Persistent memory in network topologies following temporary stimuli

Molecular memory in signaling and gene regulatory networks shapes how cells respond to transient inputs. Here, we present a mathematical framework to quantify memory as changes in system state after temporary stimulation. Using computational models, we show that circuits with positive feedback loops, particularly those enabling bistability, sustain long-term memory, while certain negative feedbacks can erase it. We further identify minimal network motifs that reliably confer memory, revealing symmetry between activating and inactivating mechanisms. In addition, oscillatory circuits can encode memory even without positive feedback, storing information in the phase of their oscillations. Applying this approach to mouse embryonic stem cells exposed to transient differentiation cues, we find that different genes display distinct degrees of memory retention, with some reflecting partial reversion and others indicating commitment to differentiation. This framework provides a unified way to compare memory across systems and highlights how circuit architecture influences information storage in biology.