Computational Model of the Serotonergic Modulation of Sensory Neurons in Aplysia

Douglas A. Baxter,1 Carmen C. Canavier,1 John W. Clark, Jr.,2 and John H. Byrne1

 1Laboratories of Origin, Department of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas-Houston Medical School, Houston, 77225; and  2Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Baxter, Douglas A., Carmen C. Canavier, John W. Clark Jr., and John H. Byrne. Computational Model of the Serotonergic Modulation of Sensory Neurons in Aplysia. J. Neurophysiol. 82: 2914-2935, 1999. Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is a useful model system for studies of neuronal plasticity that contributes to learning and memory. The effects of serotonin (5-HT) are mediated, in part, via two protein kinases (protein kinase A, PKA, and protein kinase C, PKC), which in turn, modulate at least four membrane currents, including a S ("serotonin-sensitive") K+ current (IK,S), a steeply voltage-dependent K+ current (IK-V), a slow component of the Ca2+-activated K+ current (IK,Ca-S), and a L-type Ca2+ current (ICa-L). The present study investigated how the modulation of these currents altered the spike duration and excitability of sensory neurons and examined the relative contributions of PKA- and PKC-mediated effects to the actions of 5-HT. A Hodgkin-Huxley type model was developed that described the ionic conductances in the somata of sensory neurons. The descriptions of these currents and their modulation were based largely on voltage-clamp data from sensory neurons. Simulations were preformed with the program SNNAP (Simulator for Neural Networks and Action Potentials). The model was sufficient to replicate empirical data that describes the membrane currents, action potential waveform and excitability as well as their modulation by application of 5-HT, increased levels of adenosine cyclic monophosphate or application of active phorbol esters. In the model, modulation of IK-V by PKC played a dominate role in 5-HT-induced spike broadening, whereas the concurrent modulation of IK,S and IK,Ca-S by PKA primarily accounted for 5-HT-induced increases in excitability. Finally, simulations indicated that a PKC-induced increase in excitability resulted from decreases of IK,S and IK,Ca-S, which was likely the indirect result of cross-talk between the PKC and PKA systems. The results provide several predictions that warrant additional experimental investigation and illustrate the importance of considering indirect as well as direct effects of modulatory agents on the modulation of membrane currents.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

By changing the waveform of action potentials and excitability, serotonin (5-HT)-induced modulation of membrane currents in the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is believed to be a key mechanism underlying short-term heterosynaptic facilitation (for recent review, see Byrne and Kandel 1996). The first-discovered "serotonin-sensitive" current was a novel K+ current that was termed the S current (IK,S) (Klein et al. 1982). Acting via elevated levels of intracellular adenosine cyclic monophosphate (cAMP) and the subsequent activation of protein kinase A (PKA), application of 5-HT decreased the magnitude of IK,S (Fig. 1A) (Baxter and Byrne 1990a; Bernier et al. 1982; Jarrard et al. 1993; Ocorr and Byrne 1985; Pollock and Camardo 1987; Pollock et al. 1985; Shuster and Siegelbaum 1987; Shuster et al. 1985; Siegelbaum et al. 1982; Sugita et al. 1997a; Walsh and Byrne 1989). Because 5-HT produced a broadening of the action potential and enhanced the excitability of sensory neurons, both of these changes originally were attributed to the reduction of IK,S (e.g., Klein et al. 1986). It has become clear, however, that the mechanisms underlying the 5-HT-induced changes in the biophysical properties of sensory neurons are more complicated than the activation of a single second-messenger/protein kinase system and the modulation of a single K+ current.



View larger version (25K):
[in this window]
[in a new window]
 
Fig. 1. Serotonergic modulation of sensory neurons. A: early view of serotonergic modulation. In this scheme, adenosine cyclic monophosphate (cAMP) and protein kinase A (PKA) are the only second messenger/kinase system activated by serotonin (5-HT). PKA-mediated reduction of a S-type K+ channel conductivity, gK,S, is considered to underlie the modulation of 2 physiological properties of the sensory neuron: spike broadening and enhanced excitability. B: current view of serotonergic modulation. Serotonin binds to >= 2 distinct receptors, which in turn lead to the activation of >= 2 kinases, PKA and protein kinase C (PKC). These kinases modulate a host of membrane conductances. There is overlap between the 2 kinases and their targets as well as cross-talk between the 2 second-messenger/kinase systems. +, enhancement or positive regulation; -, decrease or negative regulation. See text for additional details.

Several additional components contribute to 5-HT-induced modulation of action potentials and excitability of sensory neurons (Fig. 1B). First, elevated levels of cAMP modulate at least three currents in addition to IK,S. Walsh and Byrne (1989) described a slow component of the Ca2+-activated K+ current (IK,Ca-S) that was active near the resting potential of the cell and that was decreased by intracellular injection of cAMP (or application of 5-HT). Braha et al. (1993; see also Edmonds et al. 1990; Eliot et al. 1993) reported that intracellular injection of cAMP (or application of 5-HT) enhanced a dihydropyridine-sensitive and slowly inactivating component of the Ca2+ current similar to the L-type Ca2+ current (ICa-L). Baxter and Byrne (1989; see also White et al. 1994) reported that application of 5-HT decreased the conductance and slowed the kinetics of a large, steeply voltage-dependent K+ current (IK-V). Goldsmith and Abrams (1992) reported that application of analogues of cAMP partially mimicked the 5-HT-induced slowing of the activation kinetics of IK-V. Similarly, Hochner and Kandel (1992) reported that specific blockers of PKA partially blocked the 5-HT-induced slowing of the activation kinetics of IK-V. These results indicate that the 5-HT-induced modulation of IK-V is mediated, at least in part, by the cAMP/PKA system. Moreover, studies of Goldsmith and Abrams (1992; see also Shuster et al. 1991) suggested that the originally described IK,S consisted of two components, a moderately voltage-dependent and slowly-activating component (IK,S-V), and an instantaneous (i.e., time-independent) "steady-state" component that was activated at the resting potential (IK,S-I). Thus 5-HT-induced increases in the levels of cAMP can lead to the modulation of a complex array of membrane currents with diverse biophysical properties.

Second, in addition to the cAMP/PKA system, application of 5-HT activates protein kinase C (PKC) (Sossin 1997; Sossin and Schwartz 1992; Sossin et al. 1994; see also Sacktor and Schwartz 1990).1 Moreover, pharmacological activation of PKC [i.e., application of active phorbol esters such as 4beta -12-deoxyphorbol 13-isobutyrate (DPB), 4beta -phorbol 12,13-diacetate (PDAc), phorbol dibutyrate (PDBu), phorbol myristate (PMA)] mimics some aspects of 5-HT-induced modulation of membrane currents. Braha et al. (1993) reported that activation of PKC mimicked the 5-HT-induced increase of ICa-L and that blockers of PKC blocked 5-HT-induced modulation of ICa-L. Sugita et al. (1994a) found that activation of PKC mimicked and partially occluded the 5-HT-induced modulation of IK-V.2 Thus 5-HT-induced modulation of membrane current appears to involve at least two kinase systems (i.e., PKA and PKC) that act on an array of membrane conductances.

Third, recent studies indicate that there is cross-talk between the PKC and PKA cascades. Sugita et al. (1997a) reported that activation of PKC induced an increase in the level of cAMP in sensory neurons. It is likely that the PKC-induced increase in cAMP leads to activation of PKA and subsequent PKA-mediated modulation of membrane currents. For example, activators of PKC induced a modest increase in the excitability of sensory neurons, thereby partially mimicking a well know cAMP effect (Sugita et al. 1997a; see also Baxter and Byrne 1990a; Manseau et al. 1998). In contrast, biochemical evidence indicates that translocation of PKC was not induced by analogues of cAMP (Sacktor and Schwartz 1990). These results suggest that some of the biophysical effects that have been attributed directly to the PKC cascade may be indirect effects that result from cross-talk between the PKC and PKA cascades.

Because of overlapping responses to electrical and pharmacological stimulation and because of cross-talk between second messenger/protein kinase cascades, it is difficult to accurately assess the how the modulation of specific membrane currents (i.e., IK,S, IK-V, IK,Ca-S, ICa-L) or how the PKA- versus PKC-mediated modulation of membrane currents contribute to 5-HT-induced spike broadening and excitability enhancement. The present study addresses these issues by developing and analyzing a Hodgkin-Huxley-type mathematical model of the sensory neuron. First, previously published voltage-clamp data were used to develop mathematical descriptions of the ionic conductances in the somata of sensory neurons. Second, simulations investigated whether the known modulatory actions of 5-HT on membrane currents are sufficient to account for the empirically observed increases in spike duration and excitability. Third, simulations investigated the relative contributions of individual currents to the overall effects of 5-HT. Fourth, simulations investigated the consequences of cross-talk between the PKC and PKA cascades. Finally, an empirical study was conducted to test the predicted contribution of IK,Ca-S to accommodation. The results indicated that the model was sufficient to simulate the basic features of action potential and excitability data from sensory neurons; concurrent modulation of IK,S and IK,Ca-S contributed significantly to 5-HT-induced increases in excitability; and modulation of IK-V contributed significantly to 5-HT-induced spike broadening. The simulations also provided several predictions that can help guide future experimental analysis, and the results illustrate that the actions of modulatory agents and second messengers cannot be understood on the basis of their direct effects alone. It is also necessary to consider indirect effects that occur through cross-talk between second-messenger systems and Ca2+-dependent processes.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Model development

GENERAL FEATURES. The simulations were performed with SNNAP (Simulator for Neural Networks and Action Potentials) (Ziv et al. 1994). Version 5 of SNNAP was used and the software was run under the Windows 95/NT operating systems on PC-type microcomputers (Baxter and Byrne 1999). The Euler method with a fixed time step of 30-µs was used for numerical integration. When simulations were begun, there typically was a small (<500 µV), brief (~1 s) transient before the resting membrane potential settled to its steady-state value (-50 mV). To avoid analysis during this or any other transient, >= 10 s of simulated time was allowed to elapse before data were taken.

The soma of a sensory neuron was modeled as a sphere 20 µm in diameter that had a surface area of 1.2 × 104 µm2. This surface area included a factor of 10 to account for membrane invagination (Gorman and Mirolli 1972; Mirolli and Talbott 1972). In the present study, we assumed the axon did not make a significantly contribution to the biophysical properties of the sensory neuron or to their responses to 5-HT. This assumption was based, in part, on previously published studies of action potentials, excitability, and their modulation by 5-HT in isolated somata and in ganglia preparations (cf. Sugita et al. 1992, 1997). Apparently identical results have obtained in both types of preparation. The model consisted of a membrane model represented by an equivalent circuit (Fig. 2A) coupled to equations that describe the regulation of intracellular Ca2+ (Fig. 2B). The membrane model was composed of a membrane capacitance (CM), which was assumed to be 1 µF/cm2 (Almers 1978), in parallel with three inward currents (1 Na+ and 2 Ca2+ currents), six K+ currents, and a leak current. The ionic currents in the model were described by Hodgkin-Huxley-type equations in which generalized Boltzman-type equations defined the voltage- and time-dependent activation and inactivation of conductances. In addition, the descriptions of four conductances (the 2 Ca2+ conductances and 2 of the K+ conductances) were expanded to include Ca2+-dependent regulation (e.g., Ca2+-dependent inactivation and activation, respectively; Fig. 2B). The details of the equations and parameters are given in the APPENDIX and Table 1.



View larger version (39K):
[in this window]
[in a new window]
 
Fig. 2. Model of a sensory neuron. A: equivalent electrical circuit of the cell membrane. Linear conductances are indicated by resistors and nonlinear (i.e., voltage-gated) conductances are indicated by variable resistors. Each conductance is associated with a equilibrium potential (E). In parallel with the membrane capacitance (CM) are 10 ionic conductances: a leakage conductance (gL); a fast Na+ conductance (gNa); a slowly inactivating L-type Ca2+ conductance (gCa-L); a rapidly inactivating N-type Ca2+ conductance (gCa-N); a fast transient A-type K+ conductance (gK-A); a fast voltage- and Ca2+-activated K+ conductance (gK,Ca-F); a slow voltage-independent Ca2+-activated K+ conductance (gK,Ca-S); an instantaneous, modestly voltage-dependent component of the S ("serotonin")-type K+ conductance (gK,S-I); a voltage- and time-dependent component of the S-type K+ conductance (gK,S-V); and a delayed, steeply voltage-dependent K+ conductance (gK-V). The application of extrinsic stimulating and/or bias currents is represented by IStim. B: intracellular regulatory pathways of the model. Model also incorporated a description of an intracellular pool of Ca2+. Calcium influx via gCa-L and gCa-N contributed to the Ca2+ pool. Dynamics of the Ca2+ pool were modeled as a first-order process. The intracellular pool of Ca2+, in turn, regulated several membrane conductances. Both gCa-L and gCa-N were regulated negatively by [Ca2+] (i.e., Ca2+-dependent inactivation), and both gK,Ca-S and gK,Ca-F were activated (i.e., positively regulated) by [Ca2+]. Although not explicitly modeled as biochemical components, the regulatory relationships of PKC and PKA are illustrated. See text for details. +, enhancement or positive regulation; -, decrease or negative regulation.


