- Email: [email protected]
Slowly-inactivating potassium conductances in compartmental interneuron models
Neurocomputing 44– 46 (2002) 161 – 166
www.elsevier.com/locate/neucom
Slowly-inactivating potassium conductances in compartmental interneuron models Fernanda Saragaa , Frances K. Skinnera; b;∗ a Toronto
Western Research Institute, University Health Network, Department of Physiology, University of Toronto, Toronto, Ont., Canada b Departments of Medicine (Neurology) and Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ont., Canada
Abstract Recent experimental and modelling work suggests that slowly-inactivating potassium currents might play critical roles in generating slow (delta) oscillatory behaviour in neurons. We examine the contribution of a slowly-inactivating potassium channel to the signal output in a multi-compartmental interneuron model. Depending on the distribution, density, and kinetics of this channel, we +nd a wide range of tonic and bursting behaviours. Under certain conditions, we obtain a robust (with respect to injected current) bursting pattern and in this paper we show how such robust oscillations emerge and their dependence on the slowly-inactivating potassium c 2002 Published by Elsevier Science B.V. channel. Keywords: Bursting oscillations; Compartmental models; Ion channel kinetics; Interneurons; Hippocampus
1. Introduction Interneurons are a heterogeneous group of cells in terms of morphology, neuromodulators, and electrophysiological responses, and it has been suggested that this heterogeneity might subserve functionally distinct roles for the interneuron subtypes.
This work was supported by OGSST and NSERC (F.S.); and CIHR (FKS). FKS is an MRC Scholar + CFI Researcher. ∗ Corresponding author. Toronto Western Research Institute, University Health Network, 399 Bathurst St., MP13-317, Toronto, Ont., Canada M5T 2S8. Tel.: +1-416-603-5800x5107; fax: +1-416-603-5745. E-mail address: [email protected] (F.K. Skinner). c 2002 Published by Elsevier Science B.V. 0925-2312/02/$ - see front matter PII: S 0 9 2 5 - 2 3 1 2 ( 0 2 ) 0 0 3 7 8 - 8
162
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
Speci+cally, voltage-gated ion channels have diCerent kinetic properties, densities and distributions in interneurons which leads to the various signal outputs recorded from these cells [7,9]. Recent experimental work shows that slow (¡1–4 Hz) +eld rhythms occur spontaneously or can be induced in the rodent hippocampus [14,12]. Rhythmic discharges in interneurons are correlated with the +eld rhythms implying a possible role of signal generation for the interneurons in this rhythm. Modeling work shows that the inclusion of a slowly-inactivating potassium current in a two-cell network model, coupled with both inhibitory and gap junction synapses, can produce a slow bursting behaviour similar to that seen experimentally [11]. In a previous paper [10], we look at all the +ring patterns that emerge from a simple multi-compartment model with limited ion channels. By varying the kinetics of one of the channels, a slowly-inactivating potassium channel, IKs−i , and the distribution of the channels among the compartments we are able to produce a rich variety of signals including tonic +ring, bistable tonic +ring, and bursting. Of the 15 combinations considered, two result in a robust bursting signal of ∼1 Hz. This frequency remains unchanged with changing current injection values. A bursting signal is one of the many diCerent discharge patterns measured from hippocampal interneurons and other cells [9]. Bursts are believed to have a special role in synaptic plasticity and information processing since they allow reliable transmission at a synapse [6]. The generation of bursts may depend on the interaction of synaptic input with intrinsic conductances. In this paper we examine the mechanisms behind the generation and stabilization of the robust bursting signal described in [10].
