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Simulation of rabbit A-type retinal horizontal cell that generates repetitive action potentials
Neuroscience Letters 439 (2008) 116–118
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Simulation of rabbit A-type retinal horizontal cell that generates repetitive action potentials Takaaki Shirahata ∗ Laboratory of Pharmaceutics, Faculty of Pharmaceutical Sciences at Kagawa Campus, Tokushima Bunri University, 1314-1 Shido, Sanuki, Kagawa 769-2193, Japan
a r t i c l e
i n f o
Article history: Received 9 February 2008 Received in revised form 11 April 2008 Accepted 26 April 2008 Keywords: Horizontal cell Repetitive action potentials Long-lasting depolarization Ionic current Simulation
a b s t r a c t Rabbit A-type retinal horizontal cells are classified into at least two types: cells that generate repetitive action potentials and those that do not. A mathematical model of these two types of cells based on the ionic current mechanisms has been proposed. Although the response of the former cell to 1-s positive current injection has so far been investigated by both electrophysiological and computational approaches, how this cell responds to much longer current injection has not been investigated. In the present study, I use this model to investigate the response of the former cell to a much longer current injection. Computer simulation indicates that when the stimulation period is relatively short, the membrane potential returns to the resting potential after current injection. In this case, the cell can repeatedly generate repetitive action potentials in response to stimulation. In contrast, when the stimulation period is relatively long, the membrane potential does not return to the resting potential but maintains the depolarized level even after current injection. In this case, the cell cannot repeatedly generate repetitive action potentials. When the present results were compared with those of the previous study, the difference in the response pattern after stimulation between the two types of horizontal cells was revealed. © 2008 Elsevier Ireland Ltd. All rights reserved.
Research on retinal horizontal cells has been carried out in both lower vertebrates and mammals, which suggests that mammalian horizontal cells are both structurally and functionally different from those of lower vertebrates [5,7]. Mammalian horizontal cells are morphologically classified into A- and B-type cells [3,4,8]. Electrophysiological studies indicate that rabbit A-type retinal horizontal cells are further classified into at least two types. One is a cell that generates repetitive action potentials in response to depolarizing current injection, and the other is a cell that does not generate repetitive action potentials but shows long-lasting depolarization [1,2]. In particular, the electrical properties and functional role of the former cell (the cell that generates repetitive action potentials) have attracted considerable attention [1,2]. Although voltage responses to 1-s depolarizing current injection have been investigated in the former cell [2], how this cell responds to depolarizing current injection longer than 1 s has not been investigated. It may be important to elucidate the response of this cell to longer depolarizing current injection in order to understand the electrical properties and functional role of this cell. A previous study has proposed a mathematical model of rabbit A-type retinal horizontal cell based on ionic current mechanisms
∗ Tel.: +81 87 894 5111x6508; fax: +81 87 894 0181. E-mail address: [email protected]. 0304-3940/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2008.04.087
[1]. Five types of ionic currents in the rabbit A-type retinal horizontal cell – sodium current (INa ), calcium current (ICa ), delayed rectifying potassium current (IKv ), transient outward potassium current (IA ), and anomalous rectifying potassium current (IKa ) – are described by Hodgkin–Huxley type equations based on voltage clamp experiments. This model reproduces the results of the electrophysiological experiments adequately. It is considered from their simulation that a cell that generates repetitive action potentials has comparatively large IKv conductance, and a cell that does not generate repetitive action potentials, but shows long-lasting depolarization, has comparatively small IKv conductance. The electrophysiological properties of the five types of ionic currents listed above are described in detail in the previous report [1] and summarized as follows. INa activates around −50 mV, reaches a peak at about −10 mV, and is decreased by depolarization greater than −10 mV. The current activates within a few milliseconds and completely inactivates in less than 10 ms. The current is blocked by tetrodotoxin (TTX). ICa is the sustained L-type calcium current, which is not suppressed by an accumulation of intracellular calcium. IKv slowly activates on depolarization by more than −35 mV, is blocked by tetraethylammonium (TEA), and is inactivated by a depolarizing holding potential. IA activates at depolarization of more than −40 mV, reaches a peak within a few milliseconds, and inactivates in less than a few hundred milliseconds. This current is inactivated by 4-aminopyridine (4-AP). IKa is activated by hyperpolarization below −80 mV, and shows anomalous (inward)
T. Shirahata / Neuroscience Letters 439 (2008) 116–118
rectification near the resting potential. The current is blocked by a solution with Cs or Ba. The previous study indicated that repetitive action potentials are generated by an interaction of ICa and IKv as follows [1]. A current injection depolarizes the membrane. The depolarization activates ICa , and an increase of ICa causes further depolarization. IKv is activated by the depolarization more slowly compared with ICa and hyperpolarizes the membrane, which results in a transient depolarizing response. After hyperpolarization, since the steady stimulus current induced the membrane depolarization, ICa is reactivated. ICa and IKv repeat this activation and inactivation during current injection, which generates repetitive action potentials. In the present study, I investigate the response of a horizontal cell that generates repetitive action potentials to longer depolarizing current injection by computer simulation based on a mathematical model proposed by Aoyama et al. [1]. The detail of modeling has been reported previously [1] and will be summarized briefly here. The membrane current I of a horizontal cell that generates repetitive action potentials is described as I = C dV/dt + Ii = C dV/dt + gi (V − Ei ) based on a parallel conductance model [6], where C is the membrane capacitance (nF), V is the membrane potential (mV), Ii is the ionic current (pA), gi is the conductance of the ionic current (nS), and Ei is the reversal potential (mV) of the current. The voltage-dependent ionic currents included in the model are INa , ICa , IKv , IA , and IKa . Each ionic current is described by a Hodgkin–Huxley type equation based on voltage clamp experiments. The model also includes leakage current. Details of the description of each ionic current have been described previously [1]. In the present study, differential equations are numerically solved using Scilab© INRIA-ENPC. The voltage responses of the rabbit A-type retinal horizontal cell to current injection for 1 s were simulated in a previous report [1]. I also obtained an identical simulated response, as illustrated in Fig. 1A. Fig. 1B–D illustrates the simulated responses to current injection for more than 1 s. When a current pulse was applied for a slightly longer period, the cell generated transient repetitive action
117
Fig. 1. The simulated voltage responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to depolarizing current injection. The stimulation period was 1 s (A), 4 s (B), 7 s (C), and 11 s (D). In all cases, the injections were started at time 0.1 s.
potentials but the membrane potential returned to the resting potential after stimulation (40 and 70 pA stimulation in Fig. 1B, and 70 pA stimulation in Fig. 1C). In contrast, in response to much longer stimulation, the cell generated transient repetitive action potentials followed by long-lasting depolarization even after stimulation (compare 25 pA stimulation in Fig. 1B–D with 25 pA stimulation in Fig. 1A; 40 pA stimulation in Fig. 1C and D with 40 pA stimulation in Fig. 1A and B; 70 pA stimulation in Fig. 1D with 70 pA stimu-
Fig. 2. The simulated ionic current responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to depolarizing 40 pA current injection. The voltage responses are also indicated at the top. The stimulation period was 4 s (A) and 7 s (B). In all cases, the injections were started at time 0.1 s.
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T. Shirahata / Neuroscience Letters 439 (2008) 116–118
Fig. 3. The simulated voltage responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to repeated depolarizing 40 pA current injections. The current was injected from 0.1 to 4.1 s and from 9.1 to 13.1 s (A); from 0.1 to 7.1 s and from 12.1 to 19.1 s (B).
