Non-linear leak currents affect mammalian neuron physiology

Abstract

In their seminal works on squid giant axons, Hodgkin, and Huxley approximated the membrane leak current as Ohmic, i.e., linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted) varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents) and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells.

Detection of Multiway Gamma Coordination Reveals How Frequency Mixing Shapes Neural Dynamics

“…Through frequency mixing, the integration of two oscillations by a target that activates with a nonlinear dependence on its inputs results in the emergence of novel frequency components (Fessenden, 1902;Poole, 2015). Consistent with the fact that neurons are nonlinear integrators (Hille, 2001;Huang et al, 2015;Segev and London, 2000), it was demonstrated experimentally that frequency mixing is applicable to brain oscillations (Ahrens et al, 2002;Grossman et al, 2017). However, these experimental studies induced mixing by applying stimuli at known frequencies.…”

“…As oscillatory signals converge and diverge within and between neuronal networks, they undergo multiple nonlinear transformations (Hille, 2001;Huang et al, 2015;Segev and London, 2000). In other fields such as electronics and acoustics, it has long been appreciated that applying a nonlinearity to the sum of two oscillations, S 1 and S 2 , with frequencies f 1 and f 2 , results in new oscillations.…”

T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells

“…However, it should be noted that modeling leak currents exactly (i.e. non-linearly) may affect the output of neurons ( Huang et al, 2015 ).…”

Dynamics of ramping bursts in a respiratory neuron model

“…8, 9). While our decision to treat E L as a constant allowed us to compare our model directly to earlier ones where leak strength was used to explore model behavior, E L may in reality be nonlinearly modulated by ion dynamics (Koizumi and Smith, 2008;Huang et al, 2015). The robustness of bursting that we found with respect to variations in g L supports the claim that the ramping dynamics that we have studied will persist with the inclusion of E L dependence on dynamic ion concentrations, but incorporating this effect in the model and tuning it appropriately is beyond the scope of the current study.…”