  This report formulates a minimal model based on a control theoretic framework
to best describe the dynamics of perfect adaptation shown by the hyper osmotic
shock response system in yeast. Using principles from adaptive control and
stability theory, we step by step apply system identification methods to build
a simple second order linear system with only a few parameters, that can
concisely model the High Osmolarity Glycerol (HOG) Mitogen Activated Protein
Kinase (MAPK) signaling dynamics. Validation with experimental data demonstrate
that the model is sufficient to predict response of yeast to an arbitrary
external osmotic shock stimulus.