                              
View this table:
[in this window]
[in a new window]
 
Table 1. Parameters describing membrane currents in control conditions

Whenever possible, previously published voltage-clamp data from sensory neurons were used to formulate the descriptions of the currents. These data have been collected from sensory neurons in both abdominal and pleural ganglia. In the present study, these two sets of sensory neurons were assumed to have identical biophysical properties and responses to 5-HT. This assumption was based, in part, on the work of Wright and Kirschman (1995), who made direct comparisons of the firing properties and effects of 5-HT on siphon versus tail sensory neurons. They concluded that the properties and responses to 5-HT of these two classes of sensory neurons were indistinguishable. Thus we (and others) generally have considered these two sets of sensory neurons to be experimentally interchangeable. Voltage-clamp data that illustrate the voltage- and time-dependent characteristics are available for many of the membrane currents, including the L- and N-type Ca2+ currents (ICa-L, ICa-N, respectively) (Braha et al. 1993; Edmonds et al. 1990; Eliot et al. 1993), a transient A-type K+ current (IK-A) (Baxter and Byrne 1989, 1990b), a steeply voltage-dependent K+ current (IK-V) (Baxter and Byrne 1989, 1990b; Goldsmith and Abrams 1992; Hochner and Kandel 1992; White et al. 1994), a fast component of the Ca2+-activated K+ current (IK,Ca-F) (Baxter and Byrne 1989; Critz and Byrne 1992; Walsh and Byrne 1989; see also Shuster et al. 1991), and a time- and voltage-dependent component of the S-type K+ current (IK,S-V) (Baxter and Byrne 1989, 1990a,b; Braha et al. 1993; Hochner and Kandel 1992; Klein et al. 1982; Pollock et al. 1985; Sugita et al. 1994a; Walsh and Byrne 1989). In general, the methods used to develop mathematical descriptions of these current followed those of Byrne (1980a,b) and White et al. (1994). Briefly, published voltage-clamp records were digitized with a commercially available software packages (SigmaScanPro; SPSS, Chicago, IL), nonlinear parameter estimation (SigmaPlot) was performed on the digitized data at each potential, and a Hodgkin-Huxley type description of each current was formulated that was consistent with the parameters derived from the voltage-clamp traces. The model was developed to simulate the properties of sensory neurons at 15°C. Thus when necessary, conductances and time constants that were derived from empirical data were scaled to 15°C using a Q10 of 2 (Adams and Gage 1979b; Andresen and Brown 1979; Gorman and Marmor 1970, Johnston 1980; Joyner 1981; Partidge and Connor 1978; Romey et al. 1980; Thompson et al. 1986; see also Sah et al. 1988; Thompson et al. 1985). In the present study, the parameters for IK-V were adjusted to duplicate a previous empirical-based model of IK-V (White et al. 1994). Results from patch-clamp studies indicated that the channels mediating IK,S-I have a modest voltage dependency, a low probability of being open (P < 0.1) and a single-channel conductance of ~50 pS (Brezina et al. 1987; Pollock and Camardo 1987; Shuster et al. 1991; Siegelbaum et al. 1982, 1986; see also Goldsmith and Abrams 1992). The conductance for IK,S-I was calculated assuming an average of 0.02 pores were open per square µm [i.e., gK,S-I = (0.02 × 50 pS/µm2) × 1.2 × 104 µm2 = 0.012 µS; see Table 1] and the voltage dependency of IK,S-I was matched to that of single-channel currents. Finally, the leakage conductance was set to produce a input resistance of 27 MOmega , which was based on empirical data (see RESULTS). In the present model, 61% of the outward current that flowed at the resting membrane potential was carried by gK,S-I, 25% was carried by gK,S-V and 10% was carried by carried by gK,Ca-S.3

Other aspects of the model were less constrained by available data. First, the Na+ current (INa) in sensory neurons has not been characterized. Na+ currents have been characterized in other neurons of Aplysia, however (Adams and Gage 1979a; Byrne 1980a,b; Farquharson and Jahan-Parwar 1984; Fieber 1995; Gilly et al. 1997; see also Canavier et al. 1991). Thus a Hodgkin-Huxley-type description of INa for the present sensory neuron model was formulated that was consistent with INa in these other cells. The parameters for INa in the present sensory neuron model were adjusted, within limits set by the published examples of INa in Aplysia neurons, to produce a current typical of sodium currents observed in Aplysia neurons and to match the waveform of empirically observed action potentials in sensory neurons (e.g., Baxter and Byrne 1990a; Braha et al. 1993; Critz et al. 1991; Eliot et al. 1994; Ghirardi et al. 1992; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Mercer et al. 1991; Stark et al. 1996; Sugita et al. 1992, 1994b; Wright and Kirschman 1995).

Second, the kinetics and voltage dependency of the slow component of the Ca2+-activated K+ current (IK,Ca-S) have not been characterized extensively. This current appears to be active at potentials near the resting potential of sensory neurons and to have slow kinetics, however. For example, in voltage-clamp studies of sensory neurons, low concentrations (e.g., 2-5 mM) of tetraethylammonium (TEA), which selectively blocks IK,Ca, blocked a component of membrane current that was active at membrane potentials as hyperpolarized as -40 mV and that activated with an apparent time constant >2 s (Baxter and Byrne, unpublished observations; Walsh and Byrne 1989). In the present model, the model of IK,Ca-S was developed without explicit voltage and time dependency. Rather, the activation of IK,Ca-S and its dynamics were regulated solely by the concentration and dynamics of the intracellular pool of Ca2+ (see the APPENDIX). The value for the maximum conductance of IK,Ca-S (i.e., gK,Ca-S in Table 1) was estimated from the data of Walsh and Byrne (1989), who found that manipulations blocking IK,CA (e.g., substituting Ba2+ for Ca2+; blocking Ca2+ currents; applying low concentrations of TEA) also induced an inward shift in the steady-state holding current and a decrease in the membrane conductance. Their data suggested that at membrane potentials near -30 mV, the magnitude of IK,CA-S was ~3 nA. In the present model, voltage clamping the membrane potential at -30 mV induced a steady-state IK,CA-S of 2.7 nA.

Third, the Ca2+ dependency of ICa-L and ICa-N has not been investigated in sensory neurons of Aplysia. In other systems where it has been examined, however, L- and N-type Ca2+ currents are regulated both by voltage and intracellular concentrations of Ca2+ (for reviews, see Eckert and Chad 1984; Hille 1992; Tsien et al. 1988). Thus in present the sensory neuron model, the descriptions of ICa-L and ICa-N were extended to include functions describing an inverse relationship between the Ca2+ conductances (gCa-L and gCa-N) the concentration of Ca2+ in the pool. This feature of the model made an important contribution to the firing properties of the sensory neuron under conditions of enhanced excitability, which suggests that this mechanism warrants additional experimental investigation (see following text).

SIMULATING 5-HT-INDUCED MODULATION OF MEMBRANE CURRENTS. To simulate 5-HT-induced modulation of membrane currents, selected parameters of the model were set to the values indicated in the column labeled "5-HT-induced modulation" in Table 2. The actions of 5-HT were simulated by decreasing the conductances of IK,S (both IK,S-V and IK,S-I) to ~50% of their control values and decreasing the conductance of IK,Ca-S to ~20% of its control value. The magnitudes of these changes were estimated from published data. Cell-attached patch-clamp studies of the channels mediating IK,S indicated that application of 5-HT or injection of cAMP closed between 46 and 53% of the channels in any given patch (Shuster et al. 1985; Siegelbaum et al. 1986). Thus PKA-mediated and 5-HT-induced modulation of IK,S were simulated by decreasing the conductances of IK,S-I and IK,S-V by ~50%. Similarly, the voltage-clamp studies of Walsh and Byrne (1989) indicated that application of 5-HT or injection of cAMP blocked between 30 and 100% of the total IK,Ca-S (the average was ~77 ± 8%). Thus PKA-mediated and 5-HT-induced modulation of IK,Ca-S were simulated by decreasing the conductances of gK,Ca-S to 23% of its control value. In addition, the actions of 5-HT were simulated by increasing the conductance of ICa-L to 250% of its control value, which was based on published data indicating that application of 5-HT induced an average increase in ICa of 220 ± 36% (Eliot et al. 1993). Finally, the actions of 5-HT were simulated by modifying the properties of IK-V. This modification was more complex than simply decreasing gK-V, however. White et al. (1994) reported that in addition to decreasing gK-V, 5-HT slowed the kinetics for its activation and inactivation. Thus the mathematical description of 5-HT-induced modulation of IK-V included increases in the time constants of activation and inactivation (tau A and tau B, respectively). The magnitude of these changes in the present study were adjusted so as to reproduce the data of White et al. (1994). This ensemble of modifications to the model was assumed to represent the maximal effects of 5-HT. This assumption was based on previously published dose-response curves for 5-HT-induced modulation of sensory neurons (Jarrard et al. 1993; Ocorr and Byrne 1985; Stark et al. 1996; see also Bacskai et al. 1993). The reported EC50 values for the actions of 5-HT ranged from 0.8 to 14 µM and average EC50 was 8 ± 3 µM. The previously published empirical studies, which provided the data for the present model, used an average concentration of 30 ± 5 µM 5-HT. Thus we assumed that a maximal effect was achieved in the majority of previous experimental studies, and the results of these studies were combined. Finally, this ensemble of modifications to the model that reflect 5-HT-induced modulation represented the steady-state actions of 5-HT. Thus the present study did not simulate the time dependency of 5-HT modulation (for review, see Byrne and Kandel 1996).


                              
View this table:
[in this window]
[in a new window]
 
Table 2. Parameters describing modulation of membrane currents

SIMULATING THE ACTIVATION OF PKA. Although it is not clear from the available empirical results that all of the modulatory changes that are induced by elevated levels of cAMP are mediated via activation of PKA (e.g., Braha et al. 1993), in the present study, these modulatory changes were referred to collectively as "PKA-mediated modulation." To simulate the modulatory actions of PKA, selected parameters of the model were set to the values indicted in the column labeled "PKA-mediated modulation" in Table 2. Because PKA is believed to mediate many of the actions of 5-HT, many of the PKA-mediated parameter changes were identical to those described above for 5-HT-induced modulation. For example, the conductances for IK,S (both IK,S-I and IK,S-V) and IK,Ca-S were reduced to ~50 and ~20% of their control values, respectively, and the conductance for ICa-L was increased to 250% of its control value. The modulation of IK-V was different, however. In the presence of 5-HT, the conductance as well as the activation and inactivation time constants (tau A and tau B) were modulated. The available empiric data suggest that PKA only modulates tau A, and this modulation is equivalent to ~64% of that produced by 5-HT (Goldsmith and Abrams 1992; Hochner and Kandel 1992). Thus the actions of PKA on IK-V were simulated by slowing its activation kinetics to a level 64% of that used to simulate the actions of 5-HT.

SIMULATING ACTIVATION OF PKC. To simulate the modulatory actions of PKC, selected parameters of the model were set to the values indicted in the column labeled "PKC-mediated modulation" in Table 2. Activation of PKC has been found to partially mimic and occlude the modulatory actions of 5-HT on some membrane current [e.g., ICa-L (Braha et al. 1993) and IK-V (Sugita et al. 1994a)]. Thus some of the PKC-mediated parameter changes were similar or identical to those described earlier here for 5-HT-induced modulation. Specifically, gCa-L was increased to 250% of its control value, gK-V was reduced, and the kinetics of its inactivation were slowed to match the data of White et al. (1994). As suggest by the data of Sugita et al. (1994a), the actions of PKC on IK-V were simulated by slowing its activation kinetics to a level 75% of that used to simulate the actions of 5-HT and by modifying the conductance and inactivation kinetics of IK-V to levels identical to those used to simulated the actions of 5-HT. In addition, to its direct effects on membrane conductances, activation of PKC stimulated an increase in the intracellular levels of cAMP equivalent to ~60% of the increase in cAMP that was induced by 5-HT (Sugita et al. 1997a). Thus the modulatory effects of PKC also included changes to conductances that were modulated by elevated levels of cAMP, such as gK,S-I, gK,S-V, and gK,Ca-S. The simulated actions of PKC decreased these conductances to a level equivalent to ~60% the PKA-mediated modulation (see Table 2).

