D43 Time response analysis

Topic

This temporal response analysis characterizes the receptor's processing dynamics: specifically, how quickly it tracks variations in the perceived stimulus versus how rapidly it responds to a sudden stimulus.

Conversely, the receptor's transfer function in the frequency domain serves as the most comprehensive tool for this characterization: the magnitude of the transfer function indicates the receptor's gain, while its phase angle indicates the phase lag.

The cutoff frequency establishes the upper limit of stimulus variation that the receptor can track faithfully; for instance, an insect mechanoreceptor—representing one model in this set—can achieve a considerably high cutoff frequency, whereas a cutaneous thermoreceptor—representing a different model characterized by slow adaptation—exhibits a significantly lower cutoff frequency. If the receptor responds more slowly to the stimulus, its cutoff frequency is consequently lower.

Finally, the receptor's squared coherence determines whether the relationship between stimulus and response is essentially linear or, conversely, non-linear or noisy, thereby estimating the fraction of the response explained by a simple linear model at any given frequency. As the relationship between the stimulus and the receptor's response deviates further from simple linearity, the receptor's final quadratic coherence at that specific frequency consequently decreases.

Conversely, the sensory receptor's absolute refractory period determines its maximum firing rate—a parameter that defines another model in this set: a fast insect mechanoreceptor with a very short absolute refractory period can fire at a maximum frequency comparable to the insect's wing-beat frequency. A further shortening of the sensory receptor's absolute refractory period results in a higher maximum firing rate for that receptor.

Thus, this model—characterized by its processing dynamics and its ability to track stimulus variations—demonstrates that the power law governing the sensory receptor's latency (specifically, the same family of power laws defining firing rates in another model of this set) implies that a more intense response triggers faster firing—with a significantly shorter latency—following a power-law relationship characteristic of that specific receptor. A further increase in the perceived stimulus intensity results in an even shorter firing latency, thereby bringing the receptor closer to the upper limit of temporal variation established at the outset of this model.

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