Diversity amongst human cortical pyramidal neurons revealed via their sag currents and frequency preferences

In the human neocortex coherent interlaminar theta oscillations are driven by deep cortical layers, suggesting neurons in these layers exhibit distinct electrophysiological properties. To characterize this potential distinctiveness, we use in vitro whole-cell recordings from cortical layers 2 and 3 (L2&3), layer 3c (L3c) and layer 5 (L5) of the human cortex. Across all layers we observe notable heterogeneity, indicating human cortical pyramidal neurons are an electrophysiologically diverse population. L5 pyramidal cells are the most excitable of these neurons and exhibit the most prominent sag current (abolished by blockade of the hyperpolarization activated cation current, Ih). While subthreshold resonance is more common in L3c and L5, we rarely observe this resonance at frequencies greater than 2 Hz. However, the frequency dependent gain of L5 neurons reveals they are most adept at tracking both delta and theta frequency inputs, a unique feature that may indirectly be important for the generation of cortical theta oscillations.

Neuronal resonance can be generated independently at distinct levels of organization

ABSTRACTNeuronal resonance is defined as maximal amplification of the response of a system to a periodic input at a finite non-zero input frequency band. Resonance has been observed experimentally in the nervous system at the level of membrane potentials, spike times, post-synaptic potentials, and neuronal networks. It is often assumed that resonance at one level of organization endows resonance at another level, but how the various forms of neuronal resonances interact is unknown. Here we show that a direct link of the frequency response properties across neuronal levels of organization is not necessary. Using detailed biophysical modeling combined with numerical simulations, extracellular recordings, and optogenetic manipulations from behaving mice, we show how low-pass filtering, high-pass filtering, and amplification mechanisms can generate resonance at a single level of organization. Subthreshold resonance, synaptic resonance, and spiking resonance can each occur in the lack of resonance at any other level of organization. In contrast, frequencydependent mechanisms at several levels of organization are required to generate the more complex phenomenon of network resonance. Together, these results show that multiple independent mechanisms can generate resonance in neuronal systems.

Sag currents are a major contributor to human pyramidal cell intrinsic differences across cortical layers

In the human neocortex, coherent theta (∼8Hz) oscillations between superficial and deep cortical layers are driven by deep layer neurons, suggesting distinct intrinsic electrophysiological properties of L5 neurons. We used in vitro whole-cell recordings to characterize pyramidal cells in layer 2/3 (L2/3), layer 3c (L3c) and layer 5 (L5) of the human neocortex. L5 pyramidal cells were more excitable and had a more prominent sag relative to L2/3 and L3c neurons that was abolished by blockade of the hyperpolarization activated cation current (Ih). We found a greater proportion of L5 and L3c neurons displaying subthreshold resonance relative to L2/3. Although no theta subthreshold resonance was observed in either L5 and L2/3 neurons, L5 neurons were more adept at tracking both delta (4Hz) and theta oscillations, the former being dependent on Ih. The unique features of human L5 neurons likely contribute to the emergence of theta oscillations in human cortical microcircuits.

Spectroscopic aspects of subthreshold Siegert states

The Siegert states are approached in the framework of Bloch–Lane–Robson theory of quantum collisions. Both the bound and the quasi-stationary Siegert states are subject of the equation relating the channel R-matrix element to the logarithmic derivative. The Siegert state dependence on the decay channel parameters results in channel renormalization of reduced widths, especially near threshold. The neutron subthreshold and the electron Rydberg states are examples of subthreshold Siegert states. The Siegert approach results in Heisenberg’s S-matrix formula for the bound state and the subthreshold resonance. The Siegert state residue is a spectroscopic asymptotic normalization constant. The decay width of the electron Rydberg channel resonance is, up to a factor, the electron strength function.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage regime and the spiking mechanism. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold oscillations patterns with different properties. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but functionally different (parabolic- and cubic-like). As a case study we consider a model having a persistent sodium current and a hyperpolarization-activated (h-) current. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonance. We also measure spiking phasonance, which is an extension of subthreshold phasonance to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present, but output spiking resonance is present primarily in the parabolic-like model, while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results show that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

BIOPHYSICAL PROPERTIES OF SUBTHRESHOLD RESONANCE OSCILLATIONS AND SUBTHRESHOLD MEMBRANE OSCILLATIONS IN NEURONS

Subthreshold-level activities in neurons play a crucial role in neuronal oscillations. These small-amplitude oscillations have been suggested to be involved in synaptic plasticity and in determining the frequency of network oscillations. Subthreshold membrane oscillations (STOs) and subthreshold resonance oscillations (SROs) are the main constituents of subthreshold-level activities in neurons. In this study, a general theoretical framework for analyzing the mechanisms underlying STOs and SROs in neurons is presented. Results showed that the resting membrane potential and the hyperpolarization-activated potassium channel ([Formula: see text]-channel) affect the subthreshold-level activities in stellate cells. The contribution of [Formula: see text]-channel on resonance is attributed to its large time constant, which produces the time lag between [Formula: see text] and the membrane potential. Conversely, the persistent sodium channels (Nap-channels) only play an amplifying role in these neurons.