NEURON Note #25

Goals: Create a NMODL model for the delayed rectifier potassium current (K_DR)

Introduction:

Delayed rectifier potassium current (I_DR, K_DR, or I_K) is an important outward current regulating the firing properties of excitable cells. Thus, it is wise to carefully select an available model or create one based on experimental data. I tested the models in Bianchi et al's paper (2012), Gonzalez et al's paper (2011), and Migliore's paper (1996). These models generate currents which are distinct from I_DR observed in CA1 pyramidal neurons. Thus, I created a new model based on Mohapatra et al's data (2009) and Hoffman's data (1997). This model is more suitable to simulate I_DR in CA1 pyramidal neurons.

Results:

Bianchi (2012)

	Vhalf = 13.0 (mV); k = -8.8 (mV)

Gonzalez (2011)

V_1/2 is too hyperpolarized. The absolute value of k is too small.

	Vhalf = -31.9 (mV); k = -4.1 (mV)

Migliore (1996)

V_1/2 is too hyperpolarized.

	Vhalf = -41.7 (mV); k = -1.4 (mV)

Payne's Model

g = gbar * n^4 * l

Target Activation Curve:
Vhalf = 2 (mV) (Ref: Chen (2004)
k = 7 (mV) (Ref: Chen (2004)

n (activation particle):
Vhalf = -13.9 (mV)
k = -9.1 (mV)
tau = 1.8 (ms) (Ref: Hoffman (1997))

l (inactivation particle):
Vhalf = -28.8 (mV) (Ref: Mohapatra (2009)
k = 11.4 (mV) (Ref: Mohapatra (2009)
tau = 500 (ms) (Ref: Mohapatra (2009)
P = 0.25 (1) (Ref: Mohapatra (2009)

Program used to find parameters for n: BoltzmannPowerFit.py
Command to run the program in the cmd console: ipython3 BoltzmannPowerFit.py -- pylab

NMODL file: kdr_p.mod

Results

	Vhalf = 1.9 (mV); k = -6.9 (mV)

References:

• On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Bianchi D, Marasco A, Limongiello A, Marchetti C, Marie H, Tirozzi B, Migliore M. J Comput Neurosci. 2012 Feb 5.
• Gómez González JF, Mel BW, Poirazi P. Distinguishing Linear vs. Non-Linear Integration in CA1 Radial Oblique Dendrites: It's about Time. Front Comput Neurosci. 2011;5:44.
• Modeling the attenuation and failure of action potentials in the dendrites of hippocampal neurons. Migliore M. Biophys J. 1996 Nov;71(5):2394-403.
• Regulation of intrinsic excitability in hippocampal neurons by activity-dependent modulation of the KV2.1 potassium channel. Mohapatra DP, Misonou H, Pan SJ, Held JE, Surmeier DJ, Trimmer JS. Channels (Austin). 2009 Jan-Feb;3(1):46-56.
• K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Hoffman DA, Magee JC, Colbert CM, Johnston D. Nature. 1997 Jun 26;387(6636):869-75.
• Chen X, Johnston D. Properties of single voltage-dependent K+ channels in dendrites of CA1 pyramidal neurones of rat hippocampus. J Physiol. 2004 Aug 15;559(Pt 1):187-203.