Mechanisms of Onset Responses in Octopus Cells of the Cochlear Nucleus: Implications of a Model

Yidao Cai, Edward J. Walsh, and JoAnn McGee

Developmental Auditory Physiology Laboratory, Boys Town National Research Hospital, Omaha, Nebraska 68131

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Cai, Yidao, Edward J. Walsh, and JoAnn McGee. Mechanisms of onset responses in octopus cells of the cochlear nucleus: implications of a model. J. Neurophysiol. 78: 872-883, 1997. The octopus cells of the posteroventral cochlear nucleus receive inputs from auditory-nerve fibers and form one of the major ascending auditory pathways. They respond to acoustic and electrical stimulation transiently and are believed to carry temporal information in the precise timing of their action potentials. The mechanism whereby onset responses are generated is not clear. Proposals aimed at elucidating the mechanism range from neural circuitry and/or inhibition, "depolarization block" (or inactivation of Na+ channels), and the involvement of a 4-aminopyridine (4-AP)-sensitive, low-threshold channel (KLT). In the present study, we used a compartment model to investigate possible mechanisms. The model cell contains a soma, an axon, and four passive dendrites. Four kinds of ionic channels were included in the soma compartment: the Hodgkin-Huxley-like Na+ and K+ channels, a 4-AP-sensitive, low-threshold channel, KLT, and a Cs+-sensitive, hyperpolarization-activated inward rectifier, Ih. DC currents and half-wave-rectified sinewaves were used as stimuli. Our results showed that an onset response can be generated in the absence of neuronal circuitry of any form, thus suggesting that the onset response in octopus cells is regulated intrinsically. Among the many factors involved, low-input impedance, partly contributed by Ih, appears to be essential to the basic onset response pattern; also, the KLT conductance plays a major role, whereas the inactivation of Na+ channels probably plays only a secondary role. The dynamics of Ih also can modify the response pattern, but due to its slow kinetics, its role is probably limited to longer-term regulation under the conditions simulated in this study.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Octopus cells lie in a distinct region within the posteroventral cochlear nucleus (PVCN) known as the octopus cell area (OCA) (Bawer et al. 1974; Kane 1973; Osen 1969). They have relatively large cell bodies and thick dendrites, which taper slightly in the proximal-distal dimension, distinguishing them from other cell types in the cochlear nuclei (Golding et al. 1995; Kane 1973, 1974; Morest et al. 1973; Oertel et al. 1990; Ostapoff et al. 1994; Rhode et al. 1983). Inputs from auditory-nerve fibers spanning a relatively wide range of characteristic frequencies converge onto octopus cells, and their outputs project through the intermediate acoustic stria contralaterally to the dorsal-medial periolivary nucleus and the ventral nucleus of the lateral lemniscus, forming one of the major ascending auditory pathways (Adams and Warr 1976; Smith et al. 1993; Warr 1969, 1972, 1982). Although the specific functions of such cells are not known, they are thought to carry temporal information in the precise timing of action potentials (Godfrey et al. 1975). Because it has been suggested that the timing of the action potentials underlies the perception of pitch, octopus cells probably contribute to pitch perception (Golding et al. 1995; Oertel 1991; Rhode 1995).

Octopus cells produce onset responses to acoustical and electrical stimuli, i.e., under conditions of continuous acoustic stimulation, they show a major peak near the time of stimulus onset in the poststimulus time histogram (PSTH) (Godfrey et al. 1975; Kiang et al. 1973; Rhode and Smith 1986a; Rouiller and Ryugo 1984) and sustained depolarization in intracellular recordings in vivo (e.g., Feng et al. 1994). With current injection, they usually fire one action potential at the stimulus onset followed by sustained depolarization (e.g., Feng et al. 1994; Romand 1978). These two forms of onset responses (i.e., the onset action potential under current stimulation and the onset PSTH pattern under acoustic stimulation) are related, as it has been shown that both can be recorded from the same octopus cells (Feng et al. 1994; Ostapoff et al. 1994). Although there are other cell types in the cochlear nuclei (e.g., the multipolar cell and the fusiform cell) showing onset responses (Friauf and Ostwald 1988; Rhode and Smith 1986a,b; Rhode et al. 1983; Smith and Rhode 1989), the correspondence between octopus cells and the onset response pattern has been established by structural and functional correlation (Godfrey et al. 1975) and by combined anatomic and physiological studies using labeling techniques, both in vivo (Feng et al. 1994; Ostapoff et al. 1994; Rhode et al. 1983; Rouiller and Ryugo 1984) and in brain slice preparations (Golding et al. 1995).

The mechanisms underlying the production of the onset response pattern in octopus cells, however, are not clear. An obvious possibility is that it might be due to neural circuitry involving interneuron(s). But this has been excluded virtually from consideration based on the short latency of responses (Godfrey et al. 1975; Kane 1973; Ritz and Brownell 1982). The observation that a single auditory-nerve fiber can give rise to two types of synaptic endings on a single octopus cell (Kane 1973; cf. footnote 3) raised the possibility of an interaction between excitatory and inhibitory effects in which the inhibitory inputs were provided by the thin auditory-nerve fiber collaterals (Godfrey et al. 1975; Kane 1973; Morest et al. 1973). Immunostaining studies indicated that inhibitory neurotransmitters are present in synapses located at the soma and proximal dendrites of octopus cells in cats [gamma -aminobutyric acid (GABA): Adams and Mugnaini 1987; Saint Marie et al. 1989] and guinea pigs (glycine: Wenthold et al. 1988) and in the PVCN of cats (glycine: Wenthold 1987) and guinea pigs (GABA: Wenthold et al. 1986; GABA and glycine: Wenthold et al. 1987). However, GABA staining was usually weaker in the PVCN than in other parts of the cochlear nuclei (Wenthold et al. 1986), and glycine staining was weak or even absent in the PVCN (Altschuler et al. 1986; Saint Marie et al. 1991; Wenthold et al. 1987). In mice, inhibitory postsynaptic potentials were shown to be present in other cell types in the cochlear nuclei, however, none have been recorded in octopus cells (Golding et al. 1995; Hirsch and Oertel 1988; Wu and Oertel 1986).

