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.

在第 5 层锥体细胞 (PC) 的远端躯干中启动的Ca ²⁺尖峰是细胞反应增益的非线性动态变化的基础，这对于皮质处理的自上而下控制至关重要。具有许多隔间和数十个离子通道的详细模型可以解释这种 Ca ²⁺峰值依赖性增益和相关的临界频率。然而，目前的模型并没有考虑到所有已知的 Ca ²⁺依赖性特征。以前尝试包含更多功能需要增加复杂性，从而限制了它们在研究大量人口动态方面的可解释性和实用性。我们在最小的两室生物物理模型中克服了这些限制。在我们的模型中，基底树突/体细胞室包括快速失活的 Na ⁺和延迟整流器 K ⁺电导，而顶端树突/树干隔室包括持久性 Na ⁺、超极化激活阳离子 (I _h )、缓慢失活 K ⁺、毒蕈碱 K ⁺和 Ca ²⁺ L 型。该模型复制了 Ca ²⁺尖峰形态及其临界频率以及第 5 层 PC 突触整合的其他三个定义特征：线性频率-电流关系、反向传播激活的 Ca ²⁺尖峰发射以及临界频率的偏移阻塞 I _h。^{模拟 1000 个同步的第 5 层 PC，我们再现了 Ca 2+}诱发的电流源密度模式尖峰并描述在雄性猕猴身上产生的内侧 - 额叶脑电图。_{当 I h}被阻挡时，我们再现了电流源密度的变化。因此，在顶端树突中具有五个关键离子电流的二室模型再现了这些神经元的所有特征。我们讨论了这个最小模型的效用，以研究参与认知控制并负责事件相关电位（例如与错误相关的消极性）的额叶颗粒区域的微电路。

重要性声明第 5 层锥体细胞的最小模型复制了所有已知的对这些神经元中的远端突触整合至关重要的特征。通过在模型中重新分配电压门控和返回跨膜电流，我们建立了一个理论框架来研究皮质微电路对颅内局部场电位和脑电图的贡献。这种易于处理的模型将使多尺度电生理特征的生物物理评估和皮质处理的计算研究成为可能。