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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
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Today’s contents Statistical Genetics Mathematical approach
Genotype and Phenotype Graph to understand relations Mathematical approach Dynamics and differentiation
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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
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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
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What to study? How to study?
What do you want to know? How do you want to know it?
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Genetics Genotype Phenotype
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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.
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Genotype Phenotype Intermediate phenotype Terminal phenotype
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Graph (Theory) グラフ(理論)
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Pedigree 家系図
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Pedigree 家系図 phylogenetic tree 系統樹
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Phylogety, a tree
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Distance 距離
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Distance: More than one definition
距離にもいろいろな定義がある
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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.
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Difference among graphs グラフ間の違い
Same or different as a tree?
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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?
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Items can be expressed as a tree when distance among them are given.
Different “distances” give different trees.
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Graphs for data-analyses グラフによるデータ解析
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Heatmap Data-mining approach also uses trees.
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Tree needs “distance” with its definition.
Clustering methods also need definition to make tree structure..
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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.
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Relations among columns
Original data Relations among lines Relations among columns and lines
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Pedigrees are NOT graphs 家系図はグラフでは ない
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Trees in classical genetics: Pedigrees
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Relation between humans. Relation between chromosomes.
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A human relation can be multiple chromosomal relations.
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Chromosomes have two parental chromosomes.
But a base has only one parental base.
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Sexual and Asexual Reproduction Graph 有性生殖と無性生殖、とグラフ
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Genotype Phenotype Intermediate phenotype Terminal phenotype
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Types of Data データ タイプ
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Categorical data and sets.
カテゴリ型データと集合
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Ordered and Non-ordered.
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High-dimensional data and graph
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Genotype Phenotype Intermediate phenotype Terminal phenotype
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Networks ネットワーク
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? ? ? ? ? ? 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
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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
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Networks are complex ネットワークは複雑
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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
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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
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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.
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Time,Space 時間、空間 Dimensions 次元 Dimensions of data
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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
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Closed space 閉じた空間 Populations in “Space” and “Time”.
Finite space vs. Infinite Space
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Non-linear 非線形
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Stable Equilibrium 安定 定常
Models how to handle space and time.
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生物学のための数学 微分方程式を例に Mathematics for biology with differential equations
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? 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 統計遺伝学分野 山田 亮 南部総合研究1号館5階
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