Inferring Selection Pressure from Positional Residue Conservation

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Inferring Selection Pressure from Positional
Residue Conservation

• Rose Hoberman
• Roni Rosenfeld
• Judith Klein-Seetharaman

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Sequence Conservation

• Conserved positions in proteins are of functional
  and structural importance
• Many quantitative measures of positional
  conservation
• Applications
• predict function/structure
• model protein families/domains
• evaluate and refine multiple sequence alignments

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Objective

• Given a multiple sequence alignment...
• Which positions are conserved?
• Identify specific selectional pressures at each
  position
• assume amino acids are selected based on their
  underlying physical and chemical properties

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Related Work

• Entropy
• most common measure of conservation
• amino acids as independent symbols
• Property-based
• smallest set of properties
• small number (binary) properties
• ignores amino acid frequency

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Related Work

• Mutation-based substitution matrices
• average over many positions/proteins
• Aggregate experimental scales
• build a similarity matrix
• propotypical properties via dimensionality
  reduction
• average over many properties
• By aggregating, loses specificity

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250 Properties

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250 Properties

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Multiple Sequence Alignment

• FAMLR...
• LAMLR...
• IAMLR...
• P-EL-...
• GAELR...
• PGEIR...
• L-ELY...
• L-EVR...
• I-MLK...
• WAELR...
• HAELY...
• YAILY...
• WAML-...

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Multiple Sequence Alignment

• FAMLR...
• LAMLR...
• IAMLR...
• P-EL-...
• GAELR...
• PGEIR...
• L-EVY...
• L-EVR...
• I-MLK...
• WAELR...
• HAELY...
• YAILY...
• WAML-...

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Multiple Sequence Alignment

• FAMLR...
• LAMLR...
• IAMLR...
• P-EL-...
• GAELR...
• PGEIR...
• L-ELY...
• L-EVR...
• I-MLK...
• WAELR...
• HAELY...
• YAILY...
• WAML-...

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Limitations of our approach

• Not modelling phylogenetic relationships
• Cannot identify property conservation when
  entropy is low

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Variance
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Variance

• If a property is conserved, the distribution of
  its values should have lower variance
• However, must condition on entropy

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Holes
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Unimodality

• When selection based on a single property,
  fitness is unimodal
• Look for properties for which all amino acids are
  adjacent

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Adjacency Limitations

• Definition of a hole too strict, fails to model
  unimodality
• Ignores distances between property values

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Adjacency Limitations

• Definition of a hole too strict, fails to model
  unimodality
• Ignores distances between property values
• Therefore... calculate goodness of fit to a
  Gaussian

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Gaussian Goodness-of-Fit

• Fit a maximum-likelihood Gaussian to amino acid
  frequencies in property space
• Calculate goodness-of-fit to learned Gaussian
• discretize Gaussian over 20 values
• calculate statistic

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Significance

• High false discovery rate when low entropy
• Calculate significance using shuffled properties
• For a position
• Calculate value for each shuffled property
• Tells us the likelihood of getting a particular
  value by chance
• Convert to a p-value

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Gaussian Significance I
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Gaussian Significance II
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Gaussian Significance III
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GPCR Family A

• 7 TM segments
• Cytoplasmic, TM, and extracellular domains
• Responds to a large variety of ligands
• Ligand binding allows binding and activation of a
  G protein
• Diversity in sequences
• Believed to share similar structure
• Only known structure is for Rhodopsin

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False Discovery Rate
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Computational Validation

• Predict the occurence of amino acids not yet seen
  in a position of a multiple sequence alignment
• Subsample sequences from GPCR alignment of sizes
  25, 50, 75, 100, 200
• Baseline logistic regression with only entropy
  and variability
• New model incorporates the distance of the
  residues value from the mean of the best fitting
  property Gaussian

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Computational Validation
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Results for GPCR
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Biological Validation

• Property conservation in all three domains of
  GPCR (not just TM)
• e.g. hydrophobicity conserved in interhelical
  loop regions
• Charge conserved at 134
• part of D/E R Y motif of importance to binding
  and activation of G-protein
• Size conserved at 54, 80, 87, 123, 132, 153, 299
• helix faces one or two other helices

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Biological Validation

• Helix-coil equilibrium constant conserved at 278
• a helix capping residue at the EC end of helix VI
• Dynamic properties conserved
• especially in third CP loop
• in Rhodopsin this is the most flexible
  interhelical loop
• in TM at 215 and 269
• close proximity to retinal ligand the
  ligand-binding pocket is the most rigid part of
  crystal structure

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Clustered Positions

• Positions with high property-conservation
  similarity are often close in space but distant
  in primary sequence
• 129 and 226 and 131 and 219
• 162 and 297 both face outside of the bundle at a
  similar height with respect to the membrane

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Novel Hypothesis

• 175 and 265 highly similar conservation patterns
• Both tryptophans in rhodopsin
• Trp265 in direct contact with retinal ligand, but
  when exposed to light, crosslinks to Ala169
  instead.
• Trp161 has been proposed to contribute to this
  process
• The property conservation patterns suggest Trp175
  has a more significant role
• This hypothesis can be tested experimentally

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Results
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Results
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More Detailed Results
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Future Work

• Additional evaluation
• Consider selection pressure from more than one
  property
• Use multivariate Gaussians
• Look for adjacency in 2-D property space
• Test for unimodality directly
• Model phylogenetic relationship between sequences

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Conclusions

• Method identifies positions with significant
  evidence that a particular property is conserved
• More discriminatory than entropy
• Framework is easily extendable to multiple
  properties

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Thanks!
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Entropy

• Most commonly-used measure of conservation
• Based only on frequency of each amino acid
• Treats amino acids as independent symbols
• Amino acids are not uniformly different

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Property-based Measures

• Based on Venn diagram of physical-chemical
  properties
• Find smallest set of properties that explains
  amino acids
• Considers only a small number of property
  combinations
• Only binary properties
• Ignores amino acid frequency

Livingstone Barton, CABIOS, 1993
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Hybrid Methods

• Stereochemically-sensitive entropy scores
• Divide amino acids into clusters (show example?)
• Calculate entropy on reduced alphabet
• Clustering is ad hoc
• Can only consider a limited number properties
• Still considers each amino acids in a cluster as
  uniformly distant from each amino acid in every
  other cluster
• Only models limited number of properties at a
  very coarse level

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More ...

• Substitution methods
• Physical-chemical distance matrices or aggregate
  properties
• DNA, phylogeny, mutation rates

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Adjacency Significance

• Positions with small number of amino acids will
  have a high false discovery rate
• Add equation and table

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Significance

• Problem for positions with low entropy, every
  property will have low variance
• very high false positive rate any combination of
  1 more more properties can explain this!
• actual explanation may involve several properties
• In this case, multiple property constraints
• Cannot determine which one property is conserved
• Need to condition on entropy

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Significance Testing

• What is the probability of a property having low
  variance in this position purely by chance?
• Generate a large set of random (shuffled)
  property scales
• show examples of shuffling
• Calculate variance for each random property
• The distribution of this statistic can be used to
  calculate a threshold for acceptability of
  false-positives
• Show picture here? add error bars?

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Results