核糖体流动模型的能控性分析与控制综合
Controllability analysis and control synthesis for the ribosome flow model
摘要：
沿着mRNA分子编码区的核糖体密度影响各种基本的细胞内现象，包括：蛋白质产生速率、生物体适应性、核糖体脱落和共翻译蛋白质折叠。因此，调节翻译以沿着mRNA分子获得所需的核糖体谱是一个重要的生物学问题。我们研究这个问题使用的mRNA翻译模型，称为核糖体流模型（RFM）。在RFM中，mRNA分子被建模为n个位点的链。n个状态变量描述了沿着mRNA分子的核糖体密度分布，而从每个位点到下一个位点的转换速率由n+1个正常数控制。为了研究控制密度分布的问题，我们考虑一些或所有的过渡率随时间变化的控制。我们考虑以下问题：给定一个初始的和所需的核糖体密度分布，确定引导RFM到这个密度分布的过渡率的时变值，如果它们存在的话。具体来说，我们考虑两个控制问题。在第一种情况下，所有的转换速率都可以被调节，目标是将核糖体密度分布和蛋白质产生速率从给定的初始值引导到期望值。在第二种情况下，控制单个转换速率，目标是将生产速率引导到期望值。在第一种情况下，我们表明，该系统是可控的，即控制是足够强大的，以引导RFM到任何所需的值，我们提供了封闭形式的表达式恒定的控制功能（或过渡率）渐近引导RFM到所需的值。对于第二个问题，我们表明，生产率可以被引导到任何所需的值在一个可行的区域由其他，恒定的过渡率。我们讨论了这些结果的生物学意义。
英文摘要：
The ribosomal density along the coding region of the mRNA molecule affect various fundamental intracellular phenomena including: protein production rates, organismal fitness, ribosomal drop off, and co-translational protein folding. Thus, regulating translation in order to obtain a desired ribosomal profile along the mRNA molecule is an important biological problem. We study this problem using a model for mRNA translation, called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as chain of n sites. The n state-variables describe the ribosomal density profile along the mRNA molecule, whereas the transition rates from each site to the next are controlled by n+1 positive constants. To study the problem of controlling the density profile, we consider some or all of the transition rates as time-varying controls. We consider the following problem: given an initial and a desired ribosomal density profile, determine the time-varying values of the transition rates that steer the RFM to this density profile, if they exist. Specifically, we consider two control problems. In the first, all transition rates can be regulated and the goal is to steer the ribosomal density profile and the protein production rate from a given initial value to a desired value. In the second, a single transition rate is controlled and the goal is to steer the production rate to a desired value. In the first case, we show that the system is controllable, i.e. the control is powerful enough to steer the RFM to any desired value, and we provide closed-form expressions for constant control functions (or transition rates) asymptotically steering the RFM to the desired value. For the second problem, we show that the production rate can be steered to any desired value in a feasible region determined by the other, constant transition rates. We discuss some of the biological implications of these results.
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