Homeostasis at different backgrounds: The roles of overlayed feedback structures in vertebrate photoadaptation

Abstract

We have studied the resetting behavior of eight basic integral controller motifs with respect to different but constant backgrounds. We found that the controllers split symmetrically into two classes: one class, based on derepression of the compensatory flux, leads to more rapid resetting kinetics as backgrounds increase. The other class, which directly activates the compensatory flux, shows a slowing down in the resetting at increased backgrounds. We found a striking analogy between the resetting kinetics of vertebrate photoreceptors and controllers based on derepression, i.e. vertebrate rod or cone cells show decreased sensitivities and accelerated response kinetics as background illuminations increase. The central molecular model of vertebrate photoadaptation consists of an overlay of three negative feedback loops with cytosolic calcium (Ca i 2 +), cyclic guanosine monophosphate (cGMP) and cyclic nucleotide-gated (CNG) channels as components. While in one of the feedback loops the extrusion of Ca i 2 + by potassium-dependent sodium-calcium exchangers (NCKX) can lead to integral control with cGMP as the controlled variable, the expected robust perfect adaptation of cGMP is lost, because of the two other feedback loops. They avoid that Ca i 2 + levels become too high and toxic. Looking at psychophysical laws, we found that in all of the above mentioned basic controllers Weber’s law is followed when a “just noticeable difference” (threshold) of 1% of the controlled variable’s set-point was considered. Applying comparable threshold pulses or steps to the photoadaptation model we find, in agreement with experimental results, that Weber’s law is followed for relatively high backgrounds, while Stephens’ power law gives a better description when backgrounds are low. Limitations of our photoadaption model, in particular with respect to potassium/sodium homeostasis, are discussed. Finally, we discuss possible implication of background perturbations in biological controllers when compensatory fluxes are based on activation.

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

“…Dowling interpreted the parallel lines as a result of a second adaptive mechanism in the receptor, which shifts the photoreceptor intensity-response curves along the intensity axis, thus extending the range over which the receptor responds (see page 222 in Ref[3], bottom section).Clearly, as Fig18shows, the parallel lines in panels c or d neither require the need for a background compensation mechanism nor additional adaptive mechanisms. While adaptation mechanisms compensating for a background cannot be excluded, the observation of parallel lines in semi-logarithmic or double-logarithmic plots appear not sufficient to indicate additional background compensation mechanisms besides of the negative feedbacks which lead to the responses in Fig 1[5].…”

“…For example, when studying photoreceptor cells often a constant background light is used in addition to the application of a flash or step of light [2][3][4]. In fact, motif 2 has been found [5] to describe light adaptations and the influence of different background light intensities, as shown in Fig 1, relatively well. In this paper we describe novel findings how a background can be compensated for, such that the response kinetics become independent of different but constant backgrounds.…”

“…In the following calculations we have used zero-order kinetics to implement integral control [17,[22][23][24]. However, it should be mentioned that there are other kinetics conditions to achieve integral control, such as antithetic control [21,25,26], which often will show identical resetting behaviors as in zero-order control [5,26]. Also, autocatalytic reactions can be used to obtain integral control [27][28][29], which generally will show much faster resetting kinetics in comparison when integral control is introduced by zero-order kinetics [30,31].…”

“…For non- [7]. For a theoretical description of this behavior see Ref [5] and references therein. https://doi.org/10.1371/journal.pone.0287083.g001…”

“…Homeostatic mechanisms play important roles in physiology and in the adaptation of organisms to their environments [1]. For example, vertebrate retinal photoreceptor cells contain negative feedback loops which participate in light adaptation [2][3][4][5]. A hallmark of vertebrate photoadaptation is that resetting kinetics accelerate and response amplitudes decrease as backgrounds increase [5,6].…”