More recently, attention has focused on the intrinsic properties of octopus cells. There have been suggestions (Feng et al. 1994; Ritz and Brownell 1982) that the onset response is due to the inactivation of Na+ channels (Hodgkin and Huxley 1952a) or "depolarization block." Because an octopus cell receives inputs from many auditory-nerve fibers, the multiple inputs maintain the cell in a depolarized state after the initial spike, thus inactivating the voltage-sensitive Na+ channels and preventing the cell from firing additional spikes. Intracellular recordings indeed show sustained depolarization under either acoustical stimulation (Feng et al. 1994) or current injection (Feng et al. 1994; Romand 1978), but it is unclear whether the Na+ channel is inactivated under those conditions. Another suggestion (Feng et al. 1994) implicates the 4-aminopyridine (4-AP)-sensitive, low-threshold K+ channel (KLT), a channel that is similar to that found in type II neurons of the ventral cochlear nucleus (Manis and Marx 1991) and in neurons of the medial nucleus of the trapezoid body (MNTB) (Banks and Smith 1992) as well as in octopus cells (Golding et al. 1995). As intracellular recordings from octopus cells are complicated by low input impedance (Golding et al. 1995), we have implemented a compartment model to test the above hypotheses with the intention of gaining insight into the mechanism by which onset responses are generated in octopus cells.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Octopus cell model

The octopus cell model used in this study was based on available anatomic and physiological data (Golding et al. 1995; Kane 1973, 1974; Oertel et al. 1990; Rhode 1985; Rhode et al. 1983; Schwartz and Kane 1977). As schematized in Fig. 1A, the model cell has a soma, an axon, and four identical dendrites. We chose a soma diameter of 32 µm, which is about the lower-median for cats and upper boundary for mice. Given the fact that there is no evidence suggesting major differences in axon morphology of different neuron types in the cochlear nucleus, we modeled the axon as in the stellate cell model of Banks and Sachs (1991) (i.e., 3 µm in diam and 70 µm in length). This axonal model is not intended to represent the entire axon in an octopus cell. Dendrites were modeled as cylinders for simplicity, each being 200 µm in length and 5 µm in diam, even though the dendrites of octopus cells taper slightly (Golding et al. 1995; Kane 1973, 1974; Morest et al. 1973; Oertel et al. 1990; Ostapoff et al. 1994; Rhode et al. 1983; Schwartz and Kane 1977).


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FIG. 1. A: a schematic representation of octopus cell model (d, diameter; l, length). B: compartmental representation of model. Soma and axon are each represented by one compartment (square ), while each dendrite is divided into 20 sections of equal length and thus represented by same number of compartments. Compartments are interconnected with resistors. C: details inside each square  (compartment). Each compartment contains a membrane capacitor (Cm) and a leakage branch consisting of a resistor (conductance gleak) and a battery (leakage equilibrium potential Eleak). It also may contain other branches (gi-Ei) representing active channels (e.g., Na+ and K+ channels).

The basic electrical parameters of the model were chosen within the widely accepted ranges measured for various cell types and adjusted to fit available physiological data. Specifically, the membrane capacitance density (Cm) was set to 1 µF/cm2, which is typical for cell membranes (Jack et al. 1983). The membrane time constant (tau m) was set to 1 ms, consistent with values observed in slice preparations (Golding et al. 1995). Consequently, the membrane resistivity (Rm) was calculated to be 1 kOmega /cm2, which is in the lower bound of standard values (Jack et al. 1983). We selected an axial resistivity (Ri) of 100 Omega /cm, a value that is standard in such cell models (Jack et al. 1983). As will be shown, these basic electrical parameters, together with the morphological parameters, determine other passive electrical parameters used in the model.

Although there is increasing evidence suggesting that dendrites can be active and that active dendrites play important roles in neuronal signal processing (e.g., Lipowsky et al. 1996; Wilson 1995; see Cai et al. 1997 for review), we chose to model the dendrites as passive for simplicity. The dendrites have a space constant (lambda ) of 354 µm (the electrotonic length, i.e., the length expressed in terms of the space constant, is 0.565). Each dendrite is divided into 20 compartments (Fig. 1B). Thus each compartment is 10 µm long with an electrotonic length of 0.0282. On the other hand, the soma and axon contain active channels and each are represented by a single compartment.

In addition to the Hodgkin-Huxley type Na+ and K+ channels (Hodgkin and Huxley 1952b), there are two other major types of ionic conductances in octopus cells: KLT and a Cs+-sensitive conductance, Ih (Golding et al. 1995). The latter is a hyperpolarization-activated inward rectifier and is responsible for the low input impedance of this neuronal type. It bears resemblance to the Ih found in a variety of other cell types (e.g., in Purkinje fibers, DiFrancesco 1981; in thalamic relay neurons, McCormick and Pape 1990; and in retinal ganglion cells, Tabata and Ishida 1996), including MNTB neurons (Banks et al. 1993). Because there is no quantitative data characterizing the kinetics of channels in octopus cells, the kinetics of the Hodgkin-Huxley type Na+ and K+ channels were modeled in accordance with those in models of stellate cells (Banks and Sachs 1991) and pyramidal cells (Hewitt and Meddis 1995) of the dorsal cochlear nucleus. The kinetics of KLT were modified from those of the type II neurons in ventral cochlear nucleus (Manis and Marx 1991). The kinetics of Ih vary greatly from one neuron type to another (Banks et al. 1993; McCormick and Pape 1990; Tabata and Ishida 1996). Although Banks et al. (1993) have reported second-order kinetics for Ih associated with MNTB cells, studies of other cell types revealed first-order kinetics. In our representation, we emphasized their slow dynamics and different time courses of activation and deactivation and chose to use only first-order kinetics. The detailed kinetics of each channel type can be found in the APPENDIX.

