Julius B. Lucks/Meetings and Notes/SMBE2007/models protein evolution 2

Ziheng Yang : A mutation selection model of codon substitution

Tue Jun 26 14:02:43 EDT 2007

• first one to propose codon models - analyze codon changes dN/dS (rather than nucleotides and AAs)
• UCL
• Rasmus Nielsen - Univ. Copenhagen
• Alan Moses thinks this will be a revolutionary talk

Talk

• Goldman & Yang 1994 model - codon substitution model
  • Mol. Biol. Evol., 11, 725, 1994
  • Yang and Nielsen, 1998, J. Mol. Evol.
  • Subst. rate to codon j proportional to equil. freq of codon j
  • does not separate mutational bias and selection on codon usage
  • Bierne & Eyre-Walker, 2003, Genetics, 165, 1587
  • Yang 2006, Computational Molecular Evolution, Oxford, 284
  • TTT,TTC,TCT,TCC transitions - only 2 rates
    • TTC, TCC preferred, others rare
    • realistically want 3 rates
• model with 3 rates - Neilsen et al. - 20007, Mol. Biol. Evol., 24, 228
  • large rate from unpreferred to pref
  • smal rate for reverse
  • middle rate from pref to pref and unpref to unpref
    • requires a prioir partitioning of codons (Hiroshi Akashi)
• Codon usage gen believed to be under selection in bacteria and Drosophila
  • mammals case is less clear
  • Akashi H, 1994, Genetics
  • synonymous changes change protein structure and function
    • Kimchi-Sarfaty, 2007, Science, 315, 525
    • Komar AA, 2007, Scienc, 315, 466
    • protein folding co-translational
    • silent SNP - altered protein translation kinetics - final protein diff conformation and function

Model

1. mutation rate from nucl i to j described by HKY85 or GTR (REV) applied to all 3 processes
   • [math]\displaystyle{ \mu_{ij} = a_{ij}\pi_j^* }[/math] - a's symmetric
   • [math]\displaystyle{ \pi^* }[/math] mutational bias parameters
   • codons [math]\displaystyle{ I = i_1i_2i_3 }[/math]
2. fixation probability function of selection coefficient
   • Kimura M, 1962, Genetics, 47, 713 - use Kimura formula
     • [math]\displaystyle{ S_{ij} = 2Ns_{ij} = 2N(f_j - f_i) }[/math]
     • N number of chromosomes
3. Selection on protein is modeled using [math]\displaystyle{ \omega }[/math]

• parameters in the model
  • 4 mutation rates
  • 60 codon fitness parameters
  • sequence distance or branch lengths
• time reversible
  • markov change tr iff rate matrix is product of symmetrical matrix and diagonal matrix
  • equil rate of codon [math]\displaystyle{ \pi_j \propto (\pi_{j1}^*\pi_{j2}^*\pi_{j3}^*)e^{F_J} }[/math]
• comments
  • use of omega to detect selection on the protein does not rely on assump that synon sites evolve neutrally
  • old medels in codeml such as F1x4, F3x4, Fcodon - not special cases of mutation selection model
  • Muse and Gaut, 1994 ,mBE , 11, 715

Results

• why little correlation between [math]\displaystyle{ \omega_{human-macaque} }[/math] and [math]\displaystyle{ \omega_{mouse-rat} }[/math]?
• liklihood ration test of selection on synonymous codon usage
  • null model assumes synonymous codons have same fitness
  • most genes are under selection of codon usage

Summary

• estimation of distances using old models fine
• in most (90%) genes - sig evidence for nat selection driving evol of codon usage
• most mutations have fitness in range |S| < 1 or 2, implying weak selection on codon usage or nearly neutral evolution

Questions

• drosophila and bacteria - codon bias and gene expression found
  • expts - optimal codons can use in bacteria - use to translate more eff
  • mammals not as clear

Tal Pupko : An evolutionary model that accounts for selection on synonymous mutations

Tue Jun 26 14:03:00 EDT 2007

• Cell Res Immunology - Tel-Aviv
• Ka/Ks webserver
• collaborated with Nir Friedman

