Männikkö R , Pandey S , Larsson HP , Elinder F .

NS043259 NINDS NIH HHS , R01 NS043259 NINDS NIH HHS

	Figure 1. . Voltage protocols to measure hysteresis. In the present investigation, different voltage protocols were used to measure the different effects of voltage hysteresis: (A) Q(V) shifts, (B) the development of tail current changes, (C) the development of activation current changes, (D) G(V) shifts, and (E) hysteresis during voltage-clamp ramps.
	Figure 2. . Q(V) shifts in spHCN channels. (A) Gating currents in response to voltage steps between −10 and −120 mV (ΔV = −10 mV) for ZD7288-blocked wt spHCN channels. Cut-open oocyte voltage-clamp technique; holding potential VH = −10 mV. (B) Gating currents for a voltage protocol as in A for nonconducting P435Y spHCN channels. Two-electrode voltage clamp technique. (C) Currents in response to a voltage step to −80 mV from uninjected (control) oocytes and oocytes injected with nonconducting P435Y spHCN cRNA. Cut-open oocyte voltage-clamp technique. VH = −10 mV. (D) Total gating charge (integral of gating currents) moved at the different voltage steps in (A) (•) and in (B) (○). (E) Gating currents in P435Y spHCN channels in response to voltage steps between −80 and +50 mV (ΔV = +10 mV), VH = −80 mV. (F) Total gating charge (integral of gating currents) from P435Y spHCN channels, moved at different voltage steps from VH = −10 mV (○) and from VH = −80 mV (•), and fitted to Q(V) = Qmax/(1 + exp(−ze0(V − V1/2)/kT). V1/2 = −73 mV (○) and +6 mV (•). Qmax = −24.5 nC (○) and +20.1 nC (•), z = 2.1 for both curves. (G) The gating charge in F was normalized as Q(V) = (Q(V) + Qmin)/(Qmax − Qmin). (H) Off (return) gating current of P435Y spHCN channels at −40 mV, after varying the lengths of activating pulses to −80 mV (raw data shown in inset). Note that the off (tail) gating charge paradoxically reduces (vertical arrow) while the on gating charge increases with increasing prepulse length (i.e., the shorter pulses curtail the on-gating currents). (I) The charge of the off-gating currents (from H) versus prepulse durations, fitted to an exponential decay with τ = 74 ms.
	Figure 3. . spHCN channels have multiple open states. (A) Development of a delay in the tail currents at +50 mV, in response to the increasing length of the −80 mV activation pulse. (B) Normalized tail current amplitudes from A. The prepulse length is increased with 40 ms for each trace. Arrow indicates increasing prepulse lengths. (C) Time course of development of the delay, measured as the tail current amplitude 10 ms after the onset of the tail potential (arrow in B), fitted with a single exponential with τ = 75 ms. (D) The tail currents were fitted to I(t) = I0(1 − (1 − exp(−t/τ))w), where w = 3.2. (E) Tail currents at −15 mV for spHCN channels. The prepulse length is increased with 50 ms for each trace. Arrow indicates increasing prepulse lengths. (F) Normalized currents, first and last trace, from E. Arrow indicates increasing prepulse lengths. τ = 81.2 ± 10.4 ms (n = 3) for the first trace and τ = 639 ± 32 ms (n = 3) for the last trace.
	Figure 4. . Activation kinetics is altered by negative prepulses. (A) A double-pulse protocol showing the change in both tail kinetics (at +80 mV) and activation kinetics (at −100 mV) induced by a 225-ms step to −100 mV versus a 25-ms step to −100 mV. Currents shown are the subtraction of the currents from the same cell in response to identical voltage protocols with and without 0.5 mM ZD7288. (B) Currents during the second −100-mV step in a double-pulse protocol (inset) used to measure the time course of the change in activation kinetics: −100 mV (step increase 25 ms), +80 mV for 50 ms, −100 mV for 50 ms, and +80 mV for 25 ms. Arrow indicates increasing prepulse lengths. (C) Time course of the change in activation time constant in B, fitted by a single exponential. τ = 73 ms. (D) Activation time constant during the second step in B for different voltages during the second negative voltage step. The remainder of the double-pulse protocol was as in B. Activation time constant (▪) after a 25-ms prepulse and (○) after a 300-ms prepulse. The data were fitted to t = t0 exp(−zV/kT). (▪) z = 0.74 ± 0.04 and (○) z = 0.70 ± 0.04. Arrow shows the voltage shift that superimposes the two lines (=28 mV in this cell). (E) Recovery of the activation time constant during the second negative voltage step in response to an increased duration of the step to +80 mV in the double-pulse protocol: −100 mV for 300 ms, +80 ms (25-ms step increase), −100 mV for 50 ms, and +80 ms for 25 ms. Arrow indicates increasing prepulse lengths. (F) Time constant during the second step to −100 mV in E after different durations at +80 mV. The data were fit to an exponential with τ = 58 ms.