lation in Fig. 1A–C). Fig. 1 also indicates that when the intensity of a current pulse decreased (70 pA → 40 pA → 25 pA), the period of stimulation necessary for generation of long-lasting depolarization shortened. Fig. 2 illustrates the ionic current responses to 40 pA current injection. In response to longer stimulation (Fig. 2B), activation of ICa , IKv , and IA lasted even after stimulation, which contributed to long-lasting depolarization. In contrast, in response to shorter stimulation (Fig. 2A), these three currents became inactivated after stimulation, which led to the membrane potential returning to the resting potential after stimulation. Fig. 3 shows the voltage responses to repetitive current injection. When the first stimulation was relatively short (4 s) and long-lasting depolarization did not appear, repetitive action potentials appeared in response to the second stimulation. In contrast, when the first stimulation was relatively long (7 s), once long-lasting depolarization appeared, repetitive action potentials did not appear in response to the second stimulation. The following electrical properties of a horizontal cell that generates repetitive action potentials were clarified from the present study. Repetitive action potentials generated in this cell were transient. When the stimulation period was relatively short, the membrane potential returned to the resting potential after current injection. In this case, the cell can repeatedly generate repetitive action potentials in response to stimulation. In contrast, when the stimulation period was relatively long, the membrane potential did not return to the resting potential but maintained the depolarized level even after current injection. In this case, the cell cannot repeatedly generate repetitive action potentials. Three ionic currents, ICa , IKv , and IA , played an important role in these electrical behaviors. After stimulation, activation of neither INa nor IKa was
observed irrespective of whether or not long-lasting depolarization appeared. In contrast, although ICa , IKv , and IA became inactivated after stimulation when long-lasting depolarization did not appear, activation of these three currents continued after stimulation when long-lasting depolarization appeared. Therefore, long-lasting depolarization after stimulation depends on the balance of sustained activation of ICa , IKv , and IA . As the intensity of injected current decreased, long-lasting depolarization occurred because of the shorter period of stimulation. The previous study indicated that a horizontal cell with comparatively small IKv conductance shows long-lasting depolarization even after stimulation once the membrane potential becomes positive in response to depolarizing current injection [1]. In contrast, as described above, whether a horizontal cell that generates repetitive action potentials (a cell with comparatively large IKv conductance) shows long-lasting depolarization after stimulation is greatly influenced by the stimulation condition even if the membrane potential becomes positive. The interesting point is that the present study, through comparison with the previous one [1], clarified this difference in the response pattern after stimulation between the two types of cells. Horizontal cells are depolarized in the dark by the glutamate release from photoreceptors [9]. Therefore, it might be possible that the cell that generates repetitive action potentials plays an important role in responding repeatedly to the dark under certain limited conditions. Although the present study predicts the new dynamics of a horizontal cell that generates repetitive action potentials, it is important to clarify in the future whether or not this dynamics can be verified experimentally. References [1] T. Aoyama, Y. Kamiyama, S. Usui, R. Blanco, C.F. Vaquero, R. de la Villa, Ionic current model of rabbit retinal horizontal cell, Neurosci. Res. 37 (2000) 141–151. [2] R. Blanco, C.F. Vaquero, R. de la Villa, Action potentials in axonless horizontal cells isolated from the rabbit retina, Neurosci. Lett. 203 (1996) 57–60. [3] S.A. Bloomfield, R.F. Miller, A physiological and morphological study of the horizontal cell types of the rabbit retina, J. Comp. Neurol. 208 (1982) 288–303. ¨ [4] B.B. Boycott, L. Peichl, H. Wassle, Morphological types of horizontal cell in the retina of the domestic cat, Proc. R. Soc. B (Lond.) 203 (1978) 229–245. [5] D.M. Dacey, B.B. Lee, D.K. Stafford, J. Pokorny, V.C. Smith, Horizontal cells of the primate retina: cone specificity without spectral opponency, Science 271 (1996) 656–659. [6] D. Johnston, S.M. Wu, Foundations of Cellular Neurophysiology, MIT Press, Cambridge, MA, 1995, pp. 143–181. [7] A. Kaneko, The functional role of retinal horizontal cells, Jpn. J. Physiol. 37 (1987) 341–358. [8] H. Kolb, The connections between horizontal cells and photoreceptors in the retina of the cat: electron microscopy of Golgi preparations, J. Comp. Neurol. 6 (1974) 131–153. [9] S.C. Massey, Cell types using glutamate as a neurotransmitter in the vertebrate retina, in: N. Osborne, G. Chader (Eds.), Progress in Retinal Research, vol. 9, Pergamon Press, Oxford, 1990, pp. 399–425.
