Algorithmic complexity and thermodynamics of sequence-structure relationships in proteins

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Abstract
The information contained in a protein’s amino acid sequence dictates its three-dimensional structure. In this situation a frozen or embedded structure, the sequence, contains information that ultimately influences a thermodynamic entity, the protein structure. The interplay between information and thermodynamics is explored by considering the algorithmic complexity and Kolmogorov’s universal probability of the sequence and of the structure. It is shown that the algorithmic complexity of a microstate of a polymer is given by its configurational entropy. Using this result and a lattice protein model, a quantitative estimate of the information contained in a protein’s structure is made. This is compared to the information content of the sequence. The information content of the sequence is approximately 2.5 bits per amino acid, while the content in the structure is approximately 0.5 bits per amino acid. It is estimated that virtually all the information contained in the protein structure is shared with the sequence. A deeper connection can be made between the shared information content and the thermodynamic entropy governing the system. Using Kolmogorov’s universal probability, it is possible to establish statistical-mechanical relationships for objects without resorting to a probabilistic ensemble formalism. This allows the thermodynamics of microstates of objects of known configurations to be determined. Using this formalism, the connection between sequence information and the structural thermodynamics of a protein can be made. This connection has strong implications for how protein sequences evolve over evolutionary time and demonstrates that this evolution is constrained by the thermodynamic evolution of the protein structure.

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