Modeling the calcium spike as a threshold triggered fixed waveform for synchronous inputs in the fluctuation regime

A Minimal Biophysical Model of Neocortical Pyramidal Cells: Implications for Frontal Cortex Microcircuitry and Field Potential Generation

Ca²⁺ spikes initiated in the distal trunk of layer 5 pyramidal cells (PCs) underlie nonlinear dynamic changes in the gain of cellular response, critical for top-down control of cortical processing. Detailed models with many compartments and dozens of ionic channels can account for this Ca²⁺ spike-dependent gain and associated critical frequency. However, current models do not account for all known Ca²⁺-dependent features. Previous attempts to include more features have required increasing complexity, limiting their interpretability and utility for studying large population dynamics. We overcome these limitations in a minimal two-compartment biophysical model. In our model, a basal-dendrites/somatic compartment included fast-inactivating Na⁺ and delayed-rectifier K⁺ conductances, while an apical-dendrites/trunk compartment included persistent Na⁺, hyperpolarization-activated cation (I _h ), slow-inactivating K⁺, muscarinic K⁺, and Ca²⁺ L-type. The model replicated the Ca²⁺ spike morphology and its critical frequency plus three other defining features of layer 5 PC synaptic integration: linear frequency-current relationships, back-propagation-activated Ca²⁺ spike firing, and a shift in the critical frequency by blocking I _h Simulating 1000 synchronized layer 5 PCs, we reproduced the current source density patterns evoked by Ca²⁺ spikes and describe resulting medial-frontal EEG on a male macaque monkey. We reproduced changes in the current source density when I _h was blocked. Thus, a two-compartment model with five crucial ionic currents in the apical dendrites reproduces all features of these neurons. We discuss the utility of this minimal model to study the microcircuitry of agranular areas of the frontal lobe involved in cognitive control and responsible for event-related potentials, such as the error-related negativity.SIGNIFICANCE STATEMENT A minimal model of layer 5 pyramidal cells replicates all known features crucial for distal synaptic integration in these neurons. By redistributing voltage-gated and returning transmembrane currents in the model, we establish a theoretical framework for the investigation of cortical microcircuit contribution to intracranial local field potentials and EEG. This tractable model will enable biophysical evaluation of multiscale electrophysiological signatures and computational investigation of cortical processing.

Effects of Calcium Spikes in the Layer 5 Pyramidal Neuron on Coincidence Detection and Activity Propagation

The role of dendritic spiking mechanisms in neural processing is so far poorly understood. To investigate the role of calcium spikes in the functional properties of the single neuron and recurrent networks, we investigated a three compartment neuron model of the layer 5 pyramidal neuron with calcium dynamics in the distal compartment. By performing single neuron simulations with noisy synaptic input and occasional large coincident input at either just the distal compartment or at both somatic and distal compartments, we show that the presence of calcium spikes confers a substantial advantage for coincidence detection in the former case and a lesser advantage in the latter. We further show that the experimentally observed critical frequency phenomenon, in which action potentials triggered by stimuli near the soma above a certain frequency trigger a calcium spike at distal dendrites, leading to further somatic depolarization, is not exhibited by a neuron receiving realistically noisy synaptic input, and so is unlikely to be a necessary component of coincidence detection. We next investigate the effect of calcium spikes in propagation of spiking activities in a feed-forward network (FFN) embedded in a balanced recurrent network. The excitatory neurons in the network are again connected to either just the distal, or both somatic and distal compartments. With purely distal connectivity, activity propagation is stable and distinguishable for a large range of recurrent synaptic strengths if the feed-forward connections are sufficiently strong, but propagation does not occur in the absence of calcium spikes. When connections are made to both the somatic and the distal compartments, activity propagation is achieved for neurons with active calcium dynamics at a much smaller number of neurons per pool, compared to a network of passive neurons, but quickly becomes unstable as the strength of recurrent synapses increases. Activity propagation at higher scaling factors can be stabilized by increasing network inhibition or introducing short term depression in the excitatory synapses, but the signal to noise ratio remains low. Our results demonstrate that the interaction of synchrony with dendritic spiking mechanisms can have profound consequences for the dynamics on the single neuron and network level.