BIOL 7020 Special Topics Cell/Molecular: Molecular Phylogenetics. Spring 2010 Section A

Transcription

1 BIOL 7020 Special Topics Cell/Molecular: Molecular Phylogenetics. Spring 2010 Section A Steve Thompson: stthompson@valdosta.edu 1

2 Similarity searching and homology First, just what is homology and similarity are they the same? No. Don t confuse homology with similarity: there is a huge difference! Similarity is a statistic that describes how much two (sub) sequences are alike according to some set scoring criteria. It can be normalized to ascertain statistical significance, but it s still just a number. 2

3 Homology, in contrast and by definition... Implies an evolutionary relationship more than just everything evolving from the same primordial ooze. Reconstruct the phylogeny of the organisms or genes of interest to demonstrate homology. Better yet, show experimental evidence structural, morphological, genetic, and/or fossil that corroborates your claim. There is no such thing as percent homology; something is either homologous or it is not. Walter Fitch said homology is like pregnancy you can t be 45% pregnant, just like something can t be 45% homologous. You either are or you are not. Highly significant similarity can argue for homology, never the inverse. 3

4 OK, so how can we see if two sequences are similar? First, to introduce the concept, a graphical method... One way dot matrices. Provide a Gestalt of all possible alignments between two sequences. To begin very simple 0, 1 (match, nomatch) identity scoring function. Put a dot wherever symbols match. 4

5 S E Q U E N C E A N A L Y S I S P R I M E R S E Q U E N C E P R I M E R Identities and insertion/deletion events (indels) identified (zero:one match score matrix, no window). 5

6 S E Q U E N C E A N A L Y S I S P R I M E R A N A L Y Z E S E Q U E N C E S Noise due to random composition effects contributes to confusion. To clean up the plot consider a filtered windowing approach. A dot is placed at the middle of a window if some stringency is met within that defined window size. Then the window is shifted one position and the entire process is repeated (zero:one match score, window of size three, and a stringency level of two out of three). 6

7 Exact alignment but how can we see the correspondence of individual residues? We can compare one molecule against another by aligning them. However, a brute force approach just won t work. Even without considering the introduction of gaps, the computation required to compare all possible alignments between two sequences requires time proportional to the product of the lengths of the two sequences. Therefore, if the two sequences are approximately the same length (N), this is a N 2 problem. To include gaps, we would have to repeat the calculation 2N times to examine the possibility of gaps at each possible position within the sequences, now a N 4N problem. There s no way! We need an algorithm. 7

8 But... just what the heck is an algorithm? Merriam-Webster s says: A rule of procedure for solving a problem [often mathematical] that frequently involves repetition of an operation. So, you could write an algorithm for tying your shoe! It s just a set of explicit instructions for doing some routine task. 8

9 Enter the dynamic programming (optimal substructure) algorithm! Computer scientists figured it out long ago; Needleman and Wunsch applied it to the alignment of the full lengths of two sequences in An optimal alignment is defined as an arrangement of two sequences, 1 of length i and 2 of length j, such that: 1) you maximize the number of matching symbols between 1 and 2; 2) you minimize the number of indels within 1 and 2; and 3) you minimize the number of mismatched symbols between 1 and 2. Therefore, the actual solution can be represented by: Si-1,j-1 or max Si-x,j-1 + wx-1 or Si,j = si,j + max 2 < x < i max Si-1,j-y + wy-1 2 < y < I Where Si,j is the score for the alignment ending at i in sequence 1 and j in sequence 2, si,j is the score for aligning i with j, wx is the score for making a x long gap in sequence 1, wy is the score for making a y long gap in sequence 2, allowing gaps to be any length in either sequence. This roughly brings the solution back to N 2. Whatever.... How about... 9

