Computational Biology: More on Sequence Operations, Slides of Computational Biology

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Computational Biology, Part A

More on Sequence Operations

Robert F. Murphy

Representation and Matching of

Sequences

Matching one character - with

character variables

 Assume two character variables "C” and “Q” test for exact match  If(Q=C) {...} need complicated statements to handle wildcards  If(Q=C | (Q=„A‟&(C=„A‟|C=„R‟‟| C=„W‟ | C=„M‟ | C=„D‟ | C=„H‟‟| C=„V‟ | C=„N‟)|Q=„C‟&...)) {...} can build into a function  If(TestBase(Q,C)) {...}

Efficient method to match one

character

 Convert char to int 0-

 Create 26x26 matrix showing which matches which

 Lookup two characters to be compared to find value

Matching one character - with bit

coding

 Assume two integer variables “I” and “J”  test for exact match  If(I=J) {...}  test for match with wildcards (no lookup!)  If(I&J) {...}

Matching more than one

character - pattern matching

 Example: recognition site for a restriction enzyme  Input sequence string into variable Seq  Define Site as string of characters or masks  EcoRI recognizes GAATTC  AccI recognizes GTMKAC  Create function to search a sequence for that site  Find(Site,LenSite,Seq,LenSeq)  for each position in Seq, see if Site matches starting there

Automating the Calculation

 Goal: Calculate probability of occurrence of a sequence that may include ambiguous bases

 What we need is a way to consider all possible allowed nucleotides at each position in all allowed combinations

 When using dinucleotide probabilities, have to be careful about how the probabilities are combined

Illustration

 Question: What is the probability of observing sequence feature ART (A followed by a purine {either A or G}, followed by a T) using dinucleotide probabilities?

Expansions

 pART=pA(pAA+pAG)(pAT+pGT) [eq.1]

 pART=pApAApAT + pApAApGT

• pApAGpAT + pApAGpGT)

 pART=pA(pAApAT+pAGpGT) [eq.2]

 pART= pApAApAT + pApAGpGT

Proof

 pART=pAAT+pAGT

 pAAT=pApAApAT

 pAGT=pApAGpGT

 pART= pApAApAT + pApAGpGT

 This matches equation 2 on previous slide

More complicated probability

illustration

 What is the probability of observing the sequence feature ARYT (A followed by a purine {either A or G}, followed by a pyrimidine {either C or T}, followed by a T)?

 Using equal mononucleotide frequencies

 pA = pC = pG = pT = 1/ pARYT = 1/4 * (1/4 + 1/4) * (1/4 + 1/4) * 1/ = 1/

Illustration (continued)

 Using observed mononucleotide frequencies: pARYT = pA (pA + pG) (pC + pT) pT

 Using dinucleotide frequencies:

pARYT = pA (pAA (pACpCT + pATpTT) + pAG (pGCpCT + pGTpTT) )

Multiply then add

 We conclude that for such strings our rule should be “multiply dinucleotide probabilities along each allowed path and then add the results”

How do we program this?

 “for” loops?

 Nested “if” structure?

 Other?