Specific protein-protein binding in many-component mixtures of proteins

Proteins must bind to specific other proteins in vivo in order to function. The proteins are required to bind to only one or a few other proteins of the few thousand proteins typically present in vivo. To quantify this requirement we introduce a property of proteins called the capability. The capability is the maximum number of specific-binding interactions possible in a mixture, or in other words the size of largest sustainable interactome. This calculation of the maximum number possible is closely analogous to the work of Shannon and others on the maximum rate of communication through noisy channels. Using a simple model of proteins, we find specific binding to be a demanding function in the sense that it demands that the binding sites of the proteins be encoded by long sequences of elements, and the requirement for specific binding then strongly constrains these sequences.