10 It may be easier to visualize with an oversimplified example. c T A T A t A a g g c g 0 0+1= = = = = = = =1 1 +0=1 T =1 0 +1= = = = = = = =1 A =0 1 +1=2 0 +1=1 1 +1= =0 1 +1= = = =0 t = =0 1 +2=3 0 +1=1 1 +2= =1 0 +2=2 0 +1= =0 A =0 1 +1= =1 1 +3= =2 1 +3= =3 0 +2=2 0 +1=1 a = =1 0 +2= =3 0 +4= =4 1 +4=5 0 +3=3 0 +2=2 T = =0 1 +1=2 0 +2=2 1 +3=4 0 +4=4 0 +4=4 0 +5= =4 total penalty = gap opening penalty {zero here} + ([length of gap][gap extension penalty {one here}]) 10

11 Do the math and trace-back the optimum route(s) that got you there. c T A T A t A a g g c g T A t A a T Also see 11

12 Optimum Alignments There may be more than one best path through the matrix (and optimum doesn t guarantee biologically correct). Starting at the top and working down, then tracing back, the two best traceback routes define the following two alignments: ctatataagg ctatataagg and cg.tataat..cgtataat. With the example s scoring scheme these alignments have a score of 5, the highest bottom-right score in the trace-back path graph, and the sum of six matches minus one interior gap. This is the number optimized by the algorithm, not any type of a similarity or identity percentage, here 75% and 62% respectively! Software will report only one optimal solution. This was a Needleman Wunsch global solution. Smith Waterman style local solutions use negative numbers in the match matrix and pick the best diagonal within the overall graph. 12

13 What about proteins conservative replacements and similarity as opposed to identity. The nitrogenous bases are either the same or they re not, but amino acids can be similar, genetically, evolutionarily, and structurally! The BLOSUM62 table (Henikoff and Henikoff, 1992) (and remember PAM). A B C D E F G H I K L M N P Q R S T V W X Y Z A B C D E F G H I K L M N P Q R S T V W X Y Z Identity values range from 4 to 11, some similarities are as high as 3, and negative values for those substitutions that rarely occur go as low as 4. The most conserved residue is tryptophan with a score of 11; cysteine is next with a score of 9; both proline and tyrosine get scores of 7 for identity. 13

14 We can imagine screening databases for sequences similar to ours using the concepts of dynamic programming and substitution scoring matrices and some yet to be described algorithmic tricks. But what do database searches tell us; what can we gain from them? Why even bother? Inference through homology is a fundamental principle of biology! When a sequence is found to fall into a preexisting family we may be able to infer function, mechanism, evolution, perhaps even structure, based on homology with its neighbors. 14

15 Independent of all that, what is a good alignment? So, first significance: when is any alignment worth anything biologically? An old statistics trick Monte Carlo simulations: Z score = [ (actual score) - (mean of randomized scores) ] (standard deviation of randomized score distribution) 15

16 The Normal distribution... Many Z scores measure the distance from the mean using this simplistic Monte Carlo model assuming a Gaussian distribution, a.k.a. the Normal distribution ( mathworld.wolfram.com/ NormalDistribution.html), in spite of the fact that sequence-space actually follows what is know as the Extreme Value distribution. However, the Monte Carlo method does approximate significance estimates fairly well. 16

17 Sequence-space (Huh, what s that?) actually follows the Extreme Value distribution ( ExtremeValueDistribution.html). < :== : := :* :* :* :===* :=========* :==================*== :===============================*===== :===========================================*==== :=====================================================*=== :==========================================================* :===========================================================* :======================================================== * :=================================================== * :=============================================* :====================================== * :============================== * :========================= * :=====================* :=================* :=============*= :==========* :========* :======* :=====* :====* :===* :==* :=* :=* :=* :* :* :* :* :* :* :* :* 17 Based on this known statistical distribution, and robust statistical methodology, a realistic Expectation function, the E Value, can be calculated from database searches. The particulars of how this is done will come in just a moment, but the take-home message is the same :* :* :* :* :* :* :* :* :* > :*=

18 The Expectation Value! The higher the E value is, the more probable that the observed match is due to chance in a search of the same size database, and the lower its Z score will be, i.e. is NOT significant. Therefore, the smaller the E value, i.e. the closer it is to zero, the more significant it is and the higher its Z score will be! The E value is the number that really matters. In other words, in order to assess whether a given alignment constitutes evidence for homology, it helps to know how strong an alignment can be expected from chance alone. 18

