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2016 bioinformatics i_alignments_wim_vancriekinge

- Dynamic programming is used to find the optimal alignment between two protein sequences by recursively computing sub-alignments and storing them in a lookup table. - The example shows calculating the alignment score between a zinc-finger core sequence and a viral sequence fragment by filling a table and tracking the cumulative scores. - Filling the table from left to right and top to bottom allows reconstructing the highest scoring alignment between the two sequences.

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FBW 25-10-2016 Wim Van Criekinge
Rat versus mouse RBP Rat versus bacterial lipocalin
– Henikoff and Henikoff have compared the BLOSUM matrices to PAM by evaluating how effectively the matrices can detect known members of a protein family from a database when searching with the ungapped local alignment program BLAST. They conclude that overall the BLOSUM 62 matrix is the most effective. • However, all the substitution matrices investigated perform better than BLOSUM 62 for a proportion of the families. This suggests that no single matrix is the complete answer for all sequence comparisons. • It is probably best to compliment the BLOSUM 62 matrix with comparisons using 250 PAMS, and Overington structurally derived matrices. – It seems likely that as more protein three dimensional structures are determined, substitution tables derived from structure comparison will give the most reliable data. Overview
Available Dot Plot Programs Dotlet (Java Applet) http://www.isrec.isb- sib.ch/java/dotlet/Dotlet. html
Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
Global and local alignment Pairwise sequence alignment can be global or local Global: the sequences are completely aligned (Needleman and Wunsch, 1970) Local: only the best sub-regions are aligned (Smith and Waterman, 1981). BLAST uses local alignment.
– In order to characterize protein families, identify shared regions of homology in a multiple sequence alignment; (this happens generally when a sequence search revealed homologies to several sequences) – Determination of the consensus sequence of several aligned sequences – Help prediction of the secondary and tertiary structures of new sequences; – Preliminary step in molecular evolution analysis using Phylogenetic methods for constructing phylogenetic trees – Garbage in, Garbage out – Chicken/egg Why we do multiple alignments?
Why we do multiple alignments? • To find conserved regions – Local multiple alignment reveals conserved regions – Conserved regions usually are key functional regions – These regions are prime targets for drug developments • To do phylogenetic analysis: – Same protein from different species – Optimal multiple alignment probably implies history – Discover irregularities, such as Cystic Fibrosis gene
VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWWSNG--
Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
Algorithms and Programs • Algorithm: a method or a process followed to solve a problem. – A recipe. • An algorithm takes the input to a problem (function) and transforms it to the output. – A mapping of input to output. • A problem can have many algorithms.
Arayabhata-Euclid’s algorithm: How to find gcd(a,b), the greatest common divisor of a and b Based on a single observation: if a = b q + r, then any divisor of a and b is also a divisor of r, and any divisor of b and r is also a divisor of a, so gcd(a,b) = gcd(b,r) Euclid algorithm: use the division algorithm repeatedly To reduce the problem to one you can solve. Example: gcd(55,35) 55 = 35*1 + 20 so gcd(55,35) = gcd(35,20) 35 = 20*1 + 15 so gcd(35,20) = gcd(20,15) 20 = 15*1 + 5 done gcd(55,35) = 5
Pseudocode
GGD.py def gcd(a, b): while a != 0: a, b = b%a, a # parallel assignment return b print (gcd(55, 35))
Bubble Sort Algorithm 1. Initialize the size of the list to be sorted to be the actual size of the list. 2. Loop through the list until no element needs to be exchanged with another to reach its correct position. 2.1 Loop (i) from 0 to size of the list to be sorted - 2. 2.1.1 Compare the ith and (i + 1)st elements in the unsorted list. 2.1.2 Swap the ith and (i + 1)st elements if not in order ( ascending or descending as desired). 2.2 Decrease the size of the list to be sorted by 1. One of the simplest sorting algorithms proceeds by walking down the list, comparing adjacent elements, and swapping them if they are in the wrong order. The process is continued until the list is sorted. More formally: Each pass "bubbles" the largest element in the unsorted part of the list to its correct location. A 13 7 43 5 3 19 2 23 29 ?? ?? ?? ?? ??
Bubble Sort Implementation void BubbleSort(int List[] , int Size) { int tempInt; // temp variable for swapping list elems for (int Stop = Size - 1; Stop > 0; Stop--) { for (int Check = 0; Check < Stop; Check++) { // make a pass if (List[Check] > List[Check + 1]) { // compare elems tempInt = List[Check]; // swap if in the List[Check] = List[Check + 1]; // wrong order List[Check + 1] = tempInt; } } } } Bubblesort compares and swaps adjacent elements; simple but not very efficient. Efficiency note: the outer loop could be modified to exit if the list is already sorted. Here is an ascending-order implementation of the bubblesort algorithm for integer arrays:
"Great algorithms are the poetry of computation"
"Great algorithms are the poetry of computation" 1946: The Metropolis Algorithm for Monte Carlo. Through the use of random processes, this algorithm offers an efficient way to stumble toward answers to problems that are too complicated to solve exactly. 1947: Simplex Method for Linear Programming. An elegant solution to a common problem in planning and decision-making. 1950: Krylov Subspace Iteration Method. A technique for rapidly solving the linear equations that abound in scientific computation. 1951: The Decompositional Approach to Matrix Computations. A suite of techniques for numerical linear algebra. 1957: The Fortran Optimizing Compiler. Turns high-level code into efficient computer-readable code. 1959: QR Algorithm for Computing Eigenvalues. Another crucial matrix operation made swift and practical. 1962: Quicksort Algorithms for Sorting. For the efficient handling of large databases. 1965: Fast Fourier Transform. Perhaps the most ubiquitous algorithm in use today, it breaks down waveforms (like sound) into periodic components. 1977: Integer Relation Detection. A fast method for spotting simple equations satisfied by collections of seemingly unrelated numbers. 1987: Fast Multipole Method. A breakthrough in dealing with the complexity of n-body calculations, applied in problems ranging from celestial mechanics to protein folding. From Random Samples, Science page 799, February 4, 2000.
