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Department of Neurobiology and Behavior, Cornell University, Ithaca, New York
Submitted 10 March 2006; accepted in final form 21 March 2006
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ABSTRACT |
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INTRODUCTION |
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10 cortical and subcortical destinations via divergent axon collaterals (Cleland and Linster 2003
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METHODS |
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The mitral cell model described herein was shaped by four principal objectives. First, the model must represent cellular morphological and physiological properties with adequate accuracy and precision for its intended purposes. Second, it must be computationally efficient, such that moderately sized networks can be constructed and employed toward useful ends. Third, it should be reasonably compartmentalized, so that elements of the model can be upgraded or redesigned as required without rendering the revised model incompatible with its predecessors. Fourth, although the point of compartmental models is to depict cellular properties in biophysical detail, we hold an explicit bias against the addition of unconstrained variables; excess free parameters can improve apparent fits to data but will reduce models' predictive value.
Model morphology and passive properties
We based the present model (Fig. 1B) on the four-compartment mitral cell model of Davison and colleagues (2000)
, adding additional current mechanisms and adjusting parameters so as to replicate the complex dynamical properties of mitral cells observed in studies of rat olfactory bulb slices (Balu et al. 2004
; Chen and Shepherd 1997
; Desmaisons et al. 1999
; Heyward et al. 2001
). The Davison model abstracts the mitral cell into four isopotential compartments (glomerular tuft, apical dendrite, soma, and lateral dendrite), each possessing independent membrane properties and current complements and connected to one another by axial resistors. The complement and distribution of its membrane current mechanisms were derived from the 286-compartment model of Bhalla and Bower (1993)
, which in turn was closely based on mitral cell morphology and fit to current-clamp electrophysiological recordings under a broad variety of conditions. In Davison's reduced model, the lengths of the four compartments are identical, whereas their diameters differ so as to yield sections with empirically appropriate surface areas (glomerular tuft: 8,399.99 µm2; apical dendrite: 32,801.4 µm2; soma: 5,100.1 µm2; lateral dendrite: 53,699.2 µm2). The linking conductances between the four compartments are also unchanged from Davison: tuft to apical dendrite: 58.6 µS; apical dendrite to soma: 54.7 µS; soma to lateral dendrite: 194.0 µS. Owing to extensive parameter optimization with respect to the model of Bhalla and Bower (1993)
, the reduced model faithfully replicates many aspects of mitral cell physiology (Davison et al. 2000
).
The present model (Fig. 1B) inherits this reduced morphology and six channel mechanisms from its predecessors (Bhalla and Bower 1993
; Davison et al. 2000
): a fast sodium spike current (INa), an L-type calcium current (ICaL), two delayed rectifier potassium currents distinguished by their activation kinetics (IKf, IKs), an inactivating potassium current (nominally IA, but with slow inactivation kinetics rendering it intermediate between classical A- and D-current kinetics), and a calcium-activated potassium current (IK(Ca)). The model additionally incorporates a persistent sodium current mechanism (INaP) adapted from that of Fransén and colleagues (2004)
, pursuant to the essential role of this current in mitral cell subthreshold oscillations (Balu et al. 2004
; Desmaisons et al. 1999
) as well as a hyperpolarization-activated cation current (IH) adapted from that of Saraga and colleagues (2003)
, and an ohmic ATP-sensitive potassium current (IK(ATP)). We adjusted the potassium and sodium reversal potentials to reported values, but otherwise retained the passive properties of the Davison model (Table 1). The conductance densities and distributions of membrane mechanisms were reparameterized as described below and are summarized in Table 2.