19 Rules of thumb for a protein search Z score E Value Inference little, if any evidence for homology, but can not disprove! probably homologous, but may be due to convergent evolution strong evidence for homology The Z score represents the number of standard deviations some particular alignment is from a distribution of random alignments (often the Normal distribution). They very roughly correspond to the listed E Values (based on the Extreme Value distribution) for a typical protein sequence similarity search through a database with ~250,000 protein entries. 19

20 On to the searches How can you search the databases for similar sequences, if pairwise alignments take N 2 time?! Significance and heuristics... Database searching programs use the two concepts of dynamic programming and substitution scoring matrices; however, dynamic programming takes far too long when used against most sequence databases with a normal computer. The databases are incredibly huge! Therefore, the programs use tricks to make things happen faster. These tricks fall into two main categories, that of hashing, and that of approximation. 20

21 Corn beef hash? Huh... Hashing is the process of breaking your sequence into small words or k-tuples (think all chopped up, just like corn beef hash) of a set size and creating a look-up table with those words keyed to position numbers. Computers can deal with numbers way faster than they can deal with strings of letters, and this preprocessing step happens very quickly. Then when any of the word positions match part of an entry in the database, that match, the offset, is saved. In general, hashing reduces the complexity of the search problem from N 2 for dynamic programming to N, the length of all the sequences in the database. 21

22 A simple hash table The sequence FAMLGFIKYLPGCM and a word size of one, would produce this query lookup hash table: word A C F G I K L M P Y pos Comparing it to the database sequence TGFIKYLPGACT, would yield the following offset table: T G F I K Y L P G A C T

23 Hmmm & some interpretation The offset numbers come from the difference between the positions of the words in the query sequence and the position of the occurrence of that word in the target sequence. Then.... Look at all of the offsets equal to three in the previous table. Therefore, offset the alignment by three: FAMLGFIKYLPGCM TGFIKYLPGACT Quick and easy. Computers can compare these sorts of tables very fast. The trick is to know how far to attempt to extend the alignment out. 23

24 OK. Heuristics... What s that? Approximation techniques are collectively known as heuristics. Webster s defines heuristic as serving to guide, discover, or reveal;... but unproved or incapable of proof. In database similarity searching techniques the heuristic usually restricts the necessary search space by calculating some sort of a statistic that allows the program to decide whether further scrutiny of a particular match should be pursued. This statistic may miss things depending on the parameters set that s what makes it heuristic. Worthwhile results at the end are compiled and the longest alignment within the program s restrictions is created. The exact implementation varies between the different programs, but the basic idea follows in most all of them. 24

25 Two predominant versions exist: BLAST and Fast Both return local alignments, and are not a single program, but rather a family of programs with implementations designed to compare a sequence to a database in about every which way imaginable. These include: 1) A DNA sequence against a DNA database (not recommended unless forced to do so because you are dealing with a non-translated region of the genome DNA is just too darn noisy, only identity & four bases!); 2) A translated (where the translation is done on-the-fly in all six frames) version of a DNA sequence against a translated ( on-the-fly sixframe) version of the DNA database (not available in the Fast package); 3) A translated ( on-the-fly six-frame) version of a DNA sequence against a protein database; 4) A protein sequence against a translated ( on-the-fly six-frame) version of a DNA database; 5) Or a protein sequence against a protein database. Translated comparisons allow penalty-free frame shifts. 25

26 The BLAST and Fast programs some generalities BLAST Basic Local Alignment Search Tool, developed at NCBI. 1) Normally NOT a good idea to use for DNA against DNA searches w/o translation (not optimized); 2) Pre-filters repeat and low complexity sequence regions; 3) Can find more than one region of gapped similarity; 4) Very fast heuristic and parallel implementation; 5) Restricted to precompiled, specially formatted databases; 26 FastA and its family of relatives, developed by Bill Pearson at the University of Virginia. 1) Works well for DNA against DNA searches (within limits of possible sensitivity); 2) Can find only one gapped region of similarity; 3) Relatively slow, but parallel implementations are available; 4) Does not require specially prepared, preformatted databases.

