Supplemental Data. Starting matrix, rate constants, and channel state dwell probabilities
corresponding to the kinetic schemes shown in Figs. 7A-D. O: channel open states; C: channel
closed states. For brevity, we use C4 to denote the “low activity mode” mentioned in the main text
and Fig. 7.
Starting matrix: the following set of seven differential equations represents the general kinetic
model that is applied to all schemes described in Figure 7C & 7D of the manuscript. Note that for
schemes shown in Fig. 7A and 7B (0.3 uM calcium in absence and presence of ethanol,
respectively): kC3C4 = 0 and kC4C3 = 0.
Next, rearrangement of terms in the right hand side of each equation (so that the states C1,
C2, C3, C4, O1, O2, and O3 “line up” vertically) helps in the identification of the elements of the
square transition matrix (i.e., Sij, with i, j = 1,2,3,4,5,6,7).
1
C1
C2
C3
C4
O1
O2
O3
rendering the following transition matrix system corresponding to the kinetic scheme:
At steady-state (our experimental recording conditions), all seven derivatives on the left
hand side of the above column matrix will become zero. Therefore:
2
From which we obtain the following equalities:
that match the original equations shown above.
Rate and equilibrium constants, and channel state dwell probabilities:
Considering two channel dwell states “S1” and “S2”, we use the following notation:
kS1S2: “forward”rate constant, kS2S1: “reverse” rate constant, and rS1S2: equilibrium rate constant,
which results from: rS1S2=kS1S2/kS2S1.
Based on the schemes shown in Fig. 7A-D, and considering that P=Pc+Po=1 where
Pc: closed channel probability and Po: open channel probability, we have:
Pc=PC1+PC2+PC3+PC4, where C4=low activity mode (Figs. 7C and D);
Po=PO1+PO2+PO3
Therefore:
Pc=PC1*(1 + rC1C2 + rC1C2*rC2C3 + rC1C2*rC2C3*rC3C4), and
Po=PC1*(rC1O1 + rC1C2*rC2O2 + rC1C2*rC2C3*rC3O3), where
PC1 = 1 / [ (1 + rC1C2 + rC1C2*rC2C3 + rC1C2*rC2C3*rC3C4) + (rC1O1 + rC1C2*rC2O2 + rC1C2*rC2C3*rC3O3) ]
Please note that
rC3C4=0, only for low calcium (0.3 uM), and
rO2O3=0 because there are no O2-O3 transitions.
3
"Forward"
Rate
Constants
kC1C2 =
kC2C3 =
kC3C4 =
kC1O1 =
kC2O2 =
kC3O3 =
kO1O2 =
kO2O3 =
"Reverse"
Rate
Constants
kC2C1 =
kC3C2 =
kC4C3 =
kO1C1 =
kO2C2 =
kO3C3 =
kO2O1 =
kO3O2 =
"Equilibrium"
Rate
Constants
rC1C2 =
rC2C3 =
rC3C4 =
rC1O1 =
rC2O2 =
rC3O3 =
rO1O2 =
rO2O3 =
Steady
State
Probabilities
PC1 =
PC1 =
PC2 =
PC3 =
PC4 =
PO1 =
PO2 =
PO3 =
PClosed =
POpen =
Ptotal =
0.3 uM Ca2+
0.3 uM Ca2+
~+ Ethanol
65.7000
5.0000
0
123.1000
0.1100
0.0660
380.4000
0
515.6000
6.6000
0
133.0000
5.0000
0.0620
761.2000
0
0.3 uM Ca2+
0.3 uM Ca2+
~+ Ethanol
30 uM Ca2+
2559.8000
283.1000
55.2600
5940.8000
5.0000
8024.9000
2077.5000
0
30 uM Ca2+
30 uM Ca2+
~+ Ethanol
2099.400000
264.2000
84.4400
5209.3000
1.3000
7254.5000
1797.5000
0
30 uM Ca2+
~+ Ethanol
22.9000
4.7000
0
816.4000
1.4000
4239.5000
237.3000
0
243.4000
31.8000
0
458.0000
17.9000
144.5000
369.8000
0
905.6000
797.5000
136.8000
2906.7000
4.1000
568.4000
1223.9000
0
603.000000
639.8000
46.2600
3189.5000
2.5000
649.2000
1547.6000
0
0.3 uM Ca2+
0.3 uM Ca2+
~+ Ethanol
30 uM Ca2+
30 uM Ca2+
~+ Ethanol
2.8690
1.0638
0
0.1508
0.0786
0.0000
1.6030
0
0.3 uM Ca2+
1.37E-01
0.137036
0.393155
0.418250
0
0.020663
0.030891
0.000007
0.948440
0.051560
1.000000
2.1183
0.2075
0
0.2904
0.2793
0.0004
2.0584
0
0.3 uM Ca2+
~+ Ethanol
2.25E-01
0.225212
0.477071
0.099015
0
0.065400
0.133260
0.000042
0.801298
0.198702
1.000000
2.8266
0.3550
0.4039
2.0438
1.2195
14.1184
1.6974
0
30 uM Ca2+
4.02E-02
0.040172
0.113552
0.040309
0.016283
0.082105
0.138478
0.569101
0.210316
0.789684
1.000000
3.4816
0.4129
1.8253
1.6333
0.5200
11.1745
1.1615
0
30 uM Ca2+
~+ Ethanol
3.56E-02
0.035647
0.124109
0.051250
0.093548
0.058221
0.064536
0.572690
0.304553
0.695447
1.000000
4
Prob (C1,C2,C3,C4,O1,O2,O3)
1.00
Probability
0.90
0.80
O3
0.70
0.60
O2
0.50
C4
0.40
0.30
C3
0.20
0.10
C1
O1
C2
0.00
0.3 uM Ca2+
0.3 uM Ca
0.3 uM Ca2+
2+
0.3 uM Ca
+ Ethanol
0.3 uM Ca2+
2+
30 uM Ca
2+
0.3 uM Ca2+
2+
30 uM Ca
+ Ethanol
The bar graph shows that at submicromolar calcium (0.3 μM), an increase in the probability of the
channel dwelling in O2 and a decrease in the probability of the channel dwelling in C3 are the main
contributors to ethanol-induced increase in overall Po. At 30 μM calcium, ethanol increases the
probability of the channel to dwell in a “low activity mode” (C4) from <5% to >10%. This action,
together with a decrease in the probability of channel dwelling in O2, leads to alcohol-induced
reduction in overall Po.
5