2. Model We use the multi-compartment interneuron model described in [10]. BrieIy, the model consists of 12 compartments: an axon, a soma, and a dendrite (10 segments). The surface area (2:21 × 10−4 cm2 ), input resistance (∼290 MJ), and membrane time constant (∼6 ms) were matched to values taken from the literature [8,4,5] for oriens=alveus hippocampal interneurons. The ion channels included in the model are limited to the traditional Hodgkin–Huxley (HH) sodium, INa , and potassium, IK , currents, a persistent sodium current, INap , and a slowly-inactivating potassium current, IKs−i . The equations governing the currents are described in [10]. The general form of the steady-state activation and inactivation for the IKs−i channel are a∞ = 1={1 + exp [ − (V + V1=2 act: )=5]} and b∞ = 1={1 + exp [(V + V1=2 inact: )=6]}. V1=2 act: and V1=2 inact: are the half-activation and half-inactivation values that when varied, produce diCerent +ring patterns. The voltage range that resulted in the robust spiking pattern (−35 mV= − 65 mV) is shown in Fig. 1, along with the activation curve for the persistent sodium current p∞ = 1={1 + exp [ − (V + 51)=5]}. The activation and inactivation time constants for IKs−i are 5 and 1500 ms respectively. The conductance value used for this channel is gKs−i = 20 mS=cm2 .
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
163
Fig. 1. Steady-state activation and inactivation curves. Solid lines: activation and inactivation curves for IKs−i ; Dashed line: activation curve for INap .
3. Results Fig. 2(A) shows the voltage response of the model cell to two diCerent injected current values. All four ion channels described earlier are placed with the same conductance density in all compartments. Although the amplitude and shape of the action potentials are diCerent for each injected current value, the frequency of the bursts and the spike frequency within each burst remain the same. The burst frequency is equal to 1:05 Hz regardless of the amount of injected current into the cell. When the IKs−i current is removed from the soma and axon compartments, the resulting burst signal is again robust with respect to injected current, this time measuring at 1 Hz. The onset of the burst is governed by the persistent sodium current, INap , which acts to depolarize the membrane allowing it to reach threshold and to spike. The spikes are produced by the interplay between the HH currents, INa and IK . The termination of the burst is brought about by the IKs−i channel which, as an outward current, works to hyperpolarize the membrane thereby not allowing the membrane to reach threshold. This is shown in Fig. 2(B). This careful balance (in terms of maintaining the same frequency) between all four currents is maintained even when the membrane is depolarized by a steady injected current into the soma compartment. The activation and inactivation time constants are modi+ed individually to see the eCect on the robustness of the signal (see Table 1). The activation and inactivation time constants are modi+ed from their original values of 5 and 1500 ms respectively,
164
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
Fig. 2. (A) Voltage recordings from the soma. Thin line: Iinj = 0 nA. Thick line: Iinj = 0:1 nA. (B) Current recordings from the soma. Iinj = 0 nA. Positive=negative plots denote outward=inward currents. Thin lines: HH currents, INa and IK . Thick positive line: IKs−i . Thick negative line: INap . Table 1 Changes in burst frequency with variations in time constants and conductance values
Burst Frequency
a 4 ms
a 6 ms
b 1200 ms
b 1800 ms
gKs−i 18 mS=cm2
gKs−i 22 mS=cm2
↑
↓
↑
↓
↓
↑
2:83 Hz
0:85 Hz
2:32 Hz
1:02 Hz
0:57 Hz
1:81 Hz
Original time constant and conductance values were: a = 5 ms, b = 1500 ms, gKs−i = 20 mS=cm2 , giving rise to a burst frequency of 1:05 Hz.