27 The algorithms, in brief BLAST: Two word hits on the same diagonal above some similarity threshold triggers ungapped extension until the score isn t improved enough above another threshold: the HSP. Initiate gapped extensions using dynamic programming for those HSP s above a third threshold up to the point where the score starts to drop below a fourth threshold: yields alignment. Find all ungapped exact word hits; maximize the ten best continuous regions scores: init1. Fast: Combine non-overlapping init regions on different diagonals: initn. Use dynamic programming in a band for all regions with initn scores better than some threshold: opt score. 27

28 BLAST the algorithm in more detail 1) After BLAST has sorted its lookup table, it tries to find all double word hits along the same diagonal within some specified distance using what NCBI calls a Discrete Finite Automaton (DFA). These word hits of size W do not have to be identical; rather, they have to be better than some threshold value T. To identify these double word hits, the DFA scans through all strings of words (typically W=3 for peptides) that score at least T (usually 11 for peptides). 2) Each double word hit that passes this step then triggers a process called ungapped extension in both directions, such that each diagonal is extended as far as it can, until the running score starts to drop below a predefined value X within a certain range A. The result of this pass is called a High-Scoring segment Pair or HSP. 3) Those HSPs that pass this step with a score better than S then begin a gapped extension step utilizing dynamic programming. Those gapped alignments with Expectation values better than the user specified cutoff are reported. The extreme value distribution of BLAST Expectation values is precomputed against each precompiled database this is one area that speeds up the algorithm considerably. 28

29 The BLAST algorithm, continued The math can be generalized thus: for any two sequences of length m and n, local, best alignments are identified as HSPs. HSPs are stretches of sequence pairs that cannot be further improved by extension or trimming, as described above. For ungapped alignments, the number of expected HSPs with a score of at least S is given by the formula: E = Kmne λs This is called an E-value for the score S. In a database search n is the size of the database in residues, and m is your query s length, so N=mn is the total search space size. K and λ are supplied by statistical theory, and, as mentioned above, can be calculated by comparison to precomputed, simulated distributions. These two parameters define natural scales for the size of the database and the scoring system being used respectively. The E-value defines the significance of the search. As mentioned above, the smaller an E-value is, the more likely it is significant. A value of 0.01 to is a good starting point for significance in most typical searches. In other words, in order to assess whether a given alignment constitutes evidence for homology, it helps to know how strong an alignment can be expected from chance alone. 29

30 The Fast algorithm in more detail Fast is an older algorithm than BLAST. The original Fast paper came out in 1988, based on David Lipman s work in a 1983 paper; the original BLAST paper was published in Both algorithms have been upgraded substantially since originally released. Fast was the first widely used, powerful sequence database searching algorithm. Bill Pearson continually refines the programs such that they remain a viable alternative to BLAST, especially if one is restricted to searching DNA against DNA without translation. They are also very helpful in situations where BLAST finds no significant alignments arguably, Fast may be more sensitive than BLAST in these situations. Fast is also a hashing style algorithm and builds words of a set k-tuple size, by default two for peptides. It then identifies all exact word matches between the sequence and the database members. Note that the word matches must be exact for Fast and only similar, above some threshold, for BLAST. 30

31 The Fast algorithm, continued From these exact word matches: 1) Scores are assigned to each continuous, ungapped, diagonal by adding all of the exact match BLOSUM values. 2) The ten highest scoring diagonals for each query-database pair are then rescored using BLOSUM similarities as well as identities and ends are trimmed to maximize the score. The best of each of these is called the Init1 score. 3) Next the program looks around to see if nearby off-diagonal Init1 alignments can be combined by incorporating gaps. If so, a new score, Initn, is calculated by summing up all the contributing Init1 scores, penalizing gaps with a penalty for each. 4) The program then constructs an optimal local alignment for all Initn pairs with scores better than some set threshold using a variation of dynamic programming in a band. A sixteen residue band centered at the highest Init1 region is used by default with peptides. The score generated from this step called opt. 31

