导　　师： 庾建设;唐谟勋

学科专业： 070104

授予学位： 博士

作　　者： ;

机构地区： 广州大学

摘　　要： 基因表达是整个生命活动的中心过程，正常的生命活动，如干细胞的分化，胚胎与身体的发育，以及人体的免疫反应，都依赖于基因的正确表达;另一方面，许多疾病的产生与恶化都源于基因的突变或基因表达的紊乱。因此它的研究是当今生命科学研究的重要分支，也是分子生物学研究的核心课题。 基因表达把储存在DNA序列中的基因转变成具有生物活性的蛋白质分子，它主要包括两个过程：转录和翻译。在第一个过程中，根据碱基互补配对原则，DNA中的基因被转录成mRNA分子；在第二个过程中，mRNA分子被翻译成蛋白质分子。以前人们普遍认为基因表达是一个连续的、确定的过程。近年来由于计算机图像处理技术以及荧光蛋白技术的发展，生物学家们通过实验证实，基因表达是一个不连续的、随机的过程。在单个细胞中，基因表达的不连续性主要表现在基因的开启与闭合两种状态的更替；基因表达的随机性主要表现在开启或闭合状态下所持续时间的不确定性。为了定性地描述基因表达的随机性，生物学家们给出了多种量化方式，如噪声、噪声强度等。科学家们对基因表达的噪声与噪声强度进行了广泛的研究，但是他们一般采用两状态模型，并且认为基因开启和基因闭合这两个状态所持续的时间分别服从独立的指数分布。为了更好地描述外部环境信号对噪声与噪声强度的影响，近年来，三状态的基因转录模型被建立，并被广泛的研究，见/[17,80–82,85,86/]等。 本文是在三状态基因转录模型的基础上，计算和分析基因表达的均值、噪声与噪声强度，并重点讨论这些数值如何由基因转录的启动、mRNA和蛋白质合成和降解的随机过程等进行调节。本文的创新之处主要体现在以下几个方面： 1、利用三状态的基因转录模型，首次得到蛋白质均值的精确表达式，并发现基因表达的均值具有振动性。由于两状态模型基因表达的均值总是单调递增的，所以我们的三状态模型揭示的振动性第一次准确地模拟了生物学家们在真核细胞中观察到的蛋白质数量的振动现象。 2、当基因处于闭合状态的平均时间确定时，我们证明了，平衡状态下蛋白质的噪声随|κ-λ|的增大而增大（其中κ,λ分别表示外部环境信号的诱导强度和活化强度）。当κ=λ时，平衡状态下蛋白质的噪声最小；当κ=∞或λ=∞时，此时三状态模型退化为两状态模型，平衡状态下蛋白质的噪声最大。这也说明了，当基因处于闭合状态的平均时间确定时，平衡状态下三状态模型产生的噪声总是比两状态模型的噪声小。根据这一结果我们预测，如果细胞在确定时间内要完成一个转录周期，并使噪声变小，它可能会自然地选择由两步或更多步来完成。 3、我们得到平衡状态下蛋白质的噪声有一个很有意义的分解式。这个分解式简要地解释了Newman等/(2006，Nature/)，Yu等/(2006，Science/)，Raj等/(2010，Nature/)，Taniguchi等/(2010，Science/)的主要结论――蛋白质的噪声大于或等于蛋白质均值的倒数。有趣的是我们的分解式也准确地解释了Taniguchi等/(2010，Science/)另一个令人惊异的结果：在单个细胞内任何一个基因，mRNA的表达量与蛋白质的表达量总是不相关的。 4、我们证明了，平衡状态下蛋白质噪声的那个简洁分解式，在非平衡状态下不一定正确。同时我们的分析结果表明：与两状态模型相比，三状态模型蛋白质的噪声展示出更复杂的非单调的动力学行为。 本文的各章节安排如下：首先，第一章详细介绍基因表达的机制以及基因表达随机性的研究现状，同时也介绍我们的基因表达模型。其次，第二章我们得到蛋白质平均表达量的精确表达式。通过分析，我们发现对于三状态模型，基因表达的均值可能出现振动现象。这就意味着，三状态模型基因表达的均值能展示出非单调的复杂的动力学行为。再次，第三章我们得到平衡状态下蛋白质噪声与噪声强度的精确表达式，并对它们进行分析讨论，从而解释了一些重要的实验结果。最后，第四章主要讨论非平衡状态下基因表达噪声与噪声强度的动力学行为。与平衡状态相比，我们发现非平衡状态下基因表达的噪声与噪声强度展示出更复杂的动力学行为。 It is well known that gene expression plays a central role in the activity of life. Nor-mal life activities, such as stem cell differentiation, embryo development, physical growth,and immune response, depend on correct decoding of genes. Moreover, generation andaggravation of many diseases are caused by gene mutation or abnormal alteration of geneexpression. Therefore, the study of gene expression has been a core subject in molecularbiology, as well as an important research branch in the current study of life science. Gene expression transfers genes stored in DNA molecules to proteins. It consists oftwo main processes which are transcription and translation. In the first step, accordingto the principle of complementary base pairing, genes are transcribed to message RNA/(mRNA/) molecules. In the second step, mRNA molecules are translated into proteins. Itwas widely accepted in biology that genes were expressed in a deterministic and contin-uous way. In recent years，thanks to the development of computer image processing andfluorescent protein technique, biologists have shown that genes are expressed randomlyand discontinuously. In a single cell, the discontinuity of gene expression is reflected byrandom transition between gene off and gene on states. The stochasticity of gene expres-sion is manifested in variations of the durations in gene on or gene off states. In orderto measure quantitatively the stochasticity of gene expression, biologists have introduceda variety of statistical concepts, such as noise and noise strength. Many scientists havestudied the noise and noise strength in gene expression by using the two-state model. Inthese studies, the sojourn