An imbalance between excitation and inhibition can play an important role in the generation of epileptiform activity. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties may contribute to this imbalance. The slow Ca2+ - activated K+ currents (sIAHP) limit neuronal firing rate and excitability and are therefore of great interest for their potential role in epileptogenesis. The sIAHP is found in both excitatory and inhibitory neurons, and its effect on these neurons can influence the network behavior. Simulations show that the increased excitability caused by reduction of inhibition by the sIAHP for inhibitory interneuron generates recurrent bursting activity

Bergey, Gregory K.

Franaszczuk, Piotr J.

Yang, Keun-Hang Susan

English

Chapman University Digital Commons

Chapman UniversityChapman University Digital CommonsMathematics, Physics, and Computer ScienceFaculty Articles and ResearchScience and Technology Faculty Articles andResearch2003The Influence of Slow Calcium-ActivatedPotassium Channels on Epileptiform Activity in aNeuronal Model of Pyramidal CellsKeun-Hang Susan YangChapman University, kyang@chapman.eduPiotr J. FranaszczukJohns Hopkins UniversityGregory K. BergeyJohns Hopkins UniversityFollow this and additional works at: http://digitalcommons.chapman.edu/scs_articlesPart of the Nervous System CommonsThis Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University DigitalCommons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorizedadministrator of Chapman University Digital Commons. For more information, please contact laughtin@chapman.edu.Recommended CitationYang, Keun-Hang, Piotr J. Franaszczuk, and Gregory K. Bergey. "The Influence of Slow Calcium-Activated Potassium Channels onEpileptiform Activity in a Neuronal Model of Pyramidal Cells." Computational Neuroscience Meeting (2003).The Influence of Slow Calcium-Activated Potassium Channels onEpileptiform Activity in a Neuronal Model of Pyramidal CellsCommentsThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in the proceedings forthe Computational Neuroscience Meeting in 2003.CopyrightTNBThis article is available at Chapman University Digital Commons: http://digitalcommons.chapman.edu/scs_articles/229The Influence of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Model of Pyramidal Cells    Keun-Hang Yang, Piotr J. Franaszczuk, and Gregory K. Bergey  Department of Neurology, Johns Hopkins Epilepsy Center, Johns Hopkins  University School of Medicine, Baltimore, Maryland    Abstract               An imbalance between excitation and inhibition can play an important role in the generation of epileptiform activity. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties may contribute to this imbalance. The slow Ca2+ - activated K+ currents (sIAHP) limit neuronal firing rate and excitability and are therefore of great interest for their potential role in epileptogenesis. The sIAHP is found in both excitatory and inhibitory neurons, and its effect on these neurons can influence the network behavior. Simulations show that the increased excitability caused by reduction of inhibition by the sIAHP for inhibitory interneuron generates recurrent bursting activity.                          Background and Significance  Neuronal hyperexcitability and epileptiform activity are associated with an imbalance between excitatory and inhibitory synaptic activity and/or alterations of neuronal intrinsic properties (Bernard et al., 2000; During et al., 1995; Olsen and Avoli, 1997; Treiman, 2001). GABAergic inhibition controls neuronal excitability in such a way that a change in GABAergic inhibition is thought to be important for many forms of human or experimental epilepsy (Bernard et al., 2000; Freund and Buzsáki, 1996; Prince, 1978; Treiman, 2001). There is evidence from in vitro experiments that reduced GABAergic inhibitory synaptic activity (Federico and MacVicar, 1996; McBain, 1994; Rodriguez-Moreno et al., 1997; Wong and Miles, 1994) or increased glutamatergic excitatory synaptic activity (Federicon and MacVicar, 1996; Johnston and Brown, 1981; Traub et al., 1993) leads to epileptiform activity. The array of potassium channels expressed by a neuron is a major factor in determining its excitability.  Studies of human epileptic hippocampus indicate that changes in the properties of some potassium channels may contribute to neuronal hyperexcitability and epileptogenesis (Beck et al., 1996; Biervert et al., 1998).  The slow Ca2+- activated K+ current (sIAHP) mediates the post-spike after hyperpolarization (AHP) that limits excitability of pyramidal neurons (Alger and Nicoll, 1980; Behr et al., 2000; Empson and Jefferys, 2001; Verma-Ajuja et al., 1995).  Alger and Nicoll (1980) suggested that the Ca2+- dependent K+ current is important in preventing the development of seizure-like activity.  In addition, Empson and Jefferys (2001) suggested that Ca2+ entry through L-type Ca2+ channels activates a K+ current that helps terminate epileptiform activity.    While the studies summarized above suggest that sIAHP controls the excitatory output of neuronal networks by altering intrinsic neuronal excitability, an unknown factor in these experiments is the role of interneurons.  Interneurons also control the excitatory output of networks by providing feedback inhibition onto excitatory neurons.  Interneurons, like pyramidal neurons, possess sIAHP (Zhang and McBain, 1995; McQuiston and Madison, 1999).  