32 The Fast algorithm, still continued 5) Next, Fast uses a simple linear regression against the natural log of the search set sequence length to calculate a normalized z- score for the sequence pair. Note that this is not the same Monte Carlo style Z score described earlier, and can not be directly compared to one. 6) Finally, it compares the distribution of these z-scores to the actual extreme-value distribution of the search. Using this distribution, the program estimates the number of sequences that would be expected to have, purely by chance, a z-score greater than or equal to the z-score obtained in the search. This is reported as the Expectation value. 7) If the user requests pair-wise alignments in the output, then the program uses full Smith-Waterman local dynamic programming, not restricted to a band, to produce its final alignments. 32

33 What s the deal with DNA versus protein for searches and alignment? All similarity searching and sequence alignment, regardless of algorithm, is far more sensitive at the amino acid level than at the DNA level. This is because proteins have twenty match criteria versus DNA s four, and those four DNA bases can generally only be identical, not similar, to each other; and many DNA base changes (especially third position changes) do not change the encoded protein. Furthermore, indels cannot occur within codons. All of these factors drastically increase the noise level of DNA against DNA search and alignment, and give protein searches a much greater look-back time, at least doubling it. Therefore, whenever dealing with coding sequence, it is always prudent to search and align at the protein level! 33

34 Conclusions The better you understand the chemical, physical, and biological systems involved, the better your chance of success in analyzing them. Certain strategies are inherently more appropriate to others in certain circumstances. Making these types of subjective, discriminatory decisions is one of the most important take-home messages I can offer! Gunnar von Heijne in his old but quite readable treatise, Sequence Analysis in Molecular Biology; Treasure Trove or Trivial Pursuit (1987), provides a very appropriate conclusion: Think about what you re doing; use your knowledge of the molecular system involved to guide both your interpretation of results and your direction of inquiry; use as much information as possible; and do not blindly accept everything the computer offers you. 34

35 References Altschul, S. F., Gish, W., Miller, W., Myers, E. W., and Lipman, D. J. (1990) Basic Local Alignment Tool. Journal of Molecular Biology 215, Altschul, S.F., Madden, T.L., Schaffer, A.A., Zhang, J., Zhang, Z., Miller, W., and Lipman, D.J. (1997) Gapped BLAST and PSI-BLAST: a New Generation of Protein Database Search Programs. Nucleic Acids Research 25, Gribskov, M. and Devereux, J., editors (1992) Sequence Analysis Primer. W.H. Freeman and Company, New York, New York, U.S.A. Henikoff, S. and Henikoff, J.G. (1992) Amino Acid Substitution Matrices from Protein Blocks. Proceedings of the National Academy of Sciences U.S.A. 89, Needleman, S.B. and Wunsch, C.D. (1970) A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins. Journal of Molecular Biology 48, Pearson, W.R. and Lipman, D.J. (1988) Improved Tools for Biological Sequence Analysis. Proceedings of the National Academy of Sciences U.S.A. 85, Schwartz, R.M. and Dayhoff, M.O. (1979) Matrices for Detecting Distant Relationships. In Atlas of Protein Sequences and Structure, (M.O. Dayhoff editor) 5, Suppl. 3, , National Biomedical Research Foundation, Washington D.C., U.S.A. Smith, T.F. and Waterman, M.S. (1981) Comparison of Bio-Sequences. Advances in Applied Mathematics 2, Wilbur, W.J. and Lipman, D.J. (1983) Rapid Similarity Searches of Nucleic Acid and Protein Data Banks. Proceedings of the National Academy of Sciences U.S.A. 80,

36 Now it s your turn! Go to the National Center for Biotechnology Information: The search box at top is a text-based search called Entrez. By default it will search all of the databases at NCBI. Go ahead and type something related to your potential project. You ll probably find way more than you wanted! Let s play. I ll start with gopher tortoise. 36

37 Once you find a sequence of interest... Go to the BLAST pages. But don t just BLAST off yet. One of the most helpful things you can do is limit your search to a taxonomic group. This makes the statistics much more sensitive, makes the search run faster, and excludes stuff you re not interested in! Watch, then play on your own. 37