Models of subthreshold membrane resonance in neocortical neurons
Authors: Hutcheon B. , Miura R. M. , Puil E. 
Published: December 2017

1. We obtained whole cell data from sensorimotor cortical neurons of in vitro slices (juvenile rats) and observed a low-frequency resonance (1-2 Hz) in their voltage responses. We constructed models of subthreshold membrane currents to determine whether a hyperpolarization-activated cation current (IH) is sufficient to account for this resonance. 2. Parameter values for a basic IH (BH) model were estimated from voltage-clamp experiments at room temperature. The BH model formed a component of a reduced membrane (RM) model. On numerical integration, the RM model exhibited voltage sags and rebounds to injected current pulses; maximal voltage responses to injected oscillatory currents occurred near 2 Hz. 3. We compared the experimentally measured frequency-response curves (FRCs) at room temperature with the theoretical FRCs derived from the RM model. The theoretical FRCs exhibited resonant humps with peaks between 1 and 2 Hz. At 36 degrees C, the theoretical FRCs peaked near 10 Hz. The characteristics of theoretical and observed FRCs were in close agreement, demonstrating that IH is sufficient to cause resonance. Thus we classified IH as a resonator current. 4. We developed a technique, the reactive current clamp (RCC), to inject a computer-calculated current corresponding to a membrane ionic current in response to the membrane potential of the neuron. This enabled us to study the interaction of an artificial ionic current with living neurons (electronic pharmacology or EP-method). Using the RCC, a simplified version of the BH model was used to cancel an endogenous IH (electronic antagonism) and to introduce an artificial IH (electronic expression) when an endogenous IH was absent. Antagonism of IH eliminated sags and rebounds, whereas expression of IH endowed neurons with resonance and the frequency-selective firing that accompanies resonance in neurons with an endogenous IH. Previous investigations have relied on the specificity of pharmacological agents to block ionic channels, e.g., Cs+ to block IH. However, Cs+ additionally affects other currents. This represents the first time an in vitro modeling technique (RCC) has been used to antagonize a specific endogenous current, IH. 5. A simplified RM model yielded values of the resonant frequency and Q (an index of the sharpness of resonance), which rose almost linearly between -55 and -80 mV. Resonant frequencies could be much higher than fH = (2 pi tau H) - 1 where tau H is the activation time constant for IH. 6. In the FRCs, resonance appeared as a hump at intermediate frequencies because of low- and high-frequency attenuations due to IH and membrane capacitance, respectively. Changing the parameters of IH altered the low-frequency attenuation and, hence, the resonance. Changes in the leak conductance affected both the low- and high-frequency attenuations. 7. We modeled an inwardly rectifying K+ current (IIR) and a persistent Na+ current (INaP) to study their effects on resonance. Neither current produced resonance in the absence of IH. We found that IIR attenuated, whereas INaP amplified resonance. Thus IIR and INaP are classified as attenuator and amplifier currents, respectively. 8. Resonators and attenuators differ in that they have longer and shorter time constants, respectively, compared with the membrane time constant. Therefore, an increase in the leak conductance decreases the membrane time constant, which can transform an attenuator into a resonator, altering the frequency response. This suggests a novel mechanism for modulating the frequency responses of neurons to inputs. 9. These investigations have provided a theoretical framework for detailed understanding of mechanisms that produce resonance in cortical neurons. Resonance is one aspect of the intrinsic rhythmicity of neurons. The rhythmicity due to IH resonance is latent until it is revealed by oscillatory inputs. (ABSTRACT TRUNCATED)