Figure 4
Processes underlying emergent memory and reverberatory dynamics in the MAPK cascade. (a) A characteristic time-series for the normalized concentrations of singly and doubly phosphorylated MAPK (\({n}_{{K}^{\ast }}\) and \({n}_{{K}^{\ast \ast }}\), respectively) following the removal of an applied stimulus of amplitude S = 2.0 × 10−6 μM at t = 0. The numbers (1–4) represent the sequence of events that lead to the emergence of the post-stimulus large-amplitude spiking activity shown schematically in Fig. 1(b). (b) Normalized chemical flux NFlux of MAPK and MAP2K** shown for the segment of the time-series where the spiking behavior in \({n}_{{K}^{\ast \ast }}\) is observed following the withdrawal of the stimulus to MAP3K [demarcated by broken vertical lines in (a)]. (c) Normalized chemical flux NFlux of MAPK** shown along with the difference between the normalized fluxes of MAP2K** and MAPK for the duration indicated by broken vertical lines in (b) corresponding to the peak in the spiking activity of MAPK**. For both panels (b) and (c), normalization of flux is with respect to the maximum of the flux for MAPK**. (d) Characteristic time-series for the reverberatory activity of MAPK following the withdrawal of a stimulus of amplitude S = 1.2 × 10−6 μM at t = 0, showing the normalized concentration of MAPK** (\({n}_{{K}^{\ast \ast }}\)) along with that of the protein complex MAP2K**.MAPK (\({n}_{2{K}^{\ast \ast }\mathrm{.}K}\) = [MAP2K**.MAPK]/[2K]tot). The reference line shows that the peak normalized concentration of the protein complex eventually decreases over time. For details of parameter values see Supplementary Information. The steady state of the system prior to the withdrawal of the stimulus is represented by a red marker [panels (a) and (d)], while the grey marker in (d) corresponds the final time point in Fig. 3(d).