In contrast to pyramidal neurons, reducing sIAHP and thereby increasing excitability in inhibitory interneurons would be expected to reduce rather than enhance the overall excitability of the network.  When this added complexity is considered, it becomes less clear how various modulators may affect network behavior. Experiments employing simultaneous intracellular recordings of pyramidal neurons and interneurons to determine how changes in sIAHP may correlate with epileptogenesis would require a universally accepted model of epilepsy and the capability to perform complex data analysis.  This type of experiment may be modeled using a small network of pyramidal cells and an interconnected inhibitory interneuron. Using the computational approach will allow the simultaneous monitoring of individual neurons’ membrane behavior as well as the behavior of the entire network.  In addition, the individual conductance on each cell membrane can be modified and the resulting effect on network behavior tested. In this way, a carefully controlled study of the role of sIAHP and its modulation in epileptogenesis can be performed.  The results of this study may guide the design of biological experiments to verify where alterations or abnormal regulation of these important channels may occur in epilepsy, and may suggest key targets for therapeutic intervention.   Methods  We have built a circuit pyramidal cell model using the simulation software GENESIS (http://www.genesis-sim.org/GENESIS/). Three simplified pyramidal neurons and an interneuron later added are modeled in this study: two neurons synaptically connected with excitatory synapses forming a loop (neuron 1 and neuron 2 in Fig. 1), a neuron where random input is applied to generate action potentials (neuron 0 in Fig. 1), and an inhibitory interneuron (neuron 3 in Fig. 1) in a negative feedback loop with one of the modeled pyramidal neurons (neuron 2 in Fig. 1).  The generated action potentials stimulate one of the other neurons (neuron 1 in Fig. 1), which is connected to the other one (neuron 2 in Fig. 1) with an excitatory synapse as a recurrent loop. The synaptic inputs on each main dendrite of two pyramidal neurons are connected with an excitatory synapse (Fig. 1A).  An inhibitory interneuron (neuron 3 in Fig. 1) forms a negative feedback loop with one of the two pyramidal neurons (neuron 2 in Fig. 1). This inhibitory interneuron synapses on the main dendrites of neuron 2 (Fig. 1B).  Each pyramidal neuron with 17 compartments is comprised of a soma, a main dendrite, and two branch dendrites. The soma and dendrite have a fast sodium (INa), delayed potassium (IKDR), transient potassium (IA), high-threshold calcium (ICa), and slow calcium activated potassium (sIAHP) channels, and a short-duration voltage and calcium dependent potassium channel (IKC). The equations for these channels are the same as in the Traub et al. (1991, 1994) multicompartmental CA3 pyramidal cell model. In this model the soma, main, and branch dendrites have excitatory and inhibitory synaptic channels, which connect two neurons as a loop. The soma and dendrites have a fast GABAergic inhibitory synapse and a slow GABAergic inhibitory synapse. The kinetics of these fast and slow GABAergic components are the same as for GABAA inhibitory and GABAB inhibitory synapses, respectively, in a model of piriform cortex pyramidal cells (Protopapas et al., 1998). The inhibitory interneuron has a soma with the same channels as in the soma of two neurons synaptically connected with excitatory synapses. The soma, main, and branch dendrites have excitatory and inhibitory synaptic channels, which connect two neurons in a loop. The parameters for these excitatory and inhibitory synaptic conductance and cellular dimensions of the soma and dendrites are the same as in the reduced models of piriform cortex pyramidal cell in Protopapas et al. (1998).     Figure 1. Schematic representation of neural connections. A. Neuron 1 andneuron 2 are connected with an excitatory synapse as a loop. Synaptic inputsare on the main dendrite of these two neurons connected with an excitatorysynapse. B. An inhibitory interneuron in a negative feedback loop with themodeled pyramidal neuron 2 is added to the circuit in A. This inhibitoryinterneuron synapses on the main dendrite of neuron 2.  The synaptic connection between neurons is modeled by a synaptic channel, Isyn (Bhalla and Bower, 1993).  The synaptic conductance is modeled as an alpha function with the maximum value of 0.5 nS.  The synaptic weight represents the overall strength of a connection and the synaptic delay represents all delays between neurons. Simulations were performed for 10 sec using GENESIS version 2.2 on a LINUX operating system. The simulation time step is 0.05 ms, which is the same value as in the Traub et al. (1991, 1994) multicompartmental CA3 pyramidal cell model provided with GENESIS.  In order to examine the role of the sIAHP on bursting activity caused by the increased excitability, simulations were performed with different values of the maximum conductance of the sIAHP   for the inhibitory interneuron. The synaptic weight and delay of the excitatory neuron sufficient to generate bursting activity without the inhibitory interneuron were used. For the inhibitory interneuron, the synaptic weight and delay that completely block bursting activity were used. Then with these synaptic weight and delay of the excitatory neuron and inhibitory interneuron, simulations were run for different values of the maximum conductance of the sIAHP.     