Hysteresis in voltage gating of HCN channels (Elinder et al 2006, Mannikko et al 2005)

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Accession:82758
We found that HCN2 and HCN4 channels expressed in oocytes from the frog Xenopus laevis do not display the activation kinetic changes that we (previously) observed in spHCN and HCN1. However, HCN2 and HCN4 channels display changes in their tail currents, suggesting that these channels also undergo mode shifts and that the conformational changes underlying the mode shifts are due to conserved aspects of HCN channels. With computer modelling, we show that in channels with relatively slow opening kinetics and fast mode-shift transitions, such as HCN2 and HCN4 channels, the mode shift effects are not readily observable, except in the tail kinetics. Computer simulations of sino-atrial node action potentials suggest that the HCN2 channel, together with the HCN1 channel, are important regulators of the heart firing frequency and that the mode shift is an important property to prevent arrhythmic firing. We conclude that although all HCN channels appear to undergo mode shifts – and thus may serve to prevent arrhythmic firing – it is mainly observable in ionic currents from HCN channels with faster kinetics. See papers for more and details.
Reference:
1 . Elinder F, Männikkö R, Pandey S, Larsson HP (2006) Mode shifts in the voltage gating of the mouse and human HCN2 and HCN4 channels. J Physiol 575:417-31 [PubMed]
2 . Männikkö R, Pandey S, Larsson HP, Elinder F (2005) Hysteresis in the voltage dependence of HCN channels: conversion between two modes affects pacemaker properties. J Gen Physiol 125:305-26 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Na,t; I L high threshold; I T low threshold; I K; I M; I h;
Gap Junctions:
Receptor(s):
Gene(s): HCN2; HCN4;
Transmitter(s):
Simulation Environment: QBasic/QuickBasic/Turbo Basic/VBA;
Model Concept(s): Ion Channel Kinetics; Action Potentials; Heart disease;
Implementer(s): Elinder, Fredrik [fredrik.elinder at ibk.liu.se];
Search NeuronDB for information about:  I Na,t; I L high threshold; I T low threshold; I K; I M; I h;
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modeshift
readme.txt
SAN-MODE.BAS
                            
10 REM "SA-NODE ACTION POTENTIAL" BY FREDRIK ELINDER, LINK™PINGS UNIVERSITET
11 REM  REFERENCES: MŽNNIKK™, PANDEY, LARSSON & ELINDER. 2005. J GEN PHYSIOL 125:305-326
12 REM              ELINDER, MŽNNIKK™, PANDEY & LARSSON. 2006. J PHYSIOL 575:417-431
13 REM  UPDATED SEPTEMBER 13, 2006
14 REM  BASED ON THE MODEL BY ZHANG ET AL., 2000, AM J PHYSIOL 279:H397-H421
15 REM  DIFFERENCES FROM ZHANG ET AL: NEW DESCRIPTION OF HCN + CORRECTION OF EQ 42
20 SCREEN 9
30 CLS

40 OPEN "C:\DATA\X.PRN" FOR OUTPUT AS #1
45 OPEN "C:\DATA\Y1.PRN" FOR OUTPUT AS #2
50 OPEN "C:\DATA\Y2.PRN" FOR OUTPUT AS #3
55 OPEN "C:\DATA\Y3.PRN" FOR OUTPUT AS #4
60 OPEN "C:\DATA\Y4.PRN" FOR OUTPUT AS #5
65 OPEN "C:\DATA\Y5.PRN" FOR OUTPUT AS #6

80 FOR WW=0 TO 1		:REM HYSTERESIS (1) OR NOT (0)

100 REM CONSTANTS FOR PROGRAM CONTROL AND SAMPLING CARACTERISTICS
110 	DT=0.000005		:REM STEP LENGTH TIME (s) = 5 us
120 	MAXCOUNT=400000		:REM TOTAL TIME = 2 s
130 	R = 8.31		:REM GENERAL GAS CONSTANT
140 	T = 293			:REM TEMPERATURE (K)
150 	F = 96480/1000		:REM FARADAYS CONSTANT (C/MOL) CORRECTED FOR mV

