Abstract

Information in neuronal networks is thought to be represented by the rate of discharge and the temporal relationship between the discharging neurons. The discharge frequency of neurons is affected by their afferents and intrinsic properties, and shows great individual variability. The temporal coordination of neurons is greatly facilitated by network oscillations. In the hippocampus, population synchrony fluctuates during theta and gamma oscillations (10–100 ms scale) and can increase almost 10-fold during sharp wave bursts. Despite these large changes in excitability in the sub-second scale, longer-term (minute-scale) firing rates of individual neurons are relatively constant in an unchanging environment. As a result, mean hippocampal output remains stable over time. To understand the mechanisms responsible for this homeostasis, we address the following issues: (i) Can firing rates of single cells be modified? (ii) Once modified, what mechanism(s) can maintain the changes? We show that firing rates of hippocampal pyramidal cells can be altered in a novel environment and by Hebbian pairing of physiological input patterns with postsynaptic burst discharge. We also illustrate a competition between single spikes and the occurrence of spike bursts. Since spike-inducing (suprathreshold) inputs decrease the ability of strong (‘teaching’) inputs to induce a burst discharge, we propose that the single spike versus burst competition presents a homeostatic regulatory mechanism to maintain synaptic strength and, consequently, firing rate in pyramidal cells.

Long-term Stability of Firing Rates in the Hippocampus

In an unchanging environment, sensory inputs activate a defined subset of the neuronal population. If a rat explores a testing apparatus repeatedly, the same sets of hippocampal pyramidal cells are re-activated even days and weeks later (O’Keefe and Nadel, 1978; Thompson and Best, 1990; McNaughton et al., 1996). This may be so because synaptic connectivity, relative synaptic weights and intrinsic properties of the neurons involved do not substantially change over time. Since during the intervening period the animal spends a great deal of time in sleep, it follows that neuronal network activity during sleep does not alter the connectivity of the network. A possible explanation for the lack of an interfering effect of sleep activity on the firing patterns of single cells is that the subpopulation which was activated by sensory information in the awake animal is commensurately more active in the absence of external sensory signals (e.g. during sleep) than those cells which were not active for an extended period of time in the preceding awake period. In short, wake and sleep episodes can cooperate and maintain network activity in a predictable manner. Several experiments support this conjecture. In an early work, pairs of pyramidal cells were recorded simultaneously and the rat was confined to the place field of one of the neurons in an otherwise familiar environment. In the subsequent sleep period, the neuron with the sustained activation in the awake state fired more action potentials compared to the control neuron (Pavlides and Winson, 1989). In a more recent experiment, firing rates of ‘place’ cells and ‘non-place’ cells were compared in a subsequent sleep period. The firing rates of the two cell populations were significantly different in both awake and slow-wave sleep states (Kudrimoti et al., 1999).

Discharge frequency of pyramidal cells can remain stable across several sleep–wake cycles, as illustrated in Figure 1. The minute-scale firing frequency of neurons remained stable across various states in both the waking and sleeping animal. In a different experiment, neurons with high firing rates during wheel running (associated with theta oscillation) continued to fire at a high rate (relative to other neurons) while the rat was drinking or staying immobile. Similarly, fast-firing pyramidal neurons in slow-wave sleep sustained their relative high rates during REM sleep (Hirase et al., 2001). When firing rates of neuronal populations were compared in two subsequent sleep episodes, interrupted by awake session in a familiar wheel or exploration in a familiar large box, discharge frequencies of individual cells robustly correlated (Fig. 2A, familiar and Fig. 2B).

What determines the long-term firing rates of individual neurons? When the animal is exposed to a novel environment, different subsets of neurons become active (O’Keefe and Nadel, 1978; Wilson and McNaughton, 1993; Kudrimoti et al., 1999). Such an exposure may result in long-lasting changes in the firing rate distributions of the recorded pyramidal cells. In line with this expectation, when firing rates of individual neurons in a novel environment and subsequent sleep episode were compared, their correlation was stronger than correlation of firing rates between exploration in the novel environment and the preceding sleep episode. Importantly, firing rates observed in the sleep episodes preceding and following exposure to novelty were poorly correlated (Fig. 2A, novel). Intervening novelty can have an impact on firing rates even in a familiar environment. When rats were tested repeatedly in the same apparatus during exploration, the firing patterns were sometimes substantially re-organized after the animals were exposed to a series of novel environments. The interpretation of the ‘re-mapping’ of neuron discharges in the familiar environment was that synaptic weights in the CA3 axon collateral system were altered substantially by novelty in a different environment (McNaughton et al., 1996). In support of this interpretation, tetanic stimulation of intrahippocampal synapses modified firing rates and maps of hippocampal place cells in an unchanging environment (Dragoi and Buzsáki, 2001).