	Figure 5. . Kinetic models used in the present study. (A) O denotes open states, and C denotes closed states. The rate constants are described by Eqs. 1 and 2 in materials and methods, with the values given in Table I. All models have a steady-state open probability of 50% at −45 mV. (B) To obtain similar activation rates, the models (continuous line) were adjusted to fit to experimental data (○) at −80 mV.
	Figure 6. . Q(V) curves simulated for the models in Fig. 5. The gating charge, Q, was measured as the amount of charge that moved during a 200-ms pulse. (A-–E) Simulations of the models in Fig. 5. Holding voltage VH = 0 mV for the left curve in each panel, VH = −80 mV for the right curve. (F) Time courses of the OFF gating charge at −45 mV after different prepulses to −100 mV (protocol similar to that shown in Fig. 2 H).
	Figure 7. . Simulated tail currents. (A–E) Simulations of the models in Fig. 5. Holding voltage is 0 mV. The channel-opening prepulse is −120 mV for 50, 100, 150, 200, 250, or 300 ms, and the following tail current is simulated at +50 mV. The tail currents that are shown are normalized to 1 for the first data point. Arrows indicate increasing prepulse lengths. (F) Development of the tail current for the model in A.
	Figure 8. . Simulated prepulse-dependent activation kinetics. (A–E) Double-pulse protocol simulations of the models in Fig. 5. Holding voltage is 0 mV. Prepulse to −100 mV for 50, 100, 150, 200, 250, or 300 ms, followed by a closing step at +80 mV for 30 ms, and then followed by a second step to −100 mV. The activation kinetics shown were measured during the second pulse to −100 mV. Arrows indicate increasing prepulse lengths. See G for an example of a simulation. (F) Development of the activation kinetics for the simulations in A measured as single exponentials (see dotted lines in A). (G) Simulations shown for prepulse lengths of 25 and 225 ms. (H) Voltage dependence of activation time constants following no prepulse or a 225-ms long prepulse to −100 mV. The slopes correspond to z = 0.91 (with prepulse) and z = 1.04 (no prepulse). See legend to Fig. 4 for an explanation of voltage protocol.
	Figure 9. . Slow equilibration at −40 mV in spHCN channels. (A) Currents in response to voltage steps to −40 mV, with or without a 100-ms prepulse to −100 mV. VH = −10 mV. 100-K bath solution. (B–F) Computer simulations of the different models shown in Fig. 5, in response to the protocol used in A.
	Figure 10. . Prepulse-dependent shift of G(V). (A and B) Ionic currents through spHCN channels in response to voltage steps in 10-mV increments between +50 mV and −100 mV, from VH = −10 mV with (A) or without (B) a 50-ms prepulse to −100 mV. Tail currents at +50 mV. 100-K bath solution. The relatively large “leak” currents seen in A and B are a property of spHCN channels (compare recording in Fig. 4, which is the result of a subtraction of identical recordings executed on the same cell before and after an application of the HCN-channel blocker ZD7288; even in these ZD7288-subtracted currents, there was an instantaneous current component when the voltage was stepped from a 0-mV holding potential). (C) G(V) curves for spHCN after prepulses with durations of 0 (□), 10 (○), 25 (▵), 50 (▿), and 100 (⋄) ms, measured from an instantaneous tail current at +50 mV. Fitted to G(V) = A + B/(1 + exp(−ze0(V − V1/2)/kT). V1/2 = −43, −30, −12, −3, +2. z = 1.59, 1.33, 1.37, 1.87, and 2.10. 100-K bath solution. (D) V1/2 versus prepulse duration from C, fitted with a single exponential with τ = 24 ms. (E–H) Computer simulations of G(V) shifts for the models in Fig. 5. Holding potential is 0 mV followed by prepulses to −100 mV for 0, 75, 150, 225, 300, and 375 ms (from left to right), followed by equilibrium steps of 200 ms to the voltages indicated on the x axis. Compared with the other models, the four-state model exhibits the largest and the slowest shifts. (I) G(V) shifts for the four-state (open symbols) and the two-state (closed symbols) models for different prepulse potentials (circle, −180 mV; triangle, −140 mV; square, −100 mV; diamond, −60 mV). The continuous curves are best fits of single exponentials through origin. (J) Time constants from I. Note that the time constants from the four-state model, in contrast to the two-state model, levels out as was found in the experiments.
