A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in al...A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.展开更多
One of the most complex questions in quantitative biology is how to manage noise sources and the subsequent consequences for cell functions. Noise in genetic networks is inevitable, as chemical reactions are probabili...One of the most complex questions in quantitative biology is how to manage noise sources and the subsequent consequences for cell functions. Noise in genetic networks is inevitable, as chemical reactions are probabilistic and often, genes, mRNAs and proteins are present in variable numbers per cell. Previous research has focused on counting these numbers using experimental methods such as complex fluorescent techniques or theoretical methods by characterizing the probability distribution of mRNAs and proteins numbers in cells. In this work, we propose a modeling based approach;we build a mathematical model that is used to predict the number of mRNAs and proteins over time, and develop a computational method to extract the noise-related information in such a biological system. Our approach contributes to answering the question of how the number of mRNA and proteins change in living cells over time and how these changes induce noise. Moreover, we calculate the entropy of the system;this turns out to be important information for prediction which could allow us to understand how noise information is generated and expanded.展开更多
基金Supported by the National Science Foundation of China.
文摘A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.
基金Supported by National Natural Science Foundation of China(11471071)Natural Science Fundation of Shanghai(14ZR1401200)+1 种基金Shanghai Pujiang Program(16PJ1408000)Natural Science Fund of Shanghai Normal University(SK201603)
文摘One of the most complex questions in quantitative biology is how to manage noise sources and the subsequent consequences for cell functions. Noise in genetic networks is inevitable, as chemical reactions are probabilistic and often, genes, mRNAs and proteins are present in variable numbers per cell. Previous research has focused on counting these numbers using experimental methods such as complex fluorescent techniques or theoretical methods by characterizing the probability distribution of mRNAs and proteins numbers in cells. In this work, we propose a modeling based approach;we build a mathematical model that is used to predict the number of mRNAs and proteins over time, and develop a computational method to extract the noise-related information in such a biological system. Our approach contributes to answering the question of how the number of mRNA and proteins change in living cells over time and how these changes induce noise. Moreover, we calculate the entropy of the system;this turns out to be important information for prediction which could allow us to understand how noise information is generated and expanded.
