The Levinthal paradox of the interactome
Peter Tompa George D. Rose
First published: 10 October 2011
The number of possible interactomes increases exponentially with proteome size. The number of possible different states (patterns of pairwise interactions) of the interactome increases exponentially with the number of its constituent proteins. In the simple case of four proteins (A), the number of possible different arrangements is only three. Five proteins (B) may already engage in 15 different pairwise interactions. The first pair (red‐blue, red‐purple, red‐yellow, red‐green) is connected by a solid line, followed by any of three possible secondary pairs (with connections indicated by dotted lines), plus three remaining possibilities (not illustrated) in which the first protein (red) is unpaired. The theoretical number for n proteins is n!/2n/2 × n/2! (cf. text and Supporting Information), which for a realistic interactome of 4500 proteins gives 107200 different possibilities.
Abstract
The central biological question of the 21st century is: how does a viable cell emerge from the bewildering combinatorial complexity of its molecular components? Here, we estimate the combinatorics of self‐assembling the protein constituents of a yeast cell, a number so vast that the functional interactome could only have emerged by iterative hierarchic assembly of its component sub‐assemblies. A protein can undergo both reversible denaturation and hierarchic self‐assembly spontaneously, but a functioning interactome must expend energy to achieve viability. Consequently, it is implausible that a completely “denatured” cell could be reversibly renatured spontaneously, like a protein. Instead, new cells are generated by the division of pre‐existing cells, an unbroken chain of renewal tracking back through contingent conditions and evolving responses to the origin of life on the prebiotic earth. We surmise that this non‐deterministic temporal continuum could not be reconstructed de novo under present conditions.
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