生物的調制包含了細胞內基因的調控與細胞間的訊息交換。充分瞭解基因調控系統的機制，再進一步操縱與使用，是現今生命科學最期待能有突破的重大課題。基因調控和基因的表現本質上是一種隨機程序，這種隨機行為的起源，可以歸結到在離散的操縱子狀態(處於自由態或是與一些轉錄因子結合的狀態)間的隨機躍遷，以及在調控單元 (指一個細胞、細菌或病毒)中所包含的去氧核糖核苷酸、核糖核苷酸、和調控蛋白質等一些相關的重要分子成分之個數很少所造成的高變異性。近年來，原核生物間集體感應機制的瞭解也為以實驗技術研究細胞間如何交換訊息帶來了突破性的進展。訊息交換後細胞便可藉著多數個體內的調控機制產生集體在基因表現態的變換。本計畫所要探討的就是因為這種生化反應本質上的隨機性對於生物族群的集體表現所造成的定性與定量影響。在對於主要的生化反應先給出一全面的概略描述後，再藉由詳細的電腦模擬與解析計算掌握系統的微觀特性的動態變化，進一步的了解隨機性與系統動態行為的相互作用。對於所得的結果，我們將嘗試以最大熵原理的觀念加以分析，試圖單以賦予適當測度的相空間、微觀反應式的守恆條件與系統和外界相互作用的關係重新檢視整個結果。 genetic regulation. Today the fully understanding, as well as the further manipulation, of the interwoven action of genes, mRNA, and proteins, commonly known as genetic regulatory networks, is one of the main issues in life science. Gene regulation and gene expression are inherently random processes. The origins of this stochastic behavior can be traced back to the random transitions among discrete chemical states (free or binding to some particular transcription factors) that dictate the transcription rates and to the very low copy number of many components, including DNA, mRNA and important regulatory protein molecules in a regulation unit (a cell, a bacterial, or a virus). The intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large influences on the response of biochemical networks. On the other hand, the recent explosion of advances in the fields of inter-cell communication in bacteria has shown that many bacteria release chemical signals to coordinate the behavior of the group. We are thus motivated to investigate what kind of quantitative and qualitative impact can the innate stochastic nature have on the behavior of gene-regulatory networks and the collective behavior of the group. We will first approach this problem by describing the key biochemical reactions in the biochemical networks in terms of rate laws. Then, the corresponding master equations for all the components in the network will be studied extensively by both numerical and analytical approaches. We plan to explore many facets of the interplay between the stochastic nature and the dynamics of the system. After the results come out, we will analyze the very problem through applying the Maximum Entropy principle on the phase space with appropriately assigned measure, constrained by some external conditions and conservation laws derived from the mass-action law equations.