In vitro preparation

Experimental procedures to measure the excitability of sensory neurons have been described in detail previously (Baxter and Byrne 1990a). Briefly, all experiments were performed on clusters of somata of sensory neurons that were surgically isolated from the ventrocaudal cluster of pleural ganglia in A. californica. Dissections were performed after anesthetizing the animals by injecting a volume of isotonic MgCl2 equal to about one-half of the volume of the animal. An isolated cluster was pinned to the floor of a recording chamber, which was coated with a silicon elastomer and had a volume of ~300 µl. The static bathing solution of artificial sea water (ASW; Instant Ocean, Aquarium Systems, Mentor, OH) was buffered to pH 7.6 with 10 mM Trizma (Sigma Chemical, St. Louis, MO) and was maintained at 15°C. Conventional two-electrode current-clamp techniques were used. Sensory neurons were impaled with two glass capillary microelectrodes that were filled with 3 M potassium acetate and that had resistances of 2-6 MOmega . The membrane potential of the sensory neuron was monitored and was maintained at -45 mV by manually adjusting the constant DC current output of the current passing electrode. Excitability was measured by counting the number of action potentials elicited during a 1-s, 2-nA constant-current pulse. These stimulating current pulses were separated by 60 s. To ensure that the responses to the stimulating current were stable, at least three examples of excitability were recorded before and after bath application of TEA (Eastman Kodak, Rochester, NY). Small, concentrated aliquots TEA were added to the bath such that the final bath concentration of TEA was 2 mM. Data were collected from the last stimulus in ASW and from the first stable response after bath application of TEA.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Simulating membrane currents, action potentials, and excitability in control conditions

The first test of the model was to examine how well it simulated the biophysical properties of sensory neurons under control conditions. To simulate control conditions, the parameters of the model were set the values indicated in Table 1. These values produced a model sensory neuron with a resting membrane potential of -50 mV and an input resistance of 27 MOmega . (The input resistance was measured by injecting a hyperpolarizing current pulse from a resting potential of -50 mV.) These values are within the range of previously reported empirically measured values. A survey of the published literature indicated that in vitro preparations of sensory neurons have resting membrane potentials ranging from -38 to -55 mV and input resistances ranging from 10 to 50 MOmega . The available published data suggested that sensory neurons have an average resting potential of about -48 mV and an average input resistance of ~27 MOmega (Baxter and Byrne 1989, 1990a,b; Cleary et al. 1998; Pollock et al. 1985; Walsh and Byrne 1989; White et al. 1994; Wright and Kirschman 1995).4 Figure 3 illustrates simulated membrane currents that were elicited by voltage-clamp protocols similar to those used in previous empiric studies. The current responses of the model were in general agreement, both in time course and magnitude, with published examples of isolated ionic currents in sensory neurons (cf. Baxter and Byrne 1989, 1990a,b; Braha et al. 1993; Edmonds et al. 1990; Eliot et al. 1993; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Klein et al. 1980, 1982; Pollock et al. 1985; Scholz and Byrne 1987; Sugita et al. 1994a,b; Walsh and Byrne 1989; White et al. 1994; see also Adams and Gage 1979a; Byrne 1980a; Farquharson and Jahan-Parwar 1984, Fieber 1995; Gilly et al. 1997).



View larger version (23K):
[in this window]
[in a new window]
 
Fig. 3. Voltage-clamp simulations of membrane currents in control conditions. Membrane currents were described by voltage-gating equations of the Hodgkin-Huxley type and were modified when necessary to include Ca2+ dependence. With the exception of INa, the model currents were based on experimental data from Aplysia sensory neurons and corresponded well to experimentally measured currents both in time course and magnitude. Model of INa was derived from experimental data for Na+ current in other identified neurons of Aplysia, and the parameters were adjusted to match the waveform of the action potential of the sensory neuron. Traces illustrate simulated current responses elicited by 200-ms voltage-clamp steps from a holding potential of -70 mV. To ensure that steady-states conditions existed in the model, >= 10 s of simulated time was allowed to pass before any experimental manipulation and data collection in this and all subsequent figures. A: simulation of INa elicited by voltage-clamp steps to 0 mV (a), 10 mV (b), and 20 mV (c). Note, to illustrate the fast kinetics of INa, only the 1st 15 ms of the voltage-clamp step are illustrated. B: simulation of ICa-N elicited by voltage-clamp steps to -20 mV (a), 0 mV (b), and 20 mV (c). C: simulation of IK-V elicited by voltage-clamp steps to 0 mV (a), 10 mV (b), and 20 mV (c). D: simulation of IK,S elicited by voltage-clamp steps to 0 mV (a), 10 mV (b), and 20 mV (c). These currents are a combination of both the instantaneous (IK,S-I) and the voltage-dependent (IK,S-V) components of IK,S. E: simulation of ICa-L elicited by voltage-clamp steps to -20 mV (a), 0 mV (b), and 20 mV (c). F: simulation of IK-A elicited by voltage-clamp steps to -20 mV (a), -10 mV (b), and 0 mV (c). G: simulation of IK,Ca elicited by voltage-clamp steps to 0 mV (a), 10 mV (b), and 20 mV (c). These currents are a combination of both the fast (IK,Ca-F) and the slow (IK,Ca-S) components of IK,Ca.

The simulated voltage-clamp experiments illustrated that the model accurately reproduced the data from which it was derived. The more complex biophysical properties of sensory neurons (e.g., the waveform of the action potential and its excitability), however, emerge from interactions among this ensemble of membrane currents and from interactions between the membrane conductances and the intracellular concentration of Ca2+. To examine how well the present model simulated these emergent properties, single actions potentials were elicited with a brief (3 ms) depolarizing current pulse (15 nA) (Fig. 4A) and the excitability of the cell was measured as the number of spikes elicited by a series of 1-s depolarizing current pulses of increasing amplitude (Fig. 4B). These techniques closely mimicked protocols used in previous experimental studies (e.g., Baxter and Byrne 1990a; Braha et al. 1993; Hochner and Kandel 1992; Stark et al. 1996; Sugita et al. 1992; Wright and Kirschman 1995) and allowed for analysis of the waveform of the action potential without contamination from the stimulating current.



View larger version (12K):
[in this window]
[in a new window]
 
Fig. 4. Simulations of an action potential and excitability in control conditions. Responses of the model sensory neuron to stimulation corresponded well to experimentally measured action potentials and excitability both in time course and magnitude. A: resting membrane potential of the model sensory neuron was -50 mV. Single spike was elicited by injecting a 3-ms, 15-nA depolarizing current pulse (bar). Action potential had a peak amplitude of ~41 mV and a duration of 4.9 ms. Duration of the spike was measured as the time between the peak of the spike and the point of the repolarizing phase at which the membrane potential was 10% of the peak amplitude. B: excitability of the model sensory neuron was measured as the number of action potentials elicited by a series of 1-s depolarizing current pulses (bar) of increasing magnitude (1 nA, B1; 2 nA, B2; and 3 nA, B3). In all 3 examples, the resting membrane potential of the model sensory neurons was -50 mV. Response of the model cell accommodated during the sustained depolarization, and thus only a brief burst of spikes was elicited at the beginning of the stimulus.

From the resting potential of -50 mV, the model produced an action potential that reached a voltage of ~41 mV at its peak (i.e., the spike had a total amplitude of 91 mV; Fig. 4A). The duration of the simulated spike, which was measured as the time between the peak voltage and the point on the falling phase at which the membrane potential was 10% of the peak, was 4.9 ms. There are many examples of sensory neuron action potentials in the published literature with which to compare the results of the present simulation (e.g., Baxter and Byrne 1990a; Braha et al. 1993; Critz et al. 1991; Eliot et al. 1994; Ghirardi et al. 1992; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Jarrard et al. 1993; Klein 1993; Mercer et al. 1991; Stark et al. 1996; Sugita et al. 1992, 1994b, 1997b; Wright and Kirschman 1995). Results from these empirical studies indicated that in vitro preparations of sensory neurons generally have an action potential with a total amplitude of ~90 ± 14 mV and a duration of ~5.1 ± 2.7 ms (means ± SE). In response to 1-s depolarizing current pulses, the model sensory neuron exhibited accommodation similar to that observed empirically (Fig. 4B). The simulated responses to 1-, 2-, and 3-nA depolarizing current pulses were 1, 3, and 6 spikes, respectively. A survey of the published literature indicated that in vitro preparations of sensory neurons generally produced an average of ~1.8 ± 1.4 spikes in response to a 1-nA pulse; ~3.6 ± 0.9 spikes in response to a 2-nA pulse and ~5.4 ± 1.3 spikes in response to a 3-nA pulse (cf. Baxter and Byrne 1990a; Braha et al. 1993; Cleary et al. 1998; Critz et al. 1991; Dale et al. 1987; Eliot et al. 1994; Ghirardi et al. 1992; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Jarrard et al. 1993; Klein et al. 1986; Manseau et al. 1998; Mercer et al. 1991; Stark and Carew 1999; Stark et al. 1996; Sugita et al. 1992; Wright and Kirschman 1995; Wright et al. 1996). The close agreement between the simulated responses of the model (i.e., membrane currents, spike waveform, and excitability) and empiric results indicated the mathematical descriptions of the available empirical data were sufficient to reproduce several key biophysical properties of sensory neurons in control conditions and that additional simulations of the model may provide insights into the mechanisms underlying serotonergic modulation of spike duration and excitability of sensory neurons.

Simulating serotonergic modulation of membrane currents, action potentials, and excitability

A second test of the model was to examine how well it simulated the 5-HT-induced modulation of the biophysical properties of sensory neurons. The simulated actions of 5-HT induced a steady-state depolarization of the resting membrane potential of ~4.1 mV and an increase in the input resistance of the model sensory neuron to ~34 MOmega (i.e., an increase to ~126% of the control value). A survey of previously published empirical results indicated that in sensory neurons, 5-HT induces depolarizations ranging from 2.9 to 5.7 mV (the average depolarization was ~4.5 mV) and increases in input resistance ranging from 110 to 140% of control values (the average increase was ~130% of control) (cf. Braha et al. 1993; Stark et al. 1996; Walsh and Byrne 1989; Wright and Kirschman 1995). The simulated responses were in general agreement with empirical observations in that 5-HT induced a decrease in resting membrane conductance and a depolarizing of the resting membrane potential.

SEROTONERGIC MODULATION OF SPIKE DURATION. To allow for direct comparisons between action potentials (and measurements of excitability) simulated in control conditions and in the simulated presence of 5-HT, a constant bias current (-0.11 nA) was applied to the model to maintain the resting membrane potential at -50 mV during 5-HT-induced modulation. In the simulated presence of 5-HT and from a resting potential of -50 mV, the model produced an action potential with a total amplitude of ~96 mV and a duration of 6.8 ms (i.e., the duration was increased to ~139% of control; Fig. 5A). Although 5-HT-induced increases in spike amplitude are not a parameter generally investigated in empirical studies, a review of the published literature indicated that on average 5-HT induces an increase of ~3 mV in the amplitude of spikes. Thus the simulated increase in spike amplitude was consistent with empirical studies. Similarly, the simulated increase in spike duration was in general agreement with empirical studies. A survey of the published literature indicated that on average 5-HT induced an increase in spike duration to ~140% of control (cf. Baxter and Byrne 1990a; Braha et al. 1993; Critz et al. 1991; Eliot et al. 1994; Ghirardi et al. 1992; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Hochner et al. 1986a,b; Jarrard et al. 1993; Mercer et al. 1991; Pollock et al. 1985; Stark and Carew 1999; Stark et al. 1996; Sugita et al. 1992, 1994a; Wright and Kirschman 1995; Wright et al. 1996). The close agreement between the empirical and simulated results suggest that our current understanding of the 5-HT-induced modulation of membrane currents is sufficient to account for 5-HT-induced spike broadening. The relative contribution of the various modulatory actions of 5-HT to spike broadening will be considered in the following text.



