Extrinsic Noise Of CI Expression In Phage λ Lysogen

The specific protein level in a single cell is controlled by the gene regulatorynetwork, which is a complex stochastic process occurring in a cell. However, Thenoise along with the process is still a"mysterious thing". And many researchers foundit difficult to explain the noise within the existing theoretical framework. Several yearsago, Zhu et al [1] used 2-d Langevin equation and raised up a new method of potentialfunction to solve it, and it's better to explain the stability, robustness and switchingefficiency. Based on such a successful model, we remodel the system and calculatethe result to solve extrinsic noise and DNA looping event which was found by Zhu etal [1].In the recent paper by Anderson and Yang [2], we try to apply the stochasticdynamic model to this new experimental data. The mathematic form of this stochasticdynamical analysis method to model the system, Langevin equation, shows generalconsistency with the experimental results e.g. mean number of CI. However, thereis still variation between theoretical and experimental CI distributions of each strain,which we denote as the extrinsic noise outside the system, corresponding to intrinsicnoise inherent to the process itself. Thus we found the extrinsic noise can finallyenlarge the variation of distribution remarkably.As we extended our minimal 1-d Langevin model into 2-d stepwise Langevinmodel, mRNA acts an important role in making contribution to variation of CI dis-tribution, that could explain 40% to 70% of total variation. And we found noisy cellgrowth rate could also contribute to variation of CI distribution by enlarging about10% of variation, that is, 80% more or less for 4 mutants and near 50% for wild type.With more noise factors considered, we can better explain the experimental data andthe unknown extrinsic noise will be much smaller.