These findings indicate that (i) experience can alter the minute-scale firing rates of neurons although (ii) the changes are not all-or-none since some residual correlation was still present between exploration and the preceding sleep session.

Hebbian Modification of Discharge Probability

A potential mechanism of modifying firing rates and patterns is synaptic plasticity (Bliss and Lømo, 1973). To examine the contribution of synaptic potentiation, we hypothesized that pairing a physiologically relevant afferent pattern with consistent burst discharge of pyramidal cells can lead to potentiation of the afferent synapses. We chose sharp wave bursts as a natural activation pattern to CA1 because this population pattern is known to arise in the excitatory recurrent circuit of the CA3 region (Buzsáki et al., 1983; Csicsvari et al., 2000). A single or small group of CA1 pyramidal cells were discharged by either direct current injection via an intracellular electrode in anesthetized animals or via extracellular micro-stimulation through a recording tetrode in behaving rats (King et al., 1999). Following the pairing between physiological activation of the Schaffer collaterals to CA1 and burst discharge of the target cells by artificial means, the discharge probability of neurons, associated with the sharp wave bursts, increased significantly (Fig. 3) (King et al., 1999). Similar pairing-induced changes in neuronal excitability have been observed in other systems, including the amygdala (Rogan et al., 1997) and auditory cortex (Ahissar et al., 1992). These findings suggest that changing the weights of synaptic afferents is one mechanism for altering firing rates of single neurons.

Homeostatic Maintenance of Synaptic Inputs by Burst Discharges: a Hypothesis

Cortical pyramidal cells fire single spikes and complex spike bursts (Kandel and Spencer, 1961; Thach, 1968; Connors et al., 1982; Gray and McCormick, 1996). In hippocampus, pyramidal cells exhibit bursts of two to six spikes of decreasing extra-cellular amplitude at short (≤6 ms) intervals (Ranck, 1973). Bursts are often assumed to have functions different from single spikes (Lisman, 1997). Bursts can have a differential impact ‘downstream’ (i.e. on postsynaptic targets) or can provide a feedback signal to the synapses that initiated the burst. Bursts of spikes have been shown to cause supra-linear summation of EPSPs at pyramidal–pyramidal synapses and pyramidal–interneuron synapses (Thomson, 2000). Burst patterns discharged postsynaptic targets more reliably than the same number of single spikes separated by longer intervals (Miles and Wong, 1987; Csicsvari et al., 1998; Thomson, 2000). Due to their prolonged effects, bursts may be able to activate postsynaptic N-methyl-d-aspartate (NMDA) receptors, in contrast to sparse spikes (Lisman, 1997). Nevertheless, the exact downstream (i.e. postsynaptic) role of bursts is not clear. If bursts convey the same information as single spikes, just stronger, then the behavioral conditions that bring about burst discharges should correspond to the maximum excitation of the bursting neurons (Otto et al., 1991; Lisman, 1997; Livingstone et al., 1996). In this framework, the burst would simply ensure that the information conveyed from a presynaptic neuron to its postsynaptic target does not get lost in noise, due to the stronger impact of the burst. However, the importance of bursts carrying downstream information is not straightforward, since bursts generally do not carry more information than single spikes (Bair et al., 1994). When a neuron is strongly depolarized and discharges high rates of single spikes, the frequent occurrence of spikes decreases the probability of burst occurrence (Harris et al., 2001).