In the axon compartment, only Hodgkin-Huxley type Na+ and K+ channels were included, as in the stellate cell model of Banks and Sachs (1991). For the soma, in addition to the Na+ and K+ channels, we also included KLT and the Cs+-sensitive, hyperpolarization-activated inward rectifier Ih, which are known to exist in octopus cells (Golding et al. 1995). The maximum conductances of the soma Na+ and K+ channels are much lower than those used in the stellate (chopper) cell model in Banks and Sachs (1991), because the Na+ and K+ channels are responsible for generating spikes (Hodgkin and Huxley 1952b), and it was suggested that the action potentials in octopus cells are generated at the axon stage (Golding et al. 1995).

The dendritic compartments are interconnected with serial resistors (cf. Fig. 1B), the conductance of which, as calculated from the geometric data of the dendritic compartments and Ri, is 1.96 × 10-6 S. The conductance between the soma and the first dendritic compartments is twice that of the interdendritic compartments, because the soma is considered to have zero electrotonic length. The axon compartment is connected to the soma compartment with a serial resistor, which has a conductance calculated to be 1.3 × 10-7 S.

As shown in Fig. 1C, there are at least two branches in the circuit representation of each compartment: the capacitance branch representing Cm and the leakage branch (gleak-Eleak) representing the leakage channel. In each dendritic compartment, the leakage branch has a conductance of 1.57 × 10-9 S (calculated using the membrane area of the compartment and Rm) and a leakage equilibrium potential, chosen to be equal to the resting membrane potential of -62 mV. The axon and soma compartments contain active channels (represented by gi-Ei branches in Fig. 1C). Following the usual practice (e.g., Rothman et al. 1993), we fixed the soma leakage conductance (at 3.217 × 10-8 S, a value calculated using the membrane area of the soma and Rm) and adjusted the leakage equilibrium potential (about -58.4 mV) to maintain a stable resting membrane potential of -62 mV. For the axon compartment, we fixed the leakage equilibrium potential (at -53 mV) instead and adjusted the leakage conductance (~2.57 × 10-9 S). The value of the resting potential is somewhat arbitrary, considering the wide range of values reported for octopus cells in the literature (in vivo: -10 to -70 mV in Romand 1978; about -30 mV in Rouiller and Ryugo 1984; -35 to -70 mV in Feng et al. 1994; in slice: -50 to -70 mV in Golding et al. 1995).

Stellate cell model

The stellate (chopper) cell is known to fire regularly to stimulation even at low levels (Oertel 1983; Oertel et al. 1988; Rhode and Smith 1986a). It would help us gain insight into the mechanisms of onset responses if the chopper response associated with the stellate cell models could be converted into an onset response by modifying a specific set of model parameters. Thus we implemented a stellate cell model based on that of Banks and Sachs (1991). The morphological and basic electrical parameters were as described in their paper. Specifically, the model cell has a 25-µm-diam soma, an axon 70 µm in length and 3 µm diam, and six dendrites each 600 µm in length and 2.2 µm diam. Cm was 1 µF/cm2, Rm was 10 kOmega /cm2 and Ri was 150 Omega /cm. The only modification was in relation to the Na+ and K+ channel kinetics. We chose the kinetics specified by Hewitt and Meddis (1995) for pyramidal cells of dorsal cochlear nucleus, but made minor adjustments in parameters to produce responses to current inputs that were similar to those reported in Banks and Sachs (1991).1

Simulation program

Simulations were performed on either a PC under DOS or unix workstations with a program developed in our laboratory (Cai et al. 1997). The program automatically configures the model according to information available in a parameter file, which was used to store model parameters. To simulate different models and/or conditions, the parameter file can be adjusted, and no change in the simulation program is necessary. Notice that all compartments, whether they contain active channels or not, are treated uniformly (cf. Fig. 1C). One differential equation then can be written for each compartment. Due to the uniform treatment of all compartments, these equations have the same form. The conductances of the active channels are treated the same way as fixed conductances in the equations, but the conductance values are updated at each time step according to the kinetics of the channels. The equations were solved numerically using the modified Crank-Nicolson method (Hines 1984) and a simple approach for solving equations with branching geometries (Cai et al. 1997). DC currents and half-wave-rectified sinewaves were used as stimuli. The results were obtained at a resolution of 10 µs. However, the data shown in the figures were further subsampled at a rate of 1:16. With our model configuration, it takes a few seconds to finish one simulation on a Pentium-130 PC under DOS.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Stellate cell model can demonstrate onset responses

As described in METHODS, we implemented a stellate cell model based on that of Banks and Sachs (1991) in an effort to generate onset responses by adjusting appropriate model parameters, hoping to gain insight into the mechanisms underlying the production of onset responses. With the original parameters, the model fires regularly in response to depolarizing current (Fig. 2A), even at threshold levels.


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FIG. 2. Response from a stellate (chopper) cell model, modified from that of Banks and Sachs (1991) (see METHODS). A: membrane voltage of soma. B: changes of m (- - -) and h () parameters of soma Na+ channel. Model parameters shown (top of figure) are for soma compartment except otherwise noted, and injected current into soma is shown schematically below voltage response. This convention holds for all other figures in this paper. Vm, membrane voltage; Iinj, injected current; freq, stimulus frequency; leakage, soma leakage channel; gNa, gK, conductances of Na+ and K+ respectively; gmax, maximum channel conductance. Refer to the descriptions of channel kinetics in APPENDIX for meanings of Msh, Hsh, etc.

