Article Figures & Data
Figures
- Fig. 3.
A mathematical model, which accurately simulates IAdepol, illustrates the role of cumulative inactivation in the evolution ofIAdepol traces during a spike train.A, The recovery from inactivation of recordedIAdepol has two time constants. A two-pulse protocol (inset) was used to determine the recovery from inactivation caused by the first 100 msec pulse from −50 to +30 mV. The peak current during the second pulse, normalized to that during the first one (filled circles), was plotted against the time interval between the two pulses. The curve (smooth line) was fit by a double exponential function; the major component had a τh value of 0.9 sec, whereas τh for the minor component was 18.5 sec. To simulate IAdepol, the recovery from inactivation was approximated by using just the faster time constant, which was 1.1 sec at −50 mV, averaged from four experiments. The accuracy of this approximation was tested by using the same double-pulse protocol (inset) to drive the dynamic-clamp circuit in open-loop mode. The peak current calculated during the second pulse, normalized to that during the first pulse (open circle), was plotted against the time interval between two pulses, which was fit by a single exponential curve (dotted line). B, The model simulates IAdepol during rectangular depolarizing steps. B1, Empirically measuredIAdepol in response to 200 msec depolarizing steps in 10 mV increments from −40 to +30 mV from a holding potential of −50 mV. B2, IAdepol was simulated by driving the dynamic-clamp circuit in open-loop mode with the same set of depolarizing steps as those used in B1.C, The simulated IAdepol traces during action-potential trains were quite similar to those recorded as 4-AP difference current. C1, An action-potential train evoked by injecting brief, depolarizing current pulses into the soma was recorded for use as a command signal. The holding potential was −40 mV.C2, IAdepol was recorded as a 4-AP difference current under voltage clamp while playing back the spike train recorded in C1.C3, C4,IAdepol was simulated by playing back the action-potential train from C1 to the dynamic-clamp circuit in open-loop mode with two different versions of the model. C3,IAdepol waveforms that were simulated with the unmodified version of the model matched the empirically determined values in C2.C4, When noninactivatingIAdepol was simulated by fixingh = 1, the same command led to greatly enhanced values of IAdepol. C5, Changes in peak values of recorded and simulated IAdepol fromC2–C4 are plotted against spike number.IAdepol was measured as a 1 mm 4-AP difference current after 60 μm TTX, 2 mmCdCl2, and 40 mm TEA had been added to blockINa, IK-Ca, andIK-V. The value of Gmaxused in the simulations C3, C4 was 1900 nS. The first and last traces in C are indicated by thewhite and black arrows, respectively.
- Fig. 1.
The dynamic clamp was used in open-loop mode to simulate current waveforms off-line in response to predetermined voltage commands consisting of either (1) a train of recorded spike waveforms, (2) rectangular voltage steps, or (3) in closed-loop mode to inject, block, or modify currents on-line.
- Fig. 10.
Addition of either IAdepolor IK-V with the dynamic clamp was sufficient to cause spike broadening in a cell in which K+ currents had been preblocked pharmacologically. An action-potential train was evoked: A, In normal ASW. B, After 50 mm TEA and 10 mm 4-AP had been added to blockIK-V, IK-Ca, andIAdepol. C, With bothIAdepol and IK-V added back. D, With IAdepol added back.E, With IK-V added back.F, With IK-V, modified to express only the slow, nonstate-dependent inactivation, added back. Resting potential was −47 mV. Gmax forIAdepol, 1500 nS; Gmaxfor IK-V, 1500 nS (n = 6).
- Fig. 2.