Bursts also play an important role in synaptic plasticity but whether the impact of the burst is downstream or upstream (i.e. affecting the inputs of the bursting cell rather than its targets) is still debated (Rose and Dunwiddie, 1986; Staubli and Lynch, 1987; Huerta and Lisman, 1993; Holscher et al., 1997). Recent experiments in hippocampal pyramidal neurons indicate that a necessary condition for the induction of long-term potentiation is the temporal coordination of presynaptic activity with postsynaptic burst discharge in such a way that presynaptic activity should coincide or precede the burst (Fig. 4) (Jester et al., 1995; Magee and Johnston, 1997; Thomas et al., 1998; Pike et al., 1999). Importantly, presynaptic bursting appears neither necessary nor sufficient to induce synaptic plasticity in hippocampal pyramidal cells (Paulsen and Sejnowski, 2000).

One possible mechanism how bursts may contribute to synaptic plasticity is through soma-dendritic backpropagation of action potentials. Successfully backpropagating action potentials are much wider in the dendrites than their axonal-somatic counterparts (Spruston et al., 1995; Kamondi et al., 1998) and these wide backpropagation spikes, together with coincident synaptic depolarization, may trigger Ca2+ spikes (Magee and Johnston, 1997). In turn, Ca2+ spikes lead to burst firing (Wong et al., 1979; Traub et al., 1994). Both the Ca2+ event and the multiple wide dendritic Na+ spikes, associated with the burst, can provide the necessary depolarization, with or without activation of NMDA receptors, for the induction of synaptic potentiation (Bliss and Collingridge, 1993).

If bursts play a critical role in synaptic plasticity, it is important to reveal the network/behavioral conditions that favor their occurrence. In a recent experiment, we examined the occurrence of complex spike bursts in CA1 pyramidal cells in different behaviors. If bursting is produced by strong afferent excitation alone, we hypothesized that the ratio of bursts to single spikes should be largest in the center of the place field (O’Keefe and Nadel, 1978) where the strongest depolarization is expected. However, the information about spatial position carried by bursts and single spikes was often different (Harris et al., 2001). Furthermore, burst occurred during both theta and non-theta associated behaviors (e.g. sleep), although the incidence of bursts was significantly higher during non-theta states. Similar state-dependence of burst probability has been observed in neocortical pyramidal cells as well (Steriade et al., 2001).

These findings indicate that the occurrence of bursts is not under the control of particular behaviors or stimuli. Instead, it is the intrinsic properties of the pyramidal cell and its recent spiking history that appear to primarily determine the incidence of bursts (Harris et al., 2001). Examination of the temporal relationship between single spikes and complex spike bursts revealed that the highest burst probability occurred at times when the neuron discharged at theta (6–8 Hz) frequency, independent of the animal’s spatial position. The probability of burst and burst length correlated with the duration of pre-burst neuronal silence during both theta and non-theta network states (Fig. 5). These observations suggested that the ideal condition for burst production is strong dendritic depolarization coupled with a preceding period of non-spiking activity.

Because a main cause of spike backpropagation failure is Na+ channel inactivation (Jung et al., 1997; Colbert et al., 1997; Mickus et al., 1999), we can hypothesize that spiking-associated prolonged Na+ channel inactivation (Henze and Buzsáki, 2001) may account for the suppression of burst discharges. Supporting this suggestion, burst length, induced by depolarizing current steps in the soma in vivo, correlated with the rising slope of the intracellular action potential (Harris et al., 2001). Furthermore, the burst probability and burst length correlated with the extra-cellular amplitude of the burst-initiator spike, which reflects the maximum slope (i.e. the maximum Na+ influx) of the intra-cellular action potential (Henze et al., 2000). Thus, preceding non-spiking history of the pyramidal cell prepares the neuron for its maximum ability to produce a burst in response to a sufficiently strong depolarizing input.

The proposed importance of spike burst in synaptic plasticity and the intrinsic regulatory mechanisms of burst discharge in pyramidal cells provide some interesting possibilities for the regulation of discharge rate in these neurons (Fig. 6). Several experiments support the importance of the temporal coordination of presynaptic and postsynaptic activity in neuronal plasticity (Levy and Steward, 1983; Markram et al., 1997; Bi and Poo, 1998; Sjostrom et al., 2001). A weak input, eliciting an EPSP, followed by a strong, burst-inducing input is a necessary and sufficient condition for strengthening the weak input in hippocampal pyramidal neurons (Paulsen and Sejnowski, 2000). The shorter the time interval between the weak and strong input, the larger the magnitude of synaptic potentiation. Conversely, reversing the temporal order of the weak and strong inputs can lead to depression of the weak input or depotentiating its previously gained weight increase.

