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Proteins display a hierarchy of structural features at primary, secondary, tertiary, and higher-order levels, an organization that guides our current understanding of their biological properties and evolutionary origins. Here, we reveal a structural organization distinct from this traditional hierarchy by statistical analysis of correlated evolution between(More)
The maintenance of "public" or "common good" producers is a major question in the evolution of cooperation. Because nonproducers benefit from the shared resource without bearing its cost of production, they may proliferate faster than producers. We established a synthetic microbial system consisting of two Escherichia coli strains of common-good producers(More)
A fundamental problem in biology is understanding the evolutionary emergence and maintenance of altruistic behaviors. A well-recognized conceptual insight is provided by a general mathematical relation, Hamilton's rule. This rule can in principle be invoked to explain natural examples of cooperation, but measuring the variables that it involves is a(More)
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long-standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check codes on the binary(More)
The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit(More)
Allosteric coupling between protein domains is fundamental to many cellular processes. For example, Hsp70 molecular chaperones use ATP binding by their actin-like N-terminal ATPase domain to control substrate interactions in their C-terminal substrate-binding domain, a reaction that is critical for protein folding in cells. Here, we generalize the(More)
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the(More)
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. However, although evolution by natural selection requires new heritable traits to be produced and transmitted, it does not prescribe, per se, the mechanisms by which this is operated. The mechanisms of inheritance are not,(More)
The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary constraints may take is important to interpret the information in protein sequences. To study this problem, we introduce a(More)