-
Notifications
You must be signed in to change notification settings - Fork 1
/
cain2_par.txt
239 lines (167 loc) · 8.26 KB
/
cain2_par.txt
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Modeling of Ca-dependent inactivation by changing Ca affinity of the pore %
% %
% Roman Shirokov, UMDNJ, Victor Matveev, NJIT %
% January, 2006 %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% PARAMETERS %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%---- Charge1 - Charge2 parameters-------------
V1 = -10; V2 = -110; K = 8 % mV
a1 = 0.3; a2 =0.0033 % ms^-1, parameters "a" and "b" are used to define
b = 0.1 % voltage-dependent rates of Charge1 and Charge2 movements
tauIna = 2000 % ms, onset of inactivation without Ca
extIna = 5 % extent of inactivation without Ca, extIna=1/K.A in the paper
tauRec = 100 % ms, recovery from inactivation without Ca
kIna = 1 / tauIna % ms^-1, rate of inactivation without Ca
kRec = 1 / tauRec % ms^-1, rate of recovery without Ca
extRec = extIna exp((V2 - V1)/K) % extent of recovery without Ca, extRec=1/K.R in the paper
%-----Whole-cell parameters--------------------
Cm = 20 % pF, cell capacitance
Rs = 5 % MOhm, series resistance
CHD = 500 % pF^-1, density of channels
Nch = Cm CHD
%-----Ca parameters----------------------------
Ca.out = 10000 % microM, concentration of extracellular Ca
Ca.in = 0.1 % microM, concentration of intracellular Ca
ECa = 12.5 log( Ca.out/Ca.in ) % mV, equilibrium potential for Ca
X = 0.08 % i.s.ch scaling factor for GHK to make i.s.ch=0.5pA at 0mV 10Ca.out
Y = 0.008 % i.s.ch scaling factor for Ohmic to make i.s.ch=0.5pA at 0mV 10Ca.out
%-----Ca binding to inactivation site--------
k.on = 0.1 % microM^-1 ms^-1, the ON rate for Ca
delta = 0.5 % electrical position of the binding site
Kd = 10000 % microM, dissociation constant of the site
Gamma = 50
Epsilon= 200 % dependence of Gamma on i.s.ch
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% RATE CONSTANTS %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
k.RP.AP := a1 exp( (V - V1) / (2 K) - b ( (V - V1) / (2 K) )^2 )
k.AP.RP := k.RP.AP exp( (V1 - V) / K )
k.RI.AI := a2 exp( (V - V2) / (2 K) - b ( (V - V2) / (2 K) )^2 )
k.AI.RI := k.RI.AI exp( (V2 - V) / K )
% To limit the rate increase,
% the free energy difference between starting and transitional states
% is assumed to be a second order function of voltage
% (as done by Simon & Beam, 1985. J Gen Physiol, 85, 21-42.)
k.AI.AP = kIna / (1 + extIna )
k.AP.AI = kIna - k.AI.AP
k.RI.RP = kRec / (1 + extRec )
k.RP.RI = kRec - k.RI.RP
Kd.eff := Kd exp(delta V/12.5) (1+exp(-V/25)) / (1+exp((V - 2 ECa)/25))
PoCa:= 1 / ( 1 + (Kd.eff/Ca.out) )
%%PiCa:= 1 / ( 1 + (Kd.eff/(Gamma Ca.out)) )
%% Strictly, it should be :
%%
%% PiCa := 1 / ( 1 + Kd.eff/(Ca.out (Gamma - Epsilon i.s.ch.I (i.s.ch.I < 0))) )
%% PiCa := 1 / ( 1 + Kd.eff/(Ca.out (Gamma - Epsilon F (1-PiCa)) )
%%
%% (1-PiCa)^2 Epsilon F - (1-PiCa) (Gamma+(Kd.eff/Ca.out)) + (Kd.eff/Ca.out) = 0
%% However, the quadratic correction is small:
%% (1-PiCa) (Epsilon F)/(Gamma+(Kd.eff/Ca.out)) <<< 1
%% Since PiCa is close to 1, i.e., AI <<< AICa, even without the small contribution of
%% current through inactivated states, the correction can be ommited
aa:= Epsilon F %% F<0
bb:= -(Gamma + Kd.eff/Ca.out)
cc:= Kd.eff/Ca.out
x.positive := ( -bb - sqrt(bb^2 - 4 aa cc) )/(2 aa)
PiCa:= ( 1 - x.positive ) (F<0)
PinnCa = 1 / ( 1 + (Kd/(Gamma Ca.out)) )
PcCa = 1 / ( 1 + (Kd/Ca.out) )
k.RPCa.APCa := k.RP.AP
k.APCa.RPCa := k.AP.RP
% Gamma is increased due to current through open channels:
k.APCa.AICa := k.AP.AI ( Gamma - Epsilon i.s.ch.P (i.s.ch.P < 0) )
k.AICa.APCa = k.AI.AP
k.RICa.AICa := k.RI.AI
k.AICa.RICa := k.AI.RI
k.RPCa.RICa = k.RP.RI Gamma
k.RICa.RPCa = k.RI.RP
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% KINETIC SCHEMA %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
AP := O ( 1 - PoCa )
APCa := O PoCa
F.O :=(-k.AP.RP -k.AP.AI ) AP +k.RP.AP RP +k.AI.AP AI ...
