An extracellular electric field (EF) induces transmembrane polarizations on extremely inhomogeneous spaces Evidence shows that EF-induced somatic polarization in pyramidal cells can modulate the neuronal input-output (I/O) function. However, it remains unclear whether and how dendritic polarization participates in the dendritic integration and contributes to the neuronal I/O function. To this end, we built a computational model of a simplified pyramidal cell with multi-dendritic tufts, one dendritic trunk, and one soma to describe the interactions among EF, dendritic integration, and somatic output, in which the EFs were modeled by inserting inhomogeneous extracellular potentials. We aimed to establish the underlying relationship between dendritic polarization and dendritic integration by analyzing the dynamics of subthreshold membrane potentials in response to AMPA synapses in the presence of constant EFs. The model-based singular perturbation analysis showed that the equilibrium mapping of a fast subsystem can serve as the asymptotic subthreshold I/O relationship for sublinear dendritic integration. This allows us to predict the tendency of EF-mediated dendritic integration by showing how EF changes modify equilibrium mapping. EF-induced hyperpolarization of distal dendrites receiving synapses inputs was found to play a key role in facilitating the AMPA receptor-evoked excitatory postsynaptic potential (EPSP) by enhancing the driving force of synaptic inputs. A significantly higher efficacy of EF modulation effect on global AMPA-type dendritic integration was found compared with local AMPA-type dendritic integration. During the generation of an action potential (AP), the relative contribution of EF-modulated dendritic integration and EF-induced somatic polarization was determined to show their collaboration in promoting or inhibiting the somatic excitability, depending on the EF polarity. These findings are crucial for understanding the EF modulation effect on neuronal computation, which provides insight into the modulation mechanism of noninvasive brain modulation.

Pyramidal neurons consume most signaling-related energy to generate action potentials (APs) and perform synaptic integration. Dendritic Ca2+ spike is an important integration mechanism for coupling inputs from different cortical layers. Our objective was to quantify the metabolic energy associated with the generation of Ca2+ APs in the dendrites. We used morphology-based computational models to simulate the dendritic Ca2+ spikes in layer 5 pyramidal neurons. We calculated the energy cost by converting Ca2+ influx into the number of ATP required to restore and maintain the homeostasis of intracellular Ca2+ concentrations. We quantified the effects of synaptic inputs, dendritic voltage, back-propagating Na+ spikes, and Ca2+ inactivation on Ca2+ spike cost. We showed that much more ATP molecules were required for reversing Ca2+ influx in the dendrites than for Na+ ion pumping in the soma during a Ca2+ AP. Increasing synaptic input increased the rate of dendritic depolarization and underlying Ca2+ influx, resulting in higher ATP consumption. Depolarizing dendritic voltage resulted in the inactivation of Ca2+ channels and reduced the ATP cost, while dendritic hyperpolarization increased the spike cost by de-inactivating Ca2+ channels. A back-propagating Na+ AP initiated in the soma increased Ca2+ spike cost in the apical dendrite when it coincided with a synaptic input within a time window of several milliseconds. Increasing Ca2+ inactivation rate reduced Ca2+ spike cost, while slowing Ca2+ inactivation increased the spike cost. The results revealed that the energy demand of a Ca2+ AP was dynamically dependent on the state of dendritic activity. These findings were important for predicting the energy budget for signaling in pyramidal cells, interpreting functional imaging data, and designing energy-efficient neuromorphic devices.

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