Assuming that the synaptic modification rule also applies to the intact brain, synaptic connections between the same sets of pyramidal neurons would grow to saturation in a familiar environment with stereotypic behavior. Unless some intrinsic normalizing mechanisms exist to counteract synaptic potentiation (Turrigiano et al., 1998), the hippocampal network could eventually become epileptic. We speculate that such an ever-growing excitation may be prevented by the relationship between single spikes and bursts. In essence, we propose that bursts may be conceived as a homeostatic mechanism to maintain synaptic strength and, in turn, synaptically evoked discharge rate. This proposal is based on the observed competition between single spikes and bursts and the postulated role of burst discharge in synaptic plasticity. Once a weak input becomes suprathreshold by the ‘teaching’ effect of the burst, the consequent reduction of Na+ channel availability, as a result of the action potential, will reduce the ability of strong inputs to induce a burst. The shorter the time between the weak (but now suprathreshold) and strong inputs, the stronger the ‘veto effect’ of the single spike. Thus, the Hebbian rule of synaptic plasticity is ‘put on hold’ once the weak (subthreshold) input becomes suprathreshold. Should the strength of the synapse decay spontaneously with time or get depotentiated actively because of ‘improper’ timing of the inputs, the weak synaptic input may become subthreshold again. At this point, the strong input becomes instantly effective in inducing a burst, which event then re-potentiates the weakened synapse. In short, we propose that the veto effect of a properly timed single spike on burst probability is a potential mechanism for regulating synaptic strength. The suggested homeostatic mechanism is operative in a single cell and depends primarily on the spiking history of the neuron (Henze and Buzsáki, 2001). This hypothesis may explain why bursts in different neurons occur relatively independent from each other and why their occurrence does not require network coordination.

The above scenario is based on the assumption that bursts are necessary for the induction of synaptic plasticity. Work on neocortical pyramidal neurons, however, indicates that under some circumstances single spikes may be sufficient (Markram et al., 1997; Sjostrom et al., 2001). Nevertheless, the homeostatic mechanisms outlined above could also apply to these neurons because spike discharge by one input decreases the likelihood of future spikes by other inputs (Henze and Buzsáki, 2001). Thus, a subthreshold (weak) input followed by a strong (teaching) input will lead to strengthening of the weak synapse. Once the weak inputs becomes suprathreshold, it will decrease the effectiveness of the strong input to initiate a spike or, if elicited, its soma-dendritic backpropagation.

Supported by NIH (NS34994, MH54671).

Figure 1.

Long-term preservation of discharge frequency of individual pyramidal cells. (A) A 10_h record of movement activity of a rat in a rectangular box. Horizontal lines indicate low activity (immobility and presumed sleep) periods. (B) Firing rates of six simultaneously recorded pyramidal neurons. Place correlates of cells 3 and 6 are shown in (D). Note constant firing frequency of neurons during sleep–wake episodes. (C) The first principal component (1st PC) of cell 6, used for unit clustering (Csicsvari et al., 1998), is shown for each of the tetrode wires. Note recording stability as a function of time. (D) Place fields of cells 3 and 6. Occupancy map (right) shows locomotor activity. Only activity during the first hour of recording is shown to facilitate visibility of traces. The upper left corner (place field of cell 3) was frequently visited whereas the rat only rarely visited place field of cell 6.

Figure 1.

Long-term preservation of discharge frequency of individual pyramidal cells. (A) A 10_h record of movement activity of a rat in a rectangular box. Horizontal lines indicate low activity (immobility and presumed sleep) periods. (B) Firing rates of six simultaneously recorded pyramidal neurons. Place correlates of cells 3 and 6 are shown in (D). Note constant firing frequency of neurons during sleep–wake episodes. (C) The first principal component (1st PC) of cell 6, used for unit clustering (Csicsvari et al., 1998), is shown for each of the tetrode wires. Note recording stability as a function of time. (D) Place fields of cells 3 and 6. Occupancy map (right) shows locomotor activity. Only activity during the first hour of recording is shown to facilitate visibility of traces. The upper left corner (place field of cell 3) was frequently visited whereas the rat only rarely visited place field of cell 6.

Figure 2.