The maximum conductance of the sIAHP for the inhibitory interneuron, which synapses on the excitatory neuron in a negative feedback, was varied to investigate bursting activity caused by the increased excitability provided by reduced inhibition.   Results In previous studies, we have demonstrated that a simplified pyramidal neuron model can produce bursting activity by changing the synaptic connectivity represented by the synaptic weight and delay in a circuit pyramidal cell model with neuronal connections as illustrated in Fig. 1 (Yang et al., 2001 and 2002). Figure 2 shows that bursting activity can be generated without the inhibitory interneuron. Figure 3 shows that bursting activity can be completely blocked by the inhibitory interneuron. We chose the synaptic weight and delay of the excitatory neuron, which generate bursting activity without the inhibitory interneuron, shown in Fig. 2. The synaptic weight and delay of the inhibitory interneuron, which completely block bursting activity shown in Fig. 3, were also chosen for the further simulations. The present study with this circuit pyramidal cell model indicates that the sIAHP of the inhibitory interneuron regulates bursting activity. Figures 4 and 5 show that the increased activity of the sIAHP regenerates bursting activity. When the maximum conductance of the sIAHP for the inhibitory interneuron, which synapses on the main dendrite of the excitatory neuron 2, is increased from 35.0 nS to 52.5 nS (50 % increase) bursting activity is regenerated (Fig. 4). Duration of the burst is 1.03 sec. When the maximum conductance of the sIAHP for the inhibitory interneuron is increased to 70.0 nS (100% increase), recurrent bursting activity is also generated (Fig. 5). Duration of the burst is 1.23 sec, which is longer than in Fig. 4. The increased maximum conductance of the sIAHP for the inhibitory interneuron produces reduction of inhibition of the negative feedback that results in the increased neuronal excitability of the pyramidal neuron. Then this increased excitability regenerates epileptiform activity in the pyramidal neuron. The duration of the burst is increased as the maximum conductance of the sIAHP for the inhibitory interneuron increases.  In conclusion, simulations show that the slow Ca2+-activated K+ current (sIAHP) regulates bursting activity in pyramidal neurons. The increased excitability caused by reduction of the inhibition provided by the sIAHP for inhibitory interneuron generates recurrent bursting activity. The present study may provide the basis for future investigations into the cellular mechanisms of epilepsy.       A: The generated action potentials in neuron 0 in Fig. 1 from random inputs. B: Thepatterns of bursting activity in neuron 1 in Fig. 1. C: The patterns of bursting activity inneuron 2 in Fig. 1.            Figure 2. Traces of membrane potentials forall neurons. Bursting activity occurs inneuron 1 and neuron 2 when there is noinhibitory interneuron in the circuitpyramidal cell model (Fig. 1A). C. B. A. Vm (mV) Vm (mV) Vm (mV) Time (sec) C. B. A. Vm (mV) Vm (mV) Vm (mV) Time (sec) Figure 3. Traces of membrane potentials for allneurons. The excitatory synaptic weight and delay arethe same as in Fig. 2. When the inhibitory interneuronis added to the excitatory neuron, inhibition blocksbursting activity in neuron 1 and neuron 2 (Fig. 1B).          Vm (mV) Time (sec) Vm (mV) A. B. Vm (mV) C. Figure 4. Traces of membrane potentials for allneurons. When the maximum conductance of thesIAHP for the inhibitory interneuron is increasedfrom 35.0 nS to 52.5 nS (50 % increase) with thesame synaptic weight and delay of the excitatoryand inhibitory neurons as in Fig. 3, recurrentbursting activity is generated in neuron 1 andneuron 2. Duration of the burst is 1.03 sec.Vm (mV) Vm (mV) A. B. Vm (mV) C. Time (sec) Figure 5. Traces of membrane potentials for allneurons. When the maximum conductance of thesIAHP for the inhibitory interneuron is increasedfrom 35.0 nS to 70.0 nS (100 % increase) withthe same synaptic weight and delay of theexcitatory and inhibitory neurons as in Fig. 3,recurrent bursting activity is generated in neuron1 and neuron 2. Duration of the burst is 1.23 sec.References  B.E. Alger and R.A. Nicoll, Epileptiform burst afterhyperolarization: calcium-dependent potassium potential in hippocampal CA1 pyramidal cells. Science, 210(1980): 1122-4.  H. Beck, I. Blümcke, T. Kral, H. Clusmann, J. Schramm, O.D. Wiestler, and U. Heinemann, Properties of delayed rectifier potassium current in dentate granule cells from the hippocampus of patients with chronic temporal lobe epilepsy. Epilepsia, 37(1996): 892-901.  J. Behr, T. Gloveli, and U. Heinemann. Kindling induces a transient suppression of afterhyperpolarization in rat subicular neurons. Brain Res., 867(2000): 259-264.  C. Bernard, R. Cossart, J.C. Hirsch, M. Esclapez, Y. 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The Influence of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Model of Pyramidal Cells

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The Influence of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Model of Pyramidal Cells

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