View larger version (20K):
[in this window]
[in a new window]
 
Fig. 5. Simulating the effects of 5-HT on spike duration and excitability. In the simulated presence of 5-HT, the resting membrane potential of the model sensory neurons was maintained at -50 mV by applying constant bias current (see Table 2). Stimuli used to elicit a single action potential and to measure excitability are indicated by the bars and were identical to those described in Fig. 4. Simulated effects of 5-HT corresponded well to experimentally measured increases in spike duration and excitability both in time course and magnitude. A: 2 simulated action potentials are illustrated. Spike labeled "control" (- - -) was identical to the action potential illustrated in Fig. 4A. Spike labeled "5-HT" (---) was elicited in the simulated presence of 5-HT (see Table 2). In the simulated presence of 5-HT, the peak amplitude of the action potential was increased slightly and its duration was increased to 6.8 ms. B: simulated effects of 5-HT greatly enhanced excitability (1 nA, B1; 2 nA, B2; 3 nA, B3) as compared with the control excitability of the model sensory neuron (see Fig. 4B).

SEROTONERGIC MODULATION OF EXCITABILITY. As described previously (see Fig. 4B), the excitability of the model cell was measured as the number of spikes elicited by a series of 1-s depolarizing current pulses of increasing amplitude. In the simulated presence of 5-HT, the model no longer exhibited accommodation (Fig. 5B). Rather, the model fired spikes throughout the 1-s depolarizing current pulses. The simulated responses to 1-, 2-, and 3-nA depolarizing current pulses were 4, 8, and 11 spikes, respectively. A survey of the published literature indicated that in the presence of 5-HT, sensory neurons fired an average of ~7, ~9, and ~10 spikes during 1-, 2-, and 3-nA depolarizing current pulses, respectively (cf. Baxter and Byrne 1990a; Braha et al. 1993; Critz et al. 1991; Eliot et al. 1994; Ghirardi et al. 1992; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Jarrard et al. 1993; Klein et al. 1986; Mercer et al. 1991; Stark and Carew 1999; Stark et al. 1996; Sugita et al. 1997b; Wright and Kirschman 1995; Wright et al. 1996). Although there was a small difference between the simulated response to a 1-nA current pulse and the average empirical response (see DISCUSSION), there was a general agreement between the model and the empirical data in that sensory neurons did not exhibit accommodation in the presence of 5-HT. The specific membrane currents that mediated the 5-HT-induced anti-accommodation will be considered in the following text.

In the present study, a constant bias current was used to maintain the membrane potential at -50 mV during measurements of 5-HT-induced increases in spike duration and excitability. This procedure also was used in some, but not all, empirical studies. To examine whether the 5-HT-induced depolarization of the membrane potential influenced measurements of spike duration and excitability, a separate set of simulations was performed without the bias current. The results were essentially identical to those described in the preceding text, which suggested the 5-HT-induced depolarization does not play an important role in increasing excitability or spike duration.

SEROTONERGIC MODULATION OF MEMBRANE CURRENTS. As a first step toward gaining an understanding of which 5-HT-modulated currents mediated changes in excitability and spike duration, simulations investigated the relative contributions of IK,S, IK-V, IK,Ca-S, and ICa-L to 5-HT difference currents. In previous voltage-clamp studies (cf. Baxter and Byrne 1989, 1990b; Braha et al. 1993; Critz et al. 1992; Hochner and Kandel 1992; Klein et al. 1982; Sugita et al. 1994a,b; White et al. 1994), 5-HT difference currents were generated by subtracting currents in the presence of 5-HT from control currents. This subtraction yields the net total current modulated by 5-HT. Figure 6 illustrates a simulated voltage-clamp experiment from which 5-HT difference currents were generated. Membrane currents in the model were elicited by voltage-clamp pulses from a holding potential of -70 to -20 mV (Fig. 6A) and to 20 mV (Fig. 6B). Currents were elicited first while the parameters of the model were set to their control values (see Table 1) and again after the parameters had been adjusted to reflect the simulated presence of 5-HT (see Table 2). The 5-HT difference currents were generated by subtracting the 5-HT responses from the control responses. Thus 5-HT-induced decreases in net outward membrane currents were represented as upward deflections in the difference currents, and conversely, downward deflections represented 5-HT-induced increases in net outward current.



View larger version (20K):
[in this window]
[in a new window]
 
Fig. 6. Simulating the effects of 5-HT on total membrane current at 2 different membrane potentials. Simulated effects of 5-HT on total membrane currents corresponded to similar experimental effects both in time course and magnitude. Total membrane current represented the sum of individual ionic currents in the model sensory with the exception of INa and IL. Simulated voltage-clamp protocol was similar to that used in Fig. 1 of Baxter and Byrne (1989). A1: total membrane currents in the model sensory neuron were elicited by 200-ms voltage-clamp steps from -70 to -20 mV in simulated control conditions (a) and in the simulated presence of 5-HT (b). A2: 5-HT difference current was isolated by subtracting the current response elicited in the simulated presence of 5-HT from the control response (i.e., a - b). The dashed line labeled IK,S illustrates the contribution of the decrease in IK,S (both IK,S-I and IK,S-V) to the 5-HT difference current. B1: total membrane currents elicited by 200-ms voltage-clamp steps from -70 to 20 mV, 1st in control conditions (a) and in 5-HT conditions (b). B2: 5-HT difference current was isolated by subtracting the 5-HT trace from the control trace (i.e., a - b). The dashed line labeled IK-V illustrates the contribution of the modulation of IK-V to the 5-HT difference current.

Throughout the voltage-clamp step to -20 mV, 5-HT-induced modulation produced a decrease in the net outward membrane current (Fig. 6A1), as indicated by the upward deflection in the 5-HT difference current (Fig. 6A2). This 5-HT difference current had several components, including modulation of IK,S, ICa-L, IKCa-S, and IK-V. These various components did not contribute equally to the 5-HT difference current, however. By examining the 5-HT-induced modulation of these currents individually, it was possible to determine the relative contribution that each current made to the 5-HT difference current. The primary component of the 5-HT difference current resulted from the decrease in the outward current IK,S (both IK,S-I and IK,S-V). The contribution of the modulatory changes in IK,S (both IK,S-I and IK,S-V) was indicated by the dashed line in Fig. 6A2, which was generated by subtracting the simulated IK,S in the presence of 5-HT from the control IK,S. At the end of the 200-ms voltage-clamp pulse, modulation of IK,S accounted for 70% of the 5-HT difference current, whereas, modulation of IK,Ca-S and IK-V accounted for 15 and 3%, respectively. An additional component resulted from the enhancement of the inward current ICa-L. An enhanced inward current would decrease the net outward current and thus would be represented as an upward deflection in the 5-HT difference current. Modulation of ICa-L accounted for 12% of the 5-HT difference current at the end of the voltage-clamp pulse.

The result that modulation of IK,Ca-S made a relatively minor contribution to a brief voltage-clamp pulse to -20 mV agreed with the previous empirical observations of Walsh and Byrne (1989). They found that manipulations that block IK,Ca (e.g., applying low concentrations of TEA; substituting Ba2+ for Ca2+; or intracellular injection of Ca2+ chelators) blocked only ~10% of the net total current modulated by 5-HT during brief voltage-clamp pulses. In contrast, during long voltage-clamp steps, blocking IK,Ca reduced the response to 5-HT by 51-68%. This empirical observation suggested that the relative contributions of individual currents to the 5-HT difference current varied dramatically over time. To examine this possibility, the duration of the simulated voltage-clamp step was extended to 1 s, and a 5-HT difference current was generated (Fig. 7). The contributions to the 5-HT difference current that were made by modulation of IK,S (both IK,S-I and IK,S-V) and IK,Ca-S were indicated by the dashed lines labeled IK,S and IK,Ca-S, respectively. During the first half of the 1-s voltage-clamp step, modulation of IK,S was the predominant component of the 5-HT difference current, and because IK,S did not inactivate, the amplitude of the IK,S component was constant throughout the later portions of the voltage-clamp step. In contrast, modulation of IK,Ca-S made very little contribution early in the voltage-clamp step. Because of its slow kinetics, however, the contribution of IK,Ca-S continued to grow throughout the voltage-clamp step. The relative contribution that modulation of IK,Ca-S made to the 5-HT difference current eventually exceeded that of IK,S. At the end of the 1-s voltage-clamp step, modulation of IK,Ca-S accounted for 58% of the 5-HT difference current, whereas IK,S accounted for 37%. The observation that modulation of IK,S and IK,CA-S could account for the majority of the 5-HT difference current at membrane potentials near the resting potential suggested that modulation of these currents may play a key role in mediating 5-HT-induced increases in excitability (see following text).



View larger version (9K):
[in this window]
[in a new window]
 
Fig. 7. Relative contribution of IK,S and IK,Ca-S to long-duration voltage-clamp pulses. Total membrane currents in the model sensory neuron were elicited by a 1-s voltage-clamp pulses from -70 to -20 mV, 1st in control conditions and again in the simulated presence of 5-HT (not shown). 5-HT difference current (solid line) was generated by subtracting the current response in 5-HT from the control response and thus represented the total net current modulated by 5-HT. Short-dashed line, contribution of 5-HT-induced modulation of IK,S (both IK,S-I and IK,S-V) to the 5-HT difference current and was generated by subtracting the 5-HT-modulated IK,S response from the control IK,S response. Long-dashed line, contribution of 5-HT-induced modulation of IK,Ca-S to the 5-HT difference current and was generated by subtracting the 5-HT-modulated IK,Ca-S response from the control IK,Ca-S response.

In contrast to voltage-clamp steps to membrane potentials <0 mV, voltage-clamp steps to 20 mV revealed a complex 5-HT difference current that represented both decreases and increases in the net outward current during modulation by 5-HT. The rate of rise of the total membrane current was slowed in the simulated presence of 5-HT and thus decreased the net outward current early during the voltage-clamp pulse (Fig. 6B1). In addition, the simulated actions of 5-HT slowed the inactivation of the outward current and thus increased the outward current later during the voltage-clamp pulse. The early upward defection in the 5-HT difference current reflected the initial decrease in the outward current, whereas, the downward defection represented the late increase in outward current (Fig. 6B2).

The complexity of the 5-HT difference current at depolarized membrane potentials resulted primarily from the modulatory changes in IK-V, which was the predominant outward current at membrane potentials more depolarized than ~0 mV (see Fig. 3) (see also White et al. 1994). The contribution of modulatory changes in IK-V was indicated by the dashed line, which was generated by subtracting the simulated IK-V in the presence of 5-HT from the control IK-V. Examination of Fig. 6B2 revealed that modulation of IK-V accounted for the majority of the 5-HT-induced decrease in the outward current during the first ~10 ms of the voltage clamp. The observation that the early component of the 5-HT difference current was due mainly to changes in IK-V suggested that serotonergic modulation of IK-V may be the key contributor to 5-HT-induce spike broadening (see following text).

Simulating the effects of elevated levels of cAMP

To gain additional insights into how the modulation of specific currents and the activation of different second-messenger/protein kinase cascades contribute to 5-HT-induced changes in spike duration and excitability, simulations examined how the currents modulated as a consequence of elevated levels of cAMP effected the biophysical properties of the model sensory neuron. A survey of the published literature indicated that in the presence of elevated levels of cAMP, sensory neurons fired an average of ~7, ~11, and ~12 spikes during prolonged depolarizing current pulses of 1, 2, and 3 nA, respectively (cf. Baxter and Byrne 1990a; Braha et al. 1993; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Jarrard et al. 1993; Klein et al. 1986; see also Sugita et al. 1997a). Thus elevated levels of cAMP fully mimicked, and to some degree exceeded, the actions of 5-HT on accommodation in sensory neurons. In contrast, elevated levels of cAMP did not appear to fully mimic the actions of 5-HT on spike broadening. A survey of the published literature indicated that on average elevated levels of cAMP induced an increase in spike duration to ~119% of control (cf. Baxter and Byrne 1990; Goldsmith and Abrams 1992; Hochner and Kandel 1992; Klein 1993; Sugita et al. 1992, 1994b; see also Abrams et al. 1984; Jarrard et al. 1993). These empirical observations suggested that currents modulated by elevated levels of cAMP preferentially modulate accommodation and to a lesser degree spike duration.

