# Intro - Computational Molecular Biology Introduction and...

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Computational Molecular Biology Introduction and Preliminaries

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My T. Thai [email protected] 2 Preliminaries in Computer Science Strings and alphabet Basic notations in graph theory Algorithms and Complexity
My T. Thai [email protected] 3 Strings Consist of a sequence of letters: DNA: four nucleotides A, C, G, T Proteins: 20 symbol alphabet of animo acids Given a string s , we have the following notations: Length: | s | Substring: ACT is a substring of ATGACTG Superstring: ATGACTG is a superstring of ACT Index and interval: s [ i ] and s [ i..j ] Prefix and suffix: s [ 1..j ] and s [ i.. | s |]

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My T. Thai [email protected] 4 Graphs G = (V, E) where V is a set of vertices and E is a set of edges Undirected graph: edges are undirected Directed graph: edges are directed Weighted graph G = (V, E, w ) where each edge has some weight Some special graphs: complete graph, bipartite graph, tree, and interval graph Subgraph, spanning tree, steiner tree
My T. Thai [email protected] 5 Interval Graphs Intersection graph of a set of intervals on the real line A vertex represents an interval and an edge (u, v) exists if intervals u and v intersect

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My T. Thai [email protected] 6 Some Problems in Graphs Euler circuit : Given a graph, find a cycle that passes through each edge exactly once Hamiltonian circuit : Given a graph, find a cycle that passes through each vertex exactly once Minimum Spanning Tree : Given a weighted undirected graph, find a spanning tree with minimum total weight Maximum Matching : Given an undirected graph, find a maximum cardinality matching, which is a subset of edges such that no two edges in the subset share an endpoint
My T. Thai [email protected] 7 P vs. NP Class of P : Set of problems solvable by polynomial-time algoirthms Class of NP : Set of problems whose solutions, once found, can be verified in polynomial time NP-complete (NP-hard) problems : cannot obtain an optimal solutions in polynomial time

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My T. Thai [email protected] 8 Some approaches for NP-complete Problems Special-case method : Work on the problem with a restricted class of inputs Exhaustive search : Design an exponential-time algorithms that may perform well in practice Approximation algorithms : Design a polynomial- time algorithm that is guaranteed to find near-optimal solutions (with a good approximation ratio) Heuristics : Fast algorithms that produce satisfactory solutions most of the time but without guarantee
My T. Thai [email protected] 9 Preliminaries in Molecular Biology

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My T. Thai [email protected] 10 DNA and Base Pairs Double helix consisting of two dual strands Has four types of nucleotides: Adenine, Thymine, Guanine, Cytosine Base Pairs: A↔T , C↔G Two ends of a strand are marked with 3 and 5 The entire DNA of a living organism is called its genome
My T. Thai [email protected] 11 DNA Sequences

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My T. Thai [email protected] 12 DNA Replication Strands are separated Each strand is replicated using one of the parental strands as a template
My T. Thai [email protected] 13 Cell, Chromosome, and DNA

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My T. Thai [email protected] 14 Cell Classification
My T. Thai

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Intro - Computational Molecular Biology Introduction and...

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