Structural features of RNA phenotype networks – Applications to biological evolution – Biological Evolution

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Structural features of RNA phenotype networks – Applications to biological evolution – Biological Evolution

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Structural features of RNA phenotype networks

Applications to biological evolution

NetSci 2015-Zaragoza

Carlos A Lugo-The Sainsbury Laboratory @kupkasmalehttp://calugo.github.io

Biological Evolution

Evolutionary Theory:

Robustness and Evolvability

Multi-scale

Novel uses of known solutions

Accounts for the multiple origin of innovations

Provides insights about the role of changes in the environment

A. Wagner, Trends in Genetics (2011)

Image title:"Evolución" by Roberto Gomes http://isignrob.deviantart.com/

Oh hey, these are some notes. They'll be hidden in your presentation, but you can see them if you open the speaker notes window (hit 's' on your keyboard).

Phenotypic innovations

Are the result of microscopic changes in:

  • Macromolecules (Nucleic Acids, Proteins)
  • Genetic circuits
  • Metabolic Networks

Systematically can be studied by the theory of: Genotype-Phenotype Maps

Every change occurs at DNA level, the G-P framework is a very clever approach Mention case by case is bad Computational

Genotype-Phenotype Maps

Features:

Genotype spaces are composed by large neutral sets (Connected Networks of elements with the same pheotype)

Neighborhoods of genotypes exhibit great phenotypic diversity.

Genotypes:

Sequences: $g_i=\{\sigma_{i,j}\}_{j=1}^{L}$, $\sigma_{i,j}\in[C,G,A,U]$ $\Omega_L=\{g_i\}_{i=1}^{4^L}$ Metabolic Networks and GRN.

Phenotypes:

Folding and Assembly structures

Mention sizes 10^80, mingesize l=800 Oh hey, these are some notes. They'll be hidden in your presentation, but you can see them if you open the speaker notes window (hit 's' on your keyboard).

Phenotypes:

Protein Structure by Holger87. CC BY-SA 3.0 via Wikimedia Commons

Genotype:GGGCUAUUAGCUCAGUUGGUUAGAGCGCACCCCUGAUAAGGGUGAGGUCGCUGAUUCGAAUUCAGCAUAGCCCA

RNA Phenotype proxy (Has a distance):

(((((((..((((.........)))).(((((.......))))).....(((((.......)))))))))))).

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Example: The genetic code (L=3): 64 sequences, 21 Aminoacids. Network of codons at $d_{ij}=1.0$

Neutral sets networks only

Phenotype Neighourhoods: Proline

Arginine

RNA NETWORKS (L=12)

J. Aguirre et al, PLOS ONE (2011)

$\left| \Omega _L \right|=4^L=16777216$

$i:$ Phenotype, $n_i:$Phenotype Size

Mean degree: $k_i \simeq \ln ( n_{i} )$

Clustering:$C_{k_i}\sim {k_i}^{-1}$ $C_{n_i}\sim ln (n_i)^{-1}$

Number of phenotypes $\simeq$ 50

Number of connected sets $\simeq$ 500

Degree Distributions $p_i(k)$ Unimodal

Assortativity: $k_{n,n}$ increasing (r>0)

Degree distributions

Mean degree $k_i\simeq \ln (n_i)$

Phenotype Landscape:

L=12 RNA Phenotype Landscape

Phenotypes: p27: ((.(....).)) and p34: ((....)).... connections

Adjacency Relationships.

Evolutionary Walks.

Low lengths have diluted and fragmented phenotype spaces (For L=12 only 12% of the sequences fold).

Random walks, context free grammars and sampling allow us to:

• Quantify the long term features of random walks in the phenotype landscape. •Total number of non-empty phenotypes. •Phenotype size distributions. •Dwelling time distributions.

EFFECTIVE THEORY OF MOLECULAR EVOLUTION!

S. Manrubia and J. Cuesta, Interface (2014)

Cumulative jump distributions

Phenotype generation: Context free grammars.

Generate all the possible words of length $L$ using the alphabet $\{(,•,)\}$ and the constraints:

- The secondary structure does not have pseudo-knots.

- Base triplets are not allowed

- Minimal number of upaired nucleotides is 3

W. A. Lorenz et al, Asymptotics of RNA Shapes (2007)

P Clote et al, J of Bioinformatics and Comp Biol (2009)

Statistical estimates of phenotype sizes:

$d_{ph}(a,b)$ distance between phenotypes a and b.

Let $j_{t}$: target phenotype of size $\left|\omega_{j_{t}}\right|$ and $\lambda_{d}=\{j | d_{ph}(j,j_{t})\leq d\}$

Then: $\left| \omega_{j_{t}}\right|=\left|\lambda_{0}\right|=\Pi_{k=0}^{d_{max-1}}\frac{\left|\lambda_{k}\right|}{\left|\lambda_{k+1}\right|}\left|\lambda_{d_{max}}\right|$

Allow us to know $\left|\lambda_{0}\right|$ by sampling the fractions $\frac{\left|\lambda_{k}\right|}{\left|\lambda_{k+1}\right|}$ ($\left| \lambda_{d_{max}} \right| =4^{L}$)

T. Jorg et al, BMC Bioinformatics (2008)

Final Comments

Combinatorics, inverse folding and sampling allow us:

- To characterise jumps between phenotypes.

- Determine the phenotype sizes and size distribution.

Broad jump-sizes and dwelling time distributions lead to Non-Markovian dynamics.

Transitions between phenotypes depend on the neutral network size.

An effective dynamical theory of evolution seems achievable if we have a good idea of the topological details induced by the genotype-phenotype mapping.

Analytical and numerical evidence suggest that these “evolutionary searches” can be described by “Levy-like" processes.

More on this subject:

M. C. Cowperthwaite et al, PLOS Comp. Biol. (2008)

B. S. Khatri et. al, PNAS (2009)

J. Aguirre et al PRE (2009)

E. Ibañez-Marcelo and T. Alarcón, J. Theor. Biol. (2014)

S. F. Greebury et. al J. R. Soc. Interface (2014)

C. F. Arias et al, Scientific Reports (2014)

C. A. Lugo et al (in preparation)

Acknowledgments

Susanna Manrubia (CNB-CSIC, Madrid, Spain)

Jacobo Aguirre (CNB-CSIC, Madrid, Spain)

Jose Cuesta (Universidad CIII, Madrid, Spain)

Iván Dotu (Boston College, Boston USA)

Martin Page (TSL, Norwich U.K.)

FIN

THANKS!

Structural features of RNA phenotype networks Applications to biological evolution NetSci 2015-Zaragoza Carlos A Lugo-The Sainsbury Laboratory @kupkasmalehttp://calugo.github.io