生物学中随机过程与渠化耦合降噪
Noise reduction by coupling of stochastic processes and canalization in biology
摘要：
由于化学反应物以低拷贝数存在，随机性是细胞内环境的不可避免的特征。Delbrück在\cite{delbruck40}很久以前就预测了这种现象，在荧光技术发展之后，在原核\cite{elowitz02,cai06}和真核\cite{blake03}细胞中都检测到了这种现象。另一方面，发育中的生物体，例如{ \em D. melanogaster），显示出蛋白质/mRNA浓度\cite{gregor07b,manu09a,manu09b,boettiger09}的惊人精确的时空模式。生物体的这两个特征显然是矛盾的：蛋白质浓度的精确模式是多种相互作用的随机化学反应的结果。主要的问题是建立耦合随机反应的生化机制，以便进行渠化，或波动减少而不是放大。在这里，我们探讨了一个模型耦合两个随机过程的噪声可以小于孤立的。当且仅当模型的随机变量之间存在负协方差时，才会发生这种渠道化。我们的研究结果是在一个负自我调节-或外部调节-二元基因的主方程的框架中获得的，并表明由于负自我调节\cite{becskei00}的精确控制是因为它可能产生负协方差。我们的研究结果表明，负协方差，在随机化学反应的耦合，是一个理论机制的发展过程的精度。
英文摘要：
Randomness is an unavoidable feature of the intracellular environment due to chemical reactants being present in low copy number. That phenomenon, predicted by Delbrück long ago \cite{delbruck40}, has been detected in both prokaryotic \cite{elowitz02,cai06} and eukaryotic \cite{blake03} cells after the development of the fluorescence techniques. On the other hand, developing organisms, e.g. {\em D. melanogaster}, exhibit strikingly precise spatio-temporal patterns of protein/mRNA concentrations \cite{gregor07b,manu09a,manu09b,boettiger09}. Those two characteristics of living organisms are in apparent contradiction: the precise patterns of protein concentrations are the result of multiple mutually interacting random chemical reactions. The main question is to establish biochemical mechanisms for coupling random reactions so that canalization, or fluctuations reduction instead of amplification, takes place. Here we explore a model for coupling two stochastic processes where the noise of the combined process can be smaller than that of the isolated ones. Such a canalization occurs if, and only if, there is negative covariance between the random variables of the model. Our results are obtained in the framework of a master equation for a negatively self-regulated -- or externally regulated -- binary gene and show that the precise control due to negative self regulation \cite{becskei00} is because it may generate negative covariance. Our results suggest that negative covariance, in the coupling of random chemical reactions, is a theoretical mechanism underlying the precision of developmental processes.
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