PKA-MEDIATED MODULATION OF SPIKE DURATION AND EXCITABILITY. As described previously, a constant bias current (see Table 2) was applied to the model to maintain the resting membrane potential at -50 mV during PKA-mediated modulation. In the simulated presence of elevated levels of cAMP and from a resting potential of -50 mV, the model produced an action potential with a total amplitude of ~93 mV and a duration of 5.7 ms (i.e., the duration was increased to 116% of control; Fig. 8A). Although very little empirical data is available regarding PKA-mediated increases in spike amplitude, that which are available suggest that PKA-mediated modulation induces a slight increase in spike amplitude (Baxter and Byrne 1990a; Goldsmith and Abrams 1992; Sugita et al. 1994b). The magnitude of the simulated PKA-mediated spike broadening was ~40% of the simulated effect of 5-HT on spike duration (see preceding text). This intermediate response to PKA by the model was similar to the available empirical data, which suggested that magnitude of the spike broadening induced by elevated cAMP was ~47% of the average response to 5-HT (see preceding text).



View larger version (20K):
[in this window]
[in a new window]
 
Fig. 8. Simulating the PKA-dependent modulation of spike duration and excitability. During the simulated activation of PKA, the resting membrane potential was maintained at -50 mV by applying a constant bias current (see Table 2). Stimuli used to elicit a single action potential and to measure excitability are indicated by the bars were identical to those described in Figs. 4 and 5. Simulated activation of PKA corresponded well to experimentally measured increases in spike duration and excitability both in time course and magnitude. A: 2 simulated action potentials are illustrated. Spike labeled control (- - -) was identical to the action potential illustrated in Fig. 4A. Spike labeled PKA (---) is an action potential elicited during the simulated activation of PKA (see Table 2). Activation of PKA slightly increased the peak amplitude of the action potential and increased its duration to 5.7 ms. B: simulated effects of activating PKA greatly enhanced excitability (1 nA, B1; 2 nA, B2; 3 nA, B3) as compared with the control excitability of the model sensory neuron (see Fig. 4B).

In the simulated presence of elevated cAMP, the model produced 4, 9, and 11 spikes in response to 1-s depolarizing current pulses of 1, 2, and 3 nA, respectively. Thus the changes in the excitability of the model that were induced by PKA were similar to those produced by the simulated actions of 5-HT. Indeed, in response to the 2-nA pulse, the model produced an additional spike in the simulated condition of PKA activation, which suggested that some aspect of 5-HT-induced modulation may slightly decrease excitability.

RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKA-MEDIATED SPIKE BROADENING. To evaluate which currents mediated PKA-induced changes in spike duration (and excitability, see following text) the modulation of individual currents was removed selectively from the ensemble of PKA-mediated actions, and simulation tested the effects of these manipulations on PKA-mediated spike broadening (and excitability enhancement). For example, previous qualitative models attributed 5-HT-induced spike broadening to PKA-mediated decreases in IK,S (e.g., Kandel and Schwartz 1982; for review, see Byrne and Kandel 1986). A prediction of such a model would be that spike broadening would be blocked if the modulation of IK,S was removed from the ensemble of PKA-mediate actions (see Table 2). A simulation to test this predication found that removing only the modulation of IK,S (both IK,S-I and IK,S-V) had no effect on PKA-mediated spike broadening (not shown). Alternatively, enhancement of an inward current (e.g., ICa) has been suggested to mediate spike broadening (e.g., Klein and Kandel 1978). A simulation to test this predication found that removing only the modulation of ICa-L had no effect on PKA-mediated spike broadening (not shown). The only manipulation that was found to block PKA-mediated spike broadening was the removal of modulation of IK-V (i.e., slowing of its activation kinetics; Fig. 9A). When only modulation of IK-V was removed (i.e., PKA-mediated modulation of IK,S, IK,Ca-S, and ICa-L remained as indicated in Table 2 but the parameters for IK-V were set to the control values indicated in Table 1), the control spike and the "modulated" spike were virtually indistinguishable. Thus the simulations indicated that modulation of IK-V played the key role in PKA-mediated increases of spike duration.



View larger version (19K):
[in this window]
[in a new window]
 
Fig. 9. Different membrane currents mediate PKA-induced spike broadening and excitability enhancement. A: modulation of IK-V mediated PKA-induced spike broadening. Stimulus used to elicit a single action potential was identical to that described in Figs. 4, 5, and 7. Note, however, that the stimulus and initial rising phase of the action potentials have been omitted and that the time scale has been expanded to allow more detailed comparisons of spike duration. Spikes labeled control (short-dashed line) and PKA (long-dashed line) were identical to the spikes illustrated in Figs. 4A and 7A, respectively. Solid line, simulated spike with all but one of the PKA-mediated effects described in Table 2 (i.e., the parameter values that described IK-V were set to their control values). To maintain the resting membrane potential at -50 mV, a constant bias current of -0.18 nA was applied. B: modulation of both IK-S and IK,Ca-S contributed to PKA-induced enhancement of excitability. In all 4 traces, excitability was measured as the number of spikes elicited by a 1-s, 1-nA depolarizing current pulse (bar). B1: for purposes of comparison, the PKA-induced increase in excitability that was illustrated in Fig. 8B1 was reproduced in the present figure. B2: only the PKA-mediated increase of ICa-L was removed from the simulated activation of PKA (i.e., the parameters for ICa-L were set to their control values and all other parameters reflected the simulated activation of PKA; see Table 2). Constant bias current was -0.19 nA, which maintained the resting membrane potential at -50 mV. B3: only the PKA-mediated decrease of IK,S (i.e., both IK,S-I and IK,S-V) omitted. All other parameters were as indicated in Table 2. A constant bias current of -0.02 nA was applied to maintain the resting membrane potential at -50 mV. B4: all of the modifications described in Table 2 for PKA-mediated modulation were made, except that parameters for IK,Ca-S remained at their control value (i.e., only the PKA-mediated decrease of IK,Ca-S was removed from the simulated activation of PKA). A constant bias current of -0.11 nA was applied to maintain the resting membrane potential at -50 mV. Results similar to those obtained with the 1-s, 1-nA stimulus were obtained with 2- and 3-nA stimuli (not shown).

RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKA-MEDIATED INCREASES OF EXCITABILITY. A similar set of simulations was used to examine which currents and their modulation contributed to PKA-mediated increases in excitability of the model cell, and the results suggested that increases in excitability emerged from a complex interactions among several contributing factors.

First, simulations considered the contribution of PKA-mediated increase of ICa-L. One might predict that enhancing an inward current would help to increase excitability and that removing the modulation of ICa-L would reduce PKA-mediated increases in excitability. Simulations found, however, that removing only modulation of ICa-L increased the magnitude of PKA-mediated changes in excitability. In previous simulations in which all PKA-mediated actions were included, a 1-s, 1-nA depolarizing current pulse elicited four spikes (Fig. 9B1), whereas an identical pulse elicited five spikes after the modulation of ICa-L was removed (Fig. 9B2).

This result can be explained, in part, when one considers the indirect effects of increased Ca2+ influx via the enhanced component of ICa. Removing the PKA-mediated enhancement of ICa-L decreased the total intracellular levels of Ca2+ during the stimulating current pulse to 77% of the levels that were obtained when ICa-L was modulated. Note, that this decrease occurred despite the fact that five spikes were elicited by the test pulse (Fig. 9B2) rather than the four spikes that occurred were when all of the PKA-mediated actions were simulated (Fig. 9B1). The decreased levels of intracellular Ca2+, in turn, produced less activation of IK,Ca-S. In the simulation without modulation of ICa-L, the amplitude of IK,Ca-S at end of the 1-s stimulating current pulse was reduced to 75% of the amplitude of IK,Ca-S at the same point in time in the simulation with all of the PKA-mediated actions in place. And, as illustrated in the following text, IK,Ca-S is a current that tended to reduce excitability.

These results suggested that modulation ICa played an important, albeit indirect, role in regulating excitability. Thus additional simulations were preformed to test some of the assumptions that were incorporated into the model descriptions of ICa (see METHODS). Simulations examined the role of Ca2+-dependent inactivation of Ca2+ currents (both ICa-L and ICa-N). If Ca2+-dependent inactivation of ICa was removed from the model and all other parameters were set to the values for PKA-mediated modulation (Table 2), then a 1-s, 1-nA depolarizing current pulse elicited only three spikes (not shown). In addition, simulations examined the consequences of increasing the magnitude of PKA-mediated modulation of ICa-L. If the magnitude of PKA-mediated modulation of ICa-L was increased from 250 to 500% and all other parameters were set to the values for PKA-mediated modulation (Table 2), then a 1-s, 1-nA depolarizing current pulse elicited only three spikes (not shown).5 Both of these manipulations (i.e., removing Ca2+-dependent inactivation and increasing the magnitude of PKA-mediated modulation) increased Ca2+ influx and thereby increased the activation of IK,Ca-S and decreased excitability.

Second, simulations considered the contribution of IK,S (both IK,S-I and IK,S-V) to PKA-induced increases of excitability. These currents were active near the resting potential of the model cell and did not inactivate. Thus one might predict that reducing an outward current would help to increase excitability and that removing the modulation of IK,S would reduced PKA-mediated increases in excitability. Simulations confirmed this prediction. In the simulation without modulation of IK,S (Fig. 9B3), a 1-s, 1-nA depolarizing current pulse elicited only two spikes, whereas four spikes were elicited when all of the PKA-mediated actions were included (Fig. 9B1).

Third, simulations considered the contribution of IK,Ca-S to PKA-induced increases of excitability. As with IK,S, IK,Ca-S was active near the resting potential of the model cell and did not inactive. Moreover, the activation of IK,Ca-S was indirectly regulated by the level of spiking activity in the model cell. As more spikes were generated, the intracellular levels of Ca2+ increased and the activation of IK,Ca-S increased, and this increase in outward current opposed further spiking. Thus one might predict that down regulating this negative feedback loop (i.e., IK,Ca-S) would help to increase PKA-induced enhancement of excitability. Simulations confirmed this prediction. In the simulation without decrease of IK,Ca-S (Fig. 9B4), a 1-s, 1-nA depolarizing current pulse elicited only one spike, whereas four spikes were elicited when all of the PKA-mediated actions were included (Fig. 9B1). These results and those described above indicated that concurrent decreases of IK,S and IK,Ca-S were necessary for PKA-induced increases of excitability to occur.

ROLES OF IK,S AND ICA-L IN PKA-INDUCED BROADENING OF TEA SPIKES. The simulations described in the preceding text indicated the modulation of IK,S and ICa-L did not play important roles in PKA-induced spike broadening (see Fig. 9A). Previous empirical studies, however, have suggested that modulation of these two currents should contribute significantly to spike broadening (e.g., Abrams et al. 1984; Belardetti et al. 1986; Castellucci et al. 1982; Klein and Kandel 1978; Klein et al. 1982; Pieroni and Byrne 1992; Pollock et al. 1985; Siegelbaum et al. 1986). The discrepancy between the results of the present simulation study and previous empirical studies may be explained, in part, by differences in the conditions under which the modulation of spike broadening were studied. Often empirical studies examined spike broadening in the presence of high concentrations of TEA and thereby blocking IK-V and IK,Ca and maximizing the relative contributions of IK,S and ICa-L to PKA-mediated spike broadening. Simulations examined whether the presence of high (100 mM) concentrations of TEA created conditions in which the roles of modulation of IK,S and ICa-L in spike broadening were enhanced (Fig. 10).



View larger version (17K):
[in this window]
[in a new window]
 
Fig. 10. Simulating the PKA-dependent modulation of spike duration in the presence of 100 mM TEA. Stimulus used to elicit individual single action potentials was identical to that described in previous figures. Actions of 100 mM TEA were simulated by reducing the conductances of IK,Ca and IK-V by >= 90% (i.e., gK-V = 0.45 µS; gK,Ca-F = 0.001 µS; gK,Ca-S = 0.0079 µS) and the conductances of IK,S by ~40% (i.e., gK,S-I = 0.0072 µS; gK,S-V = 0.33 µS). To maintain the resting membrane potential at 50 mV, a constant bias current of -0.16 nA was applied. Spike labeled control (- - -) was identical to the action potential illustrated in Fig. 4A. Simulated presence of 100 mM TEA increased the duration of the action potential to 16.3 ms (spike labeled TEA). To simulate PKA-mediated modulation in the presence of TEA, the conductances of IK,S were reduced by an additional ~50% (i.e., gK,S-I = 0.0034 µS; gK,S-V = 0.158 µS), gK,Ca-S was reduced to 0.0019 µS, the time constant for activation of IK-V was slowed (see Table 2), and the conductance of ICa-L was increased by 250% (i.e., gCa-L = 0.2 µS). To maintain the resting membrane potential at -50 mV, a constant bias current of -0.27 nA was applied. Simulated action of PKA-mediated modulation increase the duration of the spike to 34.4 ms (spike labeled PKA). Finally, all of the modifications described the preceding text were made, except that gK,S-I and gK,S-V remained at their control values (i.e., gK,S-I = 0.0072 µS; gK,S-V = 0.33 µS). A constant bias current of -0.26 nA was applied to maintain the resting membrane potential at -50 mV. Without the modulation of IK,S, the duration of the spike was 20.4 msec (spike labeled PKA without modulation of IK,S).