Algorithm Properties • An algorithm possesses the following properties: – It must be correct. – It must be composed of a series of concrete steps. – There can be no ambiguity as to which step will be performed next. – It must be composed of a finite number of steps. – It must terminate. • A computer program is an instance, or concrete representation, for an algorithm in some programming language.
Measuring Algorithm Efficiency • Types of complexity – Space complexity – Time complexity • Analysis of algorithms – The measuring of the complexity of an algorithm • Cannot compute actual time for an algorithm – We usually measure worst-case time
Measuring Algorithm Efficiency Three algorithms for computing 1 + 2 + … n for an integer n > 0
Measuring Algorithm Efficiency The number of operations required by the algorithms
Measuring Algorithm Efficiency The number of operations required by the algorithms as a function of n
Big Oh Notation • To say "Algorithm A has a worst-case time requirement proportional to n" – We say A is O(n) – Read "Big Oh of n" • For the other two algorithms – Algorithm B is O(n2) – Algorithm C is O(1) • O is derived from order (magnitude)
Picturing Efficiency O(n) algorithm
Picturing Efficiency An O(n2) algorithm.
Picturing Efficiency Another O(n2) algorithm.
Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
The best alignment: The one with the maximum total score
• Exhaustive … – All combinations: • Algorithm – Dynamic programming (much faster) • Heuristics – Needleman – Wunsh for global alignments (Journal of Molecular Biology, 1970) – Later adapated by Smith-Waterman for local alignment Overview
• Score of an alignment: reward matches and penalize mismatches and spaces. – eg, each column gets a (different) value for: • a match: +1, (both have the same characters); • a mismatch : -1, (both have different characters); and • a space in a column: -2. – The total score of an alignment is the sum of the values assigned to its columns.
A metric … GACGGATTAG, GATCGGAATAG GA-CGGATTAG GATCGGAATAG +1 (a match), -1 (a mismatch),-2 (gap) 9*1 + 1*(-1)+1*(-2) = 6
Dynamic programming Reduce the problem: the solution to a large problem is to simplify … if we first know the solution to a smaller problem that is a subset of the larger problem Overview P P2P1 P3 P
Dynamic Programming • Finding optimal solution to search problem • Recursively computes solution • Fundamental principle is to produce optimal solutions to smaller pieces of the problem first and then glue them together • Efficient divide-and-conquer strategy because it uses a bottom-up approach and utilizes a look-up table instead of recomputing optimal solutions to sub- problems P P2P1 P3 P
the best alignment between • a zinc-finger core sequence: –CKHVFCRVCI • and a sequence fragment from a viral polyprotein: –CKKCFCKCV
C K H V F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 1 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 2 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 0 K | 1 0 0 C | 1 1 1 0 F | 1 0 0 C | 1 1 1 0 K | 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 1 0 K | 1 1 0 0 K | 1 1 0 0 C | 1 1 1 1 0 F | 1 1 0 0 C | 1 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 1 1 1 1 0 K | 1 1 1 0 0 K | 1 1 1 0 0 C | 1 1 1 1 1 0 F | 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 2 1 1 1 0 K | 1 1 1 1 0 0 K | 1 1 1 1 0 0 C | 1 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 2 2 1 1 1 0 K | 1 2 1 1 1 0 0 K | 1 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 3 2 2 1 1 1 0 K | 1 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 1 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
C K H V F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
Needleman-Wunsch-Simple.py
Needleman-Wunsch-Simple.py The Score Matrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1
The Score Matrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 Needleman-Wunsch-Simple.py
The Score Matrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 a bc A: matrix(i,j) = matrix(i-1,j-1) + (MIS)MATCH if (substr(seq1,j-1,1) eq substr(seq2,i-1,1) B: up_score = matrix(i-1,j) + GAP C: left_score = matrix(i,j-1) + GAP Needleman-Wunsch-Simple.py
The Score Matrix ---------------- Seq1(j)1 2 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 Needleman-Wunsch-Simple.py
Needleman-Wunsch-Simple.py
Seq1:CKHVFCRVCI Seq2:CKKCFC-KCV ++--++--+- score = 0 Needleman-Wunsch-Simple.py
Extensions to basic dynamic programming method use gap penalties – constant gap penalty for gap > 1 – gap penalty proportional to gap size • one penalty for starting a gap (gap opening penalty) • different (lower) penalty for adding to a gap (gap extension penalty) use blosum62 • instead of MATCH and MISMATCH Dynamic Programming: Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Needleman-Wunsch-Complete.py
Uses of Needleman-Wunsch-Complete.py • Time Complexity • Use random proteins to generate histogram of scores from aligned random sequences
Time complexity with Needleman-Wunsch-Complete.py Sequence Length (aa) Execution Time (s) 10 0:00:00.001500 25 0:00:00.005340 50 0:00:00.020112 100 0:00:00.081580 500 0:00:01.960721 1000 0:00:07.720884 10000 0:11:36.344549 100000 Memory could not be written
Simple version (Match/Mismatch) – no gap extension
Complete version !
