Memory functions reveal structural properties of gene regulatory networks
Fig 4
Memory amplitude and temporal dynamics.
(A) Amplitude of memory (memory function at Δt = 0) of Nkx2.2 to itself along the neural tube. There are multiple lines as the analysis was performed at all possible stable steady states. The vertical axis is logarithmic to make the range of amplitudes easier to appreciate. Colours identify the memory amplitude contribution from each of the two possible bulk channels, via Irx3 and Pax6, respectively. Thick lines indicate physiological states, while thin lines indicate states that are not usually observed in vivo. (B) Linear memory amplitude of (past) Olig2 on Nkx2.2 along the neural tube. The memory via Pax6 is for the most part below the memory via Irx3 in each pair of corresponding curves. (C,D) Memory amplitudes of Olig2 to Nkx2.2 (C) and to itself (D). No channel decomposition is performed as Olig2 receives memory only via the Irx3 channel. (E) Nonlinear memory of (past) Olig2 squared on Nkx2.2 in the p3 domain, where dynamics are dominated by Irx3; memory via Pax6 is negligible by comparison. (F) Nonlinear memory function of (past) Olig2 squared on Nkx2.2 from position 0.2 in (E), plotted to show that the relative contribution of the Pax6 channel is small also for all time differences. (G,H) Nonlinear memory functions of Olig2 to Nkx2.2 (G) and itself (H) in the p2 domain at position 0.7, exemplifying the potential for nontrivial time dependences (including non-monotonicity and sign changes) in the nonlinear memory functions.