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) and time constant (
), both of which are functions of voltage. The exception is the gating parameter for the IK(Ca) current, which is a function of both voltage and the internal perimembrane calcium concentration. Perimembrane calcium concentration is modeled as decaying exponentially to a base level after calcium influx, using a mechanism modified from that of Destexhe and colleagues (1998)Computational methods and parameterization
All simulations were run in NEURON version 5.6 (http://www.neuron.yale.edu) (Carnevale and Hines 2006
; Hines and Carnevale 1997
, 2001
) with a 0.01-ms time step. The change in voltage in each compartment was calculated as the sum of all ionic currents, injected currents, and currents flowing from the neighboring compartments. For example, in the apical dendrite:
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Ionic conductance densities in each compartment were fit using a semiautomated parameterization process broken down into two stages. First, we parameterized the model so as to replicate subthreshold activity, specifically the voltage-dependent frequency of subthreshold oscillations reported by Desmaisons et al. (1999)
. Six ionic conductances exhibiting voltage dependence within this narrow subthreshold voltage window (INaP, IH, IA, and IK(Ca) in apical dendrite; IA and IK(Ca) in soma) were varied over a parameter space encompassing circa 60,000 combinations; the remaining conductances were held constant at existing levels. For each parameter set, the simulation was run for 13,000 ms. Starting at 3,000 ms to permit the settling of initial conditions, increasing quantities of depolarizing current were injected into the apical dendrite in steps of 1,000-ms duration, the injected current increasing in amplitude by 0.2 nA at each step. Membrane potential time series for each trial were recorded as a series of discrete data vectors. The vectors were then analyzed using Matlab version 6.1 (The Mathworks, Natick, MA; http://www.mathworks.com). Each of the
60,000 trials was broken into 11 separate time segments, each 1,000 ms in duration, corresponding to the levels of current injection and disregarding the first 2,000 ms of each simulation. The oscillation frequency for each 1,000-ms segment was taken to be the frequency at which the peak in the Fourier transform of the time series occurred. The peak frequency, mean voltage, and oscillation amplitude within each segment were measured, and all 33 calculated values (11 frequencies, 11 mean voltages, 11 mean amplitudes) for a given trial were stored as a row in the data output matrix. Using data from Desmaisons et al. (1999)
, a search of the output matrix of this analysis program was then performed to find a best-fit row of values, corresponding to a distinct point in the model parameter space. Second, after establishing a best-fit set of parameters for subthreshold behavior, a similar parameterization technique was used to tune the remaining active currents on the basis of the cell's observed suprathreshold activity; specifically, the number of spikes elicited per burst as a function of stimulus current. The result of this two-step procedure is the parameter set reported in Table 2.
Synaptic inputs were delivered to the distal end of the dendritic tuft compartment using NEURON's AlphaSynapse mechanism. This mechanism generates simple synaptic inputs with single-exponential kinetics and identical onset and offset time constants. GABAA-ergic inhibitory synapses were modeled with a time constant of 2.5 ms and a reversal potential of 65 mV. Glutamatergic excitatory synapses [combining AMPA and N-methyl-D-aspartate (NMDA) effects as discussed in RESULTS AND DISCUSSION] were modeled with a 50-ms time constant and a reversal potential of 0 mV.
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RESULTS AND DISCUSSION |
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Basic properties
Mitral cells at rest in a slice preparation exhibit mean resting potentials of 55 to 65 mV under typical recording conditions with resting potential measurements in individual cells ranging from roughly 50 to 75 mV or greater (Balu et al. 2004
; Chen and Shepherd 1997
; Desmaisons et al. 1999
; Heyward et al. 2001
; Nickell et al. 1996
). Although sharp electrode recordings (Chen and Shepherd 1997
; Desmaisons et al. 1999
) have tended to report slightly more hyperpolarized mean potentials (62 to 66 mV) than have whole cell recordings using patch electrodes, this is approximately negated by uncompensated
10-mV liquid junction potentials in the whole cell slice recordings. In in vivo recordings using whole cell patch electrodes, however, the mean resting potential after compensation (56 ± 1.2 mV) was slightly more depolarized than those observed in slice preparations (Cang and Isaacson 2003
). Somatic input resistance measurements have ranged between 115 and 280 M
in studies using patch electrodes (Cang and Isaacson 2003
; Heinbockel et al. 2004
; Nickell et al. 1996
). At rest, the present model mitral cell exhibits a mean membrane potential of 64 mV in the soma, 15-Hz subthreshold oscillations, and a somatic input resistance of 12.5 M
. The relatively low input resistance of the model cell is a consequence of the process of reducing its morphological complexity, during which the accurate replication of input/output properties was emphasized over the preservation of absolute parameter values (Davison et al. 2000
).