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Simulation of rabbit A-type retinal horizontal cell that generates repetitive action potentials Takaaki Shirahata ∗ Laboratory of Pharmaceutics, Faculty of Pharmaceutical Sciences at Kagawa Campus, Tokushima Bunri University, 1314-1 Shido, Sanuki, Kagawa 769-2193, Japan
a r t i c l e
i n f o
Article history: Received 9 February 2008 Received in revised form 11 April 2008 Accepted 26 April 2008 Keywords: Horizontal cell Repetitive action potentials Long-lasting depolarization Ionic current Simulation
a b s t r a c t Rabbit A-type retinal horizontal cells are classified into at least two types: cells that generate repetitive action potentials and those that do not. A mathematical model of these two types of cells based on the ionic current mechanisms has been proposed. Although the response of the former cell to 1-s positive current injection has so far been investigated by both electrophysiological and computational approaches, how this cell responds to much longer current injection has not been investigated. In the present study, I use this model to investigate the response of the former cell to a much longer current injection. Computer simulation indicates that when the stimulation period is relatively short, the membrane potential returns to the resting potential after current injection. In this case, the cell can repeatedly generate repetitive action potentials in response to stimulation. In contrast, when the stimulation period is relatively long, the membrane potential does not return to the resting potential but maintains the depolarized level even after current injection. In this case, the cell cannot repeatedly generate repetitive action potentials. When the present results were compared with those of the previous study, the difference in the response pattern after stimulation between the two types of horizontal cells was revealed. © 2008 Elsevier Ireland Ltd. All rights reserved.
Research on retinal horizontal cells has been carried out in both lower vertebrates and mammals, which suggests that mammalian horizontal cells are both structurally and functionally different from those of lower vertebrates [5,7]. Mammalian horizontal cells are morphologically classified into A- and B-type cells [3,4,8]. Electrophysiological studies indicate that rabbit A-type retinal horizontal cells are further classified into at least two types. One is a cell that generates repetitive action potentials in response to depolarizing current injection, and the other is a cell that does not generate repetitive action potentials but shows long-lasting depolarization [1,2]. In particular, the electrical properties and functional role of the former cell (the cell that generates repetitive action potentials) have attracted considerable attention [1,2]. Although voltage responses to 1-s depolarizing current injection have been investigated in the former cell [2], how this cell responds to depolarizing current injection longer than 1 s has not been investigated. It may be important to elucidate the response of this cell to longer depolarizing current injection in order to understand the electrical properties and functional role of this cell. A previous study has proposed a mathematical model of rabbit A-type retinal horizontal cell based on ionic current mechanisms
∗ Tel.: +81 87 894 5111x6508; fax: +81 87 894 0181. E-mail address: [email protected]. 0304-3940/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2008.04.087
[1]. Five types of ionic currents in the rabbit A-type retinal horizontal cell – sodium current (INa ), calcium current (ICa ), delayed rectifying potassium current (IKv ), transient outward potassium current (IA ), and anomalous rectifying potassium current (IKa ) – are described by Hodgkin–Huxley type equations based on voltage clamp experiments. This model reproduces the results of the electrophysiological experiments adequately. It is considered from their simulation that a cell that generates repetitive action potentials has comparatively large IKv conductance, and a cell that does not generate repetitive action potentials, but shows long-lasting depolarization, has comparatively small IKv conductance. The electrophysiological properties of the five types of ionic currents listed above are described in detail in the previous report [1] and summarized as follows. INa activates around −50 mV, reaches a peak at about −10 mV, and is decreased by depolarization greater than −10 mV. The current activates within a few milliseconds and completely inactivates in less than 10 ms. The current is blocked by tetrodotoxin (TTX). ICa is the sustained L-type calcium current, which is not suppressed by an accumulation of intracellular calcium. IKv slowly activates on depolarization by more than −35 mV, is blocked by tetraethylammonium (TEA), and is inactivated by a depolarizing holding potential. IA activates at depolarization of more than −40 mV, reaches a peak within a few milliseconds, and inactivates in less than a few hundred milliseconds. This current is inactivated by 4-aminopyridine (4-AP). IKa is activated by hyperpolarization below −80 mV, and shows anomalous (inward)
T. Shirahata / Neuroscience Letters 439 (2008) 116–118
rectification near the resting potential. The current is blocked by a solution with Cs or Ba. The previous study indicated that repetitive action potentials are generated by an interaction of ICa and IKv as follows [1]. A current injection depolarizes the membrane. The depolarization activates ICa , and an increase of ICa causes further depolarization. IKv is activated by the depolarization more slowly compared with ICa and hyperpolarizes the membrane, which results in a transient depolarizing response. After hyperpolarization, since the steady stimulus current induced the membrane depolarization, ICa is reactivated. ICa and IKv repeat this activation and inactivation during current injection, which generates repetitive action potentials. In the present study, I investigate the response of a horizontal cell that generates repetitive action potentials to longer depolarizing current injection by computer simulation based on a mathematical model proposed by Aoyama et al. [1]. The detail of modeling has been reported previously [1] and will be summarized briefly here. The membrane current I of a horizontal cell that generates repetitive action potentials is described as I = C dV/dt + Ii = C dV/dt + gi (V − Ei ) based on a parallel conductance model [6], where C is the membrane capacitance (nF), V is the membrane potential (mV), Ii is the ionic current (pA), gi is the conductance of the ionic current (nS), and Ei is the reversal potential (mV) of the current. The voltage-dependent ionic currents included in the model are INa , ICa , IKv , IA , and IKa . Each ionic current is described by a Hodgkin–Huxley type equation based on voltage clamp experiments. The model also includes leakage current. Details of the description of each ionic current have been described previously [1]. In the present study, differential equations are numerically solved using Scilab© INRIA-ENPC. The voltage responses of the rabbit A-type retinal horizontal cell to current injection for 1 s were simulated in a previous report [1]. I also obtained an identical simulated response, as illustrated in Fig. 1A. Fig. 1B–D illustrates the simulated responses to current injection for more than 1 s. When a current pulse was applied for a slightly longer period, the cell generated transient repetitive action
117
Fig. 1. The simulated voltage responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to depolarizing current injection. The stimulation period was 1 s (A), 4 s (B), 7 s (C), and 11 s (D). In all cases, the injections were started at time 0.1 s.
potentials but the membrane potential returned to the resting potential after stimulation (40 and 70 pA stimulation in Fig. 1B, and 70 pA stimulation in Fig. 1C). In contrast, in response to much longer stimulation, the cell generated transient repetitive action potentials followed by long-lasting depolarization even after stimulation (compare 25 pA stimulation in Fig. 1B–D with 25 pA stimulation in Fig. 1A; 40 pA stimulation in Fig. 1C and D with 40 pA stimulation in Fig. 1A and B; 70 pA stimulation in Fig. 1D with 70 pA stimu-
Fig. 2. The simulated ionic current responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to depolarizing 40 pA current injection. The voltage responses are also indicated at the top. The stimulation period was 4 s (A) and 7 s (B). In all cases, the injections were started at time 0.1 s.
118
T. Shirahata / Neuroscience Letters 439 (2008) 116–118
Fig. 3. The simulated voltage responses of the rabbit A-type retinal horizontal cell that generates repetitive action potentials to repeated depolarizing 40 pA current injections. The current was injected from 0.1 to 4.1 s and from 9.1 to 13.1 s (A); from 0.1 to 7.1 s and from 12.1 to 19.1 s (B).
