Neutral evolution of Protein-protein interactions: a computational study using simple models

Josselin Noirel, Thomas Simonson

Protein-protein interactions are central to cellular organization, and must have appeared at an early stage of evolution. To understand better their role, we consider a simple model of protein evolution and determine the effect of an explicit selection for Protein-protein interactions. In the model, viable sequences all have the same fitness, following the neutral evolution theory. A very simple, two-dimensional lattice representation of the protein structures is used, and the model only considers two kinds of amino acids: hydrophobic and polar. With these approximations, exact calculations are performed. The results do not depend too strongly on these assumptions, since a model using a 3D, off-lattice representation of the proteins gives results in qualitative agreement with the 2D one. With both models, the evolutionary dynamics lead to a steady state population that is enriched in sequences that dimerize with a high affinity, well beyond the minimal level needed to survive. Correspondingly, sequences close to the viability threshold are less abundant in the steady state, being subject to a larger proportion of lethal mutations. The set of viable sequences has a "funnel" shape, consistent with earlier studies: sequences that are highly populated in the steady state are "close" to each other (with proximity being measured by the number of amino acids that differ). This bias in the the steady state sequences should lead to an increased resistance of the population to environmental change and an increased ability to evolve.