Mitral cells exhibit intrinsic subthreshold membrane potential oscillations and intrinsic bursting properties, even in an olfactory bulb slice preparation and when pharmacologically isolated with blockers of glutamatergic and GABAergic transmission (Balu et al. 2004
; Chen and Shepherd 1997
; Desmaisons et al. 1999
). The frequency of subthreshold oscillations is highly correlated to the membrane potential, increasing in response to membrane depolarization from 10 Hz at 67 mV to as high as 40 Hz at 59 mV (Desmaisons et al. 1999
), a phenomenon replicated by the present model (Fig. 2A). During extended stimulation, mitral cells fire clusters, or bursts, of action potentials (Fig. 2B). The number of spikes in each burst can be variable in both living and model neurons, but the spike count per burst tends to increase with increased depolarization while the interburst interval is modestly reduced (Fig. 2C) (Balu et al. 2004
; Desmaisons et al. 1999
). Furthermore, in the perithreshold regime, intraburst spike frequency directly reflects the frequency of subthreshold oscillations; the reduction in frequency when spikes are present is attributable to the additional potassium current activated in response to spiking (Fig. 2D). Spontaneous action potentials in mitral cells are correspondingly phase-constrained with respect to these underlying oscillations (Desmaisons et al. 1999
), irrespective of their frequency (Fig. 2E).
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In the perithreshold regime, spontaneous inhibitory postsynaptic currents (IPSCs) or small hyperpolarizing current pulses generate phase resets of mitral cell subthreshold oscillations, without affecting their amplitude or frequency, and can also evoke rebound spikes (Desmaisons et al. 1999
). In contrast to cerebellar interneurons and Purkinje cells (Häusser and Clark 1997
), the latency of evoked spikes in mitral cells is not dependent on IPSC amplitude; hence, rebound spikes evoked in mitral cells can reliably occur within restricted time windows independent of the potentially variable amplitudes of incoming IPSCs (Desmaisons et al. 1999
). Notably, the latency of such a rebound spike is considerably more reliable than that of a spike evoked by a depolarizing step (Balu et al. 2004
). In the present model, both small hyperpolarizing current pulses delivered to the apical dendrite and GABAA-like chloride shunt conductances opened in the glomerular tuft replicated these effects. Brief, low-amplitude hyperpolarizing pulses or inhibitory synaptic inputs reset the phase of subthreshold oscillations (Fig. 3A), whereas larger inputs could also evoke a rebound spike. Model mitral cells generated rebound spikes within narrow time windows in response to either hyperpolarizing current pulses (Fig. 3B) or synaptic shunt inhibition in the tuft (Fig. 3C) such as would be delivered by stimulus-activated periglomerular cells (Cleland and Sethupathy 2006
). Characteristic of true phase resets, the latency of rebound spikes was relatively independent of the state of the mitral cell at the time of stimulation. Rebound spike timing was not strongly influenced by the baseline membrane potential or corresponding intrinsic oscillation frequency (Fig. 3D) nor by the amplitudes of the hyperpolarizing current or shunt conductance (Fig. 3E). Furthermore, spike latency was largely independent of the phase of subthreshold oscillations at the time of delivery of the current pulse (Fig. 3F) or the shunt conductance (Fig. 3G); the exception being when the inhibitory current or IPSC coincided directly with the normal phase of spike firing (0 or 2
radians; Fig. 3, F and G).