	Figure 11. . Voltage ramps. (A) Conductance of spHCN channels during voltage ramps from −10 mV to −100 mV, and back to −10 mV, using different ramp speeds. 100-K bath solution. The conductance was normalized to 1 at −100 mV. (B) Conductance of Shaker channels during voltage ramps from −80 mV to +20 mV, and back to −80 mV, using different ramp speeds. The conductance was normalized to 1 at +20 mV. 1-K bath solution. Note that with a slower ramp speed, voltage hysteresis decreases in Shaker channels, whereas it increases in spHCN channels. With slower voltage ramps, the two limbs in the G(V) curve approach each other in Kv channels, but in HCN channels, the two limbs are well separated even for slow ramps. (C–F) Computer simulations of voltage-ramp currents for the models in Fig. 5. The ramp speed is 125, 250, 500, 1,000, and 2,000 mV/s (from periphery to center). (G and H) Hysteresis measured as the voltage separation between the upward and downward limbs at 50% relative conductance (relative to the conductance at −100 mV).
	Figure 12. . The change in tail kinetics is present in a COOH terminal–deleted spHCN channel. (A) Tail currents in Δ472 spHCN channels at +50 mV after increasingly longer (62.5–625 ms) activation prepulses to −150 mV in 1-K solution. Arrow indicates increasing prepulse lengths. (B) Tail currents at 0 mV after increasingly longer activation prepulses to −150 mV in 100-K solution. Arrow indicates increasing prepulse lengths. Note that the tails mainly develop a sigmoidal delay in A but mainly become slower in B after longer-activating prepulses.
	Figure 13. . History-dependent, tail current kinetics. A similar development in (A) HCN1 channels and (B) spHCN channels, of a delay in the tail currents at +50 mV in response to the increasing length of the activation pulse. Pulse potential: −100 mV (A) and −80 mV (B). Extracellular K concentration: 10 mM (A) and 100 mM (B). (C) Normalized tail current amplitudes from A, showing the slowing of the tail kinetics. Arrow indicates increasing prepulse lengths. (D) Time course of the development of the delay, measured as the tail current amplitude, 10 ms after the onset of the tail potential (arrow in C), fitted with a single exponential with τ = 250 ms. (E) Tail currents at −80 mV for HCN1 after increasing prepulses to −160 mV. The prepulse length is increased with 50 ms between each trace. Arrow indicates increasing prepulse lengths. (F) Normalized currents, first and last trace, from E. Arrow indicates increasing prepulse lengths. τ = 98.3 ± 5.2 ms (n = 3) for the first trace and τ = 211 ± 16 ms (n = 3) for the last trace.
	Figure 14. . History-dependent activation kinetics. A similar change in both (A) HCN1 channels and (B) spHCN channels in tail kinetics and activation kinetics induced by a long-versus-short activation step in a double-pulse protocol. Activation potential: −100 mV (A) and −80 mV (B). Tail potential: +80 mV. (C) Currents from HCN1 channels during the second −100-mV step in a double-pulse protocol (inset), used to measure the time course of the change in activation kinetics: −100 mV (step increase 160 ms), +80 mV for 150 ms, −100 mV for 750 ms, and +80 mV for 150 ms. Arrow indicates increasing prepulse lengths. (D) Time course of the change of activation constant in C fitted by a single exponential. τ = 352 ms. (E) Activation time constant during the second step in C for different voltages during the second negative voltage step. The remainder of the double-pulse protocol was as in C. Activation time constant (▪) after a 160-ms prepulse and (○) after a 1,600-ms prepulse. The data were fitted to t = t0exp(−zV/kT). (▪) z = 0.96 ± 0.02 and (○) z = 0.90 ± 0.06. Arrow shows the voltage shift that superimposes the two lines (=12 mV in this cell). (F) Recovery of the activation time constant during the second negative voltage step in response to an increased duration of the step to +80 mV in the double-pulse protocol: −100 mV for 1,600 ms, +80 mV (durations of 160–1,600 ms, in 160-ms step increase), −100 mV for 750 ms, and +80 ms for 160 ms. (G) Enlargement of the currents during the second step to −100 mV in F. Arrow indicates increasing prepulse lengths. (H) Time constant during the second step to −100 mV in E after different durations at +80 mV. The data were fit to an exponential with τ = 380 ms.
