Necessary conditions for a minimal model of receptor to show adaptive response over a wide range of levels of stimulus

Sensory systems respond to temporal changes in the stimulus and adapt to the new level when it persists, this pattern of response being maintained in a wide range of levels of stimulus. Here we use a simple model of adaptation developed by Segel et al. (J. Theor. Biol. 120 (1986) 151–179) and extended by Hauri and Ross (Biophys. J. 68 (1995) 708–722) to study the conditions in which it shows wide range of response. The model consists of a receptor that switches between a variable number of states, either by mass action law or by covalent modification. Using a global optimization procedure, we have optimized the adaptive response of the alternatives of the model with different number of states. We find that it is impossible to obtain a wide range of response if the receptor switches between states following mass-action laws, irrespective of the number of states. Instead, a wide range (of five orders of magnitude of ligand concentration) can be obtained if the receptor switches between several states by irreversible covalent modification, in agreement with previous models. Therefore, in this model, expenditure of energy to maintain a large number of covalent modification cycles operating outside equilibrium is necessary to achieve a wide range of response. The optimal values of the parameters present similar patterns to those reported for specific receptors, but there is no quantitative agreement. For instance, ligand affinity varies several orders of magnitude between the different states of the receptor, what is unlikely to be fulfilled by real systems. To see if the minimal model can show adaptive response and range with quantitatively plausible parameter values a sub-optimal receptor was studied, finding that adaptive response of high intensity can still be obtained in at least three orders of magnitude.