times in the gene on and gene off states are often assumed tobe independently and exponentially distributed. To better describe how the environmentalsignals contribute to the stochasticity of gene transcription, the three-state model of genetranscription has been recently proposed and broadly studied, see for example/[17,80–82,85,86/]. In this thesis, we calculate and analyze the mean, the noise, and the noise strengthof stochastic gene expression by employing the three-state model, and discuss how thesevalues are regulated by gene transcription, random birth and death processes of mRNAand protein. The main innovations of this thesis are as follows: 1. It is the first time in the literature to obtain the exact formula of the mean of protein numbers by using the three-state model, and show that the mean is of oscillatory behavior.As the two-state model always produces monotone growing curve for the mean expressionlevel, it is also the first time to provide the simulation of oscillatory phenomena observedin eukaryotic cells by the oscillatory dynamics exhibited by the three-state model. 2. We show that, given the same average gene off duration, the protein noise in-creases with the difference|κ-λ|under the equilibrium state /(where κ and λ denote theinduction strength and the activation strength of the environmental signals respectively/).The noise is minimal when κ=λ, and is maximal when either κ=∞orλ=∞,for which the three-state model is reduced to the two-state model. For the same averagegene off duration, the three-state model always produces less noises than the two-statemodel does. We conjecture that, to avoid higher expression noise, which may be deleteri-ous to cells, natural selection may favor two or more rate-limiting steps to complete onetranscription cycle in a given time. 3. Our analysis also gives a decomposition of the protein noise under the equilib-rium state, the far-reaching decomposition helps us explain why protein noise has beenrepeatedly found to be greater than or equal to the inverse of the mean protein levels inNewman el al./(2006，Nature/), Yu el al./(2006，Science/), Raj el al./(2010，Nature/) andTaniguchi el al./(2010，Science/). Also, it explains the striking findings of Taniguchi elal./(2010/) that the numbers of protein and mRNA for any given gene within the individualcells are uncorrelated. 4. We show that the interesting decomposition of the protein noise is not alwaysvalid under the nonequilibrium state. Our results indicate that the protein noise of thethree-state model is capable of producing non-monotonic dynamical complexity. This thesis is organized as follows: In Chapter1, we introduce the biological back-ground of stochastic gene expression and the three-state model. In Chapter2, we calculatethe exact formula of the average protein level from the three-state model, and then showthat it oscillates in some cases. This indicates, in principle, that the three-state modelis capable of producing non-monotonic dynamical complexity. In Chapter3, we obtainthe exact formulae of the noise and noise strength from the three-state model. We ex-plain many important experimental phenomena by analyzing our main results. In Chapter4, the dynamical behaviors of the noise and noise strength are discussed. We find that,comparing with the equilibrium state, the dynamical behavior is more complex.

关 键 词： 随机基因表达 噪声与噪声强度 动力学行为 数值模拟

分 类 号： [Q811.4]

领　　域： [生物学]