Using physical-chemical properties of amino acids to model site-specific substitution propensities.

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Using physical-chemical properties of amino
acids to model site-specific substitution
propensities.

• Rose Hoberman
• Roni Rosenfeld
• Judith Klein-Seetharaman

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HeterogeneityAcross Sites

• Substitution rate varies across sites
• rate parameter assumed to follow a gamma
  distribution
• mathematically convenient
• little biological justification
• provides little explanation

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HeterogeneityAcross Sites

• Rate of substitution varies across sites
• rate parameter distributed according to a gamma
  distribution
• mathematically convenient
• little biological justification
• provides little explanation
• Substitution propensities vary across sites
• leads to an explosion of parameters (400)
• still no biological explanation

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Explaining Why Substitution Propensities Vary

• Differing substitution propensities are a result
  of different amino acid preferences (Halpern
  Bruno, Koshi Goldstein)
• e.g. substitutions to deleterious amino acids are
  unlikely
• Learning amino acid preferences at each site (20
  vs 400 parameters)
• still too many parameters to estimate accurately
• still not biologically informative

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Our Modeling Assumption

• Amino acids preferences are based on which
  physical and chemical properties are important at
  each site to the function or structure of the
  protein
• restricts the parameter space (3-5)
• provides more explanation

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A New Statistical Model of Site-Specific
Molecular Evolution

• Learn which properties are important at each site
  
• Model amino acid preferences as a function of
  their properties
• Determine a mapping from amino acid preferences
  to substitution propensities
• Combine property-based substitution propensities
  with other factors that effect substitutions
• nucleotide mutation processes
• different distances between codons

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A New Statistical Model of Site-Specific
Molecular Evolution

• Learn which properties are important at each site
• dont rely on structural knowledge about the
  protein
• do not artificially restrict to a few preselected
  physical features
• Model amino acid preferences as a function of
  their properties
• Determine a mapping from amino acid preferences
  to substitution propensities
• Combine substitution propensities with codon
  distance and nucleotide mutation rates

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250 Amino Acid Properties
1 Hydrophobicity
2 Volume
3 Net charge
4 Transfer free energy
...
248 Average flexibility
249 Alpha-helix propensity
250 Number of surrounding residues

(Downloaded from http//www.scsb.utmb.edu/comp
biol.html/venkat/prop.html)
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250 Amino Acid Properties
1 Hydrophobicity
2 Volume
3 Net charge
4 Transfer free energy
...
248 Average flexibility
249 Alpha-helix propensity
250 Number of surrounding residues

A C D E F G H I K L 0.66 2.87 0.10 0.87 3.15 1.64 2.17 1.67 0.09 2.77
M N P Q R S T V W Y 0.67 0.87 1.52 0.00 0.85 0.07 0.07 1.87 3.77 2.67
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Visualizing the Amino Acid Distribution

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

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Variance

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

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Limitations of Variance
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Limitations of Variance
Our assumption when selection is based on a
single property, distribution should be unimodal
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Using Gaussian Goodness-of-Fit to Test for
Property Conservation

• Fit a maximum-likelihood Gaussian to amino acid
  frequencies in property space
• From (discretized) Gaussian calculate expected AA
  frequencies
• Calculate goodness-of-fit to learned
  Gaussian
• identifies unimodal distributions
• penalizes missing amino acids (holes)
• Use Monte-Carlo method to calculate significance
• Otherwise will have high false discovery rate
  when entropy is low

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GPCR-A Family

• Characterized by 7 TM segments
• 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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Results for GPCR
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Estimating the False Discovery Rate (FDR)
Properties Tested Significance Threshold Significant Positions Significant Positions FDR
Properties Tested Significance Threshold Number Expected Number Detected FDR
5 0.0005 0.63 76 0.8
5 0.001 1.26 85 1.5
5 0.005 6.26 136 4.6
50 0.0005 6.25 103 6.1
50 0.001 12.34 130 9.5
240 0.0005 28.61 154 18.6
FDR false positives / predicted positives
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Initial Validation

• 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
• Cluster of dynamics properties conserved in third
  cytoplasmic loop
• in Rhodopsin this is the most flexible
  interhelical loop

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Continuing Work

• Use multivariate Gaussian to model selection
  pressure from multiple properties
• Derive substitution propensities from amino acid
  preferences and combine these with codon distance
  effects and nucleotide mutation rates

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Thank YouRoni RosenfeldJudith
Klein-SeetharamanNSF
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Summary

• Proposed a new approach for modeling
  heterogeneity of the evolutionary process across
  sites
• Designed a test that is able to identify which
  properties are conserved at different sites
• Promising approach for modeling site-specific
  substitution propensities in a biologically-realis
  tic and computationally tractable way

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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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Gaussian Significance I
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Related Work
Koshi Goldstein 1998
Halpern Bruno 1997
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New Model
Model of One Fitness Class
Model of Multiple Sequences from one Protein
Family
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Abstract

• Existing models of molecular evolution capture
  much of the variability in mutation rates across
  sites. More biologically realistic models also
  seek to explain site-specific differences in
  substitution propensities between residue pairs,
  leading to more accurate and informative models
  of evolutionary dynamics. Toward this end, we
  describe a procedure for systematically
  characterizing the conservation of each position
  in a multiple sequence alignment in terms of
  specific physical and chemical properties. We use
  a Monte-Carlo method to ascertain the statistical
  significance of the findings and to control the
  False Discovery Rate. We use our method to
  annotate the diverse GPCRA family with a
  selection pressure profile. We demonstrate the
  computational and statistical significance of the
  properties we have identified, and discuss the
  biological significance of our findings. The
  latter include confirmation of experimentally
  determined properties as well as novel testable
  hypotheses.

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Results
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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