Dynamical hysteresis in multisite protein modification

Multisite protein modification is a ubiquitous mechanism utilized by cells to control protein functions. We have recently proposed a dynamical description of multisite protein modification which embodies all the essential features of the process (E. Milotti, A. Del Fabbro, C. Dalla Pellegrina, and R. Chignola, Physica A, in press), and we have used this model to analyze the stability and the time-scales of this mechanism. The same model can be used to understand how the system responds to stimuli: here we show that it displays frequency-dependent dynamical hysteresis. This behavior closely parallels -- with the due differences -- what is observed in magnetic systems. By selecting model parameters that span the known biological ranges, we find that the frequency-dependent features cover the band of the observed oscillations of molecular intracellular signals, and this suggests that this mechanism may have an important role in cellular information processing.