by a 20% diCerence. For the activation time constant, simulations with 4 and 6 ms are done, and for the inactivation time constant, simulations with 1200 and 1800 ms are done. For each simulation run, only one time constant is modi+ed from its original value. Although the frequencies of the bursts and the number of spikes per burst change with the modi+ed time constants, the robustness of each signal with respect to injected current value remains the same. This implies that the robustness of the signal is not a result of the time constants chosen for the IKs−i channel. The robust pattern results from the interplay between slowly-inactivating potassium channels, the persistent sodium channels and the HH channels in a multi-compartment model with active dendrites. Without the inclusion of the IKs−i , we do not see a bursting pattern at all. The conductance value for the IKs−i channel plays a signi+cant role in the generation of the burst pattern. The model interneuron can only produce a burst pattern when the gKs−i value falls within the range 18 and 22 mS=cm2 . That means that only a 10% change in the maximal conductance value is allowed to maintain a burst pattern. When simulations are run with gKs−i modi+ed from its original value of 20 mS=cm2 , the frequency of the bursts remains robust with respect to injected current. When the maximal conductance of IKs−i is decreased, the burst frequency increases. With
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
165
the smaller outward current that results from the decreased maximal conductance, the membrane voltage no longer remains at the same hyperpolarized value and lies closer to the threshold value. Therefore, we see an increase in the burst frequency. We see the opposite eCect happening when we increase the maximal conductance of IKs−i (see Table 1). From these results we can see that we need a relatively speci+c amount of IKs−i to oCset INap and produce a bursting pattern. Too little will result in a depolarized membrane voltage that cannot repolarize in order to spike and too much of the current will result in a hyperpolarized membrane voltage that cannot reach threshold. 4. Discussion In this paper we show how a slowly-inactivating potassium current with speci+c channel kinetics along with Hodgkin–Huxley currents, and a persistent sodium current, can generate a robust bursting pattern in a model interneuron. The robustness of the signal is maintained when the activation and inactivation time constants are modi+ed from their original values. The burst pattern is lost if gKs−i does not lie within a narrow range of values, but within that range the signal is robust. The interplay between the four ion channels allows the signal to be maintained with changing injected current. Many diCerent slowly-inactivating potassium channels, that activate at diCerent voltages, have been found to exist in interneurons [1,2,9,13]. These currents are known to delay the onset of spike discharge and aid in spike repolarization. We previously explored the role of the slowly-inactivating potassium channel that was active in three diCerent voltage ranges. Although the middle voltage range has not at present been found to exist in physiological systems, it does give insight into how such a channel with these kinetics could produce a robust signal pattern. Given the wide variety of potassium channels that are known to exist in neurons and the discovery of new ones on a continuous basis, perhaps a potassium channel with similar kinetics to those described here does exist. A neuron’s ability to generate a robust bursting signal could give it a special role in the network. A signal whose frequency is independent of its input may allow a reliable transfer of information in the face of many changing factors. Although interneurons are a small population of cells in the hippocampus (∼10%), a single interneuron can form over 1000 synapses onto multiple pyramidal cells [3]. Therefore, interneurons can exert a strong inIuence on the +eld rhythm, which is the synchronized +ring of many pyramidal cells. Individual interneurons capable of producing a robust bursting signal may play a signi+cant role in maintaining the +eld rhythms measured in the hippocampus. Given the known heterogeneity of interneurons in the hippocampus, their diCerent signal patterns could have a functional signi+cance. We can try to understand this heterogeneity in terms of the dynamical outputs of the cells. The possible outputs are less diverse than the many other factors distinguishing interneurons such as neuromodulatory responses, current distributions, and morphologies. Understanding the generation and maintenance of various +ring patterns in single cells can lead to a better understanding of network dynamics and behaviours.
166
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
A. Chikwendu, C.J. McBain, J. Neurophysiol. 76 (1996) 1477–1490. J. Du, et al., J. Neurosci. 16 (1996) 506–518. T.F. Freund, G. BuzsOaki, Hippocampus 6 (1996) 347–470. J.-C. Lacaille, et al., J. Neurosci. 7 (1987) 1979–1993. J.-C. Lacaille, S. Williams, Neurosci. 36 (1990) 349–359. J.E. Lisman, Trends Neurosci. 20 (1997) 38–43. C.J. McBain, A. Fisahn, Nature Rev. Neurosci. 2 (2001) 11–23. F. Morin, et al., J. Neurophysiol. 76 (1996) 1–16. P. Parra, et al., Neuron 20 (1998) 983–993. F. Saraga, F.K. Skinner, Neurosci., 2002, in press. F.K. Skinner, et al., J. Neurophysiol. 81 (1999) 1274–1283. C. Wu, et al., J. Physiol. (2002), in press. L. Zhang, C.J. McBain, J. Physiol. 488 (1995) 661–672. Y. Zhang, et al., J. Neurosci. 18 (1998) 9256–9268.