190 GOTO 400                    :REM GOTO 200 TO GET CENTRAL NODAL CELLS, OTHERWISE PERIPHERAL

200 REM CENTRAL NODAL CELL CONDUCTANCES (S, A, F)
210 	GNA  = 0
220 	GCAL = 0.58   * 10^-2 * 10^-6
230 	GCAT = 0.43   * 10^-2 * 10^-6
240 	GTO  = 4.91   * 10^-3 * 10^-6
250 	GSUS = 6.65   * 10^-5 * 10^-6
260 	GKR  = 7.97   * 10^-4 * 10^-6
270 	GKS  = 5.18   * 10^-4 * 10^-6
280 	GHNA = 0.0548 * 10^-2 * 10^-6
290 	GHK  = 0.0548 * 10^-2 * 10^-6
300 	GBNA = 5.8    * 10^-5 * 10^-6
310 	GBCA = 1.32   * 10^-5 * 10^-6
320 	GBK  = 2.52   * 10^-5 * 10^-6
330 	IPMAX= 4.78   * 10^-2 * 10^-9	:REM (A)
340 	KNACA= 0.27   * 10^-5 * 10^-9	:REM (A)
350 	CM   = 20             * 10^-12	:REM (F)

390 GOTO 600

400 REM PERIPHERAL NODAL CELL CONDUCTANCES (S, A, F)
410	GNA  = 1.2    * 10^-6 * 10^-6
420	GCAL = 6.59   * 10^-2 * 10^-6
430	GCAT = 1.39   * 10^-2 * 10^-6
440	GTO  =36.49   * 10^-3 * 10^-6
450	GSUS = 1.14   * 10^-2 * 10^-6
460	GKR  = 1.60   * 10^-2 * 10^-6
470	GKS  = 1.04   * 10^-2 * 10^-6
480	GHNA = 0.69   * 10^-2 * 10^-6
490	GHK  = 0.69   * 10^-2 * 10^-6
500	GBNA = 1.89   * 10^-4 * 10^-6
510	GBCA = 4.3    * 10^-5 * 10^-6
520	GBK  = 8.19   * 10^-5 * 10^-6
530	IPMAX= 0.16           * 10^-9	:REM (A)
540	KNACA= 0.88   * 10^-5 * 10^-9	:REM (A)
550	CM   = 65             * 10^-12	:REM (F)

600 REM CONCENTRATIONS (mM = mol/m^3)
610 	NAO = 140
620 	NAI =   8
630 	CAO =   2
640 	CAI =   0.0001
650 	KO  =   5.4
660 	KI  = 140

700 REM REVERSEL POTENTIALS (mV)
710 	ENA = R*T/   F  * LOG(NAO/NAI)
720 	ECA = R*T/(2*F) * LOG(CAO/CAI)
730 	EK  = R*T/   F  * LOG(KO/KI)
740 	ECAL= 46.4
750 	ECAT= 45
760 	EKS = R*T/   F  * LOG((KO+0.12*NAO)/(KI+0.12*NAI))

800 REM OTHER CONSTANTS
810 	DNACA    = 0.0001
820 	KMK      = 0.621
830 	KMNA     = 5.64
840 	GNACA    = 0.5		

900 REM INITIAL VALUES (MEAN OF CENTRAL AND PERIPHERAL CELLS)
905 	V  = -60		:REM (mV)

910 	DL = 0.07
915 	FL = 0.90
920 	DTT= 0.06
925 	FT = 0.25

930 	RR = 0.03
935 	Q  = 0.50
940 	XS = 0.07

945 	PAF= 0.44
950 	PAS= 0.48
955 	PI = 0.98

960 	M  = 0.12
965 	H1 = 0.59
970 	H2 = 0.05

975 	HO1 = 0.025
980 	HO2 = 0.025
985 	HC1 = 0.475
990 	HC2 = 0.475

995 GOSUB 1000

998 GOTO 2000

1000 REM L-TYPE CA CURRENT
1010 	IF V=-35 THEN V=-35.001
1012 	IF V= 5  THEN V=5.001
1014 	IF V= 0  THEN V=0.001
1016 	IF V=-28 THEN V=-28.001
1018 	ADL   = -14.19*(V+35)/(EXP(-(V+35)/2.5)-1) - 42.45*V/(EXP(-0.208*V)-1)
1020 	BDL   =   5.71* (V-5) /(EXP(0.4*(V-5))-1)
1022 	TDL   = 1/(ADL+BDL)
1024 	DLINF = 1/(1+EXP(-(V+23.1)/6))
1026 	DDL   = ((DLINF-DL)/TDL) * DT
1028 	DL    = DL + DDL
1030 	AFL   = 3.12*(V+28)/(  EXP( (V+28)/4)-1)
1032 	BFL   = 25         /(1+EXP(-(V+28)/4))
1034 	TFL   = 1/(AFL+BFL)
1036 	FLINF = 1          /(1+EXP( (V+45)/5))
1038 	DFL   = ((FLINF-FL)/TFL) * DT
1040 	FL    = FL + DFL