To simulate the presence of 100 mM TEA, the conductances of IK-V and IK,Ca (both IK,Ca-F and IK,Ca-S) were reduced to 10 and 5% of their control values, respectively, and the conductances of IK,S (both IK,S-I and IK,S-V) reduced to 60% of their control values. The magnitude of these changes were estimated from published dose-response relationships that describe the effects of TEA on these currents (Baxter and Byrne 1989; Herman and Gorman 1981; Shuster and Siegelbaum 1987; see also Walsh and Byrne 1989). The simulated presence of 100 mM TEA broadened the duration of the spike to ~333% of control. The actions of PKA in the presence or TEA were simulated by further reductions in the conductances for IK,S (both IK,S-I and IK,S-V) and IK,Ca-S, by slowing the activation kinetics of IK-V, and by increasing the conductance for ICa-L. These manipulations dramatically broadened the spike. In the simulated presence of 100 mM TEA, activation of PKA increased the spike duration to ~211% of the initial spike duration (i.e., the duration of the spike labeled TEA in Fig. 10). If the decrease of IK,S (both IK,S-I and IK,S-V) was removed from the ensemble of PKA-mediated actions, then the duration of the spike decreased to only 125% of the initial spike duration. If the increase of ICa-L also was removed, the duration of the spike returned to the initial TEA-broadened spike (not shown). These results indicated that the relative contribution of currents to PKA-induced spike broadening can be altered by the experimental conditions and that in the presence of high concentrations of TEA, the modulation of both IK,S and ICa-L play a key role in PKA-induced spike broadening.

Simulating PKC-mediated modulation of action potentials and excitability

The results described above indicated that modulation of IK,Ca-S and IK,S via PKA could completely account for 5-HT-induced increases in excitability, but that PKA-mediated modulation of IK-V could accounted for only ~50% of 5-HT-induced spike broadening. To determine whether PKC-mediated modulation of IK-V could more completely account for 5-HT-induced spike broadening, simulations examined how the currents modulated by activation of PKC effected the biophysical properties of the model sensory neuron.

In the simulated presence of activated PKC and from a resting potential of -50 mV, the model produced an action potential with a total amplitude of ~96 mV and a duration of ~6.4 ms (i.e., the duration was increased to ~134% of control; Fig. 11A). The data of Sugita et al. (1992; see also Bhara et al. 1993; Sugita et al. 1994a, 1997b) indicated that activation of PKC induced an average increase in spike duration to ~126% of control and a slight increase in the spike amplitude. In addition to increasing the duration of the action potential, the simulated actions of PKC also induced a slight increase in the excitability of the model. In response to 1-s current pulses of 1, 2, and 3 nA, the model produced two, four, and seven spikes, respectively (compare with Fig. 4B). A survey of the published literature indicated that in response to a 1-s, 2-nA current pulse, sensory neurons produced between three and nine spikes while in the presence of active phorbol esters (the average response was ~5 spikes) (cf. Braha et al. 1993; Manseau et al. 1998; Sugita et al. 1992, 1997a). Thus the results of the model were in general agreement with the available empirical data. Moreover, results indicated that activation of PKC closely mimicked the actions of 5-HT on spike broadening and, to a lesser degree, the actions of 5-HT on accommodation in sensory neurons. These observations suggested that currents modulated by activation of PKC preferentially modulate spike duration.



View larger version (16K):
[in this window]
[in a new window]
 
Fig. 11. Simulating the PKC-dependent modulation of spike duration and excitability. During the simulated activation of PKC, the resting membrane potential was maintained at -50 mV by applying a constant bias current (see Table 2). Stimuli used to elicit a single action potential and to measure excitability were identical to those described in previous figures. Simulated activation of PKC corresponded well to experimentally measured increases in spike duration and excitability both in time course and magnitude. A: 2 simulated action potentials are illustrated. Spike labeled control (- - -) was identical to the action potential illustrated in Fig. 4A. Spike labeled PKC (---) is an action potential elicited during the simulated activation of PKC (see Table 2). Activation of PKC slightly increased the peak amplitude of the action potential and increased its duration to 6.6 ms. B: simulated effects of activating PKC produced a moderate increase in the excitability of the model sensory neuron (1 nA, B1; 2 nA, B2; 3 nA, B3) as compared with simulations of excitability in control conditions (see Fig. 4B).

RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKC-MEDIATED SPIKE BROADENING. To evaluate which currents mediated PKC-induced changes in spike duration, the modulation of individual currents was selectively removed from the ensemble of PKC-mediated actions and simulation tested the effects of these manipulations on PKC-mediated spike broadening. As with similar investigations of which current mediated PKA-induced spike broadening (see preceding text), removing only the modulation of ICa-L, or only IK,S (both IK,S-I and IK,S-V), or only IKCa-S had no effect on PKC-mediated spike broadening (not shown). The only manipulation that blocked PKC-mediated spike broadening was the removal of modulation of IK-V (Fig. 12A). When only modulation of IK-V was removed, the control spike and the modulated spike were virtually indistinguishable. Thus the simulations indicated that modulation of IK-V played the key role in modulation of spike duration by both PKA and PKC.



View larger version (24K):
[in this window]
[in a new window]
 
Fig. 12. Different membrane currents mediate PKC-induced spike broadening and excitability enhancement. A: modulation of IK-V mediated PKC-induced spike broadening. Stimulus used to elicit a single action potential was identical to that described in previous figures. Note, however, that the stimulus and initial rising phase of the action potentials have been omitted and that the time scale has been expanded to allow more detailed comparisons of spike duration. Spikes labeled control (short-dashed line) and PKC (long-dashed line) were identical to the spikes illustrated in Figs. 4A and 11A, respectively. Spike labeled PKC without modulation of IK-V (solid line) illustrates a simulated spike with all but 1 of the PKC-mediated effects described in Table 2 (i.e., the parameter values that described IK-V were set to their control values). To maintain the resting membrane potential at -50 mV, a constant bias current of -0.09 nA was applied. B: modulation of both IK,Ca-S and IK-S contributed to PKC-induced enhancement of excitability. In all 4 traces, excitability was measured as the number of spikes elicited by a 1-s, 3-nA depolarizing current pulse (bar). B1: for purposes of comparison, the PKC-induced increase in excitability that was illustrated in Fig. 11B3 was reproduced in the present figure. B2: only the PKC-mediated increase of ICa-L was omitted. Constant bias current was -0.13 nA. B3: only the PKC-mediated decrease of IK,S (i.e., both IK,S-I and IK,S-V) was removed from the simulated activation of PKC. A constant bias current of 0.01 nA was applied to maintain the resting membrane potential at -50 mV. B4: all of the modifications described in Table 2 for PKC-mediated modulation were made, except that parameters for IK,Ca-S remained at their control values. A constant bias current of -0.06 nA was applied to maintain the resting membrane potential at -50 mV. Results similar to those obtained with the 1-s, 3-nA stimulus were obtained with 1- and 2-nA stimuli (not shown).

RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKC-MEDIATED INCREASES OF EXCITABILITY. Because activation of PKC can induce an increase in levels of cAMP, PKC can have both direct effects on some conductances (i.e., gK-V and gCa-L) and indirect effects that results from activation of PKA (see Fig. 1B). Individual components of the ensemble of PKC-mediated actions were removed selectively, and simulations examined how these manipulations altered PKC-induced increases of excitability. First, simulations considered the contribution of PKC-induced increase of ICa-L (i.e., a direct effect of PKC). If only the increase of ICa-L was removed from the ensemble of PKC-mediated actions, then the number of spikes elicited by the test pulse was increased from seven (Fig. 12B1) to nine (Fig. 12B2). Similar results were obtained if only the modulation of IK-V was removed; i.e., the test pulse elicited nine spikes (not shown). Second, simulations considered the contribution of IK,S (both IK,S-I and IK,S-V) to PKC-induced increases of excitability. If only the PKC-induced decrease of IK,S was removed (i.e., an indirect effected mediated via cross-talk with the cAMP/PKA system), the number of spikes elicited by the test pulse was decreased from seven (Fig. 12B1) to five (Fig. 12B3). Finally, simulations considered the contribution of IK,Ca-S. If only the decrease of IK,Ca-S was removed (i.e., an indirect effect mediated via cross-talk), the number of spikes elicited by the test pulse was reduced to only four (Fig. 12B4). These results indicated that the direct actions of PKC on membrane conductances do not contribute to increased excitability of the model cell. Indeed, PKC-mediated modulation of IK-V and ICa-L contributed to a reduction of excitability. Rather, PKC-induced increases in excitability resulted from its indirect actions on membrane conductances that were modulated via PKA (i.e., IK,S and IK,Ca-S).

Simulating biophysical correlates of long-term sensitization

Modulation of the intrinsic cellular properties of sensory neurons in Aplysia is believed to be an important mechanism contributing to several examples of learning, and previous studies have demonstrated that long-term sensitization training affected at least two biophysical properties of tail sensory neurons (Cleary et al. 1998; Scholz and Byrne 1987). Specifically, training reduced the net outward current elicited by brief depolarizing voltage-clamp steps and the kinetics and voltage-sensitivity of the modulated outward current were similar to IK,S (Scholz and Byrne 1987). In addition, training increased the excitability of sensory neurons (Cleary et al. 1998). Although an increase in excitability is consistent with modulation of IK,S, it is not known whether modulation of IK,S alone is sufficient to account for the twofold increase in excitability that is observed after training. To address this issue, simulations examined the increase in excitability that was induced by decreasing only IK,S (Fig. 13). In simulated control conditions, a 1-s, 2-nA current pulse elicited three spikes (Fig. 13A). After the values for gK,S-I and gK,S-V were reduced to reflect their modulation by 5-HT (see Table 2), an identical test elicited four spikes (Fig. 13B), which is less than the twofold increase previously reported (Cleary et al. 1998). This result suggests that modulation of an additional current(s) may be necessary to fully account for the effects of training. One possibility is IK,Ca-S, which like IK,S makes an important contribution to excitability. After both IK,S and IK,Ca-S were reduced, the 1-s, 2-nA test pulse elicited the expected twofold increase in excitability (i.e., 6 spikes; Fig. 13C). These results suggest that decreases of IK,S alone cannot fully account for the observed increase in sensory neuron excitability after behavioral training and that an addition current, possibly IK,Ca-S, is modulated.



View larger version (22K):
[in this window]
[in a new window]
 
Fig. 13. Simulating correlates of long-term sensitization training in sensory neurons. Simulations mimicked the experimental procedures of Cleary et al. (1998). Excitability was measured as the number of spikes elicited by a 1-s, 2-nA depolarizing current pulse. These test pulses were applied at the resting membrane potential of the cells, which has an average of -50 mV in cells from ganglia on the control side of the animal and -54 mV in cells from ganglia on the sensitized side of the animal. A: simulation of excitability under control conditions. All parameters were set to their control values (see Table 1). Simulation of excitability in control conditions was identical to that illustrated in Fig. 4B. B: simulating the effects on excitability of decreasing only IK,S. Values for gK,S-I and gK,S-V were set to 0.006 and 0.25 µS, respectively (see Table 2). All other parameters were set to their control values (see Table 1). A constant bias current of -0.28 nA was applied to maintain the resting potential of the model at -54 mV. C: simulating the effects on excitability of the concomitant decreases of IK,S and IK,Ca-S. Values for gK,S-I and gK,S-V were as in B and value for gK,Ca-S. was set to 0.1 µS. All other parameters were at their control values. A constant bias current of -0.29 nA was applied to maintain the resting potential of the model at -54 mV. Essentially identical results were obtained if the membrane potentials in B and C were held at -50 mV (not shown).