True positives False positives False negatives Sequences reported as related Sequences reported as unrelated True negatives homologous sequences non-homologous sequences Sensitivity: ability to find true positives Specificity: ability to minimize false positives
If the sequences are similar, the path of the best alignment should be very close to the main diagonal. Therefore, we may not need to fill the entire matrix, rather, we fill a narrow band of entries around the main diagonal. An algorithm that fills in a band of width 2k+1 around the main diagonal.
Local alignment • The concept of ‘local alignment’ was introduced by Smith & Waterman in 1981 • A local alignment of 2 sequences is an alignment between parts of the 2 sequences Two proteins may one share one stretch of high sequence similarity, but be very dissimilar outside that region A global (N-W) alignment of such sequences would have: (i) lots of matches in the region of high sequence similarity (ii) lots of mismatches & gaps (insertions/deletions) outside the region of similarity It makes sense to find the best local alignment instead
Smith-Waterman.py • Three changes – The edges of the matrix are initialized to 0 instead of increasing gap penalties – The maximum score is never less than 0, and no pointer is recorded unless the score is greater than 0 – The trace-back starts from the highest score in the matrix (rather than at the end of the matrix) and ends at a score of 0 (rather than the start of the matrix)
Smith-Waterman.py
Smith-Waterman.py
Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
The best alignment: The one with the maximum total score Multiple Aligment: n>2
2 to 3: hyperlattice
On its top-left side, the cube is "covered" by the polyhedron. The edges 1, 2, 3, 6 and 7 are coming from the inside, and edges 4 and 5 can be ignored (and are therefore not labeled in the figure).
• Each node in the k-dimensional hyperlattice is visited once, and therefore the running time must be proportional to the number of nodes in the lattice. – This number is the product of the lengths of the sequences. – eg. the 3-dimensional lattice as visualized. Computational Complexity of MA by standard Dynamic Programming
• The memory space requirement is even worse. To trace back the alignment, we need to store the whole lattice, a data structure the size of a multidimensional skyscraper. – In fact, space is the No.1 problem here, bogging down multiple alignment methods that try to achieve optimality. – Furthermore, incorporating a realistic gap model, we will further increase our demands on space and running time
Size/Time limits…
• The most practical and widely used method in multiple sequence alignment is the hierarchical extensions of pairwise alignment methods. • The principal is that multiple alignments is achieved by successive application of pairwise methods. – First do all pairwise alignments (not just one sequence with all others) – Then combine pairwise alignments to generate overall alignment Multiple Alignment Method
• The steps are summarized as follows: – Compare all sequences pairwise. – Perform cluster analysis on the pairwise data to generate a hierarchy for alignment. This may be in the form of a binary tree or a simple ordering – Build the multiple alignment by first aligning the most similar pair of sequences, then the next most similar pair and so on. Once an alignment of two sequences has been made, then this is fixed. Thus for a set of sequences A, B, C, D having aligned A with C and B with D the alignment of A, B, C, D is obtained by comparing the alignments of A and C with that of B and D using averaged scores at each aligned position. Multiple Alignment Method
Multiple Alignment Method
Multiple Alignment Method
• Automatic multiple alignemnt – extend dynamic programming (MSA - Lipman) • limit: computing power: length and number of sequences (e.q. 2000^8) – progressive alignment (Feng & Doolittle) • use “guide tree” (PileUp, ClustalW etc) • Dedicated alignment editing program – Boxshade – SeaView – SeqPup (Java) • Combination (Biology – Computation) Multiple Sequence Alignment programs
• ClustalW is a general purpose multiple alignment program for DNA or proteins. • ClustalW is produced by Julie D. Thompson, Toby Gibson of European Molecular Biology Laboratory, Germany and Desmond Higgins of European Bioinformatics Institute, Cambridge, UK. Algorithmic • Improves the sensitivity of progressive multiple sequence alignment through sequence weighting, positions-specific gap penalties and weight matrix choice. Nucleic Acids Research, 22:4673-4680. ClustalW
****** MULTIPLE ALIGNMENT MENU ****** 1. Do complete multiple alignment now (Slow/Accurate) 2. Produce guide tree file only 3. Do alignment using old guide tree file 4. Toggle Slow/Fast pairwise alignments = SLOW 5. Pairwise alignment parameters 6. Multiple alignment parameters 7. Reset gaps between alignments? = OFF 8. Toggle screen display = ON 9. Output format options S. Execute a system command H. HELP or press [RETURN] to go back to main menu Your choice: Running ClustalW
• The final product of a PILEUP run is a set of aligned sequences, which are stored in a Multiple Sequence File (called .msf by GCG). This msf file is a text file that can be formatted with a text editor, but GCG has some dedicated tools for improving the looks of msf files for easier interpretation and for publication. • Consensus sequences can be calculated and the relationship of each character of each sequence to the consensus can be highlighted using the program PRETTY Formatting Multiple Alignments