It was hypothesized that the Na+ channel can be opened by three activating particles, each with a probability m of being in the right place and inactivated with a probability (1 - h) when blocked by one inactivating particle (Hodgkin and Huxley 1952b). Thus the conductance of the Na+ channel is proportional to m3h (cf. equation in the APPENDIX), and the smaller the value of h, the more inactivated the Na+ channel. Shown in Fig. 2B are the changes of m and h parameters of the Na+ channel during the action potentials. During each action potential, the h parameter changes from a high value (noninactivated status) to near zero (inactivated status), then back to a high value after each spike occurs.

Electrical parameters of the model then were modified in an effort to change the sustained spike train into one exhibiting onset spikes only. Most modifications only affected the firing rate and/or the morphology of the action potential, but the basic chopper pattern was unaffected. Increasing the leakage conductance (decreasing Rm), however, produced onset responses.

Figure 3 shows the response of the model to a 40-ms depolarizing current injection, when the leakage conductance in the dendrites was increased by a factor of 10. Other parameters were the same as in Fig. 2. As can be seen, the model responded with only one action potential at the onset of the stimulus, followed by a sustained steady-state depolarization. The values of the h parameter dropped transiently during the action potential but rapidly returned to a high level and maintained a slightly decreased value relative to rest during the steady state. Although it is difficult to determine the exact contribution of depolarization block (the decrease of h) in the generation of the onset response, it is clear that the larger membrane conductance (contributed by the leakage channel) in the dendrite played a key role in the production of the onset response.


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FIG. 3. Stellate cell model that produced responses in Fig. 2 was modified to give rise to an onset response; i.e., membrane leakage conductance of dendrites was increased by a factor of 10. A: membrane voltage of soma. Same 0.15-nA DC current (threshold level) as in Fig. 2 was used as stimulus. B: changes of m and h parameters of soma Na+ channel. Note that Na+ channel is not inactivated (h parameter remains high).

Basic onset responses from the octopus cell model

Although onset responses were successfully produced by modifying the stellate cell model, the response was not realistic. For example, the soma spike is large, and the response reverts to regular firing when the stimulus level is increased slightly. Additionally, the morphology of the model cell is different from that of the octopus cell, and the model does not include the ionic channels that are known to exist in octopus cells.

In our octopus cell model, we set the membrane conductivity to be 10 times that of the stellate cell model (the resistivity, or inverse of conductivity, is 1 kOmega /cm2, or 1/10 of that of the stellate cell model, see METHODS). Because it has been suggested that in octopus cells action potentials are generated at the axon hillock (Golding et al. 1995), we used relatively low maximum conductances for soma Na+ and K+ channels (0.01 nS/cm2 for both, while the corresponding values in the stellate cell model were 0.17 and 0.04 nS/cm2, respectively). The responses of the model neuron to current injections at the soma are shown in Figs. 4 and 5. Due to the large membrane area and large resting membrane conductance (including those contributed by Ih and KLT), the current level used was much higher than that used in the stellate model. With low-level DC current injection, the model neuron fired one action potential at the onset of the stimulus, followed by a steady-state depolarization (Fig. 4). The soma spike is small, reaching only about -25 mV, whereas the axon spike is large. These characteristics are similar to those observed experimentally (Feng et al. 1994; Golding et al. 1995). Notice that although the value of the h parameter decreased transiently, it remains at a high sustained level, suggesting that the Na+ channel was only slightly inactivated. Instead, there was a significant increase in the conductance of KLT.


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FIG. 4. Responses of octopus cell model to a 1.8-nA (slightly above threshold) current injection into soma. In this and subsequent figures, results were obtained with octopus cell model. Model parameters that produced responses in this figure are considered to be reference for those of subsequent figures. A: membrane voltages of soma (low amplitude, , &cjs0681;) and axon (high amplitude, , &cjs0681;). B: changes of m and h parameters of soma Na+ channel. C: change in conductance of low-threshold, 4-AP-sensitive K+ channel (KLT).


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FIG. 5. Responses of octopus cell model to a 300-Hz, half-wave rectified sinewave stimulus. Peak amplitude was 1.9 nA, and current was injected into soma. Model parameters were same as those in Fig. 4. A: membrane voltages of soma (low amplitude, ) and axon (high amplitude, ). Below voltage responses is schematic waveform of stimulus. B: changes of m and h parameters of soma Na+ channel. C: change in conductance of KLT.

Due to the rectifying characteristic of the transfer functions of the inner hair cells (e.g., Dallos 1986; Russell et al. 1986), auditory-nerve fibers fire preferably during half of a stimulus cycle in response to low-frequency stimulation, as evidenced from the phase-locking in the responses of auditory-nerve fibers (e.g., Rose et al. 1967). Thus the use of half-wave-rectified sinewaves as stimuli mimicked, in some aspect, the inputs of the ensemble of auditory-nerve fibers, because octopus cells are thought to converge inputs from many auditory-nerve fibers based on their broad tuning and their high threshold (e.g., Godfrey et al. 1975; Rhode and Smith 1986a). In Fig. 5, we show the response of the model octopus cell when a 300-Hz, half-wave-rectified sinewave current was used as the stimulus. The model parameters were the same as those used in the DC current simulation in Fig. 4. The result was also similar to that shown in Fig. 4. The model responded with only one action potential at the first stimulus cycle. Subsequent cycles of stimulation only evoked small membrane depolarizations, although the sustained value of the h parameter remained at a high level throughout stimulation. The conductance of KLT was, however, increased, as with DC current stimulation in Fig. 4 (but the sustained level of KLT in Fig. 5 was lower than that in Fig. 4, due to the less effective stimulation in the case of the half-wave-rectified sinewave current).

