An Evolutionary SpaceTime Model with Varying AmongSite Dependencies

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An Evolutionary Space-Time Model with Varying
Among-Site Dependencies

• Adi Stern Tal Pupko

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Evolutionary models

• The aim of an evolutionary model to describe
  (often in probabilistic terms) the evolutionary
  biological reality

http//tolweb.org
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Likelihood

• An evolutionary model enables us to compute the
  likelihood that a certain scenario describes the
  biological reality we observe.
• For instance, what is the likelihood that

GVLLMEIFALTQFQRRGNQANAFSFGKDIFIRQFVPGCIRDGYTFVGPV
GVLLTELLALTKIKQRANDKFAFSFGKESFIEPFVPGCVSEPYAIMIFV
GVLLMRFTTLNPIHKRGSKAFAFSFGKDSLVGTFVPGCIPLAYSIVTPV
GVLLMRLATLSLMHQRGSKASAFSFGKDSLIGPFVPGCIQLAYNVISPV
GVVLVALITLIPIKKRGTQVFAFSFGHDEFIRTFVPGCVEDNFDQILRI
GVVLMVLYTLSRIKKRGTQPVTFSFGEDEFLRIFVPGCANDTFELLMQL
GVLLMGLFPMKHIEKRGFQALAFSFGNDAFIRPFVPGCIEEGYPVLAPL
describes
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Markov process

• Most models today assume a Markov process over
  time, i.e. over the phylogenetic tree

Time
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Inference with a model

• Using the evolutionary model we can compute the
  likelihood of the data, and we can use this to
  infer different biological properties-
  phylogenetic tree- ancestral states-
  evolutionary rate

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Site-specific evolutionary rates

• High rate fast-evolving site ? variable
• Low rate slow-evolving site ? conserved

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Space-time sites in a protein are dependent

• Sites are independent
• Sites are dependent conserved regions in a
  protein there is an interaction amongst sites

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Space and time

• A Markov process is assumed both in time and in
  space (spatial relation)

Time
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Space and time

• A Markov process is assumed both in time and in
  space (spatial relation)

Time
Position 2
Position 3
Position 1
Space
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A Markov process over the rates

• If we have 4 possible rate categories, the Markov
  process is described by

positioni
positioni1
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A Markov process over the rates

• If we have 4 possible rate categories, the Markov
  process is described by

positioni
positioni1
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A Hidden Markov model (HMM)

• This leads to an HMM over the evolutionary rates

Yang 1995Churchill and Felsenstein 1996
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But are adjacent sites dependent?
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But are adjacent sites dependent?
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An HMM with hyper-states
Dependence

Independence
positioni
positioni1
Stern and Pupko 2006
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An HMM with hyper-states
Dependence

Independence
Stern and Pupko 2006
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An HMM with hyper-states
D model
Dependence

I model
Independence
Stern and Pupko 2006
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An HMM with hyper-states
DI model

D model
Dependence

I model
Independence
Stern and Pupko 2006
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Validating the model

• Likelihood analysis
• In-depth study of biological examplerate
  inference and dependence inference
• Simulation studies

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Likelihood analysis

• 84 protein datasets analysed in 60 of 84 the DI
  model outperformed the D model, in 81 of 84 the
  DI model outperformed the I model (LRT AIC)
• Datasets where the improvement was not
  significant tended to be small (few sequences or
  short sequence length)

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In-depth analysis of the Potassium channel
Extracellular
Tetrameric pore-forming protein
Intracellular
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In-depth analysis of the Potassium channel
View from extracellular side
Extracellular
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Using DI to analyse the K-channel
Dark conserved
Light variable
Variable Conserved
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Dependence inference

• The DI model enables not only inferring the rate
  at each site but also inferring whether this
  position is dependent or independent of the
  previous position

position 1
position 2
position 1
position 2
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Sites which were inferred as independent
Dark conserved
Light variable
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Summary

• DI model may more accurately model the
  biological reality, but requires a larger dataset
  to support it.
• The DI model enables implicit study of relations
  between structure and evolutionary rate.

Stern and Pupko, 2006 Mol. Biol. Evol.
Future enhancements

• Explicitly model dependencies along the 3D
  structure of the protein belief propagation.

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Acknowledgements

• Dr. Tal Pupko
• Lab members Itay MayroseAdi Doron-FaigenboimNi
  mrod Rubinstein Eyal PrivmanOsnat ZomerThis
  study was supported by an Israeli Science
  Foundation grant
• THANK YOU!