Adaptive Neural Coding Dependent on the Time-Varying Statistics of the Somatic Input Current

It is generally assumed that nerve cells optimize their performance to reflect the statistics of their input. Electronic circuit analogs of neurons require similar methods of self-optimization for stable and autonomous operation. We here describe and demonstrate a biologically plausible adaptive algorithm that enables a neuron to adapt the current threshold and the slope (or gain) of its current-frequency relationship to match the mean (or dc offset) and variance (or dynamic range or contrast) of the time-varying somatic input current. The adaptation algorithm estimates the somatic current signal from the spike train by way of the intracellular somatic calcium concentration, thereby continuously adjusting the neuronś firing dynamics. This principle is shown to work in an analog VLSI-designed silicon neuron

A universal model for spike-frequency adaptation

Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neuron's onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current