Multi-Pathway Gene Transcription Model And Analysis On Modulation Of Transcription Noises

Gene expression and regulation are the core problems of molecular biology as well as important branches in the present study of life science. As global popular topics, they have caused wide public concern from biology, physics, chemistry, medicine and so on. Many scientists have done profound research and have achieved great successes, and some of them were awarded the Nobel Prize for their outstanding contribution. For example, the2011Nobel Prize went to Beutler and Hoffmann for their discoveries concerning the activation of innate immunity.Gene transcription is the first and the most pivotal step in gene expression. It trans-fers the genetic information stored in the encoding DNAs to an instruction for the pro-duction of RNA molecules, and it determines the synthesis and structure of protein. Gene transcription is one stochastic process, and the stochasticity of gene transcription has been studied in both experiments and theory. With the development of RNA detection techniques, such as real-time monitoring of RNA synthesis in individual living cells, bi-ologists have found that genes are transcribed in a random, discontinuous and bursting fashion. The stochasticity leads asymmetrical and irregular distribution of RNAs and proteins.Some scientists are very interested in the stochasticity of gene expression and make intensive studies via mathematical methods. In order to characterize the stochasticity, some of them utilize statistical analysis [1,2] and numerical simulation [3], and some found mathematical models of gene transcription [4-6].As the development of biological technology, theoretical study on transcription has been developing quickly and many transcription models have been founded to illustrate the stochasticity. But the gene transcription was activated by a single signaling pathway at steady-state in their models. As transcription of many genes is involved with multiple distinct signal transduction pathways, the transcription factors (abbreviated as TF) will compete at their shared DNA binding sites, and modulate gene transcription with various binding patterns.In this thesis, we found the first multi-pathway gene transcription model based on experimental data obtained in experiments by biologists, then we study transcript level and distribution of RNA in cell. We make the following main improvements and inno-vations.-1. We found the first multi-pathway gene transcription model, which extends two or three state model;2. We study the gene transcription at transcription beginning by using three quantities:transcription efficiency, noise and noise strength, to characterize the stochasticity and analyze how the transcription efficiency and the noise strength are affected by the system parameters;3. We found the multi-pathway transcription model of RNA expression level according to the birth and death of RNA. The chapters of this thesis are arranged as follows:Firstly, we introduce the stochasticity of gene expression, transcription mechanisms and transcription process in detail in Chapter one. It was widely accepted that, in tran-scription process, gene was always activated [7] or the transcription system was assumed to be residing in two different functional states [8], i.e. the gene on state and the gene off state. More and more experimental data and studies revealed that the transcription system is residing in three functional states[9-13], so we found multi-pathway gene transcription model with two or three states in Chapter two.Secondly, we respectively study the gene transcription noise under the situation when the transcription system is at transcription beginning or steady state in Chapters three and four. In most of earlier studies, the gene transcription is activated by one single signaling pathway at steady state. But we find that the transcription process exhibits more complicated dynamics at transcription beginning. Using the renewal theorem and Laplace transform, we derive the analytical forms of transcription efficiency and noise strength. Our numerical examples demonstrate that the transcription system exhibits highly non-trivial dynamics, and the noise strength varies gradually over most values of the system parameters, but changes abruptly over a narrow range near some critical parameter values. One numerical simulation demonstrates that cross-talking signaling pathways are capable of inducing more cells to transcribe than the steady-state level after a short time period of signal transduction.With the help of the elementary renewal theorem and the central limit theorem, we prove that the stationary noise strength of transcription frequency is equal to the noise of the time spent in a single transcription cycle. Further analysis shows that cross-talking signaling pathways could produce noise strength of any prescribed magni-tude, in sharp contrast to the estimate [1/3,1) for transcription activated by one single pathway. If the noise is uncontrollable, the noisy transcription is detrimental to life. Thus, how to avoid these critical system parameters is critical to ensuring cells in stable state. In order to avoid unusually noisy transcription, our models and analysis give some effective mechanisms, which can control the transcription noise.Finally, combining the multi-pathway model of transcription frequency with the birth and death of RNA for the first time, we found the RNA transcript level model and derive the average transcript level, noise and noise strength in Chapter five. With the help of numerical examples, we find that they are closely related to the time spent in gene on state and transcription efficiency. We also prove that the noise strength by calculation in this part is basically consistent with the noise strength measured in experiment by Blake et al[14].