A linearized modeling framework for the frequency selectivity in neurons postsynaptic to vibration receptors

Vibration is an indispensable part of the tactile perception, which is encoded to oscillatory synaptic currents by receptors and transferred to neurons in the brain. The A2 and B1 neurons in the drosophila brain postsynaptic to the vibration receptors exhibit selective preferences for oscillatory synaptic currents with different frequencies, which is caused by the specific voltage-gated Na⁺ and K⁺ currents that both oppose the variations in membrane potential. To understand the peculiar role of the Na⁺ and K⁺ currents in shaping the filtering property of A2 and B1 neurons, we develop a linearized modeling framework that allows to systematically change the activation properties of these ionic channels. A data-driven conductance-based biophysical model is used to reproduce the frequency filtering of oscillatory synaptic inputs. Then, this data-driven model is linearized at the resting potential and its frequency response is calculated based on the transfer function, which is described by the magnitude-frequency curve. When we regulate the activation properties of the Na⁺ and K⁺ channels by changing the biophysical parameters, the dominant pole of the transfer function is found to be highly correlated with the fluctuation of the active current, which represents the strength of suppression of slow voltage variation. Meanwhile, the dominant pole also shapes the magnitude-frequency curve and further qualitatively determines the filtering property of the model. The transfer function provides a parsimonious description of how the biophysical parameters in Na⁺ and K⁺ channels change the inhibition of slow variations in membrane potential by Na⁺ and K⁺ currents, and further illustrates the relationship between the filtering properties and the activation properties of Na⁺ and K⁺ channels. This computational framework with the data-driven conductance-based biophysical model and its linearized model contributes to understanding the transmission and filtering of vibration stimulus in the tactile system.