Mahaffy J M
Department of Mathematical Sciences, San Diego State University, CA 92182.
J Theor Biol. 1993 May 21;162(2):153-86. doi: 10.1006/jtbi.1993.1081.
A growing cell is not a steady-state situation. At some point in the cell cycle each gene doubles its concentration, which may result in a doubling of the production rate of its mRNA. The variations in concentration of mRNAs and proteins in an individual exponentially growing cell are studied for a gene which is constitutive, autorepressed, or autoactivated. Analysis of the mathematical model for a constitutive gene shows a fixed variation in concentration of a stable RNA between its minimum and maximum concentration of approximately 6%, independent of cell cycle time or gene location. The variation in the concentrations of the mRNA and protein for a constitutive gene are studied as gene position, molecular stability, and cell cycle time are varied. One result shows that doubling the growth rate can more than double the percentage of product from a gene near the origin of replication compared to one near the terminus. Results from these theoretical studies compare favorably to experimental results for rRNAs and the fully induced lac gene. Additional studies were performed to determine the effects of autorepression and autoactivation on the variation of concentration of mRNAs and proteins. The studies show that RNA and protein products of an autorepressed gene have almost the same variation in concentration as products of a constitutively expressed gene though the absolute concentrations are decreased. It is shown that the stability of an mRNA or protein affects variation in its concentration throughout the cell cycle, much more than the type of genetic control. The strength of repression has no effect on the variation in concentration of RNA and protein gene products through a cell cycle. Studies of an autoactivated gene show that it is significantly more responsive to a shift up or down, such as those caused by nutritional changes. An example is provided where the autoactivated gene is not expressed at one growth rate, but turns on at a higher growth rate. Furthermore, it is shown that gene position may determine whether or not the autoactivated gene is expressed.
正在生长的细胞并非处于稳态。在细胞周期的某个阶段，每个基因的浓度会加倍，这可能导致其mRNA产生速率加倍。对于一个组成型、自抑制型或自激活型基因，研究了单个指数生长细胞中mRNA和蛋白质浓度的变化。对组成型基因数学模型的分析表明，稳定RNA的浓度在其最小浓度和最大浓度之间的固定变化约为6%，与细胞周期时间或基因位置无关。随着基因位置、分子稳定性和细胞周期时间的变化，研究了组成型基因的mRNA和蛋白质浓度的变化。一个结果表明，与靠近末端的基因相比，将生长速率加倍可使来自复制起点附近基因的产物百分比增加一倍以上。这些理论研究的结果与rRNA和完全诱导的lac基因的实验结果相比具有优势。还进行了其他研究以确定自抑制和自激活对mRNA和蛋白质浓度变化的影响。研究表明，自抑制基因的RNA和蛋白质产物浓度变化与组成型表达基因的产物几乎相同，尽管绝对浓度有所降低。结果表明，mRNA或蛋白质的稳定性在整个细胞周期中对其浓度变化的影响远大于遗传控制类型。抑制强度对细胞周期中RNA和蛋白质基因产物的浓度变化没有影响。对自激活基因的研究表明，它对向上或向下的变化（如营养变化引起的变化）反应更为显著。给出了一个例子，自激活基因在一种生长速率下不表达，但在较高生长速率下开启。此外，结果表明基因位置可能决定自激活基因是否表达。
