Evolutionary Stability of Small Molecular Regulatory Networks That Exhibit Near-Perfect Adaptation

SIMPLE SUMMARY: If a perfume is released into a room, the occupants will immediately smell it; however, after a few minutes, they will become desensitized to the odor, although it is still in the room, as would be attested by newcomers to the gathering. Such behavior is called ‘adaptation.’ In response to a stepwise increase in an incoming signal (perfume), a sensory cell (the olfactory cell in the nose) sends an output signal (nerve impulses) to an organ (the brain) that responds appropriately (attraction or repulsion, say); however, in the continued presence of the input signal, the sensory cell ceases to respond and reverts to its ‘resting’ state. There are many examples of such near-perfect adaptive responses in the physiology of living cells, and it is natural to inquire as to the underlying molecular bases of such behavior. Using an evolutionary search procedure, this paper examines a wide class of molecular interaction networks for their potential to exhibit near-perfect adaptation. Adaptive networks that are stable to evolutionary fluctuations are characterized by a simple motif with two paths: (i) an incoming signal activates a receptor molecule, which activates an output signal, and simultaneously (ii) the receptor activates a modulator component that inhibits the output. ABSTRACT: Large-scale protein regulatory networks, such as signal transduction systems, contain small-scale modules (‘motifs’) that carry out specific dynamical functions. Systematic characterization of the properties of small network motifs is therefore of great interest to molecular systems biologists. We simulate a generic model of three-node motifs in search of near-perfect adaptation, the property that a system responds transiently to a change in an environmental signal and then returns near-perfectly to its pre-signal state (even in the continued presence of the signal). Using an evolutionary algorithm, we search the parameter space of these generic motifs for network topologies that score well on a pre-defined measure of near-perfect adaptation. We find many high-scoring parameter sets across a variety of three-node topologies. Of all possibilities, the highest scoring topologies contain incoherent feed-forward loops (IFFLs), and these topologies are evolutionarily stable in the sense that, under ‘macro-mutations’ that alter the topology of a network, the IFFL motif is consistently maintained. Topologies that rely on negative feedback loops with buffering (NFLBs) are also high-scoring; however, they are not evolutionarily stable in the sense that, under macro-mutations, they tend to evolve an IFFL motif and may—or may not—lose the NFLB motif.