On the entropy of protein families

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 fixation 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.

to appear in Journal of Statistical Physics

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Cited by in corpus (9)

• Inverse Statistical Physics of Protein Sequences: A Key Issues Review
• Efficient generative modeling of protein sequences using simple autoregressive models
• Benchmarking inverse statistical approaches for protein structure and design with exactly solvable models
• Random Language Model
• Inference of compressed Potts graphical models
• Size and structure of the sequence space of repeat proteins
• Towards Parsimonious Generative Modeling of RNA Families
• Evolutionary Dynamics of a Lattice Dimer: a Toy Model for Stability vs. Affinity Trade-offs in Proteins
• Boltzmann machine learning and regularization methods for inferring evolutionary fields and couplings from a multiple sequence alignment