lation in Fig. 1A–C). Fig. 1 also indicates that when the intensity of a current pulse decreased (70 pA → 40 pA → 25 pA), the period of stimulation necessary for generation of long-lasting depolarization shortened. Fig. 2 illustrates the ionic current responses to 40 pA current injection. In response to longer stimulation (Fig. 2B), activation of ICa , IKv , and IA lasted even after stimulation, which contributed to long-lasting depolarization. In contrast, in response to shorter stimulation (Fig. 2A), these three currents became inactivated after stimulation, which led to the membrane potential returning to the resting potential after stimulation. Fig. 3 shows the voltage responses to repetitive current injection. When the first stimulation was relatively short (4 s) and long-lasting depolarization did not appear, repetitive action potentials appeared in response to the second stimulation. In contrast, when the first stimulation was relatively long (7 s), once long-lasting depolarization appeared, repetitive action potentials did not appear in response to the second stimulation. The following electrical properties of a horizontal cell that generates repetitive action potentials were clarified from the present study. Repetitive action potentials generated in this cell were transient. When the stimulation period was relatively short, the membrane potential returned to the resting potential after current injection. In this case, the cell can repeatedly generate repetitive action potentials in response to stimulation. In contrast, when the stimulation period was relatively long, the membrane potential did not return to the resting potential but maintained the depolarized level even after current injection. In this case, the cell cannot repeatedly generate repetitive action potentials. Three ionic currents, ICa , IKv , and IA , played an important role in these electrical behaviors. After stimulation, activation of neither INa nor IKa was
observed irrespective of whether or not long-lasting depolarization appeared. In contrast, although ICa , IKv , and IA became inactivated after stimulation when long-lasting depolarization did not appear, activation of these three currents continued after stimulation when long-lasting depolarization appeared. Therefore, long-lasting depolarization after stimulation depends on the balance of sustained activation of ICa , IKv , and IA . As the intensity of injected current decreased, long-lasting depolarization occurred because of the shorter period of stimulation. The previous study indicated that a horizontal cell with comparatively small IKv conductance shows long-lasting depolarization even after stimulation once the membrane potential becomes positive in response to depolarizing current injection [1]. In contrast, as described above, whether a horizontal cell that generates repetitive action potentials (a cell with comparatively large IKv conductance) shows long-lasting depolarization after stimulation is greatly influenced by the stimulation condition even if the membrane potential becomes positive. The interesting point is that the present study, through comparison with the previous one [1], clarified this difference in the response pattern after stimulation between the two types of cells. Horizontal cells are depolarized in the dark by the glutamate release from photoreceptors [9]. Therefore, it might be possible that the cell that generates repetitive action potentials plays an important role in responding repeatedly to the dark under certain limited conditions. Although the present study predicts the new dynamics of a horizontal cell that generates repetitive action potentials, it is important to clarify in the future whether or not this dynamics can be verified experimentally. References [1] T. Aoyama, Y. Kamiyama, S. Usui, R. Blanco, C.F. Vaquero, R. de la Villa, Ionic current model of rabbit retinal horizontal cell, Neurosci. Res. 37 (2000) 141–151. [2] R. Blanco, C.F. Vaquero, R. de la Villa, Action potentials in axonless horizontal cells isolated from the rabbit retina, Neurosci. Lett. 203 (1996) 57–60. [3] S.A. Bloomfield, R.F. Miller, A physiological and morphological study of the horizontal cell types of the rabbit retina, J. Comp. Neurol. 208 (1982) 288–303. ¨ [4] B.B. Boycott, L. Peichl, H. Wassle, Morphological types of horizontal cell in the retina of the domestic cat, Proc. R. Soc. B (Lond.) 203 (1978) 229–245. [5] D.M. Dacey, B.B. Lee, D.K. Stafford, J. Pokorny, V.C. Smith, Horizontal cells of the primate retina: cone specificity without spectral opponency, Science 271 (1996) 656–659. [6] D. Johnston, S.M. Wu, Foundations of Cellular Neurophysiology, MIT Press, Cambridge, MA, 1995, pp. 143–181. [7] A. Kaneko, The functional role of retinal horizontal cells, Jpn. J. Physiol. 37 (1987) 341–358. [8] H. Kolb, The connections between horizontal cells and photoreceptors in the retina of the cat: electron microscopy of Golgi preparations, J. Comp. Neurol. 6 (1974) 131–153. [9] S.C. Massey, Cell types using glutamate as a neurotransmitter in the vertebrate retina, in: N. Osborne, G. Chader (Eds.), Progress in Retinal Research, vol. 9, Pergamon Press, Oxford, 1990, pp. 399–425.