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Subthreshold oscillations constrain spike timing
In contrast to the temporal fidelity of rebound spikes evoked by inhibitory synaptic inputs or brief hyperpolarizing pulses, action potentials evoked by excitatory synaptic inputs vary substantially in latency (Balu et al. 2004
; Desmaisons et al. 1999
). Specifically, while IPSCs reset the phase of subthreshold oscillation and hence evoke rebound spikes at times that are independent of the phase prior to reset, excitatory postsynaptic currents (EPSCs) do not reset phase; rather, the timings of spikes evoked by EPSCs are constrained with respect to the phase of the underlying subthreshold oscillations (Desmaisons et al. 1999
). In the present model, simulated EPSCs delivered at different oscillatory phases evoked spikes with variable latencies but at a consistent phase (Fig. 4A). Specifically, EPSC-evoked spike latency depended on the phase of the excitatory stimulus (Fig. 4B), such that evoked spikes were constrained to a consistent, restricted phase window of the oscillation (Fig. 4C) in agreement with experimental data (Desmaisons et al. 1999
). At modest EPSC amplitudes, these phase constraints were reliable with stronger inputs evoking spikes at shorter latencies (corresponding to a relative phase lead with respect to subthreshold oscillations). Substantially stronger EPSC amplitudes, however, were able to overpower the phasing properties of the intrinsic oscillations, evoking spikes with latencies increasingly independent of the intrinsic phase (Fig. 4D). This result suggests a particular importance for GABAB-ergic (Aroniadou-Anderjaska et al. 2000
; Wachowiak et al. 2005
) and D2 dopaminergic (Berkowicz and Trombley 2000
; Ennis et al. 2001
) presynaptic inhibition delivered onto olfactory sensory neuron terminals for the regulation of olfactory input sensitivity (McGann et al. 2005
; Wei et al. 2006
; Wilson and Sullivan 1995
). Specifically, the resulting negative feedback loops, dynamically adjusted in gain in response to odor input activity (Philpot et al. 1998
), may act to keep the intensity of afferent excitatory inputs to mitral cells within this functional range so as to facilitate the intrinsic regulation of spike timing and hence the synchronization of spikes among mitral cells. Notably, within this functional range, stronger inputs are predicted to evoke leading spikes, suggesting a downstream spike-timing based mechanism for readout of the relative intensities of glomerular activation (Cleland and Linster 2002
; Linster and Cleland 2001
).
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> 30 ms or so (Fig. 4E). One straightforward synthesis of these results is that synaptic potentials must be effectively slower than the intrinsic oscillation period in order for the latter to determine spike timing (Desmaisons et al. 1999
). The observed peak latency for NMDA receptor-mediated synaptic potentials in mitral cells is 82 ± 38 ms in response to olfactory nerve shock (Ennis et al. 1998
The concordance of these phenomena enables activated mitral cells across the olfactory bulb to be rapidly synchronized by afferent inputs before evoking any action potentials. Rapid, stimulus-evoked, periglomerular cell-mediated shunt inhibition serves to reset the subthreshold oscillatory phases of mitral cells sampling from odor-activated glomeruli. The slow, concomitant excitation of these same mitral cells, if sufficient to overcome this shunt inhibition (Cleland and Sethupathy 2006
), will evoke its first action potentials within a restricted phase window of these now-synchronized subthreshold oscillations, yielding an ensemble of synchronized spikes across the bulbar population of mitral cells. Notably, it is only after spikes have been evoked in activated mitral cells that mitral-granule reciprocal synapses can participate in the generation and maintenance of field oscillations.
