“Tree alignment”的意思、由来-开放百科全书

In computational phylogenetics, tree alignment is a computational problem concerned with producing multiple sequence alignments, or alignments of three or more sequences of DNA, RNA, or protein. Sequences are arranged into a phylogenetic tree, modeling the evolutionary relationships between species or taxa. The edit distances between sequences are calculated for each of the tree's internal vertices, such that the sum of all edit distances within the tree is minimized. Tree alignment can be accomplished using one of several algorithms with various trade-offs between manageable tree size and computational effort.

Definition

Input: A set

of sequences, a phylogenetic tree

leaf-labeled by

and an edit distance function

between sequences.

Output: A labeling of the internal vertices of

such that

is minimized, where

is the edit distance between the endpoints of

Background

Sequence alignment

In bioinformatics, the basic method of information processing is to contrast the sequence data. Biologists use it to discover the function, structure, and evolutionary information in biological sequences. The following analyses are based on the sequence assembly: the phylogenetic analysis, the haplotype comparison, and the prediction of RNA structure. Therefore, the efficiency of sequence alignment will directly affect the efficacy of solving these problems. In order to design a rational and efficient sequence alignment, the algorithm derivation becomes an important branch of research in the field of bioinformatics.

Generally, sequence alignment means constructing a string from two or more given strings with the greatest similarity by adding letters, deleting letters, or adding a space for each string. The multiple sequence alignment problem is generally based on pairwise sequence alignment and currently, for a pairwise sequence alignment problem, biologists can use a dynamic programming approach to obtain its optimal solution. However, the multiple sequence alignment problem is still one of the more challenging problems in bioinformatics. This is because finding the optimal solution for multiple sequence alignment has been proven as an NP-complete problem and only an approximate optimal solution can be obtained.^[2]

Distance matrix method

Distance method measures the minimum operation number of character insertions, deletions, and substitutions that are required to transform one sequence u to the other sequence v when being operated on a pair of strings. The calculation of edit distance can be based on dynamic programming, and the equation is in O(|u|×|v|) time, where |u| and |v| are the lengths of u and v.^[3] The efficient estimation of edit distance is essential as Distance method is a basic principle in computational biology ^[4] For functions of hereditary properties “symmetrization” can be used. Due to a series of functions being used to calculate edit distance, different functions may result in different results. Finding an optimal edit distance function is essential for the tree alignment problem.

The problem of tree alignment

Tree alignment results in a NP-hard problem, where scoring modes and alphabet sizes are restricted. It can be found as an algorithm, which is used to find the optimized solution. However, there is an exponential relationship between its efficiency and the number sequences, which means that when the length of the sequence is very large, the computation time required to get results is enormously long. Using star alignment to get the approximate optimized solution is faster than using tree alignment. However, whatever the degree of multiple-sequence similarity is, the time complexity of star alignment has a proportional relationship with the square of the sequence number and the square of the sequence average length. As usual, the sequence in MSA is so long that it is also inefficient or even unacceptable. Therefore, the challenge of reducing the time complexity to linear is one of the core issues in tree alignment.

Combinatorial optimization strategy

The keyword tree theory and the Aho-Corasick search algorithm

When the combinatorial optimization strategy is used to transform the multiple sequence alignment into pair sequence alignment, the main problem is changed from "How to improve the efficiency of multiple sequence alignment" to "How to improve the efficiency of pairwise sequence alignment." The Keyword Tree Theory and the Aho-Corasick search algorithm is an efficient approach to solve the pairwise sequence alignment problem. The aim of combining the keyword tree theory and the Aho-Corasick search algorithm is to solve this kind of problem: for a given long string

and a set of short strings

,… ,

} (z∈N,z>1), find the location of all

. The keyword tree produced by set

is used, and then searched for in

with this keyword tree through the Aho-Corasick search algorithm.^[6] The total time complexity of using this method to find all

’s location in the T is O(

), where

| (the length of

=∑|

| (the sum of all

's lengths) and

means the sum of occurrence for all

Keyword tree theory

The keyword tree of the setm

,… ,

} (z∈N,z>1) mis a rooted tree, whose root denoted by K, and this keyword tree satisfies:

(2): Any two edges separated from the same node are to correspond to different letters.