www.elsevier.com/locate/neucom
Slowly-inactivating potassium conductances in compartmental interneuron models Fernanda Saragaa , Frances K. Skinnera; b;∗ a Toronto
Western Research Institute, University Health Network, Department of Physiology, University of Toronto, Toronto, Ont., Canada b Departments of Medicine (Neurology) and Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, Ont., Canada
Abstract Recent experimental and modelling work suggests that slowly-inactivating potassium currents might play critical roles in generating slow (delta) oscillatory behaviour in neurons. We examine the contribution of a slowly-inactivating potassium channel to the signal output in a multi-compartmental interneuron model. Depending on the distribution, density, and kinetics of this channel, we +nd a wide range of tonic and bursting behaviours. Under certain conditions, we obtain a robust (with respect to injected current) bursting pattern and in this paper we show how such robust oscillations emerge and their dependence on the slowly-inactivating potassium c 2002 Published by Elsevier Science B.V. channel. Keywords: Bursting oscillations; Compartmental models; Ion channel kinetics; Interneurons; Hippocampus
1. Introduction Interneurons are a heterogeneous group of cells in terms of morphology, neuromodulators, and electrophysiological responses, and it has been suggested that this heterogeneity might subserve functionally distinct roles for the interneuron subtypes.
This work was supported by OGSST and NSERC (F.S.); and CIHR (FKS). FKS is an MRC Scholar + CFI Researcher. ∗ Corresponding author. Toronto Western Research Institute, University Health Network, 399 Bathurst St., MP13-317, Toronto, Ont., Canada M5T 2S8. Tel.: +1-416-603-5800x5107; fax: +1-416-603-5745. E-mail address: [email protected] (F.K. Skinner). c 2002 Published by Elsevier Science B.V. 0925-2312/02/$ - see front matter PII: S 0 9 2 5 - 2 3 1 2 ( 0 2 ) 0 0 3 7 8 - 8
162
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
Speci+cally, voltage-gated ion channels have diCerent kinetic properties, densities and distributions in interneurons which leads to the various signal outputs recorded from these cells [7,9]. Recent experimental work shows that slow (¡1–4 Hz) +eld rhythms occur spontaneously or can be induced in the rodent hippocampus [14,12]. Rhythmic discharges in interneurons are correlated with the +eld rhythms implying a possible role of signal generation for the interneurons in this rhythm. Modeling work shows that the inclusion of a slowly-inactivating potassium current in a two-cell network model, coupled with both inhibitory and gap junction synapses, can produce a slow bursting behaviour similar to that seen experimentally [11]. In a previous paper [10], we look at all the +ring patterns that emerge from a simple multi-compartment model with limited ion channels. By varying the kinetics of one of the channels, a slowly-inactivating potassium channel, IKs−i , and the distribution of the channels among the compartments we are able to produce a rich variety of signals including tonic +ring, bistable tonic +ring, and bursting. Of the 15 combinations considered, two result in a robust bursting signal of ∼1 Hz. This frequency remains unchanged with changing current injection values. A bursting signal is one of the many diCerent discharge patterns measured from hippocampal interneurons and other cells [9]. Bursts are believed to have a special role in synaptic plasticity and information processing since they allow reliable transmission at a synapse [6]. The generation of bursts may depend on the interaction of synaptic input with intrinsic conductances. In this paper we examine the mechanisms behind the generation and stabilization of the robust bursting signal described in [10].