Ionic basis and pharmacology of subthreshold oscillations
Intrinsic membrane oscillations generally comprise at least two opposing currents with interacting dependencies. Subthreshold oscillations are of course restricted to depending on currents that are differentially activated across this limited range of membrane potentials and hence often incorporate the persistent sodium current INaP as a source of excitatory drive (Agrawal et al. 2001
; Dickson et al. 2000
; Fransén et al. 2004
; Klink and Alonso 1993
; Magistretti and Alonso 1999
; Manis et al. 2003
; Reboreda et al. 2003
; Sanhueza and Bacigalupo 2005
; Wang 1993
; Wu et al. 2005
). Like the sodium spike current, the persistent sodium current is tetrodotoxin (TTX) sensitive. However, it does not exhibit rapid inactivation; inactivation processes in INaP are substantially slower and/or less complete (Crill 1996
; Magistretti and Alonso 1999
; Wu et al. 2005
). Furthermore, the activation curves for persistent sodium currents are typically displaced 710 mV negative to those describing the inactivating sodium spike current, hence yielding a substantial voltage window for subthreshold and perithreshold resonant activity. Finally, persistent sodium currents are small, typically contributing only 0.25% of the maximum transient sodium current (Crill 1996
); this presumably helps avoid runaway depolarization by keeping the noninactivating component of the inward current comfortably under control by the cell's complement of outward currents.
Application of TTX abolishes subthreshold oscillations in mitral cells, indicating that these oscillations depend on the persistent sodium current (Balu et al. 2004
; Desmaisons et al. 1999
). In the model mitral cell, blocking GNaP entirely abolished oscillations (Fig. 5A). In contrast, eliminating voltage-activated calcium currents from the model had no effect on subthreshold oscillations (Fig. 5A) in agreement with experimental data (Desmaisons et al. 1999
).
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Direct pharmacological testing of potassium current effects under current clamp conditions is difficult, as their blockade usually results in seizure and/or excitotoxicity. We tested their contribution to the maintenance of oscillations in the model by clamping their conductances to appropriate static levels; that is, net potassium conductance levels were set so as to confer appropriate subthreshold membrane potentials but were not permitted to fluctuate, effectively converting them to ohmic leak currents reversing at EK. Specifically, Fig. 6 depicts mitral cell activity when normally voltage-dependent currents are selectively clamped to static conductances that yield the same mean membrane potential as when the cell is at normal rest (64.3 mV, corresponding to subthreshold oscillations of 15 Hz). The clamping of either subthreshold potassium current (IA or IK(Ca)) abolished subthreshold oscillations and bursting properties, instead yielding tonic spiking (Fig. 6, AC), the frequency of which varied monotonically with the level of clamped (ohmic) potassium current. Clamping of the persistent sodium current INaP at any level abolished all subthreshold oscillatory activity in the model cell (Fig. 6D). In contrast, clamping the hyperpolarization-activated inward current IH did not impair subthreshold oscillations (Fig. 6E), indicating that this current is not a necessary dynamical contributor to these oscillations.
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Slow processes regulating burst properties
When mitral cells are continuously depolarized, they evoke repetitive bursts of action potentials, the duration and spike frequency of which depend on the degree of depolarization, as replicated by the model (Fig. 2). These intermittent bursts are dependent on 4-aminopyridine (4-AP)-sensitive currents, as application of increasing concentrations of this inactivating potassium current blocker reduces and then eliminates interburst intervals in mitral cells, eventually producing tonic activity (Balu et al. 2004
). The slow process primarily responsible for the initiation and termination of bursts has not been identified but has been suggested to involve the build-up of an outward current during the burst (Balu et al. 2004
).