	Figure 15. . Prepulse-dependent activation and voltage-ramp currents. Slow equilibration at voltages close to V1/2 in both (A) HCN1 channels and (B) spHCN channels. Currents in response to voltage steps (−70 mV [A] and −45 mV [B]), with or without prepulses to −120 mV (200 ms) for HCN (A) and −100 mV (100 ms) for spHCN channels. (B). VH = −10 mV. 1-K bath solution (A) and 100-K bath solution (B). (C) Conductance (G = I/V) of HCN1 channels during voltage ramps from −10 to −130 mV, and back to −10 mV, using different ramp speeds. (D) Conductance (G = I/V) of spHCN channels during voltage ramps from −10 to −100 mV, and back to −10 mV, using different ramp speeds. 100-K bath solution.
	Figure 16. . External K affects voltage hysteresis. Tail currents at +50 mV after different durations (12.5–275 ms, Δt = 37.5 ms) of a −160 mV activation pulse in 1-K (A), 100-K (B), and 100-K + 1 mM CsCl (C) bath solutions. Arrows indicate increasing prepulse lengths. (D) Time course of the development of the current delay in HCN1 channels. 1-K (•), 100-K (▪), and 100-K + 1 mM CsCl (▴) bath solutions. Time constants are 43, 145, and 44 ms, respectively.
	Figure 17. . Hysteresis in HCN channels prevents arrhythmia. (A) Computer simulation of a model of an SA node cell (Zhang et al., 2000), incorporating the HCN channel model described in materials and methods. Simulations were made with different values of the ΔVmode (0, 20, 40, 60, and 80 mV). V1/2(I) = −75 − ΔVmode/2, V1/2(II) = −75 + ΔVmode/2. (B) Computer simulations with an external pacemaker stimulating at 6 Hz (arrows). Stimulating current was −100 pA for 30 ms.
	Figure 18. . Voltage hysteresis prevents arrhythmia. Computer simulations of the SA-node model developed by Zhang et al. (2000). The HCN channels were replaced by our HCN-channel model (materials and methods). During the 5-s simulation, k1/2 changed from 5 to 500 s−1. The change was logarithmic, which means that k1/2 = 50 in the middle of the trace. (A) No mode shift. (B) Mode shift = 60 mV. Note the clearly arrhythmic firing for the nonmode shift model at intermediate rate constants.
	Figure 19. . A four-state model for HCN channel gating. (A) Scheme for HCN kinetics. V1/2 is the voltage at which open-to-closed and closed to-open transitions are equal. Molecular models for voltage hysteresis in (B) HCN channels and (C) Shaker K channels. See discussion “Molecular Mechanism for Mode Shift” for description.
	Figure .
	Figure 20. . 20-state extension of the four-state model. (A) Each closed and open state in the four-state model have been expanded to five states, representing 0, 1, 2, 3, or 4 S4s activated (moved inward). The channels would mainly open from the states with all S4s activated and close from the states with all S4s deactivated (moved outward). Hysteresis mainly affects the α and β rates. (B and C) Simulations of tail currents after short (continuous line) and long (dotted line) activation prepulses, using a simplified version of the model in A. All channels were assumed to be in Oi4 after short prepulses and in Oii4 after long prepulses. For simplicity, all rate constants were assumed to be zero except for β and λ. The closing rate λ is set to 25 ms−1 for all traces. β was assumed to change 2.5-fold between mode I and mode II. (B) Tail currents at +50 mV, where β = 75 ms−1 in mode I. (C) Tail currents at −15 mV, where β = 25 ms−1 in mode I. These simple simulations are not supposed to be seen as a quantitative fit to our recordings, but only as a qualitative suggestion that the slowing of the tails and the development of a delay in the tails can be due to voltage hysteresis. For example, the voltage dependence in these simulations was assumed to be only in the closed–closed transitions and open–open transitions, not in the open–closed transitions. Most likely, the open–closed transitions are also voltage dependent (Altomare et al., 2001).

