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On the Entropy of Protein Families

Journal of Statistical Physics volume 162, pages 1267–1293 (2016)Cite this article

Abstract

Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely vary across organisms, giving rise to a protein family. Here, we estimate the entropy of those families based on different approaches, including Hidden Markov Models used for protein databases and inferred statistical models reproducing the low-order (1- and 2-point) statistics of multi-sequence alignments. We also compute the entropic cost, that is, the loss in entropy resulting from a constraint acting on the protein, such as the mutation of one particular amino-acid on a specific site, and relate this notion to the escape probability of the HIV virus. The case of lattice proteins, for which the entropy can be computed exactly, allows us to provide another illustration of the concept of cost, due to the competition of different folds. The relevance of the entropy in relation to directed evolution experiments is stressed.

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Acknowledgments

S.C., H.J. and R.M. were partly funded by the Agence Nationale de la Recherche Coevstat project (ANR-13-BS04-0012-01).

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Authors and Affiliations

  1. Ragon Institute of MGH, MIT & Harvard, Cambridge, MA, USA

    John P. Barton & Arup K. Chakraborty

  2. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    John P. Barton & Arup K. Chakraborty

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    John P. Barton & Arup K. Chakraborty

  4. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA

    Arup K. Chakraborty

  5. Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Arup K. Chakraborty

  6. Institute for Medical Engineering & Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    John P. Barton & Arup K. Chakraborty

  7. Laboratoire de Physique Statistique de l’ENS, UMR 8550, associé au CNRS et à l’Université P&M. Curie, 24 rue Lhomond, 75005, Paris, France

    Simona Cocco & Hugo Jacquin

  8. Laboratoire de Physique Théorique de l’ENS, UMR 8549, associé au CNRS et à l’Université P&M. Curie, 24 rue Lhomond, 75005, Paris, France

    Rémi Monasson

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  1. John P. Barton
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  2. Arup K. Chakraborty
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  3. Simona Cocco
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  4. Hugo Jacquin
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Correspondence to Simona Cocco.

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Barton, J.P., Chakraborty, A.K., Cocco, S. et al. On the Entropy of Protein Families. J Stat Phys 162, 1267–1293 (2016). https://doi.org/10.1007/s10955-015-1441-4

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  • DOI: https://doi.org/10.1007/s10955-015-1441-4

Keywords

  • Statistical inference
  • Entropy
  • Fitness landscape
  • Genomics
  • Hidden Markov models
  • Covariation
  • HIV virus