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. 2015 Nov 6;9:432. doi: 10.3389/fncel.2015.00432

Figure 2.

Figure 2

(A–C) The Goldman-Hodgkin-Katz leak-current model predicts non-linear voltage responses to DC current injections. (A) All Ohmic model simulations are colored in blue and all GHK model simulations are colored in orange. Voltage traces of passive membrane responses to +15 pA (solid lines) and −15 pA (inversed and superimposed, dotted lines) current injections for 2 seconds, at −0.3, 0 and +0.3 nA holding currents. Bottom traces: voltage responses to +15 pA current pulse at various holding currents superimposed. The Ohmic and GHK cell models have identical surface areas, Erest (−85 mV) and membrane resistances (120 kohm cm2). For the GHK model, ionic concentrations in mM are: [K+]in and [Cl−]in are 150 and 10 respectively, external [K+]out and [Cl−]out are 2.5 and 130, respectively. (B) Rn and tau at each holding potential calculated using the +15 nA traces. The holding potential values for the traces in (A) are marked by “X”. (C) The GHK model comprises two rectifying currents IK (yellow) and ICl (red). Ohmic current is colored blue. All currents are standardized to Ohmic current at −100 mV. All three current-voltage curves were constructed using the same Ohmic and GHK model as in (A). (D–E) Rn-voltage and tau-voltage relationships measured in cerebellar Purkinje neurons were non-linear, consistent with the GHK model prediction. (D) Voltage deflections in a Purkinje neuron (when major ionic currents are blocked) in response to +15 pA (orange) and −15 pA (pale orange) current pulse injections for 1 s at −30, 0, and +30 pA holding currents (corresponding holding potentials are −74, −67, and −63 mV, respectively). Bottom traces: voltage responses to +30 pA current pulse at various holding currents superimposed. (E) Rn-voltage and tau-voltage relationships of each recorded cell (represented by different color filled circles). Holding potentials of the traces in (D) are marked by “X”. The regression slope (β) for tau and Rn are −1.2 (p = 0.043) and −4.1 (p = 0.037) respectively. Individual cells were highlighted to show that non-linear passive membrane properties could be observed for all cells recorded (n > 5).