A receptor-inactivation model for single-celled habituation in Stentor coeruleus
The single-celled ciliate Stentor coeruleus demonstrates habituation to mechanical stimuli, showing that even single cells can manifest a basic form of learning. Although the ability of Stentor to habituate has been extensively documented, the mechanism of learning is currently not known. Here we take a bottom-up approach and investigate a simple biochemistry-based model based on prior electrophysiological measurements in Stentor along with general properties of receptor molecules. In this model, a mechanoreceptor senses the stimulus and leads to channel opening to change membrane potential, with a sufficient change in polarization triggering an action potential that drives contraction. Receptors that are activated can become internalized, after which they can either be degraded or recycled back to the cell surface. This activity-dependent internalization provides a potential means for the cell to learn. Stochastic simulations of this model confirm that it is capable of showing habituation similar to what is seen in actual Stentor cells, including the lack of dishabituation by strong stimuli and the apparently step-like response of individual cells during habituation. The model also can account for several habituation hallmarks that a previous two-state Markov model could not, namely, the dependence of habituation rate on stimulus magnitude, which had to be added onto the two state model but arises naturally in the receptor inactivation model; the rate of response recovery after cessation of stimulation; the ability of high frequency stimulus sequences to drive faster habituation that results in a lower response probability, and the potentiation of habituation by repeated rounds of training and recovery. The model makes the prediction that application of high force stimuli that do not normally habituate should drive habituation to weaker stimuli due to decrease in the receptor number, which serves as an internal hidden variable. We confirmed this prediction using two new sets of experiments involving alternation of weak and strong stimuli. Furthermore, the model predicts that training with high force stimuli delays response recovery to low force stimuli, which aligns with our new experimental data. The model also predicts subliminal accumulation, wherein continuation of training even after habituation has reached asymptotic levels should lead to delayed response recovery, which was also confirmed by new experiments. The model is unable to account for the phenomenon of rate sensitivity, in which habituation caused by higher frequency stimuli is more easily reversed leading to a frequency dependence of response recovery. Such rate sensitivity has not been reported in Stentor. Here we carried out a new set of experiments which are consistent with the models prediction of the lack of rate sensitivity. This work demonstrates how a simple model can suggest new ways to probe single-cell learning at an experimental level. Finally, we interpret the model in terms of a kernel estimator that the cell may use to guide its decisions about how to response to new stimuli as they arise based on information, or the lack thereof, from past stimuli.