human cancer research, and quantification of global gene expression profiles facilitates precise prediction and modeling of cancer in systems biology. We provide several efficient computational methods based on system and control theory to compare robustness and sensitivity between cancer and normal cells by microarray data. Measurement of robustness and sensitivity by linear stochastic model is introduced in this study, which shows oscillations in feedback loops of p53 and demonstrates robustness tradeoffs that cancer is a robust system with some extreme fragilities. In addition, we measure sensitivity of gene expression to perturbations in other gene expression and kinetic parameters, discuss nonlinear effects in feedback loops of p53 and extend our method to robustness-based cancer drug design

On the attenuation and amplification of molecular noise in genetic regulatory networks

BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based