Statistical Genetics 統計遺伝学 2012/04/18 Ryo Yamada Unit of Statistical Genetics Center for Genomic Medicine Graduate School of Medicine Kyoto University
Today’s contents Statistical Genetics Mathematical approach Genotype and Phenotype Graph to understand relations Mathematical approach Dynamics and differentiation
太陽 おけら てのひら みみにみみず あめんぼ みつばち とんぼ かえる 私が両手をひろげても、 お空はちっとも飛べないが、 私が両手をひろげても、 お空はちっとも飛べないが、 飛べる小鳥は私のやうに、 地面（じべた）を速くは走れない。 私がからだをゆすっても、 きれいな音は出ないけど、 あの鳴る鈴は私のやうに、 たくさんな唄は知らないよ。 鈴と、小鳥と、それから私、 みんなちがって、みんないい。 みつばち とんぼ かえる 3
瓜二つ 瓜の蔓に茄子はならぬ 鳶が鷹を生む カエルの子はカエル 4
What to study? How to study? What do you want to know? How do you want to know it?
Genetics Genotype Phenotype
Genetics Genotype Phenotype Identity Variation How to grab “Genotype” and “Phenotype” with their “Identity” and “Variation”. One way is to make a catalogue of facts among “them”. The other way is to give a strategy to make the catalogue.
Genotype Phenotype Intermediate phenotype Terminal phenotype
Graph (Theory) グラフ(理論)
Pedigree 家系図
Pedigree 家系図 phylogenetic tree 系統樹
Phylogety, a tree
Distance 距離
Distance: More than one definition 距離にもいろいろな定義がある
Make graph from distance info 距離情報からグラフを作る Distance is a way to quantitate relation. Three items that make a triangle can be connected as a star without changing their pathway-distance.
Difference among graphs グラフ間の違い Same or different as a tree?
Difference among graphs グラフ間の違い Topology (Shape) and length of edges 位相(形)と辺の距離 Same or different as a tree?
Items can be expressed as a tree when distance among them are given. Different “distances” give different trees.
Graphs for data-analyses グラフによるデータ解析
Heatmap Data-mining approach also uses trees.
Tree needs “distance” with its definition. Clustering methods also need definition to make tree structure..
Data give trees and change the order in items. When the order in items are not changed and when relation among the items are displayed, it is correlation matrix.
Relations among columns Original data Relations among lines Relations among columns and lines
Pedigrees are NOT graphs 家系図はグラフでは ない
Trees in classical genetics: Pedigrees
Relation between humans. Relation between chromosomes.
A human relation can be multiple chromosomal relations.
Chromosomes have two parental chromosomes. But a base has only one parental base.
Sexual and Asexual Reproduction Graph 有性生殖と無性生殖、とグラフ
Genotype Phenotype Intermediate phenotype Terminal phenotype
Types of Data データ タイプ
Categorical data and sets. カテゴリ型データと集合
Ordered and Non-ordered.
High-dimensional data and graph
Genotype Phenotype Intermediate phenotype Terminal phenotype
Networks ネットワーク
? ? ? ? ? ? DNA配列 次世代 シークエンス eQTL GWAS E1 E2 E3 E4 E5 D1 D1a D2 D1b エピゲノム修飾 ? 次世代 シークエンス eQTL ? ネットワーク (転写物・翻訳物) ? ? ? GWAS ? E1 E2 E3 E4 E5 疾患に共通する因子 D1 疾患とその亜分類 D1a D2 D1b D2b D3 D2a D2c D4 D5
Components of graphs グラフの部品 Concepts of regulations/interactions 制御/相互関係の概念 Graphs are being used for biology
Networks are complex ネットワークは複雑
We can not grab the graph as a whole at once グラフ全体を一発で了解することは無理
Transition of Stata 状態推移 step-by-step 順番に Markov-chain マルコフ連鎖 Bayesian networks ベイズネットワーク
Genetic Heterogeneity and Transition of Stata 遺伝的多様性と状態推移 Three components to make genetic heterogeneity 遺伝的多様性を作る３要素 Mutations Recombinations Genetic drifts 変異 組換え 遺伝的浮動 Variants will drift out from the world.
Time,Space 時間、空間 Dimensions 次元 Dimensions of data
Data analyses and space of data
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Space may not be Euclidean 空間はユークリッド的でないかも
Closed space 閉じた空間 Populations in “Space” and “Time”. Finite space vs. Infinite Space
Non-linear 非線形
Stable Equilibrium 安定 定常 Models how to handle space and time.
生物学のための数学 微分方程式を例に Mathematics for biology with differential equations
? in Statistical genetics? Welcome Any questions on how to handle bio-medical data ? Also welcome Ryo Yamada, M.D., Ph.D. Unit of Statisical Genetics 5F Nanbu-sogo-kenkyu 1st Building ryamada@genome.med.kyoto-u.ac.jp 統計遺伝学分野 山田 亮 南部総合研究１号館５階 http://www.med.kyoto-u.ac.jp/E/grad_school/introduction/1525/