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Table 1 Time and voltage dependence of model gating variables

From: A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block

x

\(x_{\mathrm{half}}\) (mV)

\(x_{k}\) (mV)

Time constants: \(\tau_{x}\) (ms)

m

−30.09

13.2

\(0.01+ \frac{1}{a + b}\),

a = −(15.6504 + 0.4043v)/[exp(−19.565 − 0.50542v)−1],

b = 3.0212exp(−7.463e − 3v)

h

−54

−12.8

\(0.4+ \frac{1}{a+b}\),

a = 5.0754e − 4exp(−6.3213e − 2v),

b = 9.7529exp(0.13442v)

\(h_{s}\)

−54.8

−1.57

20 + 580/(1 + exp(v))

n

−25

12

\(\frac{22.7165}{1+ \exp (- (v+61.1253)/4.4429 )} [ \frac{1}{1+ \exp ( (v+36.8869) /9.7083 )} +0.0052]+0.7397\)

l

−45

7.5

\(1/\{ \frac{-0.020876 ( v+39.726 )}{\exp [ - (v+39.726)/4.711 ] -1} +0.19444 \exp [-(v+15.338)/224.21]\}\)

\(m_{\mathrm{H}}\)

−77.6

17.317

26.21 + 3136/[1 + exp(−(v + 22.686)/29.597)]

p

−35.1

13.4

\(\frac{95.5813}{1+ \exp (- (v+71.5402)/26.0594 )} [ \frac{1}{1+ \exp ( (v+62.5026)/6.5199 )} -0.5108]+48.2438\)

\(q_{1}\)

−80

−6

6.1exp(0.015v)

\(q_{2}\)

−80

−6

\(294.0087+[ \frac{55.8321}{ 1+ \exp ((v+52.5933)/4.9104 )} -5.2348][ \frac{1}{ 1+ \exp ((v-84.8594)/35.3239 )} ]\)