Rectified adaptation - a variance sensor for processing time-varying inputs

The role of chemical identity and spatial distribution of biomolecules in pattern formation and cell fate decision making has long been appreciated. However, recent experiments have revealed that the temporal dynamics of molecular concentrations also plays an important role and can affect gene regulation, cell fate decisions and accelerate pattern formation. We identify a general phenomenological behavior - ``rectified adaptation'' - that plays a critical role in processing oscillatory, pulsatile and fluctuating temporal signals in these diverse biological contexts. Like conventional adaptation, rectified adaptation describes a transient response to step changes in an input signal but the response to step ups and step downs is strongly asymmetric. We show how simple implementations of rectified adaptation can sense the variance of an input signal on specific timescales, helping make decisions in immune response and in embryonic patterning.