Role of the kinetics of KLT and Ih

The results in Figs. 4 and 5 suggested a link between onset response and the rise of the conductance of KLT. In Figs. 6 and 7, we explore in more detail the effects of the kinetics of KLT on responses of the model. The results shown in Fig. 6 were obtained with the same model parameters as those that produced the results in Fig. 5. We also used the same stimulus, a 300-Hz, half-wave-rectified sinewave current, except at a higher level. A higher level stimulus evokes more spikes during the stimulation and thus affords us the chance to study the dynamics of the kinetics. As expected from the entrainment of responses of octopus cells to low-frequency acoustic stimulation (e.g., Rhode and Smith 1986a), the spikes are timed to the depolarization events (and changes in the stimulus).2


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FIG. 6. Responses of octopus cell model to a 300-Hz, half-wave rectified sinewave stimulus. Peak amplitude of current was 2.21 nA. Model parameters were same as those in Figs. 4 and 5. A: membrane voltages of soma (low amplitude, ) and axon (high amplitude, ). B and C: changes in conductances of Cs+-sensitive, hyperpolarization-activated inward rectifier (Ih) and of KLT. D: changes of m and h parameters of soma Na+ channel. E and F: changes in conductances of Na+ and K+ channels. Note that gNa, gK, gKLT, gIh are conductances of Na+, K+, KLT and Ih, respectively. See text for details about arrows.


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FIG. 7. Responses of octopus cell model. Model parameters were same as those in Fig. 6, except for Bfac of KLT channel, which was changed from 0.75 to 1.0, a modification that "slowed" kinetics of channel by a factor of 4:3. Same 2.21-nA, 300-Hz half-wave rectified sinewave stimulus was used. Format of figures is same as in Fig. 6.

Examination of the exact response pattern shows that the model responded to the first stimulus cycle with a spike, missed one, fired one spike, then missed two cycles, and so on; i.e., the pattern of missing spikes is 1, 2, 2. Examination of the h and m parameters (Fig. 6D) indicates that there was no visible difference in the values of the h parameter at the instant just before the firing of one spike and at the corresponding instant preceding a stimulus cycle (down-arrow ) that did not evoke a spike. There was also no difference in the values of the m parameter (up-arrow ) or in the conductances of Na+ and K+ channels (Fig. 6, E and F, right-arrow). However, there was a significant difference in the conductance of KLT (Fig. 6C, right-arrow), supporting our contention that KLT is a regulatory conductance.

To further establish the role of KLT in the onset response, we tried to "slow" down the kinetics of KLT and examine any possible change in the spike pattern. We used the same stimuli as in Fig. 6, but changed the Bfac of the KLT kinetics from 0.75 to 1.0, the effect of which was to proportionally increase the time constant of the B parameter at all membrane voltages and thus slow down the kinetics by a factor of 4:3 (cf. the description of KLT kinetics in the APPENDIX). In the responses shown in Fig. 7, the first two spikes occurred at the same time as did corresponding spikes in Fig. 6, but after the second spike, three depolarizing events were missed before the "cell" fired the third spike, and so on. The missing pattern is now 1, 3, 3 instead of 1, 2, 2. Because the only parameter change involved Bfac of the KLT kinetics, the results shown in Figs. 6 and 7 demonstrate that the kinetics of KLT are important in the regulation of the firing pattern of the octopus cell model and further support the idea that KLT contributes to the onset response.

In Fig. 6A, the postspike pattern of nonspiking depolarizations was 1, 2, 2 during the first 30 ms of the response. We expected the model neuron to fire a fifth spike in the third stimulus cycle after the fourth spike at the position indicated by the left-downward arrow. It did not. Examination of the kinetics of various channels implemented in the model indicates that the conductances of all channels at the beginning of the missing spike and at the beginning of the fourth spike are the same, with the exception of Ih. This led us to consider the possibility that "the missing 5th spike" resulted from a decrease in the conductance of Ih. To test this hypothesis, we fixed the conductance of Ih at its resting level and repeated the simulation (Fig. 8). Under these conditions, the fifth spike appeared on the third postspike depolarization after the fourth spike, as predicted according to the 1, 2, 2 sequence observed during the preceding 30-ms poststimulus period (Fig. 8A, left down-arrow ).


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FIG. 8. Responses of octopus cell model. Model parameters were same as those in Fig. 6, except that conductance of Ih was fixed at its resting value (B) throughout simulation. Same 2.21-nA, 300-Hz half-wave rectified sinewave stimulus was used. Membrane voltage changes of both soma (low amplitude, ) and axon (high amplitude, ) are shown (A).

Level of Na+ channel inactivation is not a major factor

In the example shown in Fig. 9, we implemented a parameter set in which the model neuron fired more than one spike at the onset of a DC stimulus, followed by a sustained depolarization. We then evaluated the status of Na+ channel inactivation during the spiking events and the steady-state by examining the values of the h parameter. Such a firing pattern was achieved by using a higher maximum conductance of Ih (0.02 nS/cm2 in this case) and higher level currents. Although no intracellular data exist suggesting that an octopus cell can fire multiple spikes at stimulus onset in response to a depolarizing current, this manipulation is nevertheless helpful. Across a relatively wide range of stimulus levels (from <1.8 to 2.9 nA), the model neuron maintained its single-spike pattern (data not shown), suggesting that the basic model parameter might not be atypical for an octopus cell. When a 3.3-nA current was used, the model neuron fired three spikes (Fig. 9). As can be seen from the figure, the values of the h parameter just before the second and third spikes are lower (Na+ channel more inactivated) than that during the steady state. This result suggests that the level of Na+ channel inactivation (or depolarization block) is not a major factor determining the temporal response pattern of octopus cells.


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FIG. 9. Responses of octopus cell model to a 3.3-nA DC current injection into soma. Model parameters were same as those in Figs. 4-6, except that maximum conductance of Ih was doubled (now 0.02 nS/cm2). A: membrane voltages of soma (low amplitude, ) and axon (high amplitude, ). B: changes of m and h parameters of soma Na+ channel. Notice that level of h parameter in steady state is actually higher (indicating that Na+ channel less inactivated) than those before 2nd and 3rd spikes were fired.