2. Model We use the multi-compartment interneuron model described in [10]. BrieIy, the model consists of 12 compartments: an axon, a soma, and a dendrite (10 segments). The surface area (2:21 × 10−4 cm2 ), input resistance (∼290 MJ), and membrane time constant (∼6 ms) were matched to values taken from the literature [8,4,5] for oriens=alveus hippocampal interneurons. The ion channels included in the model are limited to the traditional Hodgkin–Huxley (HH) sodium, INa , and potassium, IK , currents, a persistent sodium current, INap , and a slowly-inactivating potassium current, IKs−i . The equations governing the currents are described in [10]. The general form of the steady-state activation and inactivation for the IKs−i channel are a∞ = 1={1 + exp [ − (V + V1=2 act: )=5]} and b∞ = 1={1 + exp [(V + V1=2 inact: )=6]}. V1=2 act: and V1=2 inact: are the half-activation and half-inactivation values that when varied, produce diCerent +ring patterns. The voltage range that resulted in the robust spiking pattern (−35 mV= − 65 mV) is shown in Fig. 1, along with the activation curve for the persistent sodium current p∞ = 1={1 + exp [ − (V + 51)=5]}. The activation and inactivation time constants for IKs−i are 5 and 1500 ms respectively. The conductance value used for this channel is gKs−i = 20 mS=cm2 .
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
163
Fig. 1. Steady-state activation and inactivation curves. Solid lines: activation and inactivation curves for IKs−i ; Dashed line: activation curve for INap .
3. Results Fig. 2(A) shows the voltage response of the model cell to two diCerent injected current values. All four ion channels described earlier are placed with the same conductance density in all compartments. Although the amplitude and shape of the action potentials are diCerent for each injected current value, the frequency of the bursts and the spike frequency within each burst remain the same. The burst frequency is equal to 1:05 Hz regardless of the amount of injected current into the cell. When the IKs−i current is removed from the soma and axon compartments, the resulting burst signal is again robust with respect to injected current, this time measuring at 1 Hz. The onset of the burst is governed by the persistent sodium current, INap , which acts to depolarize the membrane allowing it to reach threshold and to spike. The spikes are produced by the interplay between the HH currents, INa and IK . The termination of the burst is brought about by the IKs−i channel which, as an outward current, works to hyperpolarize the membrane thereby not allowing the membrane to reach threshold. This is shown in Fig. 2(B). This careful balance (in terms of maintaining the same frequency) between all four currents is maintained even when the membrane is depolarized by a steady injected current into the soma compartment. The activation and inactivation time constants are modi+ed individually to see the eCect on the robustness of the signal (see Table 1). The activation and inactivation time constants are modi+ed from their original values of 5 and 1500 ms respectively,
164
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
Fig. 2. (A) Voltage recordings from the soma. Thin line: Iinj = 0 nA. Thick line: Iinj = 0:1 nA. (B) Current recordings from the soma. Iinj = 0 nA. Positive=negative plots denote outward=inward currents. Thin lines: HH currents, INa and IK . Thick positive line: IKs−i . Thick negative line: INap . Table 1 Changes in burst frequency with variations in time constants and conductance values
Burst Frequency
a 4 ms
a 6 ms
b 1200 ms
b 1800 ms
gKs−i 18 mS=cm2
gKs−i 22 mS=cm2
↑
↓
↑
↓
↓
↑
2:83 Hz
0:85 Hz
2:32 Hz
1:02 Hz
0:57 Hz
1:81 Hz
Original time constant and conductance values were: a = 5 ms, b = 1500 ms, gKs−i = 20 mS=cm2 , giving rise to a burst frequency of 1:05 Hz.
