Intrinsic and parameter-less gain control in rate coding by spiking neurons

Adaptation is a critical feature of neural systems, including individual neurons. In single neurons, contrast adaptation be mediated by slow processes such as a calcium influx. Here, we propose a biophysical mechanism for contrast adaptation that does not rely on changes in internal state. Our framework is motivated by observations of Drosophila olfactory receptor neurons to fluctuating stimuli: firing rates do not modulate smoothly, rather they switch more discontinuously between low and high ~40 Hz. In the language of dynamical systems, the system persistently crosses a bifurcation between spiking and quiescence. Typically, this system could only encode 1 bit of information, but we show that the conversion from spike events to a rate code encodes more than 1 bit. In addition, responses are contrast invariant: thus, bifurcation crossing amplifies small fluctuations, permitting rate codes that would otherwise be imperceptible. Such bifurcation-induced gain control is a general property of neurons with various bifurcation topologies. Our results suggest that the machinery of neuron spiking permits robust adaptation with high coding efficacy.