Onset response produced with depolarization block

Because it has been suggested that onset responses are due to depolarization block (Feng et al. 1994; Ritz and Brownell 1982), we adjusted our model parameters to simulate onset responses under conditions of depolarization block (Fig. 10A). We used the basic octopus cell model but disabled KLT and Ih and used high-level current to produce the response. In this example, the Na+ channel clearly was inactivated as evidenced by the small value of h during the current injection (Fig. 10B). At low stimulus levels, the model neuron responded with an onset response similar to that shown in Fig. 3. As the stimulus level was slightly increased, the response became regular (not shown). Because a high-level stimulus had to be used to obtain the results shown in Fig. 10 and because we did not implement KLT and Ih, which are known to exist in octopus cells (Golding et al. 1995), the onset response in Fig. 10 is probably not what would happen under physiological conditions.


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FIG. 10. An example of an onset response with Na+ channels inactivated (h low). Basic model parameters were same as those in Figs. 4-6, but KLT and Ih were disabled. A high level (7-nA DC) stimulus was used. A: membrane voltage of soma. B: changes of m and h parameters of soma Na+ channel. Notice that level of h parameter is low during steady state, indicating that Na+ channel was inactivated.

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

The low input impedance of octopus cells makes it difficult to study their properties in vivo (Golding et al. 1995), which probably explains, in part, the lack of experimental data available regarding the characteristics of these cells. Computer modeling allows the opportunity to simulate conditions that are difficult or sometimes impossible to achieve experimentally. In this study, we used a computer model to investigate possible mechanisms underlying the production of onset responses in octopus cells.

Mechanisms of onset responses in octopus cells

Although early studies focused on the possibility that neurons projecting as interneurons or inhibitory inputs played a central role in the generation of onset responses in octopus cells (see INTRODUCTION), our model included neither network nor inhibitory inputs, yet it successfully simulated the onset response. This result supports previous suggestions that the basic onset response pattern does not require the involvement of neuronal circuitry (Godfrey et al. 1975; Kane 1973; Morest et al. 1973) or inhibitory inputs (Wickesberg et al. 1991).3 Although the result does not support the idea that the onset response requires inhibitory inputs, it does not exclude the possibility that inhibitory inputs help to shape other characteristics of the response. However, results reported here support the view that the onset pattern reflects the intrinsic properties of octopus cells.

The results obtained with the stellate cell model (Figs. 2 and 3) suggest that overall membrane conductance is the key factor shaping the onset response. This agrees with the finding that the input impedance of octopus cells is usually very low (Golding et al. 1995). It should be pointed out that, under the conditions of Figs. 2 and 3 (the stellate cell model), the membrane conductance is formed by the leakage conductance alone. However, as shown in Figs. 4-9 (the octopus cell model), the contribution from different channels can be potentially significant. The membrane conductance may be formed mainly by resting conductances of different channels (probably mainly Ih) (see Golding et al. 1995).

As we have shown (Figs. 3 and 10), models that only incorporate large leakage conductances do not produce realistic onset responses and can produce a regular firing pattern at higher stimulus levels. Therefore, there must be other important factors involved in the generation and regulation of the onset responses. The results shown in Figs. 4-7 suggest that KLT plays an important role in producing and regulating the onset response pattern in octopus cells. Such a role is consistent with KLT's role in the generation of the onset-like response in type II (bushy) neurons of the ventral cochlear nucleus (Manis and Marx 1991) and in MNTB neurons (Banks and Smith 1992). Ih also plays a role in the production of the transient, onset spike among these cell types. In addition to its contribution to the membrane conductance, Ih regulates the response pattern (Figs. 6 and 8). But due to its slow kinetics, its regulatory role probably is limited mainly to longer term effects under the conditions we used in this study.

In most of our simulations (Figs. 3-9), the value of the "h" parameter was decreased only slightly during "stimulation", although sustained depolarization was evident in every example where the onset response was generated. This suggests that sustained depolarization does not necessarily lead to inactivation of the Na+ channel (or depolarization block). Furthermore, these results suggest that depolarization block is not a major factor in the generation of onset response in octopus cells, as suggested in earlier postulates (Feng et al. 1994; Ritz and Brownell 1982). The fact that Na+ channel inactivation occurred only at high stimulus levels and that KLT and Ih had to be disabled (Fig. 10), also supports this conclusion.

Model parameters

There is very little information in the literature about the specific kinetics of channels expressed in octopus cells (esp. KLT and Ih). For this reason, it is difficult to identify a set of parameters that fits the fine aspects of most of the existing experimental data. We implemented a wide range of parameters based on existing information regarding the responses of octopus cells, and, although the basic onset responses were produced routinely, the precise response characteristics differ from one set of parameters to another. As shown in Fig. 3, the basic onset response is generated as long as there is a large membrane conductance, and more realistic onset responses (e.g., small soma spikes) can be generated when the soma spike-generating mechanism is minimized (small values of Na+ and K+ channel conductances, Figs. 4 and 5). Although the model parameters selected here may not be physiologically accurate, our choice would not affect the general conclusion (i.e., that the onset response is due to intrinsic properties of octopus cells, and the underlying mechanism is determined by a combination of factors, and that depolarization block is not a major factor). Likewise, the possible exclusion of some minor ionic channels currently not yet identified also would not affect the general conclusion. To simulate the actual responses, there is no doubt that modification and fine tuning of model parameters used here will be required. On the other hand, because onset responses can be generated with a wide range of model parameters, this diversity might correspond to the diversity in characteristics of onset responses observed in vivo (e.g., Godfrey et al. 1975; Rhode and Smith 1986a).

