Computational Biology, Part 2 Sequence MotifsSlides from Chapter 4Describing features using frequency matricesSlide 4Frequency matrices (continued)Matlab DemonstrationFrequency matrixLogo ExampleLogos for displaying sequence motifsFrequency Matrices, PSSMs, and ProfilesMethods for converting frequency matrices to PSSMsPseudo-countsFinding occurrences of a sequence feature using a ProfileBlock Diagram for Building a PSSM – Aligned SequencesBlock Diagram for Building a PSSM – Unaligned SequencesBlock Diagram for Searching with a PSSMBlock Diagram for Searching for sequences related to a family with a PSSMConsensus sequences vs. PSSMsConsensus sequences vs. frequency matricesReading for next classComputational Biology, Part 2Sequence MotifsComputational Biology, Part 2Sequence MotifsRobert F. MurphyRobert F. MurphyCopyright Copyright  1996, 1999-2009. 1996, 1999-2009.All rights reserved.All rights reserved.Slides from Chapter 4Slides from Chapter 4Ch04_Motifs_mod.pptCh04_Motifs_mod.pptDescribing features using frequency matricesDescribing features using frequency matricesGoal: Describe a sequence feature (or Goal: Describe a sequence feature (or motifmotif) more quantitatively than possible ) more quantitatively than possible using consensus sequencesusing consensus sequencesNeed to describe how often particular bases Need to describe how often particular bases are found in particular positions in a are found in particular positions in a sequence featuresequence featureDescribing features using frequency matricesDescribing features using frequency matricesDefinitionDefinition: For a feature of length : For a feature of length mm using using an alphabet of an alphabet of nn characters, a characters, a frequency frequency matrix matrix is an is an nn by by mm matrix in which each matrix in which each element contains the frequency at which a element contains the frequency at which a given member of the alphabet is observed at given member of the alphabet is observed at a given position in an aligned set of a given position in an aligned set of sequences containing the featuresequences containing the featureFrequency matrices (continued)Frequency matrices (continued)Three uses of frequency matricesThree uses of frequency matricesDescribeDescribe a sequence feature a sequence featureCalculate Calculate probability of occurrenceprobability of occurrence of feature in of feature in a random sequencea random sequenceCalculate Calculate degree of matchdegree of match between a new between a new sequence and a featuresequence and a featureMatlab DemonstrationMatlab Demonstration% read some aligned sequences provided with the bioinformatics % read some aligned sequences provided with the bioinformatics toolboxtoolboxseqs = fastaread('pf00002.fa');seqs = fastaread('pf00002.fa');seqdisp(seqs);seqdisp(seqs);startposition=4; endposition=13;startposition=4; endposition=13;[P,S] = seqprofile(seqs,'limits',[startposition endposition]);[P,S] = seqprofile(seqs,'limits',[startposition endposition]);disp([' ' sprintf('%2d ',[1:size(P,2)])]);disp([' ' sprintf('%2d ',[1:size(P,2)])]);for i=1:length(S)for i=1:length(S) disp([S(i) ' ' sprintf('%4.3f ',P(i,:))])disp([S(i) ' ' sprintf('%4.3f ',P(i,:))])endendseqlogo(seqs,'startat',startposition,'endat',endposition,'alphabet','aa’);seqlogo(seqs,'startat',startposition,'endat',endposition,'alphabet','aa’);Frequency matrixFrequency matrixLogo ExampleLogo ExampleLogos for displaying sequence motifsLogos for displaying sequence motifshttp://www.ccrnp.ncifcrf.gov/~toms/sequencelogo. htmlFree logo maker at Free logo maker at http://weblogo.berkeley.edu/http://weblogo.berkeley.edu/Frequency Matrices, PSSMs, and ProfilesFrequency Matrices, PSSMs, and ProfilesA A frequency matrixfrequency matrix can be converted to a can be converted to a PPosition-osition-SSpecific pecific SScoring coring MMatrix (atrix (PSSMPSSM) ) by converting by converting frequenciesfrequencies to to scoresscores PSSMPSSMs also called s also called PPosition osition WWeight eight MMatrixes (atrixes (PWMPWMs) or s) or ProfilesProfilesMethods for converting frequency matrices to PSSMsMethods for converting frequency matrices to PSSMsUsing log ratio of observed to expectedUsing log ratio of observed to expectedwhere where m(j,i)m(j,i) is the frequency of character is the frequency of character jj observed at position observed at position i i and and f(j)f(j) is the overall frequency of character j (usually in some is the overall frequency of character j (usually in some large set of sequences)large set of sequences)Using amino acid substitution matrix (Dayhoff similarity Using amino acid substitution matrix (Dayhoff similarity matrix) [see later]matrix) [see later]€ score( j,i) = log m( j,i) / f ( j)Pseudo-countsPseudo-countsHow do we get a score for a position with How do we get a score for a position with zero counts for a particular character? Can’t zero counts for a particular character? Can’t take log(0).take log(0).Solution: add a small number to all Solution: add a small number to all positions with zero frequencypositions with zero frequencyFinding occurrences of a sequence feature using a ProfileFinding occurrences of a sequence feature using a ProfileAs with finding occurrences of a consensus As with finding occurrences of a consensus sequence, we consider all positions in the sequence, we consider all positions in the target sequence as candidate matchestarget sequence as candidate matchesFor each position, we calculate a score by For each position, we calculate a score by “looking up” the value corresponding to the “looking up” the value corresponding to the base at that positionbase at that positionBlock Diagram for Building a PSSM – Aligned SequencesBlock Diagram for Building a PSSM – Aligned Sequences PSSM builderSet of Aligned Sequence FeaturesExpected frequencies of each sequence elementPSSMBlock Diagram for Building a PSSM – Unaligned SequencesBlock Diagram for Building a PSSM – Unaligned Sequences PSSM builderSet of unaligned sequencesExpected frequencies of each sequence elementPSSMParameters for aligning (i.e., expected length)Block Diagram for Searching with a PSSMBlock Diagram for Searching with a PSSMPSSM searchPSSMSet of Sequences to searchSequences that match above thresholdThresholdPositions and scores of matchesBlock Diagram for Searching for