Lecture03 hashing blast database search

zying / December 2022 (399 Words, 3 Minutes)

Global alignment vs. Local alignment

Needleman-Wunsch and Smith-Waterman

• Needleman-Wunsch 就是lecture02讲的比对算法（find the longest common sbusequence）
  • a type of global alignment
  • usually applied in homologous comparison
  • less useful for rearrangements, inversion or aligning to reference sequences
• Comparison of global, local and semi-global alignment
  • global alignment: end-to-end alignment; local alignment: comparison of substrings from different long strings
  • application:
    • comparing conserved parts of a gene in small domains
    • searching-finding a small gene in a large chromosome
    • analyzing rearrangements in large segments
  • From computional perspects, global align that starting at (0,0) and ending at Bottom right, but local align that starting at any position and ending anywhere
  • semi-global initializing from top row/left column to bottom row/right column

It’s enssential is a type of global alignment that cannot get penalty when exist gaps in the initial or terminal position

• Smith-Waterman作为local alignment 典型例子在needleman-wunsch的基础上，反复迭代每个位置作为起始位点记分至F=0止
  • 也可以通过在对角线周围限定范围降低时间和空间复杂度，但不一定能得到最优结果，实践效果却不错
• Varying gap penalty functions
  • Linear gap penalty: w(k)=k*p (每个gap罚相同的p分, 当前index是否有gap）
  • Quadratic: w(k)=p+q*rk^2 (考虑gap的长度，由于需要计算长度，增加了复杂度）
  • 加入binary value：starting a gap or not (添加第二个已经包含gap的矩阵）
  • Length （mod 3) gap penalty for protein-coding regions (考虑编码蛋白的密码子区域）
    • 将长度能被3整除的gaps赋予更少的得分（不会导致移码）
    • 要求更多的可能性声明
    • possible state：starting， mod 1=1,mod 2=2, mod 3=0

      Linear-time exact string matching

• Karp-Rabin algrithm and semi-numerical methods
  • interpret stings as numbers (fast comparison)
  • main:
    • compute next based on precious one
    • Hashing (mod p) to keep the numbers small
    • deal with spurious hits due to hashing collisions (处理变换之后重复的问题）
• Hash functions and randomized algorithms
  • 用mod p处理时间复杂度仍然高，减少数字范围优化
    • Hashing： 用hashing func mapping keys k in smaller space
    • Hashing func examples: x=y->h(x)=h(y) [reproducibility]; $x{\neq}y{\rightarrow}P(h(x)=h(y))=\frac{1}{m}$ [uniform output distrib] (输入字符不同，变换后相同的概率为1/m-均匀分布)
    • 存在一个新的问题：Collisions （不同的输入产生了相同的输出）
  • dealing with collisions , due to hashing
    • verify that a hit correspond to valid match (把所有比对上的序列都重新计算检查一遍）[耗时]
    • avoid worst-case behavior of many collisions (Choose random m) [合理]

      The BLAST algorithm and inexact matching

• Sequence Database search
  • Given a query seq to find similar old seqs
  • query must be very fast for a new sequence
  • most sequence will be completely unrelated to query
• BLAST Overview
  • receive query
    • split query into overlapping words of length W [重要参数]
    • find neighborhood words for each word until threshold T [重要参数]
    • look in table where words occur: seeds S
    • extend seeds S until score drops off under X
  • report significance and alignment of each match
  • W choosing:
    • Sequence length: n
    • Identities: t
    • W=[n/(n-t+1)]
  • Combs and Random projections

    Probabilistic foundations of sequence alignment

• Mismatch penalties, BLOSUM and PAM matrices
  • alignment score represent
    • likelihood ratio beteewn two hypotheses
      • H1: alignment due to chance (unrelated)
      • H2:alignment due to ancestry (related)
    • calcu probability
      • Pr(x,y|U): P of alignment x,y by model U (unrelated)
      • Pr(x,y|R): P of alignment x,y by model R (related)
    • Alignment score: likelihood ratio between the two
      • P that align not due to chance = P(x,y|R)/P(x,y|U)
      • Score=log(P)
  • Key idea of substitution Matrices: trust alignments of related seqences provide information about biologically permissible mutations
• Statistical significance of an alignment score

  Deterministic linear-time exact string matching

• Key insight: gather more info from each comparison
  • Special case （all same and all diff）
  • General case
    • learn internal redundancy structure of the pattern
    • Pattern pre-processing step
• Pre-processing, Z-algorithm, Boyer-More, KMP
  • 预处理序列，找出多次重复的pattern-Z-box
  • 如果z-box不在query seq, 直接比对，如果query seq上也有，基于P移动比对