• Shading of regions of high homology can be created using the programs BOXSHADE and PRETTYBOX , but that goes beyond the scope of this tutorial. (Boxshade: http://www.ch.embnet.org/software/BOX_form.html) • In addition to these programs that run on the Alpha, the output of PILEUP (or CLUSTAL) can be moved by FTP from your RCR account to a local Mac or PC. • Since this output is a plain text file, it can be edited with any word processing program, or imported into any drawing program to add boldface text, underlining, shading, boxes, arrows, etc Formatting Multiple Alignments
http://dot.imgen.bcm.tmc.edu:9331/multi-align/multi-align.html
VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWWSNG-- An example of Multiple Alignment … immunoglobulin
• Their alignment highlights conserved residues (one of the cysteines forming the disulphide bridges, and the tryptophan are notable) • conserved regions (in particular, "Q.PG" at the end of the first 4 sequences), and more sophisticated patterns, like the dominance of hydrophobic residues at fragment positions 1 and 3. • The alternating hydrophobicity pattern is typical for the surface beta-strand at the beginning of each fragment. Indeed, multiple alignments are helpful for protein structure prediction. An example of Multiple Alignment … immunoglobulin
• Providing the alignment is accurate then the following may be inferred about the secondary structure from a multiple sequence alignment.  The position of insertions and deletions (INDELS) suggests regions where surface loops exist.  Conserved glycine or proline suggests a beta-turn. A Practical Approach: Interpretation
• Residues with hydrophobic properties conserved at i, i+2, i+4 separated by unconserved or hydrophilic residues suggest surface beta- strands.  A short run of hydrophobic amino acids (4 residues) suggests a buried beta- strand.  Pairs of conserved hydrophobic amino acids separated by pairs of unconserved, or hydrophilic residues suggests an alfa-helix with one face packing in the protein core. Likewise, an i, i+3, i+4, i+7 pattern of conserved hydrophobic residues. A Practical Approach: Interpretation
• Take out noise (GAPS) • Extra information (structure - function) • Recursive selection – first most similar to have an idea about conserved regions – manual scan for these in more distant members then include these A Practical Approach: Which sequences to use ?
Sequence Alignments Introduction Algorithms What ? Examples Properties Dynamic Programming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
L-align (2 sequences) SIM (www.expasy.ch) LALNVIEW is available for UNIX, Mac and PC on the ExPASy anonymous FTP server. very nice TWEAKING tool (70% criteria)
Length P-value SIM
SIM
SIM
How can I use NCBI to compare two sequences? Answer: Use the “BLAST 2 Sequences” program
• Go to http://www.ncbi.nlm.nih.gov/BLAST • Choose BLAST 2 sequences • In the program, [1] choose blastp (protein search) or blastn (for DNA) [2] paste in your accession numbers (or use FASTA format) [3] select optional parameters, such as --BLOSU62 matrix is default for proteins try PAM250 for distantly related proteins --gap creation and extension penalties [4] click “align” Practical guide to pairwise alignment: the “BLAST 2 sequences” website
Question #2: How can I use NCBI to compare a sequence to an entire database? BLAST!
Weblems W4.1: Align the amino acid sequence of acetylcholine receptor from human, rat, mouse, dog with ClustalW T-Coffee Dali MSA W4.2: Use BoxShade to create a word file indicating the different conserved resides in colours W4.3: Perform a LocalAlignent using SIM and Lalign on the same sequence and Blast2 W4.4: Do the different methods give different results, what are the default settings they use ? W4.5: How would you identify critical residues for catalytic activity ?

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2016 bioinformatics i_alignments_wim_vancriekinge

  • 2.
  • 4.
    Rat versus mouse RBP Ratversus bacterial lipocalin
  • 5.
    – Henikoff andHenikoff have compared the BLOSUM matrices to PAM by evaluating how effectively the matrices can detect known members of a protein family from a database when searching with the ungapped local alignment program BLAST. They conclude that overall the BLOSUM 62 matrix is the most effective. • However, all the substitution matrices investigated perform better than BLOSUM 62 for a proportion of the families. This suggests that no single matrix is the complete answer for all sequence comparisons. • It is probably best to compliment the BLOSUM 62 matrix with comparisons using 250 PAMS, and Overington structurally derived matrices. – It seems likely that as more protein three dimensional structures are determined, substitution tables derived from structure comparison will give the most reliable data. Overview
  • 6.
    Available Dot PlotPrograms Dotlet (Java Applet) http://www.isrec.isb- sib.ch/java/dotlet/Dotlet. html
  • 7.
    Sequence Alignments Introduction Algorithms What ? Examples Properties DynamicProgramming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
  • 8.
    Global and localalignment Pairwise sequence alignment can be global or local Global: the sequences are completely aligned (Needleman and Wunsch, 1970) Local: only the best sub-regions are aligned (Smith and Waterman, 1981). BLAST uses local alignment.
  • 9.
    – In orderto characterize protein families, identify shared regions of homology in a multiple sequence alignment; (this happens generally when a sequence search revealed homologies to several sequences) – Determination of the consensus sequence of several aligned sequences – Help prediction of the secondary and tertiary structures of new sequences; – Preliminary step in molecular evolution analysis using Phylogenetic methods for constructing phylogenetic trees – Garbage in, Garbage out – Chicken/egg Why we do multiple alignments?
  • 10.
