Synaptic Input and ACh Modulation Regulate Dendritic Ca²⁺ Spike Duration in Pyramidal Neurons, Directly Affecting Their Somatic Output

Nonlinear synaptic integration in dendrites is a fundamental aspect of neural computation. One such key mechanism is the Ca²⁺ spike at the apical tuft of pyramidal neurons. Characterized by a plateau potential sustained for tens of milliseconds, the Ca²⁺ spike amplifies excitatory input, facilitates somatic action potentials (APs), and promotes synaptic plasticity. Despite its essential role, the mechanisms regulating it are largely unknown. Using a compartmental model of a layer 5 pyramidal cell (L5PC), we explored the plateau and termination phases of the Ca²⁺ spike under input current perturbations, long-step current-injections, and variations in the dendritic high-voltage-activated Ca²⁺ conductance (that occur during cholinergic modulation). We found that, surprisingly, timed excitatory input can shorten the Ca²⁺ spike duration while inhibitory input can either elongate or terminate it. A significant elongation also occurs when the high-voltage-activated Ca²+ channels (Ca_HVA) conductance is increased. To mechanistically understand these phenomena, we analyzed the currents involved in the spike. The plateau and termination phases are almost exclusively controlled by the Ca_HVA inward current and the I_m outward K⁺ current. We reduced the full model to a single-compartment model that faithfully preserved the responses of the Ca²⁺ spike to interventions and consisted of two dynamic variables: the membrane potential and the K⁺-channel activation level. A phase-plane analysis of the reduced model provides testable predictions for modulating the Ca²⁺ spike and reveals various dynamical regimes that explain the robust nature of the spike. Regulating the duration of the Ca²⁺ spike significantly impacts the cell synaptic-plasticity window and, as we show, its input-output relationship.