Preservation of and perturbation of discharge frequency of individual pyramidal cells in familiar and novel environments, respectively. (A) Mean correlation values of firing rates for ‘sleep before’ vs ‘sleep after’ (SB–SA), ‘awake’ versus ‘sleep before’ (A–SB) and ‘awake’ vs ‘sleep after’ (A–SA) sessions in the well-trained (familiar) task and in a novel environment. Note the high and low correlations of firing rates between successive sleep sessions in the familiar and novel environments, respectively (black columns). (B) Firing rates of neurons with place correlates (place cells) and no detectable place fields (termed ‘silent’ cells) during a sleep episode before (SB) and 10, 20 and 30 min epochs during sleep (SA) following exploration in a familiar environment. Note stability of firing rates over time [A, modified after Hirase et al. (Hirase et al., 2001); B, modified after Kudrimoti et al. (Kudrimoti et al., 1999)].

Figure 2.

Preservation of and perturbation of discharge frequency of individual pyramidal cells in familiar and novel environments, respectively. (A) Mean correlation values of firing rates for ‘sleep before’ vs ‘sleep after’ (SB–SA), ‘awake’ versus ‘sleep before’ (A–SB) and ‘awake’ vs ‘sleep after’ (A–SA) sessions in the well-trained (familiar) task and in a novel environment. Note the high and low correlations of firing rates between successive sleep sessions in the familiar and novel environments, respectively (black columns). (B) Firing rates of neurons with place correlates (place cells) and no detectable place fields (termed ‘silent’ cells) during a sleep episode before (SB) and 10, 20 and 30 min epochs during sleep (SA) following exploration in a familiar environment. Note stability of firing rates over time [A, modified after Hirase et al. (Hirase et al., 2001); B, modified after Kudrimoti et al. (Kudrimoti et al., 1999)].

Figure 3.

Hebbian pairing can increase participation of single pyramidal neurons in sharp wave-ripple events. (A) Detection and quantification of CA1 ripples and ripple-related intracellular potentials. Upper traces: broad-band extracellular field and its filtered derivative. Third trace: rectified and smoothed ripple. Bottom trace: intracellular membrane potential changes associated with the ripple. The shaded areas in the extracellular and intracellular signals were used to calculate the relationship between the magnitude of the intracellular and extracellular ripple-related events. (B) Relationship between extracellular and intracellular ripple signals in an example cell before (filled square) and 20 min following the training protocol (circle). The solid lines are the best-fit linear regression lines for each group. During training, the extracellular signal was fed back to the impaled neuron so that the cell consistently discharged bursts of action potentials during every ripple event (50 pairings). (C,D) A similar experiment in the freely moving rat. (C) First the relationships between ripple, recorded with the control electrode, and integrated multiple unit activity, recorded by both tetrodes, were established. During training, units recorded with the training tetrode (stimulation/recording) were consistently discharged by ripple-timed stimuli (50 ms wide pulses). (D) Relationship between extracellular and ripple events and associated multiple units spikes before (filled diamond) and after training (gray circle). The slope between these events did not change under the unstimulated electrode [not shown; after King et al. (King et al., 1999)].

Figure 3.

Hebbian pairing can increase participation of single pyramidal neurons in sharp wave-ripple events. (A) Detection and quantification of CA1 ripples and ripple-related intracellular potentials. Upper traces: broad-band extracellular field and its filtered derivative. Third trace: rectified and smoothed ripple. Bottom trace: intracellular membrane potential changes associated with the ripple. The shaded areas in the extracellular and intracellular signals were used to calculate the relationship between the magnitude of the intracellular and extracellular ripple-related events. (B) Relationship between extracellular and intracellular ripple signals in an example cell before (filled square) and 20 min following the training protocol (circle). The solid lines are the best-fit linear regression lines for each group. During training, the extracellular signal was fed back to the impaled neuron so that the cell consistently discharged bursts of action potentials during every ripple event (50 pairings). (C,D) A similar experiment in the freely moving rat. (C) First the relationships between ripple, recorded with the control electrode, and integrated multiple unit activity, recorded by both tetrodes, were established. During training, units recorded with the training tetrode (stimulation/recording) were consistently discharged by ripple-timed stimuli (50 ms wide pulses). (D) Relationship between extracellular and ripple events and associated multiple units spikes before (filled diamond) and after training (gray circle). The slope between these events did not change under the unstimulated electrode [not shown; after King et al. (King et al., 1999)].