    Why we domultiple alignments? • To find conserved regions – Local multiple alignment reveals conserved regions – Conserved regions usually are key functional regions – These regions are prime targets for drug developments • To do phylogenetic analysis: – Same protein from different species – Optimal multiple alignment probably implies history – Discover irregularities, such as Cystic Fibrosis gene
  • 11.
  • 12.
    Sequence Alignments Introduction Algorithms What ? Examples Properties DynamicProgramming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
  • 13.
    Algorithms and Programs •Algorithm: a method or a process followed to solve a problem. – A recipe. • An algorithm takes the input to a problem (function) and transforms it to the output. – A mapping of input to output. • A problem can have many algorithms.
  • 15.
    Arayabhata-Euclid’s algorithm: Howto find gcd(a,b), the greatest common divisor of a and b Based on a single observation: if a = b q + r, then any divisor of a and b is also a divisor of r, and any divisor of b and r is also a divisor of a, so gcd(a,b) = gcd(b,r) Euclid algorithm: use the division algorithm repeatedly To reduce the problem to one you can solve. Example: gcd(55,35) 55 = 35*1 + 20 so gcd(55,35) = gcd(35,20) 35 = 20*1 + 15 so gcd(35,20) = gcd(20,15) 20 = 15*1 + 5 done gcd(55,35) = 5
  • 16.
  • 17.
    GGD.py def gcd(a, b): whilea != 0: a, b = b%a, a # parallel assignment return b print (gcd(55, 35))
  • 18.
    Bubble Sort Algorithm 1.Initialize the size of the list to be sorted to be the actual size of the list. 2. Loop through the list until no element needs to be exchanged with another to reach its correct position. 2.1 Loop (i) from 0 to size of the list to be sorted - 2. 2.1.1 Compare the ith and (i + 1)st elements in the unsorted list. 2.1.2 Swap the ith and (i + 1)st elements if not in order ( ascending or descending as desired). 2.2 Decrease the size of the list to be sorted by 1. One of the simplest sorting algorithms proceeds by walking down the list, comparing adjacent elements, and swapping them if they are in the wrong order. The process is continued until the list is sorted. More formally: Each pass "bubbles" the largest element in the unsorted part of the list to its correct location. A 13 7 43 5 3 19 2 23 29 ?? ?? ?? ?? ??
  • 19.
    Bubble Sort Implementation voidBubbleSort(int List[] , int Size) { int tempInt; // temp variable for swapping list elems for (int Stop = Size - 1; Stop > 0; Stop--) { for (int Check = 0; Check < Stop; Check++) { // make a pass if (List[Check] > List[Check + 1]) { // compare elems tempInt = List[Check]; // swap if in the List[Check] = List[Check + 1]; // wrong order List[Check + 1] = tempInt; } } } } Bubblesort compares and swaps adjacent elements; simple but not very efficient. Efficiency note: the outer loop could be modified to exit if the list is already sorted. Here is an ascending-order implementation of the bubblesort algorithm for integer arrays:
  • 20.
    "Great algorithms arethe poetry of computation"
  • 21.
    "Great algorithms arethe poetry of computation" 1946: The Metropolis Algorithm for Monte Carlo. Through the use of random processes, this algorithm offers an efficient way to stumble toward answers to problems that are too complicated to solve exactly. 1947: Simplex Method for Linear Programming. An elegant solution to a common problem in planning and decision-making. 1950: Krylov Subspace Iteration Method. A technique for rapidly solving the linear equations that abound in scientific computation. 1951: The Decompositional Approach to Matrix Computations. A suite of techniques for numerical linear algebra. 1957: The Fortran Optimizing Compiler. Turns high-level code into efficient computer-readable code. 1959: QR Algorithm for Computing Eigenvalues. Another crucial matrix operation made swift and practical. 1962: Quicksort Algorithms for Sorting. For the efficient handling of large databases. 1965: Fast Fourier Transform. Perhaps the most ubiquitous algorithm in use today, it breaks down waveforms (like sound) into periodic components. 1977: Integer Relation Detection. A fast method for spotting simple equations satisfied by collections of seemingly unrelated numbers. 1987: Fast Multipole Method. A breakthrough in dealing with the complexity of n-body calculations, applied in problems ranging from celestial mechanics to protein folding. From Random Samples, Science page 799, February 4, 2000.
  • 22.
    Algorithm Properties • Analgorithm possesses the following properties: – It must be correct. – It must be composed of a series of concrete steps. – There can be no ambiguity as to which step will be performed next. – It must be composed of a finite number of steps. – It must terminate. • A computer program is an instance, or concrete representation, for an algorithm in some programming language.
  • 23.
    Measuring Algorithm Efficiency •Types of complexity – Space complexity – Time complexity • Analysis of algorithms – The measuring of the complexity of an algorithm • Cannot compute actual time for an algorithm – We usually measure worst-case time
  • 24.
    Measuring Algorithm Efficiency Threealgorithms for computing 1 + 2 + … n for an integer n > 0
  • 25.
    Measuring Algorithm Efficiency Thenumber of operations required by the algorithms
  • 26.
    Measuring Algorithm Efficiency Thenumber of operations required by the algorithms as a function of n
  • 27.
    Big Oh Notation •To say "Algorithm A has a worst-case time requirement proportional to n" – We say A is O(n) – Read "Big Oh of n" • For the other two algorithms – Algorithm B is O(n2) – Algorithm C is O(1) • O is derived from order (magnitude)
  • 28.