We should also point out that, although our choice of parameters will not affect the general conclusion, it will affect discussions about the contributions of specific factors. One such area concerns the Ih conductance. If we set the Ih conductance to a larger value, even given the selection of parameters resulting in slow kinetics, it can play a more important role, and its action may be more consistent with actual physiological conditions. Golding et al. (1995) concluded that Ih contributes substantially to the low impedance of octopus cells measured in brain slice. That means that part of the leakage conductance in our model should be replaced with the Ih conductance. Another consideration involves the dendritic model. In our model, we assumed that dendrites are passive and leaky. As noted in METHODS, there is increasingly more evidence suggesting the presence of active dendrites in a variety of cell types. If the dendrites of octopus cells are active (or the proximal stages are active), part of the resting membrane conductance will be formed by the active channels instead of the leakage channel. Accordingly, the regulatory role of the active channels will increase. Only further experimentation will ascertain whether our model assumptions and parameter choices are correct, allowing us to validate the conclusions put forth in this paper.

Implications regarding mechanisms of onset responses in other cell types

As mentioned in the INTRODUCTION, there are other cell types in the cochlear nuclei producing onset responses. One such cell type is the multipolar stellate cell, found in the anterior portion of the PVCN. Although the octopus cell is associated with PSTH subtypes OI (no activity after the initial onset spikes) and OL (with low sustained activities) (Feng et al. 1994; Rhode and Greenburg 1992; Rhode et al. 1983; Rouiller and Ryugo 1984), the multipolar cell is associated with the PSTH subtype OC, as it displays two to four modes of "chopping" at stimulus onset (Palmer et al. 1996; Rhode and Greenburg 1992; Smith and Rhode 1989). This cell type shares many characteristics with the octopus cell; for example, it also has large and relatively unbranched dendrites (Rhode and Greenburg 1992; Smith and Rhode 1989), and it is also thought to achieve its temporal precision by integration from a large number of auditory inputs (Palmer et al. 1996), as in the octopus cell (Golding et al. 1995). It is natural to assume that some of the mechanisms operating in octopus cells also play a role(s) in the production of onset responses in multipolar cells. In fact, the responses shown in Fig. 9 are reminiscent of those produced by multipolar cells. Palombi and Caspary (1992) reported that bicuculline alters the postonset discharges of chinchilla PVCN neurons, suggesting that GABAergic inhibitory inputs contribute to their onset responses. However, a more recent study in guinea pigs (Evans and Zhao 1997) showed that OC units are sensitive to bicuculline but OI units (octopus cells) are not. This later result agrees with the finding that there are inhibitory projections to the multipolar cell area but not to the OCA in mice (Wickesberg et al. 1991). Computer simulations have shown that inhibitory inputs are also important in the production of onset-like responses in bushy cells (Rothman et al. 1993). The bushy cell also contains KLT, which is proposed to increase the membrane conductance and contribute to the onset response (Manis and Marx 1991). Thus it seems that different cell types share not only the basic onset response pattern but also similar mechanisms that may produce such response patterns. These seemingly different cell types may simply form a continuum of response patterns. If that is the case, one might expect stellate cells to produce onset responses as a result of a higher membrane leakage conductance (Figs. 2 and 3).

Summary

We have used a computer model to study the mechanisms of onset responses in octopus cells. Our results suggest that the basic onset response pattern does not involve neuronal circuitry or inhibitory inputs but reflects actions of the intrinsic properties of octopus cells. A large membrane conductance, partly contributed by Ih is the key factor. KLT plays a major role in the regulation of the response pattern, whereas the role of Ih, due to its slow kinetics, must be limited to a long-term regulation under the conditions used in this investigation. Depolarization block, or Na+ channel inactivation, plays only a minor role, if any. To better determine the relative importance of factors contributing to this aspect of octopus cell function, more experimental data, especially those characterizing the kinetics of different channels, is needed.

    ACKNOWLEDGEMENTS

  The authors thank Dr. M. J. Ferragamo and two reviewers for helpful criticisms of the manuscript and Drs. D. Oertel and W. S. Rhode for helpful discussions.

  This work was supported by the National Institute of Deafness and Other Communication Disorders Grant DC-01007 and also in part, Grant P60 DC-00982-06 to Y. Cai.

    APPENDIX

A general description of the parameters determining the channel conductances is given by
τ<SUB><IT>p</IT></SUB>d<IT>p</IT>/d<IT>t + p = p</IT><SUB>∞</SUB>
and
τ<SUB><IT>p</IT></SUB><IT> = P</IT><SUB>fac</SUB>/(α<SUB><IT>p</IT></SUB> + β<SUB><IT>p</IT></SUB>)
<IT>p</IT><SUB>∞</SUB> = α<SUB><IT>p</IT></SUB>/(α<SUB><IT>p</IT></SUB> + β<SUB><IT>p</IT></SUB>)
where tau p (in ms) is the time constant for parameter p(p subset  [0,1] and p is a function of both time t and membrane voltage V, in mV), pinfinity is the value of p after the membrane voltage being held at a constant level for infinite time, Pfac is the temperature factor for time constant tau p, and alpha p and beta p are rate constants and functions of membrane voltage only. The p parameter in the above equations is to be replaced by any one of m, h, n, B, or ih in the descriptions below. For example, to describe the m parameter, tau p becomes tau m, Pfac becomes Mfac, and so on.

The Na+ channel conductance is the same as in Hewitt and Meddis (1995) and is described by
<IT>g</IT>Na = <IT>g</IT>Na<SUB>max</SUB><IT>m</IT><SUP>3</SUP><IT>hS</IT>
α<SUB><IT>m</IT></SUB> = −0.1(<IT>V</IT> + 37 + <IT>M</IT><SUB>SH</SUB>)/{exp[−(<IT>V</IT> + 37 + <IT>M</IT><SUB>SH</SUB>)/10] − 1}
β<SUB><IT>m</IT></SUB> = 4 exp[−(<IT>V</IT> + 62 + <IT>M</IT><SUB>SH</SUB>)/18]
α<SUB><IT>h</IT></SUB> = 0.07 exp[−(<IT>V</IT> + 62 + <IT>H</IT><SUB>SH</SUB>)/20]
β<SUB><IT>h</IT></SUB> = 1/{exp[−(<IT>V</IT> + 32 + <IT>H</IT><SUB>SH</SUB>)/10] + 1}
where gNamax is the maximum conductance per unit area (S/cm2), m and h are the activation and inactivation parameters respectively, and S is the membrane area of the compartment. The values of gNamax, MSH, HSH, Mfac, and Hfac for the soma are given in the figures. For the axon (of both the stellate cell model and the onset cell model), gNamax = 0.17 S/cm2, MSH = 2.3, HSH = -10.8, and Mfac = Hfac = 0.1315. The Na+ equilibrium potential ENa is 55 mV.