An empirical test of a key prediction from the model

The simulations presented above made several predictions that can be used to guide experimental investigations (see DISCUSSION). One of these predictions was related to the role of IK,Ca-S in regulating the excitability of sensory neurons. A decrease in IK,Ca-S played a key role in both PKA- and PKC-mediated increases of excitability (Figs. 9B3 and 12B3). In addition, IK,Ca-S was active at the resting potential and became the predominant component of 5-HT difference current at membrane potentials <0 mV (Fig. 7). These results suggested that IK,Ca-S contributed to accommodation and that the excitability of sensory neurons could be increased by selectively reducing IK,Ca-S. Figure 14 illustrates the results of simulation and experimental studies that examined this prediction.



View larger version (17K):
[in this window]
[in a new window]
 
Fig. 14. Ca2+-activated K+ currents contribute to accommodation. In both simulation (A) and empirical (B) studies, the excitability was measured as the number of spikes elicited by a 1-s, 2-nA depolarizing current pulse. A: simulation of excitability under control conditions and in the simulated presence of a low concentration of TEA, which selectively reduces the magnitude of Ca2+-activated K+ currents (see Baxter and Byrne 1989; Walsh and Byrne 1989). A1: all parameters were set to their control values (see Table 1). Simulation of excitability in control conditions was identical to that illustrated in Fig. 4B. A2: to simulate the experimental condition of applying a low concentration of TEA (2 mM), the conductances for both the fast and slow components of IK,Ca were reduced to 25% of their control values (i.e., gK,Ca-F = 0.005 µS; gK,Ca-S = 0.04 µS) and conductance for IK-V was reduced to 80% of its control value (i.e., gK-V = 3.6 µS). Resting potential was maintained at -50 mV by applying a constant bias of -0.03 nA. B: empiric studies to measure the effects of low concentrations of TEA on the excitability of sensory neurons. Experimental methods were identical to those described in Baxter and Byrne (1990a). B1: excitability in control saline. B2: excitability of the same cell in presence of 2 mM TEA. B3: in control saline, a 1-s, 2-nA current pulse elicited an average of 3.75 ± 1.03 action potentials in 4 different preparations. After bath application of TEA (2 mM), an identical current pulse elicited an average of 7.25 ± 1.75 action potentials. Increase in excitability that followed reduction of IK,Ca was statically significant (paired t test, t3 = -4.04; 2-tailed P < 0.03).

Experimentally, one method of selectively decreasing IK,Ca is to apply low concentrations (2-5 mM) of TEA (e.g., Walsh and Byrne 1989). Empirically derived dose-response relationships between the concentration of external TEA and the magnitude of IK,Ca indicated that 2 mM should reduce IK,Ca (presumably both IK,Ca-F and IK,Ca-S) to ~25% of its control value (Baxter and Byrne 1989; Herman and Gorman 1981). In addition, 2 mM TEA should reduce the magnitude of IK-V to ~80% of its control value. Thus to simulate the presence of a low concentration of TEA, gK,Ca-F and gK,Ca-S were both reduced to 25% and gK-V was reduced to 80% of their control values. The excitability of the model cell in the simulated presence of 2 mM TEA was tested by injecting a 1-s, 2-nA depolarizing current pulse. The test pulse elicited nine action potentials in the simulated presence of a low concentration of TEA (Fig. 14A2) as compared with three action potentials that were elicited by an identical current pulse in simulated control conditions (Fig. 14A1). Thus the simulations predicted that a low concentration of TEA should block accommodation.

The effects of a low concentration of TEA on accommodation also were examined experimentally (Fig. 14B). In control saline, a 1-s, 2-nA depolarizing current pulse elicited six action potentials, whereas an identical current pulse elicited 11 spikes in the same cells after bath application of 2 mM TEA. Summary data from four similar experiments were illustrated in Fig. 14B3. The number of spikes elicited by 1-s, 2-nA current was significantly increased in the presence of 2 mM TEA. The close agreement between the simulated results and the empirical observations supports the prediction of the model that IK,Ca plays key role in regulating accommodation of sensory neurons and that its down regulation by 5-HT contributes to increases in excitability.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The present study incorporated the available voltage-clamp data on the currents in sensory neurons and their modulation by 5-HT into a Hodgkin-Huxley-type mathematical model of the soma of a sensory neuron. The model successfully mimicked key biophysical properties of the sensory neuron, such as the waveform of its action potential and accommodation of spiking during prolonged (i.e., 1 s) stimulation. Moreover, the model reproduced several types of plasticity in the sensory neuron soma, such as increases in the duration of the action potential and excitability in response to the application of 5-HT as well as the responses of sensory neurons to activation of PKA and PKC. Analyses of the model were able to differentiate the effects of the various known modulatory actions of 5-HT on membrane conductances and to evaluate their relative contribution of 5-HT-induced plasticity. In addition, the results from these simulations made several testable predictions that can help to guide future experimental studies.

Roles of IK-V, IK,S, IK,Ca-S, and ICa-L in 5-HT induced plasticity

Results from the current model indicated that IK-V was the major current responsible for repolarization of the action potential, hence, the modulation of IK,V was the key determinant of action potential broadening induced by either 5-HT, PKC, or PKA. The varying degrees to which experimental manipulations modified the properties of IK-V were reflected directly in the magnitude of spike broadening that they induced. The simulated actions of PKA modulated only the activation time constant of IK-V, and although this was sufficient to reduce the outward current early in voltage-clamp steps, it was not as effective as the actions of PKC or 5-HT, which both slowed the activation and decreased the conductance. Thus the simulated actions of PKA produced less broadening of the action potential than either PKC or 5-HT.

The modulation of excitability emerged from the complex interactions among multiple factors and required the concurrent modulation of several conductances. The roles of IK-V and ICa-L in regulating excitability were paradoxical, as modulation of these currents increased Ca2+ influx, which in turn increased the activation of IK,Ca, thus constituting a negative feedback loop in the control of excitability. This negative feedback loop was overcome to a limited degree by down regulation of other outward currents, namely IK,S. Before dramatic increases in excitability could be achieved, however, it was necessary to reduced the gain of the negative feedback loop by down regulating IK,Ca-S. Thus the results of the present study suggested a prominent role for the modulation of IK,Ca-S in mediating 5-HT-induced increases of excitability.

Relative contributions of PKA- and PKC-mediated actions to serotonergic modulation of sensory neurons

Although PKA and PKC modulated an identical set of membrane conductances, there were relatively subtle variations in the degrees to which the two protein kinases modulated the currents, and these differences could explain the different physiological response that have been attributed to PKA and PKC. Empirical studies have indicated that activation of PKA can mimic fully the actions of 5-HT on excitability but can mimic only partially 5-HT-induced spike broadening (e.g., Baxter and Byrne 1990a; Sugita et al. 1994b). Conversely, empiric studies have indicated that activation of PKC can induce spike broadening comparable with that of 5-HT but that activation of PKC induced only moderated increases in excitability (Sugita et al. 1992, 1997a). The present simulations illustrated that although PKA modulated IK-V, the degree of this modulation was inadequate to broaden the spike to the same extent as 5-HT. The PKA-mediated modulation of the currents that regulate excitability, however, was equal to that produced by 5-HT. Indeed, PKA-induced increases in excitability exceeded that induced by 5-HT in some cases. Similar results have been observed in empirical studies (e.g., Baxter and Byrne 1990a). Conversely, PKC modulated the membrane currents that regulate excitability to a lesser degree than PKA, and PKC induced greater broadening, which acted indirectly to decrease excitability. Thus the simulated actions of PKC did not produce increases in excitability comparable to 5-HT. These results indicate that no one second-messenger/protein kinase system can account fully for the actions of 5-HT. The combined actions of PKC and PKA were necessary to account for the previously described actions of 5-HT on the biophysical properties of sensory neurons.

The present study did not investigate two important features of the relative contributions of PKA and PKC to serotongeric modulation, however. These are the temporal development the PKA- and PKC-mediated modulation after application of 5-HT and the mechanisms of interactions between the PKA and PKC cascades. Implicit in the formulation of the present model was the concept that the modulation of IK,S and IK,Ca-L by PKC was indirect and ultimately was mediated via PKA, which was activated after PKC-induced increases in levels of cAMP. In such a serial interaction, some of the modulatory effects of PKC would be blocked by experimental manipulations that specifically block PKA. Specifically, PKC-induced increases in excitability would be prevented by blocking PKA if the interaction was serial in nature. These issues have not been investigated experimentally. In addition, the present model assumed that the PKC-mediated modulation of IK,V was direct and was not mediated in anyway via its interactions with the cAMP/PKA cascade. This assumption appears to be valid because many of the modulatory actions of PKC (and 5-HT) on IK-V are not mimicked by PKA (Goldsmith and Abrams 1992; Hochner and Kandel 1992; Sugita et al. 1994a) Thus the two protein kinase cascades appear to converge on IK-V and modulated this conductance via parallel pathways.

In addition to varying in the degree to which they modulate a common set of membrane conductances, the PKA and PKC cascades may differ in the rates at which they become active after application of 5-HT. The actions of PKC appear to develop relatively slowly, whereas as the actions of PKA appear to develop more rapidly (Hochner and Kandel 1992; Sugita et al. 1992; for review, see Byrne and Kandel 1996). Thus the spike broadening that is observed soon after application of 5-HT is believed to be mediated via the PKA cascade, whereas spike broadening at later times is believed to be mediated to a greater extent via the PKC cascade. Current limitations of the SNNAP software precluded developing models that could investigate the temporal development of serotonergic modulation of sensory neurons. In addition, the present model was developed from data describing the steady-state modulation of membrane currents by 5-HT, PKA, and PKC, and thus the results of the present study represent the steady-state modulation of the biophysical properties of sensory neurons.

Discrepancies between the properties of the model and empirical observations

Although the model was able to accurately simulate many key features of the biophysical properties of sensory neurons and their modulation, there were some discrepancies between the simulated properties of the cell and the available empirical data. The predicated 5-HT-induced increases in excitability during a 1-s, 1-nA current pulse were less than the average empiric observation. The model predicted a response of four spikes, whereas the empirical data suggested an average response of about seven spikes. This discrepancy may indicate that the model would benefit from additional refinements. For example, nothing is know about the Na+ current in these sensory neurons. A more accurate description of important component of the model may resolve this discrepancy. Moreover, the results of the present study indicated that IK,Ca-S played a key role in regulating excitability. The present description of this current was based on a minimum of assumptions, and it did not incorporate voltage- and/or time-dependent activation or inactivation. It may be possible to correct this discrepancy by incorporating some degree of voltage-dependent activation of IK,Ca-S that further enhances the excitability of the cell at the resting membrane potentials in the presence of 5-HT. Indeed, the data of Walsh and Byrne (1989) suggested that some nonlinear characteristics for this conductance at membrane potentials <0 mV. Given the important role of IK,Ca-S that is predicted by the present study, additional investigation of this current appears to be warranted (see following text).

Predictions from the model

The results of the present study make several predictions that can help to guide future experimental studies. First, the present study suggests that IK,Ca-S plays an important role in regulating excitability. The original work of Walsh and Byrne (1989) investigated the contribution that modulation of this current makes to the modulatory effects of 5-HT (and cAMP) on membrane currents, but they did not investigate how modulating this current might effect the spike or excitability of sensory neurons. The present study was the first to consider this issue, and as an initial step toward testing this prediction, the actions of a low concentration of TEA on excitability were investigated experimentally. The results of the experiment agreed with the prediction of the model that blocking IK,Ca would enhance excitability. The important role that IK,Ca-S played in the current model indicates that this current warrants additional empirical characterization. Second, the present study suggests that Ca2+-dependent inactivation of ICa also contributes to the regulation of excitability. This aspect of Ca2+ currents in sensory neurons has not been investigated. More generally, the simulations suggested a more comprehensive investigation is warranted of how multiple factors interact to regulate excitability. Finally, the development of this model highlights a significant deficit in the current characterization the biophysical properties of sensory neurons. Nothing is known about the Na+ current(s) in these cells or the extent to which Na+ current may be modulated. Although the current model appears to accurately simulate many properties of sensory, incorporating a more accurate description of the Na+ current may reveal new insights into the biophysical properties and modulation of sensory neurons. In summary, the present model quantifies the current state of knowledge regarding serotonergic modulation of membrane currents in sensory neurons of Aplysia and can provide a theoretical framework to use in the design and interpretation of experiments to further our understanding of these phenomenon.