Words to Look Up

• positive selection vs. purifying selection

Talk

• codon models
  • enference of evel selection forces on a protein
  • purify selection
  • phylogeny
• converting empirical AA replacement matrices into codon-based subst matrices
• methods for computing Ka/Ks
  • subst. matrix rates 61x61
• Yang's M model (2000)
  • K - transition/transversion ratio
  • [math]\displaystyle{ \Pi }[/math] - codon frequency
  • w - factor of selection
• problems
  • asummes rate of leu (UUG) to tryp (UGG) = rate leu (UUG) to phe (UUU) (single transvertion)
    • 1st 5 times more likely
    • model does not account for exact identity of AA
  • assumes instan rate betwiin two AAs that differ by one mutation ...
• propose model
  • Mechanistic Empirical Combined (MEC)
  • exapand 20x20 empirical AA matrix into 61x61 codon matrix
• assumptions
  • sum of rate of all codons = sum of rates of AAs, but take into account codon and AA probabilities
  • intensity of selection - omega - assume gamma distributed

Ks conservation

• most models assume Ks (synonymous) same for all sites(reflects neutral rate of evolution)
  • is this true?

HIV

• vif and pol overlap in diff frames - reduced Ks in these regions

Further

• large scale search for conserved ks in mammals, viruses, bacteria and yeasts
• impact of Ks conservation on positive selection inference
• charcterization of conserved Ks regions
• Goren, Mol. Cell, 2006

Claudia Kleinman : Protein structure and sequence evolution - statistical potentials for phylogeny

Tue Jun 26 14:03:26 EDT 2007

Talk

• probabilistic models of sequence evolution
• try to incorporate protein structure explicitly into the models
• site-dependant approaches
  • simulation of evolution: Parisi & Echave 2001
• statistical potential
  • knowledge-based energy function derived from analysis of known protein structures
  • [math]\displaystyle{ Q_{lm}r_le^{\beta(G_l - G_m)} }[/math]
  • coarse grain structure
  • accounts for implicitly for poorly understood complex effects
• pairwise potential that depends on distance between residues (w/ solvent accessibility potentials)
• contact potentials
• optimized for structure prediction problem

Devise stat potential for an evol context

• [math]\displaystyle{ E = E_{contact} + E_{solvent} + E_{torsion} + E_{SS} }[/math]
  • derive contact map (binary n.n.'s)
    • contact energy parameter
  • solvent accessibility - arb # of classes
  • torsion - use main chain angles
• Kleinman, BMC, 7, 326, 2006
• likelihood proportional to exp of negative of this energy (chemical potential)
  • maximize (maximum likelihood)
  • estimate gradient by MCMC - follow to find the maximum

model comparison using Bayes factors

• Rodrigue, MBE, 23, 1762, 2006
  • Poisson distr ref model
  • thermodynamic integration

Mario Fares : The three-dimensionality of molecular evolution

Tue Jun 26 14:03:53 EDT 2007

• Trinity College Dublin

Talk

• detecting selective constraints in protein-coding genes: survival of the fittest
• [math]\displaystyle{ \omega = dN/dS }[/math]
  • [math]\displaystyle{ \omega \lt 1\gt }[/math] - purifying
  • [math]\displaystyle{ \omega \gt 1\gt }[/math] - positive selection

Allan Drummond : Modeling evolution when ribosomes fail

Tue Jun 26 14:04:15 EDT 2007

• w/ Claus Wilke - UT Austin

Talk

• ribosomes fail - don't ignore when model protein evol
• near-universal observations
  • coding sequences evolve at very diff rates
  • dN and dS correlate
  • high expressed proteins evolve slowly
  • codons matching abundant tRNAs preferred
    • high expressed genes
    • conserved sites (Akashi 1994 - trans accuracy)
  • codon biased genes have fewer dS and dN
• in matrix form - matrices look like block structure
  • bad news - not independant - PCA would predict just one factor
• 1 protein in 5 mistranslated
  • can still fold
  • or can misfold
• selection can act to favor protein sequences that are robust to mistranslation
• certain codons translated 6 times more accurately (model)
• lattice protein model
  • Bloom, PNAS (2005,2006)
  • Taverna, Goldstein, Proteins (2001)
• anything within 5 kCal/mol of gs will fold
• translational selection alone sufficient to explain the observed correlation matrix patters
• Akashi 1994
  • select for speed - don't matter where opt codons are - have to go through all of them
  • select for acc - should put opt codons at most highly conserved sites
  • this allows a within gene test to see what matters most

Conclusions

• evol rate should be considered as regulatory as well as functional signal
• translational selection suffices to explain many evol patterns
• brute-force modelling of protein evol possible