+(-k.APCa.RPCa -k.APCa.AICa ) APCa +k.RPCa.APCa RPCa +k.AICa.APCa AICa
AI := In ( 1 - PiCa )
AICa := In PiCa
F.In :=(-k.AI.AP -k.AI.RI ) AI +k.AP.AI AP +k.RI.AI RI ...
+(-k.AICa.APCa -k.AICa.RICa ) AICa +k.APCa.AICa APCa +k.RICa.AICa RICa
RI := Inn (1 - PinnCa)
RICa := Inn PinnCa
F.Inn :=(-k.RI.AI -k.RI.RP ) RI +k.RP.RI RP +k.AI.RI AI ...
+(-k.RICa.AICa -k.RICa.RPCa ) RICa +k.AICa.RICa AICa +k.RPCa.RICa RPCa
C := 1 - AP - APCa - AI - AICa - RI - RICa
RP := C / (1 + PcCa)
RPCa := C PcCa / (1 + PcCa)
dO/dt = F.O
dIn/dt = F.In
dInn/dt = F.Inn
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% EFFECT OF CURRENT ON VOLTAGE %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dV/dt = (Vf - V) / (0.001 * Cm * Rs) - I.total / Cm % t in ms, I in pA, V in mV,
% Cm in pF, Rs in MOhm
V(0) = -100
%pseudo-GHK:
%i.ghk := X 12.5 (Ca.in - Ca.out) / (Ca.out + Kd) (V == 0) + ...
% X (V/(1-exp(-V/12.5))) (Ca.in - Ca.out exp(-V/12.5)) / (Ca.out + Kd)
%
%I.ionic := Nch O i.ghk
%%%
%pseudo-Ohmic:
%i.ohm := Y (V-ECa) (Ca.out-Ca.in) / (Ca.out + Kd)
%
%I.ionic := Nch O i.s.ch
%%%
%Single site a la Woodhull:
F := 2 1.6 0.0001 ( k.on Ca.in exp((1-delta) V/25) - k.on Ca.out exp(-delta V/25) )
i.s.ch.P := F (1-PoCa)
i.s.ch.I := F (1-PiCa)
i.P := Nch AP i.s.ch.P
i.I := Nch AI i.s.ch.I
I.ionic := i.P + i.I
%%%
I.gating := Nch 25 1.6 0.0001 (F.O + F.In) / K
I.total := I.gating + I.ionic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% SOLVING %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mode = ODE
verbose=0 % removes console output for speed, comment it out to compile
run T
C(0) = 1
for Pulse = 0 to 20 step 1
Vp = -100 + 10 Pulse
if Pulse == 0 then
Vf = - 100
T = 5000 % equilibration time, ms
Export T "save.dat"
else
Import "save.dat"
Vf := (-100 - Vp) * (t > 300) + Vp
T = 320
plot mute I.total "I" Vp
% plot mute i.P "IP" Vp %this could work only for the Woodhul formulation
% plot mute i.I "II" Vp %this could work only for the Woodhul formulation
% plot mute V "V" Vp
endif
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% THE END %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%