1100 REM T-TYPE CA CURRENT
1110 	ADT   = 1068*EXP( (V+26.3)/30)
1115 	BDT   = 1068*EXP(-(V+26.3)/30)
1120 	TDT   = 1/(ADT+BDT)
1125 	DTINF = 1/(1+EXP(-(V+37)/6.8))
1130 	DDTT  = ((DTINF-DTT)/TDT) * DT
1135 	DTT   = DTT + DDTT
1140 	AFT   = 15.3*EXP(-(V+71.7)/83.3)
1145 	BFT   = 15.3*EXP( (V+71.7)/15.38)
1150 	TFT   = 1/(AFT+BFT)
1155 	FTINF = 1/(1+EXP((V+71)/9))
1160 	DFT   = ((FTINF-FT)/TFT) * DT
1165 	FT    = FT + DFT

1200 REM 4-AP-SENSITIVE CURRENTS
1210 	QINF  = 1 / (1+EXP((V+59.37)/13.1))
1220 	TQ    = 10.1*10^-3 + (65.17*10^-3)/(0.57*EXP(-0.08*(V+49)) + 0.24*EXP(0.1*(V+50.93))) :REM CORRECTED FROM ZHANG ET AL., 2000
1230 	DQ    = ((QINF-Q)/TQ) * DT
1240 	Q     = Q + DQ
1250 	RINF  = 1 / (1+EXP(-(V-10.93)/19.7))
1260 	TRR   = 2.98*10^-3 + (15.59*10^-3)/(1.037*EXP(0.09*(V+30.61))+0.369*EXP(-0.12*(V+23.84)))
1270 	DRR   = ((RINF-RR)/TRR) * DT
1280 	RR    = RR + DRR

1300 REM RAPID DELAYED RECTIFYING K CURRENT
1310 	PAFINF= 1 / (1+EXP(-(V+14.2)/10.6))
1315 	PASINF= PAFINF
1320 	TPAF  = 1 / (37.2*EXP((V-9)/15.9) + 0.96*EXP(-(V-9)/22.5))
1325 	TPAS  = 1 / ( 4.2*EXP((V-9)/17)   + 0.15*EXP(-(V-9)/21.6))
1330 	DPAF  = ((PAFINF-PAF)/TPAF) * DT
1335 	PAF   = PAF + DPAF
1340 	DPAS  = ((PASINF-PAS)/TPAS) * DT
1345 	PAS   = PAS + DPAS
1350 	PIINF = 1 / (1+EXP((V+18.6)/10.1))
1355 	TPI   = 0.002
1360 	DPI   = ((PIINF-PI)/TPI) * DT
1365 	PI    = PI + DPI
1370 	FKR   = 0.4
1375 	PA    = (1-FKR)*PAF + FKR*PAS

1400 REM SLOW DELAYED RECTIFYING K CURRENT
1410 	AXS   = 14 / (1+EXP(-(V-40)/9))
1420 	BXS   = EXP(-V/45)
1430 	XSINF = AXS/(AXS+BXS)
1440 	TXS   = 1  /(AXS+BXS)
1450 	DXS   = ((XSINF-XS)/TXS) * DT
1460 	XS    = XS + DXS

1500 REM HYPERPOLARIZATION-ACTIVATED CURRENT - DIFFERENT FROM ZHANG ET AL., 2000
1505 	HCNSHIFT = WW*60
1506    MIDPOINT = -75		:REM MIDPOINT OF G(V) CURVE WITHOUT MODE SHIFT
1507    KACT  = 18		:REM ACTIVATION RATE AT MIDPOINT (/s)
1508    KMODE = 10		:REM MODE SHIFT RATE (/s)
1524 	KCO1  = KACT*EXP(-(V-(MIDPOINT-HCNSHIFT/2))*F/R/T)
1525 	KOC1  = KACT*EXP( (V-(MIDPOINT-HCNSHIFT/2))*F/R/T)
1526 	KCO2  = KACT*EXP(-(V-(MIDPOINT+HCNSHIFT/2))*F/R/T)
1528 	KOC2  = KACT*EXP( (V-(MIDPOINT+HCNSHIFT/2))*F/R/T)
1530 	KO12  = KMODE
1532 	KO21  = KO12*(KOC2*KCO1/(KOC1*KCO2))^0.5
1534 	KC21  = KO12
1536 	KC12  = KO21
1538 	HO1   = HO1 + ((-KOC1-KO12)*HO1 + KCO1*HC1 + KO21*HO2)*DT
1540 	HO2   = HO2 + ((-KOC2-KO21)*HO2 + KCO2*HC2 + KO12*HO1)*DT
1542 	HC1   = HC1 + ((-KCO1-KC12)*HC1 + KOC1*HO1 + KC21*HC2)*DT
1544 	HC2   = 1-HO1-HO2-HC1
1545 	W     = HO2+HO1