In the present model, the slow currents regulating burst parameters include an inactivating potassium current (IA) with moderate inactivation kinetics, corresponding to the 4-AP-sensitive A- and/or D-type channels (Coetzee et al. 1999
; Wu and Barish 1992
) as well as a calcium-dependent potassium current (IK(Ca)). Both of these types of currents are prominent in mitral cells (Balu et al. 2004
; Chen and Shepherd 1997
; Wang et al. 1996
). Blockade of A-like currents with 4-AP dramatically reduced the latency to first spike in response to step depolarization in both the slice (Balu et al. 2004
) and the present model (not shown). Furthermore, when the model cell was depolarized so as to fire bursts of spikes (Fig. 7A), reduction of IA eliminated the slow modulation underlying bursting: weak antagonism increased burst duration (not shown), whereas higher levels of blockade rendered spiking entirely tonic (Fig. 7B), as demonstrated experimentally (Balu et al. 2004
). Although the model cell clearly replicates many of the salient features of burst firing in mitral cells, measurements of membrane current fluctuations in the model during bursting do not support the view that a simple build-up of potassium currents is responsible for burst termination. Indeed, most potassium current levels decline over the course of each burst with IA being the prominent exception (Fig. 7C). Rather, simulations suggest that a progressive deinactivation of IA over the course of a burst is the main factor terminating clusters of spikes in the model (Fig. 7D). Specifically, the recruitment of high-threshold potassium currents IKf and IKs during spiking transiently hyperpolarizes the cell between spikes to a level that favor the cumulative deinactivation of IA until the point at which the resulting potentiation of this fast, low-threshold potassium current successfully prevents spike initiation. Of course, this theoretical hypothesis requires experimental study. For example, if calcium buffering in the model was slowed and the IK(Ca) current mechanism in the present model was rendered proportionately more dependent on perimembrane calcium levels, then another modeling solution might be found in which a gradual accumulation of this current over the course of a burst is eventually responsible for its termination.
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Infrathreshold bistability: a protective mechanism?
In addition to subthreshold oscillations, some mitral cells exhibit another form of intrinsic bistability in their membrane potentials, spontaneously alternating between an up state, which is perithreshold for spike initiation and exhibits subthreshold oscillations as described in the preceding text, and an infrathreshold down state that is
10 mV more hyperpolarized and exhibits neither oscillations nor spikes (Heyward et al. 2001
). However, the observation of this bistability is not uniform. Bistability is observed more often in cells positioned deeply within a slice than in more superficial cells (Heyward et al. 2001
) and is consistently observed by some laboratories (Hayar et al. 2001
; Heinbockel et al. 2004
; Heyward et al. 2001
) but rarely or never by others (Balu et al. 2004
; Chen and Shepherd 1997
; Desmaisons et al. 1999
; Nickell et al. 1996
; Urban and Sakmann 2002
). In all of these studies, monostable mitral cells (i.e., those not exhibiting this infrathreshold form of bistability) exhibited properties characteristic of the up state in bistable cells, indicating that it is the presence of the down state that is inconsistently observed.
The role of infrathreshold bistability in mitral cell function, and its mechanistic relationships with other complex membrane phenomena such as subthreshold oscillations and burst properties, are not clear. We employed the present model to examine potential determinants of this infrathreshold bistability. First, it has been argued that healthy cells are more likely to display bistability, thus explaining why cells deeper within a slice, which may be less disturbed by slice preparation than more superficial neurons, are more likely to be bistable. Differences in the general health of slices across laboratories are difficult to assess; however, this hypothesis may be contraindicated in that mitral cells recorded in vivo have not displayed this bistability (Cang and Isaacson 2003
). Second, cellular properties may differ among studies based on the age of the animals from which the slices are taken, particularly as the olfactory bulb continues to develop postnatally in rats for
4 wk (Altman 1969
; Mair et al. 1982
