Contextspecific Independence Mixture Modelling for Protein Families

1
Context-specific Independence Mixture Modelling
for Protein Families

• Benjamin Georgi
• Jörg Schultz
• Alexander Schliep

2
Introduction

• Protein families fall into sub families of
  similar but distinct function
• Specific function of sub families is often
  determined by a small number of residues
• functional residues
• Example Malate / Lactate dehydrogenase single
  residue determines specificity

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Functional Positions

• Multiple Sequence alignment (MSA)
• Two sub families, three functional positions
• Strong signal of subgroup specific conservation

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Functional Positions

• Multiple sequence alignment (MSA)
• Two sub families, three functional positions
• Strong signal of subgroup specific conservation

F1
F2
5
Introduction

• Problem Clustering of protein families,
  simultaneous prediction of functional residues
• Prior approaches
• Mostly supervised, requiring additional prior
  knowledge
• Mostly based on phylogenetic trees
• Our approach First unsupervised method that does
  not require a tree

Context-specific independence (CSI) mixture models
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Context-specific independence mixture models
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Mixture Models

• Given random variable
• represents row in a MSA
• K component mixture density

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Mixture Models

• Example MSA length 4 3 component
  mixture

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Mixture Models

• Model parameterization

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Mixture Models

• Model structure matrixone atomar distribution
  per feature and component

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CSI Mixture Models

• Model structure matrixvariable number of
  parameters for each feature

• reduction of model complexity
• the contribution of noise features is
  negated
• avoids overfitting
• highly descriptive model due to block
  structure

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CSI Mixture Models

• Model structure matrixvariable number of
  parameters for each feature

use model structure to predict functional
positions
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CSI for Protein Families

• Conventional mixture

F1
F2
C1
C2
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CSI for Protein Families

• CSI Structure matrix (idealized)

F1
F2
C1
C2
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CSI for Protein Families

• CSI Structure matrix (more realistic)

F1
F2
C1
C2
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Prediction of Functional Residues

• Rank features by importance for characterization
  of a cluster
• Ranking of feature j for component i by
• Take highest ranking features as putative
  functional residues

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CSI mixture structure learning
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CSI Structure Learning

• Question How to learn a CSI structure from data?
• Bayesian approach Score models by posterior
  distribution

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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
Criterion used to select structure and parameter
estimates
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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
Probability of the data under the mixture model
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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
Typically uninformative prior, acts as pseudo
counts, conjugate Dirichlet distribution
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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
Introduces preference for simpler model, acts as
a regularizer, simple factored form
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Learning Algorithm

• Structural EM framework (Friedman 1998)
• Efficiently score candidate structures based on
  the expected sufficent statistics
• Perform greedy search over structure space to
  arrive at final structure

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CSI mixtures for protein data
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Mixtures for Proteins

• Using sequences to infer structural properties of
  the proteins
• Different amino acid substitutions have different
  structural impacts
• Need notion of amino acid similarity in the model
  to guide the structure learning
• Remark related to substitution matrices in
  phylogeny

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Conceptional problem

• Example
• Aspartate (D) and Glutamate (E) much more similar
  thanLeucine (L) and Asparagine (N)
• E/D column might best be modeled with a single
  distribution in the structure

L E L E L E L E ----- N D N D N D N D
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F2
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Amino acid properties

Livingstone and Barton (1993)
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Amino acid properties

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Model extension

• Need to integrate AA properties into
• Idea Construct parameter prior which
  defines appropriate density
• Dirichlet Mixture priors

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Dirichlet Distribution

• Defines density over discrete distributions
• Example preference for

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Dirichlet Mixture Priors (DMP)

• Mixture of several Dirichlet distributions as
  parameter prior
• instead of single Dirichlet as in the
  uninformative case
• Allows for different contexts, preferences in the
  density over the parameter space
• Fits seamlessly into the mixture framework
• How to model AA properties with DMP ?

