Asymptotic Input-Output Relationship Predicts Electric Field Effect on Sublinear Dendritic Integration of AMPA Synapses.

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.