| 摘要: | 基因組包含基因、其上游調控序列和重複序列。細胞在典型條件下，並非所有的基因都被激活。胞嘧啶，即A、T、C、G 之DNA 序列中的C，可以是被甲基化或非甲基化的。 C 的甲基化狀態，因此可以被認為是C 的一種內部自由度。甲基化胞嘧啶的分佈在哺乳動物的基因組間是保守的。特別是，重複序列區域是被甲基化，以及活性基因的調控區域是非甲基化的。的確，通過無數的分子生物學實驗，生物學家已經認識到在調控區的胞嘧啶甲基化會導致基因轉錄的沉默。在整個生命過程當中，DNA 甲基化可以被添加或丟失，這種改變較之於DNA 序列的突變更為輕易、頻繁。甲基化的改變會影響細胞功能。全基因組DNA 甲基化可由高密度的DNA 微陣列來測量。我們提議研究在有機體老化過程中，DNA 甲基化模式的改變。在物理，熵是亂度的一種衡量。在信息科學，熵是信息量。在沒有任何約束或偏見的情況下，基因組某區域的甲基化可有與無。於是甲基化密度沿著基因組看起來是均勻的。這種均勻分佈有一個最大熵。換句話說，最大化熵時的分佈，是一個最少偏頗或是最有可能的分佈。然而，細胞活動有所約束，以節約資源。例如，雖然代謝相關基因大部分時間被激活，但是壓力反應的基因只有在壓力下才會激活。在老化的甲基化研究，我們提出使用約束條件下最大熵的方法，來分析甲基化的數據。有條件的最大化可以用拉格朗日待定乘數的方法來實現。由於拉格朗日乘數是約束每單位變化下最大熵的偏離，拉格朗日方法的優點是，可以將乘數解釋為造就限制的一種力量。我們設想這力量在老化中鬆懈。也就是說，鬆懈的力量反應著老化過程。我們從加拿大的合作者獲得不同年齡小鼠的基因組甲基化數據。由於其量大的技術重複，這些數據是高質量的。我們將匯總此數據至一n 乘T 的長方形矩陣Y，其中n 為基因組區域的數量，T 是不同的年齡數。限制將由n 乘n 矩陣YYT 的特徵向量得出。力量的隨年齡變動將由T 乘T 矩陣YTY 的特徵值和特徵向量得出。拉格朗日待定乘數相共軛的限制裡的基因，會用生物信息學的方法研究出其生物功能。我們預計本研究項目將使造成老化的背後黑勢力現形。 Genome consists of genes, their upstream regulatory sequences and repetitive sequences. In a cell at typical condition, not all genes are activated. Cytosines, i.e. C of the A, T, C, G DNA sequence, can be either methyled or unmethylated. The methylation status of C therefore can be considered an internal degree of freedom of C. The distributions of methylated cytosines are conserved across mammalian genomes. In particular, the regions of repetitive sequences are methylated and the regulatory regions of active genes are unmethylated. It has indeed been recognized, through numerous molecular biology experiments, that cytosine methylation in the regulatory regions leads to transcriptional silencing of the genes. DNA methylation can be added or lost throughout life with greater ease and frequency than DNA sequence mutation. Altered methylation affects cellular functions. Genome-wide DNA methylation profiles can be measured by high density DNA microarrays. We propose to study changing DNA methylation patterns during organismal ageing. Entropy is defined as a measure of randomness in physics or information content in information theory. Without any constraint or bias, a genomic region can be methylated or unmethylated with equal chance. Methylation would look uniform along the genome. Such a uniform distributions have a maximum entropy. In other words, the distribution that maximizes entropy is the one that is least biased or most probable. Cells are subject to constraints in order to conserve resources. For example, whereas metabolism genes are activated most of the time, stress response genes are only activated upon stress. In the study of ageing methylation, we propose to analyze the methylation data by the use of maximum entropy under constraints. Constrained maximization can be achieved by the method of Lagrange undetermined multipliers. Since a Lagrange multiplier is the deviation of entropy from its maximum per unit change in the constraint, the merit of the Lagrangian method is that the multipliers can be interpreted as the forces that reinforce the constraints. We envision relaxing forces during ageing. That is, the relaxing forces recapitulate the ageing processes. We obtained genome-scale methylation data of mice at six ages from our Canadian collaborator. The data are of high quality owing to its high number of replications. We will summarize the data into an n by T rectangular matrix Y where n is the number of genomic regions and T the number of ages. The constraints will be derived from the eigenvectors of the n by n matrix YYT and the dynamics of the forces will be derived from the eigenvalues and eigenvectors of the T by T matrix YTY. Together with bioinformatics research on the biological functions of the genes in the constraints, which are conjugate to the multipliers, we expect the project to shed light on the forces behind ageing. 研究期間：10008 ~ 10107 |