  • 29.
  • 30.
  • 31.
    Sequence Alignments Introduction Algorithms What ? Examples Properties DynamicProgramming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
  • 32.
    The best alignment: Theone with the maximum total score
  • 33.
    • Exhaustive … –All combinations: • Algorithm – Dynamic programming (much faster) • Heuristics – Needleman – Wunsh for global alignments (Journal of Molecular Biology, 1970) – Later adapated by Smith-Waterman for local alignment Overview
  • 35.
    • Score ofan alignment: reward matches and penalize mismatches and spaces. – eg, each column gets a (different) value for: • a match: +1, (both have the same characters); • a mismatch : -1, (both have different characters); and • a space in a column: -2. – The total score of an alignment is the sum of the values assigned to its columns.
  • 36.
    A metric … GACGGATTAG,GATCGGAATAG GA-CGGATTAG GATCGGAATAG +1 (a match), -1 (a mismatch),-2 (gap) 9*1 + 1*(-1)+1*(-2) = 6
  • 37.
    Dynamic programming Reduce theproblem: the solution to a large problem is to simplify … if we first know the solution to a smaller problem that is a subset of the larger problem Overview P P2P1 P3 P
  • 38.
    Dynamic Programming • Findingoptimal solution to search problem • Recursively computes solution • Fundamental principle is to produce optimal solutions to smaller pieces of the problem first and then glue them together • Efficient divide-and-conquer strategy because it uses a bottom-up approach and utilizes a look-up table instead of recomputing optimal solutions to sub- problems P P2P1 P3 P
  • 39.
    the best alignmentbetween • a zinc-finger core sequence: –CKHVFCRVCI • and a sequence fragment from a viral polyprotein: –CKKCFCKCV
  • 40.
    C K HV F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
  • 41.
    C K HV F C R V C I +-------------------- C | 1 1 1 K | 1 K | 1 C | 1 1 1 F | 1 C | 1 1 1 K | 1 C | 1 1 1 V | 1 1 Dynamic Programming
  • 42.
    C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 1 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 43.
    C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 K | 1 0 C | 1 1 1 0 F | 1 0 C | 1 1 1 0 K | 1 0 C | 2 1 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 44.
    C K HV F C R V C I +-------------------- C | 1 1 1 0 K | 1 0 0 K | 1 0 0 C | 1 1 1 0 F | 1 0 0 C | 1 1 1 0 K | 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 45.
    C K HV F C R V C I +-------------------- C | 1 1 1 1 0 K | 1 1 0 0 K | 1 1 0 0 C | 1 1 1 1 0 F | 1 1 0 0 C | 1 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 46.
    C K HV F C R V C I +-------------------- C | 1 1 1 1 1 0 K | 1 1 1 0 0 K | 1 1 1 0 0 C | 1 1 1 1 1 0 F | 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 47.
    C K HV F C R V C I +-------------------- C | 1 2 1 1 1 0 K | 1 1 1 1 0 0 K | 1 1 1 1 0 0 C | 1 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 48.
    C K HV F C R V C I +-------------------- C | 1 2 2 1 1 1 0 K | 1 2 1 1 1 0 0 K | 1 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 49.
    C K HV F C R V C I +-------------------- C | 1 3 2 2 1 1 1 0 K | 1 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 50.
    C K HV F C R V C I +-------------------- C | 1 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 51.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 2 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 52.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 53.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 54.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 55.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 56.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 57.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 58.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 59.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 60.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 Dynamic Programming
  • 61.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
  • 62.
    C K HV F C R V C I +-------------------- C | 5 3 3 3 2 2 1 1 1 0 K | 4 4 3 3 2 1 1 1 0 0 K | 3 4 3 3 2 1 1 1 0 0 C | 4 3 3 3 2 2 1 1 1 0 F | 3 2 2 2 3 1 1 1 0 0 C | 4 2 2 2 2 2 1 1 1 0 K | 2 3 2 2 2 1 1 1 0 0 C | 2 1 1 1 1 2 1 0 1 0 V | 0 0 0 1 0 0 0 1 0 0 C K H V F C R V C I C K K C F C - K C V C K H V F C R V C I C K K C F C K - C V C - K H V F C R V C I C K K C - F C - K C V C K H - V F C R V C I C K K C - F C - K C V Dynamic Programming
  • 63.
  • 64.
    Needleman-Wunsch-Simple.py The Score Matrix ---------------- Seq1(j)12 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1
  • 65.
    The Score Matrix ---------------- Seq1(j)12 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 Needleman-Wunsch-Simple.py
  • 66.
    The Score Matrix ---------------- Seq1(j)12 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 a bc A: matrix(i,j) = matrix(i-1,j-1) + (MIS)MATCH if (substr(seq1,j-1,1) eq substr(seq2,i-1,1) B: up_score = matrix(i-1,j) + GAP C: left_score = matrix(i,j-1) + GAP Needleman-Wunsch-Simple.py
  • 67.