Aggarwal, Contribution of the S4 segment to gating charge in the Shaker K+ channel. 1996, Pubmed, Xenbase

Aggarwal, Contribution of the S4 segment to gating charge in the Shaker K+ channel. 1996, Pubmed , Xenbase
Altomare, Integrated allosteric model of voltage gating of HCN channels. 2001, Pubmed
Armstrong, Currents related to movement of the gating particles of the sodium channels. 1973, Pubmed
Baruscotti, Pacemaker channels. 2004, Pubmed
Bezanilla, Molecular basis of gating charge immobilization in Shaker potassium channels. 1991, Pubmed , Xenbase
Bezanilla, Distribution and kinetics of membrane dielectric polarization. 1. Long-term inactivation of gating currents. 1982, Pubmed
Clapham, Not so funny anymore: pacing channels are cloned. 1998, Pubmed
COLE, Ionic current measurements in the squid giant axon membrane. 1960, Pubmed
DiFrancesco, Characterization of the pace-maker current kinetics in calf Purkinje fibres. 1984, Pubmed
DiFrancesco, Pacemaker mechanisms in cardiac tissue. 1993, Pubmed
DiFrancesco, Delayed activation of the cardiac pacemaker current and its dependence on conditioning pre-hyperpolarizations. 1983, Pubmed
Gauss, Molecular identification of a hyperpolarization-activated channel in sea urchin sperm. 1998, Pubmed
Hahin, Removal of inactivation causes time-invariant sodium current decays. 1988, Pubmed
HODGKIN, A quantitative description of membrane current and its application to conduction and excitation in nerve. 1952, Pubmed
Keynes, The screw-helical voltage gating of ion channels. 1999, Pubmed
Keynes, Kinetics and steady-state properties of the charged system controlling sodium conductance in the squid giant axon. 1974, Pubmed
Larsson, A conserved glutamate is important for slow inactivation in K+ channels. 2000, Pubmed , Xenbase
Larsson, Transmembrane movement of the shaker K+ channel S4. 1996, Pubmed , Xenbase
Larsson, The search is on for the voltage sensor-to-gate coupling. 2002, Pubmed
Liu, Dynamic rearrangement of the outer mouth of a K+ channel during gating. 1996, Pubmed
Loots, Protein rearrangements underlying slow inactivation of the Shaker K+ channel. 1998, Pubmed
López-Barneo, Effects of external cations and mutations in the pore region on C-type inactivation of Shaker potassium channels. 1993, Pubmed , Xenbase
Ludwig, A family of hyperpolarization-activated mammalian cation channels. 1998, Pubmed
Lüthi, H-current: properties of a neuronal and network pacemaker. 1998, Pubmed
Männikkö, Voltage-sensing mechanism is conserved among ion channels gated by opposite voltages. 2002, Pubmed , Xenbase
Ogielska, Cooperative subunit interactions in C-type inactivation of K channels. 1995, Pubmed , Xenbase
Olcese, A conducting state with properties of a slow inactivated state in a shaker K(+) channel mutant. 2001, Pubmed , Xenbase
Olcese, Correlation between charge movement and ionic current during slow inactivation in Shaker K+ channels. 1997, Pubmed , Xenbase
Panyi, C-type inactivation of a voltage-gated K+ channel occurs by a cooperative mechanism. 1995, Pubmed
Pape, Queer current and pacemaker: the hyperpolarization-activated cation current in neurons. 1996, Pubmed
Santoro, Molecular and functional heterogeneity of hyperpolarization-activated pacemaker channels in the mouse CNS. 2000, Pubmed , Xenbase
Santoro, The HCN gene family: molecular basis of the hyperpolarization-activated pacemaker channels. 1999, Pubmed
Seoh, Voltage-sensing residues in the S2 and S4 segments of the Shaker K+ channel. 1996, Pubmed , Xenbase
Shin, Inactivation in HCN channels results from reclosure of the activation gate: desensitization to voltage. 2004, Pubmed
Steriade, Spike-wave complexes and fast components of cortically generated seizures. II. Extra- and intracellular patterns. 1998, Pubmed
Timofeev, Cortical hyperpolarization-activated depolarizing current takes part in the generation of focal paroxysmal activities. 2002, Pubmed
Vemana, S4 movement in a mammalian HCN channel. 2004, Pubmed , Xenbase
Wainger, Molecular mechanism of cAMP modulation of HCN pacemaker channels. 2001, Pubmed
Wang, Activity-dependent regulation of HCN pacemaker channels by cyclic AMP: signaling through dynamic allosteric coupling. 2002, Pubmed , Xenbase
Yang, Molecular basis of charge movement in voltage-gated sodium channels. 1996, Pubmed
Yu, The VGL-chanome: a protein superfamily specialized for electrical signaling and ionic homeostasis. 2004, Pubmed
Zagotta, Shaker potassium channel gating. III: Evaluation of kinetic models for activation. 1994, Pubmed , Xenbase
Zhang, Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. 2000, Pubmed