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 f...