    The Score Matrix ---------------- Seq1(j)12 3 4 5 6 7 Seq2 * C K H V F C R (i) * 0 -1 -2 -3 -4 -5 -6 -7 1 C -1 1 0 -1 -2 -3 -4 -5 2 K -2 0 2 1 0 -1 -2 -3 3 K -3 -1 1 1 0 -1 -2 -3 4 C -4 -2 0 0 0 -1 0 -1 5 F -5 -3 -1 -1 -1 1 0 -1 6 C -6 -4 -2 -2 -2 0 2 1 7 K -7 -5 -3 -3 -3 -1 1 1 8 C -8 -6 -4 -4 -4 -2 0 0 9 V -9 -7 -5 -5 -3 -3 -1 -1 Needleman-Wunsch-Simple.py
  • 68.
  • 69.
  • 71.
    Extensions to basicdynamic programming method use gap penalties – constant gap penalty for gap > 1 – gap penalty proportional to gap size • one penalty for starting a gap (gap opening penalty) • different (lower) penalty for adding to a gap (gap extension penalty) use blosum62 • instead of MATCH and MISMATCH Dynamic Programming: Needleman-Wunsch-Complete.py
  • 72.
  • 73.
  • 74.
  • 75.
  • 76.
  • 77.
  • 78.
    Uses of Needleman-Wunsch-Complete.py •Time Complexity • Use random proteins to generate histogram of scores from aligned random sequences
  • 79.
    Time complexity withNeedleman-Wunsch-Complete.py Sequence Length (aa) Execution Time (s) 10 0:00:00.001500 25 0:00:00.005340 50 0:00:00.020112 100 0:00:00.081580 500 0:00:01.960721 1000 0:00:07.720884 10000 0:11:36.344549 100000 Memory could not be written
  • 80.
    Simple version (Match/Mismatch)– no gap extension
  • 81.
  • 82.
    True positives Falsepositives False negatives Sequences reported as related Sequences reported as unrelated True negatives homologous sequences non-homologous sequences Sensitivity: ability to find true positives Specificity: ability to minimize false positives
  • 83.
    If the sequencesare similar, the path of the best alignment should be very close to the main diagonal. Therefore, we may not need to fill the entire matrix, rather, we fill a narrow band of entries around the main diagonal. An algorithm that fills in a band of width 2k+1 around the main diagonal.
  • 84.
    Local alignment • Theconcept of ‘local alignment’ was introduced by Smith & Waterman in 1981 • A local alignment of 2 sequences is an alignment between parts of the 2 sequences Two proteins may one share one stretch of high sequence similarity, but be very dissimilar outside that region A global (N-W) alignment of such sequences would have: (i) lots of matches in the region of high sequence similarity (ii) lots of mismatches & gaps (insertions/deletions) outside the region of similarity It makes sense to find the best local alignment instead
  • 85.
    Smith-Waterman.py • Three changes –The edges of the matrix are initialized to 0 instead of increasing gap penalties – The maximum score is never less than 0, and no pointer is recorded unless the score is greater than 0 – The trace-back starts from the highest score in the matrix (rather than at the end of the matrix) and ends at a score of 0 (rather than the start of the matrix)
  • 86.
  • 87.
  • 89.
    Sequence Alignments Introduction Algorithms What ? Examples Properties DynamicProgramming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
  • 90.
    The best alignment: Theone with the maximum total score Multiple Aligment: n>2
  • 91.
    2 to 3:hyperlattice
  • 92.
    On its top-leftside, the cube is "covered" by the polyhedron. The edges 1, 2, 3, 6 and 7 are coming from the inside, and edges 4 and 5 can be ignored (and are therefore not labeled in the figure).
  • 93.
    • Each nodein the k-dimensional hyperlattice is visited once, and therefore the running time must be proportional to the number of nodes in the lattice. – This number is the product of the lengths of the sequences. – eg. the 3-dimensional lattice as visualized. Computational Complexity of MA by standard Dynamic Programming
  • 94.
    • The memoryspace requirement is even worse. To trace back the alignment, we need to store the whole lattice, a data structure the size of a multidimensional skyscraper. – In fact, space is the No.1 problem here, bogging down multiple alignment methods that try to achieve optimality. – Furthermore, incorporating a realistic gap model, we will further increase our demands on space and running time
  • 95.
  • 96.
    • The mostpractical and widely used method in multiple sequence alignment is the hierarchical extensions of pairwise alignment methods. • The principal is that multiple alignments is achieved by successive application of pairwise methods. – First do all pairwise alignments (not just one sequence with all others) – Then combine pairwise alignments to generate overall alignment Multiple Alignment Method
  • 97.
    • The stepsare summarized as follows: – Compare all sequences pairwise. – Perform cluster analysis on the pairwise data to generate a hierarchy for alignment. This may be in the form of a binary tree or a simple ordering – Build the multiple alignment by first aligning the most similar pair of sequences, then the next most similar pair and so on. Once an alignment of two sequences has been made, then this is fixed. Thus for a set of sequences A, B, C, D having aligned A with C and B with D the alignment of A, B, C, D is obtained by comparing the alignments of A and C with that of B and D using averaged scores at each aligned position. Multiple Alignment Method
  • 98.
  • 99.
  • 100.
    • Automatic multiplealignemnt – extend dynamic programming (MSA - Lipman) • limit: computing power: length and number of sequences (e.q. 2000^8) – progressive alignment (Feng & Doolittle) • use “guide tree” (PileUp, ClustalW etc) • Dedicated alignment editing program – Boxshade – SeaView – SeqPup (Java) • Combination (Biology – Computation) Multiple Sequence Alignment programs
  • 101.