Characteristic patterns of changes in individual currents accompany frequency-dependent spike broadening. A 7 Hz, 9.3 sec action-potential train (left, first row) was evoked by injecting brief, depolarizing current pulses into a cell with a resting potential of −48 mV. The five major ionic currents mediating the spike train were isolated by playing back the spike train as the command to the conventional voltage clamp. Between each repetition of the train, the following sequence of blocking drugs was added, one at a time, to the bath: 60 μm TTX, 3 mm TEA, 40 mm TEA, 1 mm 4-AP, or 2 mmCdCl2. The resulting difference currents measured before and after adding each compound revealed INa,IK-Ca, IK-V,IAdepol, and ICa, respectively. The five major currents during the first spike, the 27th spike (at which point IK-V reached its peak), the 43rd spike (at which point the maximum broadening was reached), and the last spike (65th) are shown. The normalized values of spike duration and of the time integrals of each current are plotted against spike number in the right-hand column.
- Fig. 4.
A mathematical model, which accurately simulatesIK-V, illustrates the role of cumulative inactivation in the evolution of IK-V traces during a spike train. A, IK-Vexhibits state-dependent inactivation, which causes it to inactivate more rapidly in response to several brief pulses than to one long pulse of equivalent duration. Depolarizing steps were from a holding potential of −50 mV to +20 mV. A1,IK-V inactivated relatively slowly during a 2 sec depolarizing step. A2, IK-Vduring four 500 msec pulses repeated at 1 Hz decayed to a lower final level than in A1. The dotted line inA1 marks the corresponding level ofIK-V at the end of four brief voltage steps inA2.B, Recorded and simulatedIK-V were similar during 50 msec repetitive depolarizing pulses (−10 to +50 mV) at 7 Hz from a holding potential of −50 mV. B1, IK-V was measured empirically as a TEA difference current using the voltage-step protocol shown in the inset. B2, IK-V was simulated by driving the dynamic-clamp circuit in open-loop mode.C, The simulated waveforms of IK-Vduring action-potential trains were similar to those recorded as TEA difference currents. C1, An action-potential train evoked by injecting brief depolarizing current pulses was recorded for use as a command signal. The holding potential was −50 mV. C2,IK-V was recorded as a TEA difference current under voltage clamp while playing back the spike train recorded inC1.C3–C5, IK-V was simulated by playing back the action-potential train from C1 to the dynamic-clamp circuit in open-loop mode with three different versions of the model.C3, Simulated IK-V had normal inactivation. C4, NoninactivatingIK-V was simulated by fixing h = 1. C5, The state-dependent nature ofIK-V inactivation was ignored; τh was estimated from the decay during long (2 sec) voltage steps (A1) rather than from high-frequency trains of steps as in B. C6, Peak values of recorded and simulated IK-V fromC3–C5 are plotted against spike number.IK-V was measured as a 40 mm TEA difference current after 60 mm TTX and 2 mmCdCl2 had been added to block INa,ICa, and IK-Ca. The value of Gmax used for the simulations in Cwas 1850 nS. The first and last traces in C are indicated by the white and black arrows, respectively.
- Fig. 5.
Blocking IAdepol activation (or inactivation) with the dynamic clamp accelerated (or eliminated) spike broadening, which in turn modified the dynamics ofIK-V activation and inactivation. A, Action-potential trains were evoked under control conditions (A1), after blocking IAdepol(A2), or after blocking inactivation ofIAdepol (A3). The dynamic clamp was used in closed-loop mode either to simply cancel outIAdepol (A2) or to replace it with a noninactivating version of IAdepol(A3). B, Simulated IK-Vchanged during a spike train recorded whileIAdepol (or its inactivation) was blocked.B1, Simulated IK-V during a control spike train showed bimodal changes. B2, SimulatedIK-V during an action-potential train recorded while IAdepol was blocked underwent cumulative inactivation from the increased initial value. B3, SimulatedIK-V during a spike train recorded while inactivation of IAdepol was blocked underwent only modest cumulative inactivation. A4, B4, Changes in spike width (A1–A3) and peak values of simulatedIK-V (B1–B3) caused by modifyingIAdepol are plotted against spike number. Resting potential was −50 mV. Gmax used by the dynamic clamp for blocking or modifying IAdepolwas 1650 nS. Gmax used for simulatingIK-V in B1–B3 was 2050 nS.