; Rosselli-Austin and Altman 1979
; Valverde et al. 1992
). However, this variable did not correlate with bistability; both bi- and monostability were observed in mitral cells taken from rats both younger (Balu et al. 2004
; Hayar et al. 2001
) and older (Chen and Shepherd 1997
; Desmaisons et al. 1999
; Heinbockel et al. 2004
; Heyward et al. 2001
; Nickell et al. 1996
) than 28 days postnatal. Third, the presence of the down state could depend on replicable experimental factors. One such factor that correlates with the observation of mitral cell bistability is the composition of the intracellular (electrode) medium. Specifically, preparations that do not include phosphocreatine in the intracellular medium show bistability in a substantial proportion of recorded mitral cells (Hayar et al. 2001
; Heinbockel et al. 2004
; Heyward et al. 2001
), whereas studies that either include intracellular phosphocreatine (Balu et al. 2004
; Cang and Isaacson 2003
; Urban and Sakmann 2002
) or utilize sharp electrodes that do not rapidly dialyze cells (Chen and Shepherd 1997
; Desmaisons et al. 1999
) do not display this bistability. In hippocampal CA1 neurons, inclusion of phosphocreatine attenuates a strong and rapid potassium conductance that is induced by even brief hypoxia (Chung et al. 1998
), implicating a class of ATP-sensitive potassium channels long associated with such a neuroprotective role. In slice preparations, where oxygen is available only via diffusion from the oxygenated saline present at the surface, cells located more deeply within a slice preparation would be more susceptible to hypoxia and hence more likely to display this form of bistability. In this interpretation, the presence of phosphocreatine in the pipette would mitigate the hypoxia-induced disinhibition of the K(ATP) conductance, thereby reducing the probability of occurrence of the down state.
Membrane potential hyperpolarization via the disinhibition of K(ATP) channels is a common response to hypoxic insult in several resistant neurons. Hypoxia can evoke runaway depolarization in mammalian neurons, a process associated with rising intracellular calcium concentrations and the excitotoxic accumulation of extracellular glutamate as well as the rapid depletion of intracellular energy stores and eventual cell death (Ballanyi 2004
; Yamada and Inagaki 2005
). Persistent sodium currents in particular are increased by hypoxia, a response thought to be one of the early causal steps in this hypoxic cascade (Hammarström and Gage 2002
). Some classes of neuron, however, are relatively tolerant of hypoxia, deploying a variety of strategies to counter its deleterious effects. In particular, the disinhibition of K(ATP) channels strongly hyperpolarizes cells, suppressing the propagation of epileptogenic activity across networks and rapidly limiting neuronal energy expenditure by reducing the requirement for ion pumping, which consumes roughly half of all energy used in the brain (Ballanyi 2004
; Yamada and Inagaki 2005
). Knockout mice lacking Kir6.2, the pore-forming subunit of the plasma membrane K(ATP) channel, are extremely susceptible to hypoxia-induced seizures (Yamada and Inagaki 2005
).
Mitral cells are likely to be particularly vulnerable to excitotoxicity. Multiple positive feedback loops are embedded within the neural circuitry of the olfactory bulb, most notably self- and mutual excitation among mitral cells (Aroniadou-Anderjaska et al. 1999
; Didier et al. 2001
; Friedman and Strowbridge 2003
; Isaacson 1999
; Nicoll and Jahr 1982
; Salin et al. 2001
; Urban and Sakmann 2002
) and among short-axon and external tufted neurons (Aungst et al. 2003
; Cleland and Sethupathy 2006
). Although useful when well regulated, such loops are inherently dangerous to network stability and invite runaway depolarization; indeed, the olfactory bulb can generate epileptic seizures (Araki et al. 1995
; McEvoy et al. 2002
), a vulnerability that may contribute to multiple chemical-sensitivity disorders (Gilbert 2001
). Furthermore, mitral cells receive direct excitatory inputs from OSNs, which are both highly convergent on mitral cell dendrites and extremely vulnerable to environmental insult, potentially leading to the rapid and uncontrolled release of glutamate onto mitral cell dendrites as compromised OSNs depolarize and die. Indeed, immunohistochemical and in situ hybridization studies reveal intense staining for Kir6.2 in olfactory bulb mitral and tufted cells (Zhou et al. 2002
), confirming the expression of K(ATP) channels therein and suggesting that this anti-excitotoxic mechanism is present and functional in mitral cells.