    APPENDIX
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The membrane potential (Vm) of the sensory neuron was given by the differential equation
−<IT>C</IT> <FR><NU><IT>d</IT><IT>V</IT><SUB><IT>m</IT></SUB></NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT><FENCE><LIM><OP>∑</OP><LL><IT>ion</IT></LL></LIM> <IT>I</IT><SUB><IT>ion</IT></SUB></FENCE><IT>−</IT><IT>I</IT><SUB><IT>stim</IT></SUB> (A1)
where Cm is the membrane capacitance (0.13 nF), Sigma Iion represents the sum of the various ionic currents (see Fig. 2A) and IStim represents an extrinsic stimuli. Each ionic current was obtained by solving the equation Iion = gion (Vm - Eion), where gion is the underlying conductance and Eion is the reversal potential associated with the conductance. Voltage- and time-dependent conductances were represented with the use of a Hodgkin-Huxley-type formulation. Each ionic conductance was evaluated by solving the general equation
<IT>g</IT><SUB><IT>ion</IT></SUB><IT>=</IT><IT>g</IT><SUB><IT>max</IT>(<IT>ion</IT>)</SUB><IT>A</IT><SUP><IT>p</IT></SUP><SUB><IT>ion</IT></SUB>(<IT>&ugr;, </IT><IT>t</IT>)<IT>B</IT><SUB><IT>ion</IT></SUB>(<IT>&ugr;, </IT><IT>t</IT>)<IT>f</IT>[<IT>REG</IT>] (A2)
where gmax(ion) is the maximal value of gion, Aion(v, t) and Bion(v, t) are functions describing the voltage- and time-dependent activation and inactivation, respectively, associated with gion, p is the power to which Aion was raised and f[REG] is a function that describes the concentration-dependent regulation of currents (e.g., Ca2+-dependent activation of a K+ conductance or Ca2+-dependent inactivation of a Ca2+ conductance; see following text). Aion and Bion were given by the solution to the general differential equations
<FR><NU>d<IT>A</IT><SUB><IT>ion</IT></SUB></NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>A</IT><SUB><IT>∞</IT>(<IT>ion</IT>)</SUB><IT>−</IT><IT>A</IT><SUB><IT>ion</IT></SUB></NU><DE><IT>&tgr;</IT><SUB><IT>A</IT>(<IT>ion</IT>)</SUB></DE></FR> (A3a)

<FR><NU>d<IT>B</IT><SUB><IT>ion</IT></SUB></NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>B</IT><SUB><IT>∞</IT>(<IT>ion</IT>)</SUB><IT>−</IT><IT>B</IT><SUB><IT>ion</IT></SUB></NU><DE><IT>&tgr;</IT><SUB><IT>B</IT>(<IT>ion</IT>)</SUB></DE></FR> (A3b)
where Ainfinity (ion) and Binfinity (ion) are the voltage-dependent steady-state values of the activation and inactivation functions, respectively. tau A(ion) and tau B(ion) are the voltage-dependent time constants of the activation and inactivation functions, respectively. The values of Ainfinity (ion), Binfinity (ion), tau A(ion), and tau B(ion) were determined from the general equations
<IT>A</IT><SUB><IT>∞</IT>(<IT>ion</IT>)</SUB><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>1+exp</IT>((<IT>V</IT><SUB><IT>m</IT></SUB><IT>−</IT><IT>h</IT><SUB><IT>A</IT>(<IT>ion</IT>)</SUB>)<IT>/</IT><IT>s</IT><SUB><IT>a</IT>(<IT>ion</IT>)</SUB>)</DE></FR> (A4a)

<IT>B</IT><SUB><IT>∞</IT>(<IT>ion</IT>)</SUB><IT>=</IT><FR><NU><IT>1−</IT><IT>B</IT><SUB><IT>min</IT>(<IT>ion</IT>)</SUB></NU><DE>(<IT>1+exp</IT>((<IT>V</IT><SUB><IT>m</IT></SUB><IT>−</IT><IT>h</IT><SUB><IT>B</IT>(<IT>ion</IT>)</SUB>)<IT>/</IT><IT>s</IT><SUB><IT>B</IT>(<IT>ion</IT>)</SUB>))<SUP><IT>p</IT><SUB><IT>B</IT>(<IT>ion</IT>)</SUB></SUP></DE></FR><IT>+</IT><IT>B</IT><SUB><IT>min</IT>(<IT>ion</IT>)</SUB> (A4b)

&tgr;<SUB><IT>A</IT>(<IT>ion</IT>)</SUB><IT>=</IT><FR><NU><IT>&tgr;</IT><SUB><IT>A</IT>(<IT>max</IT>)(<IT>ion</IT>)</SUB><IT>−&tgr;</IT><SUB><IT>A</IT>(<IT>min</IT>)(<IT>ion</IT>)</SUB></NU><DE><LIM><OP>∏</OP><LL><IT>j′=1</IT></LL><UL><IT>nexp</IT></UL></LIM> (<IT>1+exp</IT>((<IT>V</IT><SUB><IT>m</IT></SUB><IT>−</IT><IT>h</IT><SUB><IT>&tgr;A</IT>(<IT>ion</IT>)</SUB>)<IT>/</IT><IT>s</IT><SUB><IT>&tgr;A</IT>(<IT>ion</IT>)</SUB>))</DE></FR><IT>+&tgr;</IT><SUB><IT>A</IT>(<IT>min</IT>)(<IT>ion</IT>)</SUB> (A4c)

&tgr;<SUB><IT>B</IT>(<IT>ion</IT>)</SUB><IT>=</IT><FR><NU><IT>&tgr;</IT><SUB><IT>B</IT>(<IT>max</IT>)(<IT>ion</IT>)</SUB><IT>−&tgr;</IT><SUB><IT>B</IT>(<IT>min</IT>)(<IT>ion</IT>)</SUB></NU><DE><LIM><OP>∏</OP><LL><IT>j′=1</IT></LL><UL><IT>nexp</IT></UL></LIM> (<IT>1+exp</IT>((<IT>V</IT><SUB><IT>m</IT></SUB><IT>−</IT><IT>h</IT><SUB><IT>&tgr;</IT><IT>B</IT>(<IT>ion</IT>)</SUB>)<IT>/</IT><IT>s</IT><SUB><IT>&tgr;</IT><IT>B</IT>(<IT>ion</IT>)</SUB>))</DE></FR><IT>+&tgr;</IT><SUB><IT>B</IT>(<IT>min</IT>)(<IT>ion</IT>)</SUB> (A4d)
Explanations of the symbols in Eqs. A4, a-d, are given in Table 1. For IK-V, the value Bmin(ion) was 0.07. In all other cases, the value for this parameter was 0. For IK-V, the value for pB(ion) was 2.0. In all other cases, the value for this parameter was 1.0. A two-exponential model was used to solve for tau A of ICa-L, ICa-N, IK-A, and IK,S-V (i.e., n exp = 2 in Eq. A4c), and for tau B of IK-V, ICa-L, and ICa-N (i.e., n exp = 2 in Eq. A4d). In all other cases, a single-exponential model was used (see Table 1).

The model of the sensory neuron also incorporated a relatively simple description of an intracellular pool of Ca2+ (see Fig. 2B). The dynamics of this pool were described by a first order process and the concentration of Ca2+ in the pool was obtained by solving the differential equation
<FR><NU>d[Ca<SUP>2+</SUP>]</NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>K</IT><SUB><IT>Ca</IT></SUB>(−<IT>&Sgr; </IT><IT>I</IT><SUB><IT>Ca</IT></SUB>)<IT>−</IT>[<IT>Ca<SUP>2+</SUP></IT>]</NU><DE><IT>&tgr;<SUB>Ca</SUB></IT></DE></FR> (A5)
here [Ca2+] is the concentration of Ca2+ (in arbitrary units) in the pool, KCa is a scaling constant (KCa = 18), Sigma ICa is the sum of the two Ca2+ currents that contribute to the pool, and tau Ca is the time constant (tau Ca = 0.2 s). Although this description was simpler than previously published models (e.g., Blumenfeld et al. 1992; Gingrich et al. 1988), it was sufficient to simulate the empirically observed properties of IK,Ca (e.g., their thresholds for activation and kinetics), for which purpose it was primarily included. The intracellular Ca2+ contributed to the regulation of some of the ionic currents (see Fig. 2B). The conductances of these currents were either enhanced or attenuated by the intracellular concentration of Ca2+ as described by
<IT>f</IT>[<IT>REG</IT>]<IT>=</IT><FENCE><AR><R><C><IT>gbr</IT></C><C><IT>for enhancement</IT></C></R><R><C><FR><NU><IT>1</IT></NU><DE><IT>1+&bgr;·</IT><IT>gbr</IT></DE></FR></C><C><IT>for attenuation</IT></C></R></AR></FENCE> (A6)
where gbr describes the relation between the concentration of Ca2+ and the level of enhancement or attenuation and beta  is a constant. For the Ca2+-dependent activation of the two K+ currents (IK,Ca-F and IK,Ca-S), gbr was described by
<FR><NU>d(<IT>gbr</IT>)</NU><DE><IT>d</IT><IT>t</IT></DE></FR><IT>=</IT><FR><NU>[<IT>Ca<SUP>2+</SUP></IT>]<IT>−</IT><IT>gbr</IT></NU><DE><IT>&tgr;</IT><SUB><IT>gbr</IT></SUB></DE></FR> (A7)
where [Ca2+] is the concentration of Ca2+ in the intracellular pool (see Eq. A5), and tau gbr is a time constant (tau gbr = 0.01 s for IK,Ca-F and tau gbr = 3 s for IK,Ca-S). Although Ca2+-dependent inactivation of Ca2+ currents has not been investigated in sensory neurons of Aplysia, Ca2+-dependent inactivation is a general feature of L- and N-type Ca2+ conductances (for reviews, see Eckert and Chad 1984; Hille 1992; Tsien et al. 1988). Thus the descriptions of the two Ca2+ currents (ICa-L and ICa-N) were extended to include functions that described their regulation by intracellular levels of Ca2+. For the Ca2+-dependent inactivation of the two Ca2+ currents (ICa-L and ICa-N), gbr was described by
<IT>gbr</IT><IT>=</IT><FR><NU>[<IT>Ca<SUP>2+</SUP></IT>]</NU><DE><IT>K</IT><SUB><IT>Ca−</IT>(<IT>n</IT>)</SUB><IT>+</IT>[<IT>Ca<SUP>2+</SUP></IT>]</DE></FR> (A8)
where [Ca2+] is the concentration of Ca2+ in the intracellular pool (see Eq. A5), KCa-(n) is a constant (KCa-N = 60 and KCa-L = 75, and beta  = 17 for both ICa-L and ICa-N (see Eq. A6).


    ACKNOWLEDGMENTS

The SNNAP modeling software and the input files for the simulations in the present study can be obtained at http://nba19.med.uth.tmc.edu/public/publish/dbaxter.

This work was supported by grants from the National Institutes of Health (R01-RR-11626 and P01-NS-38310).

Present address of C. C. Canavier: Dept. of Psychology, University of New Orleans, New Orleans, LA 70148.


    FOOTNOTES

Address for reprint requests: D. A. Baxter, Dept. of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas-Houston Medical School, P.O. Box 20708, Houston, TX 77225.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1 Recent evidence suggests that 5-HT also activates mitogen-activated kinase (MAPK) (Michael et al. 1998) and possibly Ca2+/calmodulin-dependent kinase II (CamKII) (Nakanishi et al. 1997). There is no evidence at this time, however, that these kinases modulate membrane conductances.

2 Activation of PKC by phorbol esters also has been reported to increase the magnitude of Ca2+-activated K+ currents (IK,Ca) (Critz and Byrne 1992). This effect of phorbol esters, however, does not appear to be mimicked by 5-HT (Walsh and Byrne 1989).

3 At the resting membrane potential, there was a small, but finite, conductance to Ca2+, which in turn, lead to a small level of activation of IK,Ca-S. Using Faraday's constant and the volume of a sensory neuron with a radius of 10 µm, the Ca2+ current at the resting potential was calculated to yield a basal concentration of intracellular Ca2+ equivalent to ~21 nM (higher if one assumes smaller intracellular volumes) (see Yamada et al. 1998).

4 Note, data indicate that sensory neurons in isolated culture have input resistances >100 MOmega (e.g., Dale et al. 1987; Manseau et al. 1998). These data were not included in the present analysis.

5 Increasing the PKA-mediated modulation of ICa-L to 500% did, however, increase the duration of the PKA-modulated spike to 124% of control (not shown). Similarly, if the magnitude of 5-HT-induced modulation of ICa-L was increased to 500%, the duration of the 5-HT-modulated spike was increased to 147% of control (not shown).

Received 21 August 1998; accepted in final form 12 July 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

0022-3077/99 $5.00 Copyright © 1999 The American Physiological Society