Inferring Selection Pressure from Positional Residue Conservation

Rose HobermanRoni Rosenfeld Judith Klein-Seetharaman

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

Objective

Given a multiple sequence alignment...

1. Which positions are conserved?

2. Identify specific selectional pressures at each position assume amino acids are selected based on

their underlying physical and chemical properties

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

p pii

i

20

ln

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

250 Properties

1 Hydrophobicity

2 Volume

3 Net charge

4 Transfer free energy

...

248 Average flexibility

249 Alpha-helix propensity

250 Number of surrounding residues

250 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 Y0.67 0.87 1.52 0.00 0.85 0.07 0.07 1.87 3.77 2.67

Multiple Sequence Alignment

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

Multiple Sequence Alignment

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

Multiple Sequence Alignment

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

Limitations of our approach

Not modelling phylogenetic relationships

Cannot identify property conservation when entropy is low

Variance

Variance

If a property is conserved, the distribution of its values should have lower variance

However, must condition on entropy

Holes

Unimodality

When selection based on a single property, fitness is unimodal

Look for properties for which all amino acids are adjacent

Adjacency Limitations

Definition of a “hole” too strict, fails to model unimodality

Ignores distances between property values

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

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 2

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

2

2

Gaussian Significance I

Gaussian Significance II

Gaussian Significance III

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

False Discovery Rate

properties threshold Expected FD

Positions 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%

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 residue’s value from the mean of the best fitting property Gaussian

Computational Validation

Results for GPCR

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

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

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

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

Results

Results

More Detailed Results

Helix 1. Proportion of residues 100% buried 3. Hydrophobicity 4. Side chain interaction param 9. Polarity10. Transfer free energy to lipophilic phase20. Membrane buried helix param

Intracellular loop

1. Polarity/Grantham 2. Normalized flexibility/B-values 4. Conformational preference for antiparallel beta 5. Hydrophobicity of physiological L-alpha amino acids 9. Mobilities of amino acids on chromatography paper 10. Relative frequency of extended structure 11. Long range non-bonded energy per atom13. Information value for accessibility

Extracellular loop

1. Normalized flexibility/B-values, average 2. Flexibility param for one rigid neighbor 3. van der Waals param R0 4. Average non-bonded energy per atom 5. Polar requirement 6. Conformational preference for antiparallel beta strands

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

Conclusions

Method identifies positions with significant evidence that a particular property is conserved

More discriminatory than entropy

Framework is easily extendable to multiple properties

Thanks!

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

p pii

i

20

ln

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

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

More ...

Substitution methods Physical-chemical distance matrices

or aggregate properties DNA, phylogeny, mutation rates

Adjacency Significance

Positions with small number of amino acids will have a high false discovery rate

Add equation and table

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

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?