- Fig. 6.
Blocking IAdepol activation with the dynamic clamp accelerated spike broadening, which, in turn, enhanced the activation of IK-Ca and modified its kinetics. A, The spike trains recorded either under control conditions (A1) or withIAdepol activation blocked (A2) by the dynamic clamp were used as commands to the voltage clamp for isolating IK-Ca pharmacologically (B1, B2). B, IK-Ca was measured as 3 mm TEA difference currents under control condition (B1) and after blocking IAdepol(B2). A3, B3, The durations of the spikes of the two trains (A1, A2) and the corresponding peaks ofIK-Ca currents (B1, B2) are plotted against spike number. Resting potential was −50 mV, andGmax used for the IAdepolsimulations (A2) was 1350 nS.
- Fig. 9.
Using the dynamic clamp to block activation or inactivation of IAdepol or ofIK-V caused changes in frequency-dependent spike broadening that were measured in the same cell. A, Action-potential trains generated with K+ conductances in various different states. A1, Control; A2, withIAdepol blocked; A3, withIK-V blocked; A4, withIAdepol and IK-V blocked;A5, with inactivation of IAdepolblocked; A6, with inactivation ofIK-V blocked. B, Durations of spikes in A1–A6 are plotted against spike number. Resting potential was −50 mV. Currents were blocked or modified by usingGmax for IAdepol = 1750 nS and Gmax for IK-V = 1650 nS.
- Fig. 7.
Blocking IK-V activation (or inactivation) with the dynamic clamp accelerated (or reduced) spike broadening, which, in turn, modified the rate and extent ofIAdepol inactivation. A, Action-potential trains were evoked under control conditions (A1), after blocking IK-V(A2), or after blocking inactivation ofIK-V (A3). The dynamic clamp was used in closed-loop mode either to simply cancel outIK-V (A2) or to replace it with a noninactivating version of IK-V (A3).B, Compared with control (B1), simulatedIAdepol underwent faster inactivation during a spike train with IK-V blocked (B2) or slower and less complete inactivation with inactivation ofIK-V blocked (B3). A4, B4, Changes in spike width (A1–A3) and peak values ofIAdepol (B1–B3) caused by modifyingIK-V are plotted against spike number. Resting potential was −50 mV. Gmax used by the dynamic clamp for blocking or modifying IK-V was 1700 nS. Gmax of IAdepol used for simulating IAdepol in B1–B3 was 1950 nS.
- Fig. 8.
Replacing the rapid, state-dependent inactivation of IK-V by a slower, Hodgkin–Huxley-type version reduced both the rate and final extent of spike broadening.A, An action-potential train was evoked by injecting brief depolarizing current pulses under control conditions. B, An action-potential train was evoked after eliminating the state-dependent inactivation of IK-V, which was achieved by injecting two currents into the cell simultaneously:IK-V with normal state-dependent inactivation but with reversed sign to block the existingIK-V of the cell and IK-Vwith only slow inactivation and normal polarity to replace the endogenous current. C, The durations of spikes for these two trains are plotted against the number of spike. Resting potential was −48 mV. Gmax used by the dynamic clamp for blocking or modifying IK-V was 2100 nS.
- Fig. 11.
Summary of the predominant mechanisms underlying spike broadening in the R20 neurons, determined in this and the previous study (Ma and Koester, 1995). Some interactions that play a minor role in spike broadening are not included in this diagram. For example, spike broadening also facilitates the activation ofIAdepol (Fig. 3C4). This effect is overwhelmed by the progressive increase in inactivation, however. Broadening also enhances cumulative inactivation ofICa (Ma and Koester, 1995). This effect has two opposing effects on spike broadening: by reducing inward current it limits broadening, and by reducing the build-up ofIK-Ca, it enhances broadening.