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DMP for Amino acids

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DMP for Amino acids

Values of X and . for each component chosen by
heuristic
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DMP for Amino acids

• Yields probabilistic representation of amino acid
  property hierarchy as DMP
• Drives parameter estimation and structure
  learning to be consistent with this notion of
  similarity
• Yields improvement of model performance for
  protein clustering

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Results
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Data sets

• Method evaluation on well-studied families with
  known subgroups
• Clustering and prediction of functional residues
• Malate / Lactate dehydrogenase (MDH/LDH)
• Guanylyl / Adenylyl cyclases (GC/AC)
• (Serine/Threonine and Tyrosine Protein kinases)

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Malate / Lactate Dehydrogenase

• Oxidoreductase, part of citrate cylce
• Small, clean PFAM seed alignment for MDH/LDH NAD
  binding domain
• 29 sequences (13 MDH, 16 LDH)
• MSA of length 141 (after filtering highly gapped
  columns gt0.33 gaps)

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Malate / Lactate Dehydrogenase

• Single residue has been experimentally confirmed
  to determine substrate specificity
• Model selection Normalized entropy criterion
  (NEC) K 2
• Perfect recovery of MDH/LDH
• Consider top ranked positions for prediction of
  functional residues

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MDH/LDH

• Top 10
• Arg 81
• Met 85
• Gly 145
• Ser 88
• Leu 132
• Val 42
• Thr 123
• Ala 52
• Tyr 138
• Asn 122

Ecoli MDH chain A
White ligand interactions (NAD, SO4)
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MDH/LDH

• Top 10
• Arg 81
• Met 85
• Gly 145
• Ser 88
• Leu 132
• Val 42
• Thr 123
• Ala 52
• Tyr 138
• Asn 122

true, experimentally verified specificity
determining residue
Ecoli MDH chain A
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MDH/LDH

• Top 10
• Arg 81
• Met 85
• Gly 145
• Ser 88
• Leu 132
• Val 42
• Thr 123
• Ala 52
• Tyr 138
• Asn 122

Ecoli MDH chain A
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Guanylyl / Adenylyl Cyclases

• Catalyzes ATP-gtcAMP, GTP-gtcGMP
• 132 sequences (81 AC, 51 GC)
• MSA of length 771 (filtered for gaps)

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Guanylyl / Adenylyl Cyclases

• Group of five residues identified to influence
  substrate binding in mutation experiments
• NEC K2
• Clustering Sensitivity 83 , Specificity 87
  wrt. AC/GC separation
• Evaluation Consider top ranked positions within
  C2 domain

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AC/GC Cyclases

• Top 10
• Ile 919
• Asp 1018
• Gln 1016
• Lys 1014
• Phe 975
• Lys 938
• Thr 943
• Cys 911
• Ile 1019
• Tyr 899

Rat AC C2 domain
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AC/GC Cyclases

• Top 10
• Ile 919
• Asp 1018
• Gln 1016
• Lys 1014
• Phe 975
• Lys 938
• Thr 943
• Cys 911
• Ile 1019
• Tyr 899

Specificity determining residues
Rat AC C2 domain
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AC/GC Cyclases

• Top 10
• Ile 919
• Asp 1018
• Gln 1016
• Lys 1014
• Phe 975
• Lys 938
• Thr 943
• Cys 911
• Ile 1019
• Tyr 899

Part of C1/C2 domain interface
Rat AC C2 domain
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AC/GC Cyclases

• Top 10
• Ile 919
• Asp 1018
• Gln 1016
• Lys 1014
• Phe 975
• Lys 938
• Thr 943
• Cys 911
• Ile 1019
• Tyr 899

Next to forsoklin interaction site
Rat AC C2 domain
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Conclusion

• Clustering of protein families and simultaneous
  prediction of functional residues
• Unsupervised and does not rely on phylogeny
• DMP based on amino acid properties
• Results on well-studied families encouraging

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Future work

• Consider Machine learning approaches for DMP
  parameter estimation
• Analysis of protein families without known
  subgroup classification and functional site
  prediction

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Software

• Pymix Python Mixture Package
• http//algorithmics.molgen.mpg.de/pymix.html

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• Thank you.

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Mixture Models

• For MSA
• Each is a realization of
• Probability of D under mixture M

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CSI Structure Learning

• Bayesian data likelihood
• is the mixture density
• is a conjugate prior over parameters

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CSI Model

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
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CSI Structure Learning

• Model posterior

Structure prior
Model posterior
Likelihood
Parameter prior
Amino acid property DMP instead of uninformative
prior
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Protein kinase

• Data set of tyrosine kinases (TK) and two classes
  of serine/threonine kinases (STE, AGC)
• Stretch of three residues highly indicative for
  substrate specificity
• Three component clustering sensitivity 79,
  specificity 83

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Protein kinase

• Top 10
• Thr 201
• Lys 168
• Gly 200
• Leu 273
• Glu 170
• 15. Pro 169

cAMP dep. protein kinase, mus musculus
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Protein kinase

• Top 10
• Thr 201
• Lys 168
• Gly 200
• Leu 273
• Glu 170
• 15. Pro 169

cAMP dep. protein kinase, mus musculus
Stretch of three residues known to
determine substrate specificity