by a 20% diCerence. For the activation time constant, simulations with 4 and 6 ms are done, and for the inactivation time constant, simulations with 1200 and 1800 ms are done. For each simulation run, only one time constant is modi+ed from its original value. Although the frequencies of the bursts and the number of spikes per burst change with the modi+ed time constants, the robustness of each signal with respect to injected current value remains the same. This implies that the robustness of the signal is not a result of the time constants chosen for the IKs−i channel. The robust pattern results from the interplay between slowly-inactivating potassium channels, the persistent sodium channels and the HH channels in a multi-compartment model with active dendrites. Without the inclusion of the IKs−i , we do not see a bursting pattern at all. The conductance value for the IKs−i channel plays a signi+cant role in the generation of the burst pattern. The model interneuron can only produce a burst pattern when the gKs−i value falls within the range 18 and 22 mS=cm2 . That means that only a 10% change in the maximal conductance value is allowed to maintain a burst pattern. When simulations are run with gKs−i modi+ed from its original value of 20 mS=cm2 , the frequency of the bursts remains robust with respect to injected current. When the maximal conductance of IKs−i is decreased, the burst frequency increases. With
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
165
the smaller outward current that results from the decreased maximal conductance, the membrane voltage no longer remains at the same hyperpolarized value and lies closer to the threshold value. Therefore, we see an increase in the burst frequency. We see the opposite eCect happening when we increase the maximal conductance of IKs−i (see Table 1). From these results we can see that we need a relatively speci+c amount of IKs−i to oCset INap and produce a bursting pattern. Too little will result in a depolarized membrane voltage that cannot repolarize in order to spike and too much of the current will result in a hyperpolarized membrane voltage that cannot reach threshold. 4. Discussion In this paper we show how a slowly-inactivating potassium current with speci+c channel kinetics along with Hodgkin–Huxley currents, and a persistent sodium current, can generate a robust bursting pattern in a model interneuron. The robustness of the signal is maintained when the activation and inactivation time constants are modi+ed from their original values. The burst pattern is lost if gKs−i does not lie within a narrow range of values, but within that range the signal is robust. The interplay between the four ion channels allows the signal to be maintained with changing injected current. Many diCerent slowly-inactivating potassium channels, that activate at diCerent voltages, have been found to exist in interneurons [1,2,9,13]. These currents are known to delay the onset of spike discharge and aid in spike repolarization. We previously explored the role of the slowly-inactivating potassium channel that was active in three diCerent voltage ranges. Although the middle voltage range has not at present been found to exist in physiological systems, it does give insight into how such a channel with these kinetics could produce a robust signal pattern. Given the wide variety of potassium channels that are known to exist in neurons and the discovery of new ones on a continuous basis, perhaps a potassium channel with similar kinetics to those described here does exist. A neuron’s ability to generate a robust bursting signal could give it a special role in the network. A signal whose frequency is independent of its input may allow a reliable transfer of information in the face of many changing factors. Although interneurons are a small population of cells in the hippocampus (∼10%), a single interneuron can form over 1000 synapses onto multiple pyramidal cells [3]. Therefore, interneurons can exert a strong inIuence on the +eld rhythm, which is the synchronized +ring of many pyramidal cells. Individual interneurons capable of producing a robust bursting signal may play a signi+cant role in maintaining the +eld rhythms measured in the hippocampus. Given the known heterogeneity of interneurons in the hippocampus, their diCerent signal patterns could have a functional signi+cance. We can try to understand this heterogeneity in terms of the dynamical outputs of the cells. The possible outputs are less diverse than the many other factors distinguishing interneurons such as neuromodulatory responses, current distributions, and morphologies. Understanding the generation and maintenance of various +ring patterns in single cells can lead to a better understanding of network dynamics and behaviours.
166
F. Saraga, F.K. Skinner / Neurocomputing 44– 46 (2002) 161 – 166
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
A. Chikwendu, C.J. McBain, J. Neurophysiol. 76 (1996) 1477–1490. J. Du, et al., J. Neurosci. 16 (1996) 506–518. T.F. Freund, G. BuzsOaki, Hippocampus 6 (1996) 347–470. J.-C. Lacaille, et al., J. Neurosci. 7 (1987) 1979–1993. J.-C. Lacaille, S. Williams, Neurosci. 36 (1990) 349–359. J.E. Lisman, Trends Neurosci. 20 (1997) 38–43. C.J. McBain, A. Fisahn, Nature Rev. Neurosci. 2 (2001) 11–23. F. Morin, et al., J. Neurophysiol. 76 (1996) 1–16. P. Parra, et al., Neuron 20 (1998) 983–993. F. Saraga, F.K. Skinner, Neurosci., 2002, in press. F.K. Skinner, et al., J. Neurophysiol. 81 (1999) 1274–1283. C. Wu, et al., J. Physiol. (2002), in press. L. Zhang, C.J. McBain, J. Physiol. 488 (1995) 661–672. Y. Zhang, et al., J. Neurosci. 18 (1998) 9256–9268.