(3) Each pattern

(i=1,2,…,z) corresponds to a node

, and the path from the root K to the node

can exactly correctly spell the string

For each leaf node of this K tree, it corresponds to one of the certain patterns of set

For example, the set

={potato, tattoo, theater, other}, and the keyword tree is shown on the right. In that example, if

=potat, then

=|tat|=3, and the failure link of the node

is shown in that figure.

Establishing a failure link is the key to improve the time complexity of the Aho-Corasick algorithm. It can be used to reduce the original polynomial time to the linear time for searching. Therefore, the core of keyword tree theory is to find all failure links (which also means finding all

s) of a keyword tree in the linear time. It is assumed that every

of all nodes

, whose distance from the root node is less than or equal

, can be found. The

of the node

whose distance from the root node is

+ 1 can then be sought for. Its parent node is

, and the letter represented by the node

and

, is

(1): If the next letter of the node

, the other node of this edge can be set as

, and

(2): If all letters are not

by searching all edges between

and its child nodes,

is a suffix of

plus

. Because this suffix matches the STRING beginning with the root node (similar to prefix), the

after

can be detected or not. If not, this process can be continued until

or the root node is found.

Aho-Corasick search algorithm

After establishing all failure links in the keyword tree, the Aho-Corasick search algorithm is used to find the locations of all

(i=1,2,…,z) in the linear time. In this step, the time complexity is O(m+k).

Other strategies

In MSA, DNA, RNA, and proteins, sequences are usually generated and they are assumed to have an evolutionary relationship. By comparing generated maps of RNA, DNA, and sequences from evolutionary families, people can assess conservation of proteins and find functional gene domains by comparing differences between evolutionary sequences. Generally, heuristic algorithms and tree alignment graphs are also adopted to solve multiple sequence alignment problems.

Heuristic algorithm

Generally, heuristic algorithms rely on the iterative strategy, which is to say that based on a comparison method, optimizing the results of multiple sequence alignment by the iterative process. Davie M. proposed using the particle swarm optimization algorithm to solve the multiple sequence alignment problem; Ikeda Takahiro proposed a heuristic algorithm which is based on the A* search algorithm; E. Birney first proposed using the hidden Markov model to solve the multiple sequence alignment problem; and many other biologists use the genetic algorithm to solve it.^[8]^[9] All these algorithms generally are robust and insensitive to the number of sequences, but they also have shortcomings. For example, the results from the particle swarm optimization algorithm are unstable and its merits depend on the selection of random numbers, the runtime of the A* search algorithm is too long, and the genetic algorithm is easy to fall into local excellent.{{clarify|date=January 2019|reason=what does "local excellent" mean?}}

Tree alignment graph

Roughly, tree alignment graph aims to align trees into a graph and finally synthesize them to develop statistics. In biology, tree alignment graphs (TAGs) are used to remove the evolutionary conflicts or overlapping taxa from sets of trees and can then be queried to explore uncertainty and conflict. By integrating methods of aligning, synthesizing and analyzing, the TAG aims to solve the conflicting relationships and partial overlapping taxon sets obtained from a wide range of sequences. Also, the tree alignment graph serves as a fundamental approach for supertree and grafting exercises, which have been successfully tested to construct supertrees by Berry.^[10] Because the transformation from trees to a graph contain similar nodes and edges from their source trees, TAGs can also provide extraction of original source trees for further analysis. TAG is a combination of a set of aligning trees. It can store conflicting hypotheses evolutionary relationship and synthesize the source trees to develop evolutionary hypotheses. Therefore, it is a basic method to solve other alignment problems.^[11]