1600 REM TTX-SENSITIVE NA CURRENT
1610 	MINF  = (1/(1+EXP(-V/5.46)))^(1/3)
1612 	TM    = 4*10^-5 + 0.6247*10^-3 / (0.832*EXP(-0.335*(V+56.7))+0.627*EXP(0.082*(V+65.01)))
1614 	DM    = ((MINF-M)/TM) * DT
1616 	M     = M+DM
1618 	H1INF = 1/(1+EXP((V+66.1)/6.4))
1620 	H2INF = H1INF
1622 	TH1   = 5.977*10^-4 + 3.717*10^-6*EXP(-0.2815*(V+17.11))/(1+3.732*10^-3*EXP(-0.3426*(V+37.76)))
1624 	TH2   = 3.556*10^-3 + 3.186*10^-8*EXP(-0.6219*(V+18.8)) /(1+7.189*10^-5*EXP(-0.6683*(V+34.07)))
1626 	DH1   = ((H1INF-H1)/TH1) * DT
1628 	H1    = H1+DH1
1630 	DH2   = ((H2INF-H2)/TH2) * DT
1632 	H2    = H2+DH2
1634 	XNA   = 8.69*10^-2 + 9.52*10^-2*EXP(-6.3*10^-2*(V+34.4))/(1+1.66*EXP(-0.225*(V+63.7)))
1636 	H     = (1-XNA)*H1 + XNA*H2

1900 RETURN

2000 REM MAIN ALGORITHM
2010 FOR COUNT=0 TO MAXCOUNT-1
2020   GOSUB 1000

2100 REM CURRENTS (A)
2110   INA  = 0.001 * GNA   * M^3 * H  * NAO * F^2 * V/(R*T) * (EXP((V-ENA)*F/(R*T))-1)/(EXP(V*F/(R*T))-1)
2120   ICAL = 0.001 * GCAL  *(FL  * DL + 0.006/(1+EXP(-(V+14.1)/6))) * (V-ECAL)
2130   ICAT = 0.001 * GCAT  * DTT * FT * (V-ECAT)
2140   ITO  = 0.001 * GTO   * Q   * RR * (V-EK)
2150   ISUS = 0.001 * GSUS  *       RR * (V-EK)
2160   IKR  = 0.001 * GKR   * PA  * PI * (V-EK)
2170   IKS  = 0.001 * GKS   * (XS)^2   * (V-EKS)
2180   IH   = 0.001 *(GHNA  * W        * (V-ENA) + GHK * W * (V-EK))
2190   IBNA = 0.001 * GBNA  * (V-ENA)
2200   IBK  = 0.001 * GBK   * (V-EK)
2210   IBCA = 0.001 * GBCA  * (V-ECA)
2220   INACA=         KNACA * (NAI^3*CAO*EXP(0.03743*V*GNACA) - NAO^3*CAI*EXP(0.0374*V*(GNACA-1))) / (1+DNACA*(CAI*NAO^3+CAO*NAI^3))
2230   IP   =         IPMAX * (NAI/(KMNA+NAI))^3 * (KO/(KMK+KO))^2 * 1.6/(1.5+EXP(-(V+60)/40))

2300   IC  = 0 - (IS+INA+ICAL+ICAT+ITO+ISUS+IKR+IKS+IH+IBNA+IBCA+IBK+INACA+IP)
2310   DV  = 1000 * (IC/CM) * DT
2320   V   = V + DV

2500 REM PRINT ROUTINE
2510	X = COUNT/MAXCOUNT*500		
2520	Y = 50 - V + WW*150
2530	PSET(X,Y)
2540    Y = 50 + WW*150
2550    PSET(X,Y)

2600 IF INT(COUNT/1000)=COUNT/1000 THEN GOTO 2610 ELSE GOTO 2700
2610 IF WW=0 THEN PRINT #1, COUNT*DT
2620 IF ww=0 THEN PRINT #2, V
2630 IF ww=1 THEN PRINT #3, V
2640 IF ww=2 THEN PRINT #4, V
2650 IF ww=3 THEN PRINT #5, V
2660 IF ww=4 THEN PRINT #6, V

2700 NEXT COUNT

2800 NEXT WW

3000 END