    • ClustalW isa general purpose multiple alignment program for DNA or proteins. • ClustalW is produced by Julie D. Thompson, Toby Gibson of European Molecular Biology Laboratory, Germany and Desmond Higgins of European Bioinformatics Institute, Cambridge, UK. Algorithmic • Improves the sensitivity of progressive multiple sequence alignment through sequence weighting, positions-specific gap penalties and weight matrix choice. Nucleic Acids Research, 22:4673-4680. ClustalW
  • 102.
    ****** MULTIPLE ALIGNMENTMENU ****** 1. Do complete multiple alignment now (Slow/Accurate) 2. Produce guide tree file only 3. Do alignment using old guide tree file 4. Toggle Slow/Fast pairwise alignments = SLOW 5. Pairwise alignment parameters 6. Multiple alignment parameters 7. Reset gaps between alignments? = OFF 8. Toggle screen display = ON 9. Output format options S. Execute a system command H. HELP or press [RETURN] to go back to main menu Your choice: Running ClustalW
  • 103.
    • The finalproduct of a PILEUP run is a set of aligned sequences, which are stored in a Multiple Sequence File (called .msf by GCG). This msf file is a text file that can be formatted with a text editor, but GCG has some dedicated tools for improving the looks of msf files for easier interpretation and for publication. • Consensus sequences can be calculated and the relationship of each character of each sequence to the consensus can be highlighted using the program PRETTY Formatting Multiple Alignments
  • 104.
    • Shading ofregions of high homology can be created using the programs BOXSHADE and PRETTYBOX , but that goes beyond the scope of this tutorial. (Boxshade: http://www.ch.embnet.org/software/BOX_form.html) • In addition to these programs that run on the Alpha, the output of PILEUP (or CLUSTAL) can be moved by FTP from your RCR account to a local Mac or PC. • Since this output is a plain text file, it can be edited with any word processing program, or imported into any drawing program to add boldface text, underlining, shading, boxes, arrows, etc Formatting Multiple Alignments
  • 105.
  • 106.
  • 107.
    • Their alignmenthighlights conserved residues (one of the cysteines forming the disulphide bridges, and the tryptophan are notable) • conserved regions (in particular, "Q.PG" at the end of the first 4 sequences), and more sophisticated patterns, like the dominance of hydrophobic residues at fragment positions 1 and 3. • The alternating hydrophobicity pattern is typical for the surface beta-strand at the beginning of each fragment. Indeed, multiple alignments are helpful for protein structure prediction. An example of Multiple Alignment … immunoglobulin
  • 108.
    • Providing thealignment is accurate then the following may be inferred about the secondary structure from a multiple sequence alignment.  The position of insertions and deletions (INDELS) suggests regions where surface loops exist.  Conserved glycine or proline suggests a beta-turn. A Practical Approach: Interpretation
  • 109.
    • Residues withhydrophobic properties conserved at i, i+2, i+4 separated by unconserved or hydrophilic residues suggest surface beta- strands.  A short run of hydrophobic amino acids (4 residues) suggests a buried beta- strand.  Pairs of conserved hydrophobic amino acids separated by pairs of unconserved, or hydrophilic residues suggests an alfa-helix with one face packing in the protein core. Likewise, an i, i+3, i+4, i+7 pattern of conserved hydrophobic residues. A Practical Approach: Interpretation
  • 110.
    • Take outnoise (GAPS) • Extra information (structure - function) • Recursive selection – first most similar to have an idea about conserved regions – manual scan for these in more distant members then include these A Practical Approach: Which sequences to use ?
  • 111.
    Sequence Alignments Introduction Algorithms What ? Examples Properties DynamicProgramming for Pairwise Alignment Concept Example Needleman-Wunsch(.pl) Smith-Waterman(.pl) Multiple Alignment MSA Hierarchical Pairwise Alignent ClustalW, PileUp Formatting Interpretation Alternative Methods SIM Blast2 Dali
  • 112.
    L-align (2 sequences) SIM(www.expasy.ch) LALNVIEW is available for UNIX, Mac and PC on the ExPASy anonymous FTP server. very nice TWEAKING tool (70% criteria)
  • 113.
  • 114.
  • 115.
  • 116.
    How can Iuse NCBI to compare two sequences? Answer: Use the “BLAST 2 Sequences” program
  • 117.
    • Go tohttp://www.ncbi.nlm.nih.gov/BLAST • Choose BLAST 2 sequences • In the program, [1] choose blastp (protein search) or blastn (for DNA) [2] paste in your accession numbers (or use FASTA format) [3] select optional parameters, such as --BLOSU62 matrix is default for proteins try PAM250 for distantly related proteins --gap creation and extension penalties [4] click “align” Practical guide to pairwise alignment: the “BLAST 2 sequences” website
  • 120.
    Question #2: How canI use NCBI to compare a sequence to an entire database? BLAST!
  • 123.
    Weblems W4.1: Align theamino acid sequence of acetylcholine receptor from human, rat, mouse, dog with ClustalW T-Coffee Dali MSA W4.2: Use BoxShade to create a word file indicating the different conserved resides in colours W4.3: Perform a LocalAlignent using SIM and Lalign on the same sequence and Blast2 W4.4: Do the different methods give different results, what are the default settings they use ? W4.5: How would you identify critical residues for catalytic activity ?