Figure 4.

Bursts of spikes induce long-term potentiation (LTP). Normalized EPSP amplitude monitored over time. No increase in synaptic efficacy was seen following pairing of single pulse stimulation of the Schaffer collaterals with single postsynaptic action potentials (a), whereas robust potentiation was induced by pairing afferent stimulation with postsynaptic bursts (b). Inset above: test EPSPs from a typical experiment at the indicated time points (x, y, z) [modified after Pike et al. (Pike et al., 1999)].

Figure 4.

Bursts of spikes induce long-term potentiation (LTP). Normalized EPSP amplitude monitored over time. No increase in synaptic efficacy was seen following pairing of single pulse stimulation of the Schaffer collaterals with single postsynaptic action potentials (a), whereas robust potentiation was induced by pairing afferent stimulation with postsynaptic bursts (b). Inset above: test EPSPs from a typical experiment at the indicated time points (x, y, z) [modified after Pike et al. (Pike et al., 1999)].

Figure 5.

Single spikes ‘veto’ the occurrence of bursts. (A) Intra-burst dynamics. The pseudo-color image shows the probability of seeing a given pair of successive interspike intervals (ISI, the return map), minus the return map (previous interspike interval versus next interspike interval) for a spike train where ISIs have been shuffled (color scale: –5×10–3 to 5×10–3 arbitrary units). The red region above the diagonal indicates the decelerating tendency of intra-burst ISIs, up to a limit of ∼6 ms. (B) Probability that an ISI is less than 6ms, as a function of the preceding ISI. (C) Averaged spike frequency, aligned on the first spike of bursts of various lengths. Silent periods occur before bursts, with longer silences before longer bursts [modified after Harris et al. (Harris et al., 2001)].

Figure 5.

Single spikes ‘veto’ the occurrence of bursts. (A) Intra-burst dynamics. The pseudo-color image shows the probability of seeing a given pair of successive interspike intervals (ISI, the return map), minus the return map (previous interspike interval versus next interspike interval) for a spike train where ISIs have been shuffled (color scale: –5×10–3 to 5×10–3 arbitrary units). The red region above the diagonal indicates the decelerating tendency of intra-burst ISIs, up to a limit of ∼6 ms. (B) Probability that an ISI is less than 6ms, as a function of the preceding ISI. (C) Averaged spike frequency, aligned on the first spike of bursts of various lengths. Silent periods occur before bursts, with longer silences before longer bursts [modified after Harris et al. (Harris et al., 2001)].

Figure 6.

Bursts are hypothesized to maintain synaptic plasticity in single pyramidal neurons. A weak input (weak) is followed by a strong input (teacher). If the weak input is subthreshold (left), the strong input can trigger a burst, and can lead to strengthening of the weak input. Once the weak input becomes suprathreshold (right) as a result of weak input–strong input pairings, the evoked single spike can inhibit burst response to the same strong input. In effect, the firing in response to the potentiated weak input reduces the ability of the strong input to evoke a burst and, as a consequence, reduces further potentiation. Once the weak input becomes subthreshold, due to spontaneous decay or depotentiation of the synapse, it will allow the strong input to induce a burst; thus, potentiation will resume again (left panels). The temporal relationship between the weak and strong input and the veto effect of single spikes on bursts are suggested to maintain synaptic strength [modified after Harris et al. (Harris et al., 2001)].

Figure 6.

Bursts are hypothesized to maintain synaptic plasticity in single pyramidal neurons. A weak input (weak) is followed by a strong input (teacher). If the weak input is subthreshold (left), the strong input can trigger a burst, and can lead to strengthening of the weak input. Once the weak input becomes suprathreshold (right) as a result of weak input–strong input pairings, the evoked single spike can inhibit burst response to the same strong input. In effect, the firing in response to the potentiated weak input reduces the ability of the strong input to evoke a burst and, as a consequence, reduces further potentiation. Once the weak input becomes subthreshold, due to spontaneous decay or depotentiation of the synapse, it will allow the strong input to induce a burst; thus, potentiation will resume again (left panels). The temporal relationship between the weak and strong input and the veto effect of single spikes on bursts are suggested to maintain synaptic strength [modified after Harris et al. (Harris et al., 2001)].

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