Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

Abstract

AbstractWhen in an integral feedback controller a step perturbation is applied at a constant background, the controlled variable (described here asA) will in general respond with decreased response amplitudes ΔAas backgrounds increase. The controller variableEwill at the same time provide the necessary compensatory flux to moveAback to its set-point. A typical example of decreased response amplitudes at increased backgrounds is found in retinal light adaptation. Due to remarks in the literature that retinal light adaptation would also involve a compensation of backgrounds we became interested in conditions how background compensation could occur. In this paper we describe how background influences can be robustly eliminated. When such a background compensation is active, oscillatory controllers will respond to a defined perturbation with always the same (damped or undamped) frequency profile, or in the non-oscillatory case, with the same response amplitude ΔA, irrespective of the background level. To achieve background compensation we found that two conditions need to apply: (i) an additional set of integral controllers (here described asI1andI2) have to be employed to keep the manipulated variableEat a defined set-point, and (ii),I1andI2need to feed back to theA-Esignaling axis directly through the controlled variableA. In analogy to a similar feedback applied in quantum control theory, we term these feedback conditions as ‘coherent feedback’. When analyzing retinal light adaptations in more detail, we find no evidence in the presence of background compensation mechanisms. Although robust background compensation, as described theoretically here, appears to be an interesting regulatory property, relevant biological or biochemical examples still need to be identified.