Using the model, we tested whether the activation of an ohmic potassium conductance (IK(ATP)) could suffice to generate a down state. Indeed, on activation of a modest K(ATP) conductance (Table 2), the resting potential of the model mitral cell became more hyperpolarized and subthreshold oscillations ceased. Excitatory synaptic inputs normally sufficient to evoke spiking activity (Fig. 8A) failed to do so after IK(ATP) activation (Fig. 8B), although this inhibition could be overcome by stronger excitatory inputs (Fig. 8C) as has been demonstrated experimentally (Heyward et al. 2001
). These effects confirm the sufficiency of an IK(ATP)-like disinhibition mechanism to suppress potentially excitotoxic synaptic inputs in mitral cells. Other observed physiological properties of bistable mitral cells, such as the slow progression from the down to the up state and the voltage-dependent properties that govern the transitions between the two states (Heyward et al. 2001
), could be mediated by a number of factors, such as the declining disinhibition of K(ATP) current while in the down state because of lower ATP consumption coupled with the hypoxic potentiation of persistent sodium currents (Hammarström and Gage 2002
). However, hypoxia can exert multiple and complex effects on the properties of membrane channels (Lopez-Barneo et al. 2001
), so it remains unclear which mechanisms would be primarily responsible for the complex properties of this form of bistability. It does suggest, however, that certain membrane mechanisms such as K(ATP) channels may not be contributing to odor coding per se but rather may mediate other functions necessary for the maintenance and stable operation of the olfactory system.
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When convergent OSNs become activated, mitral cells receive direct excitatory inputs via ionotropic and metabotropic glutamate receptors as well as indirect shunt inhibition via periglomerular cells. It has long been known that even the fastest mitral cells are delayed in their responses to odor stimuli; although some of this delay is clearly due to physical factors inherent in sniffing behavior as well as odorant diffusion across the mucus layer, additional delay also can be attributed to mitral cells' relatively slow rise toward spike threshold. This slow progress toward threshold has two consequences that bear on current theories of bulbar function. First, it provides a window of time for disynaptic shunt inhibition via periglomerular cells to exert its effects on mitral cell integration before direct monosynaptic excitation can evoke action potentials (Cleland and Sethupathy 2006
), an effect sometimes observed as a fast hyperpolarization immediately preceding even the shortest-latency mitral cell responses to odors (Hamilton and Kauer 1989
; Kauer et al. 1990
; Wellis and Scott 1990
). These IPSCs will reset the phase of subthreshold oscillations in activated mitral cells, rapidly synchronizing the activated mitral cell population. Second, among mitral cells activated strongly enough to overcome this shunt inhibition, the relatively slow progress of depolarization largely delegates the determination of mitral cell spike timing to the intrinsic oscillatory phase of their subthreshold oscillations. As the mitral cell population is by this point transiently synchronized, the spikes evoked by activated mitral cells will also be correspondingly synchronized, perhaps with more strongly activated mitral cells enjoying a slight phase lead. This synchronized activation of mitral cells presumably contributes strongly to the initiation of network oscillations among mitral and granule cells that further regulate the bulbar response to odorant stimulation. In sum, the intrinsic properties of mitral cells, coupled with the circuitry of the glomerular synaptic triad, may comprise an effective engine for translating patterns of rate-coded primary olfactory receptor activity into a timing-dependent secondary representation (Cleland and Linster 2002
; Linster and Cleland 2001
) that is likely to be considerably more metabolically efficient (Baddeley et al. 1997
; Balasubramanian et al. 2001
; Levy and Baxter 1996
; Schreiber et al. 2002
) and appropriate for broad distribution within the brain (Cleland and Linster 2003
).
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: T. A. Cleland, Dept. Neurobiology and Behavior, Cornell University, Ithaca, NY 14853 (E-mail: tac29{at}cornell.edu)
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