The K+ channel conductance is also the same as in Hewitt and Meddis (1995) and is described by
<IT>g</IT>K = <IT>g</IT>K<SUB>max</SUB><IT>n</IT><SUP>4</SUP><IT>S</IT>
α<SUB><IT>n</IT></SUB> = −0.01(<IT>V</IT> + 52 + <IT>N</IT><SUB>SH</SUB>)/{exp[−(<IT>V</IT> + 52 + <IT>N</IT><SUB>SH</SUB>)/10] − 1}
β<SUB><IT>n</IT></SUB> = 0.125 exp[−(<IT>V</IT> + 62 + <IT>N</IT><SUB>SH</SUB>)/80]
where gKmax is the maximum conductance per unit area (S/cm2), and n is the activation parameter. The values of gKmax, NSH, and Nfac for the soma are given in the figures. For the axon (of both the stellate cell model and the octopus cell model), gKmax = 0.02 S/cm2, NSH = 2.65, and Nfac = 0.6575. The K+ equilibrium potential EK is -80 mV.

The kinetics of KLT are modified from Manis and Marx (1991)
<IT>g</IT>K<SUB>LT</SUB><IT> = g</IT>K<SUB>LTmax</SUB><IT>BS</IT>
α<SUB><IT>B</IT></SUB> = α<SUB><IT>B</IT></SUB>0 exp[(<IT>V − V</IT><SUB>1/2</SUB><IT> − B</IT><SUB>SF</SUB>)/<IT>K</IT><SUB>α</SUB>]
β<SUB><IT>B</IT></SUB> = β<SUB><IT>B</IT></SUB>0 exp[−(<IT>V − V</IT><SUB>1/2</SUB><IT> − B</IT><SUB>SF</SUB>)/<IT>K</IT><SUB>β</SUB>]
where V1/2 (-53 mV) is the half activation voltage. The values of gKLTmax and other parameters are given in the figures. The equilibrium potential EKLT is -77 mV. In the original description of Manis and Marx (1991), the minus sign in the exp( ) function of beta B was misplaced in that of alpha B. We also changed the form of expression so that it resembles those of the Na+ and K+ channels.

The kinetics of Ih were based on the data of McCormick and Pape (1990) and Banks et al. (1993). We did not use the activation and deactivation rate constants (as used for other channel types), although such treatment also was used for Ih (Tabata and Ishida 1996). The description is as follows
<IT>gI<SUB>h</SUB> = gI<SUB>h<UP>max</UP></SUB>i<SUB>h</SUB>S</IT>
τ<SUB><IT>ih</IT></SUB> = (110 + <IT>V</IT>)<SUP>2</SUP> + 50 for activation process,
τ<SUB><IT>ih</IT></SUB> = −1,000(5.75 + 0.11<IT>V</IT>)/3
for deactivation process,
<IT>i<SUB>h∞</SUB></IT> = 1/{1 + exp[(<IT>V − V</IT><SUB>1/2</SUB><IT> − IH</IT><SUB>SF</SUB>)/K<SUB>S</SUB>]}
where tau ihsubset [50, infinity ] and V1/2 (-75 mV) is the half activation voltage. The equilibrium potential Eih is -45 mV.

    FOOTNOTES

1   The model failed to produce the proper response patterns reported in Banks and Sachs (1991) when the K+ channel kinetics as described in their paper were implemented. So we used the kinetics of Hewitt and Meddis (1995), which lack a voltage-dependent term (not critical for the basic response pattern) used in that of Banks and Sachs (1991). The Na+ channel kinetics in both studies were almost identical. 2   When the stimulus presentation is repeated (i.e., similar to that during experiments using acoustic stimuli), the spike pattern is not likely to change in consecutive stimulus presentations, and the PSTH so produced would not be realistic. If spike trains from auditory-nerve fibers were used as stimuli, however, the spike pattern in the model output would change in consecutive stimulus presentations (due to the "randomness" in the inputs and synaptic events), producing a more realistic PSTH. Thus the use of the 300-Hz, half-wave-rectified sinewave current to simulate acoustic stimulation was not useful when a realistic PSTH was the goal. However, it is useful to study the model behavior on one-trial basis, as in our case. 3   Earlier suggestions that inhibitory inputs shaped the temporal response patterns of octopus cells were based on the presence of thin, presumably inhibitory, auditory-nerve fiber collaterals making direct contacts with octopus cells and did not involve neural circuits (Godfrey et al. 1975; Kane 1973; Morest et al. 1973). In more recent literature, it is often unclear whether "inhibitory inputs" or "inhibition" also included those mediated by neural circuitry. In our discussion, we chose not to distinguish the two, since our results do not support the role of inhibitory inputs of any kind. Due to the latency constraint (see INTRODUCTION), the more synapses the neural circuitry contains, the less likely they are involved in the generation of onset response. Golding et al. (1995) recently suggested that the presumed thin auditory-nerve fiber collaterals described by Kane (1973) might come from octopus cells.

  Address for reprint requests: Y. Cai, Boys Town National Research Hospital, 555 North 30th St., Omaha, NE 68131. E-mail: caiy{at}boystown.org

  Received 3 January 1997; accepted in final form 4 April 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society