A Frequency Domain Analysis of the Growth Factor-Driven Extra-Cellular-Regulated Kinase (ERK) Pathway

The ERK pathway is an important biochemical cascade and acts as a master regulator of myriad cell processes including cell proliferation, differentiation, and survival. Early biochemical work established that the timing of ERK phosphorylation was an important determinant of PC12 cell fate, with extended phosphorylation (with nerve growth factor treatment) linked to differentiation but rapid on-off ERK phosphorylation kinetics (with epidermal growth factor treatment) linked to cell proliferation. Recent work from several laboratories has revealed that periodic forcing the phosphorylation of ERK with growth factors, light (optogenetics) or electronically can switch cell fate from proliferative to differentiated depending on type of stimulus (amplitude and frequency). Here, we take an ERK model and analyze it from the frequency domain perspective. The key is the transfer function, which provides a compact description of input (growth factor)-output (ERK activation) behavior over a range of input frequencies, allowing an understanding of system dynamics in terms of amplitude modulations, phase shifts, and signaling bandwidths. Our analysis of transfer functions indicates that, at normal receptor levels, the ERK pathway acts as a negative feedback amplifier to growth factor fluctuations, amplifying them at low receptor occupancy but suppressing them at high receptor occupancy. The frequency dependence is best described as a resonant low pass filter, which selectively filters out high frequency input oscillations. We use the transfer function to predict how different growth factor input dynamics shape ERK activation.