Variation of Input-Output Properties along the Somatodendritic Axis of Pyramidal Neurons

Boosting of inputs at proximal and middle dendritic sites

The computer-generated inputs were first injected at dendritic locations d₁ and d₂, and the associated subthreshold voltage responses were recorded at the soma. To facilitate comparison, the amplitudes of the simulated synaptic currents (which mimic unitary EPSCs) injected at d₁ and d₂ were adjusted so that the resultant voltage deflections (which resemble unitary EPSPs) recorded with the somatic electrode were nearly identical (EPSP_d1→S, EPSP_d2→S) (Figs. 1B, 2A). To meet this condition, the EPSCs and EPSPs at d₂ were typically larger and narrower than those at d₁.

Although the individually injected EPSCs produced identical EPSPs at the soma (Fig. 2A, left), the responses to EPSC barrages delivered to d₁ and d₂ were significantly different from each other (right). The barrages were calculated by summing the synaptic inputs generated by a specified number (N_pre) of simulated presynaptic cells, each of which fired randomly with respect to each other at a given frequency (F_pre). These barrages resulted in noisy tonic depolarizations [composite EPSPs (cEPSPs)]. At low-EPSC rates (0.04 kHz), the cEPSPs recorded at the soma with stimulation at d₂ were only slightly smaller than those recorded with stimulation at d₁ (Fig. 2B, left traces). This difference increased at higher EPSC rates (Fig. 2B, middle and right traces). A plot of the average cEPSP versus EPSC rate (Fig. 2C) shows that the difference continued to grow as the membrane potential approached threshold. The cEPSPs evoked with d₁ and d₂ stimulation were larger than those evoked by directly injecting the barrages at the soma (cEPSP_S→S). The difference in the response between d₁ and d₂ stimulation was consistent across all neurons: a plot of cEPSP_d2→S versus cEPSP_d1→S for 10 cells shows that the points for large depolarizations were below the unity slope line (Fig. 2 D).

To determine whether the subthreshold differences extended to the suprathreshold range, the EPSC rate was increased until the neuron fired repetitively. In general, a higher EPSC rate was needed to evoke firing with d₂ stimulation than with d₁ stimulation. Moreover, the firing frequency was consistently lower with d₂ stimulation for the same EPSC rate (Fig. 3A, top and middle traces, B). Both responses were significantly greater than those evoked with somatic injection (Fig. 3A, bottom) (s→s, n = 7), indicating that inputs to both were boosted. Unlike subthreshold responses (Fig. 2C,D), the differences in firing rate between d₁ and d₂ stimulation remained constant for the range of EPSC rates examined; the firing rate curves are vertically shifted from each other along the firing rate axis (Fig. 3B) (n = 14). A plot of the firing rates evoked with d₂ stimulation versus those evoked with d₁ stimulation shows that approximately all of the points were below the unitary slope line (Fig. 3C). Pairwise comparison of the firing rates evoked with d₁ and d₂ stimulation confirmed that the differences were significant (p = 0.0001; n = 14; paired t test).

Boosting persists with dynamic-clamp stimulation

The change in conductance caused by synaptic inputs can substantially alter the integrative properties of neurons. For excitatory synapses, increasingly larger membrane depolarizations decrease the excitatory drive effectively shunting the inputs. To determine whether boosting persists under this condition, the inputs were injected under dynamic clamp (see Materials and Methods). To accurately perform dynamic clamp (Prinz et al., 2004), two electrodes were placed in the dendrite (or soma) spaced <10 μm apart (Fig. 4A, inset). One electrode was used to inject current (I), and the other was used to record the membrane potential (V_d). These two electrodes were placed at an average distance of 230 μm (±50 μm) from the soma. To monitor somatic membrane potential (V_s) during dynamic-clamp stimulation in the dendrite, a third recording electrode was placed at the soma.

As with current clamp, the cEPSPs evoked with dendritic stimulation were greater than those evoked with somatic stimulation (Fig. 4A, left), and this difference was significant (Fig. 4A, right) (p < 0.001; n = 5; paired t test). Likewise, suprathreshold dendritic stimulation evoked significantly (p < 0.0001; n = 5; paired t test) higher firing rates than somatic stimulation (Fig. 4B). These results indicate that boosting would still occur in the presence of synaptic shunting.

Effects of I_h blockade on boosting

Two lines of evidence suggest that the decrease in boosting observed with stimulation of the middle dendritic segments was mediated by deactivation of the hyperpolarization-activated cation current, I_h (Williams and Stuart, 2000; Berger et al., 2001). First, the falling phase of EPSP_d2 decayed faster than that of EPSP_d2→S so that the two waveforms crossed (Fig. 2A, open arrow, top left traces). The fact that crossing of the falling phases was not observed for injection at d₁ (Fig. 2A, bottom left traces) is consistent with an increase in the density of I_h with distance from the soma (Stuart and Spruston, 1998; London et al., 1999). Second, the difference between cEPSP_d2→S and cEPSP_d1→S often did not become apparent until ∼100 ms after the stimulus onset, in the same range as the deactivation time constant of I_h. To determine whether I_h does indeed contribute to the differences in the subthreshold and suprathreshold boosting between d₁ and d₂, the I_h channel blocker ZD7288 (50 μm) was bath applied. During drug application, the resting membrane potential became more hyperpolarized (ΔV_m, 10 ± 1.5 mV; n = 9), and the input resistance measured at the soma increased (control, 29 ± 10 MΩ; I_h block, 58 ± 12 MΩ; n = 9). These effects are in line with I_h being tonically active at rest.

Consistent with previous results (Williams and Stuart, 2000), the width but not the rise time of individual EPSPs recorded at the soma following d₁ and d₂ stimulation increased in the presence of ZD7288 (Fig. 5A). This effect was magnified when a barrage of EPSCs were injected into the dendrite (Fig. 5B), similar to what was observed with trains of single EPSCs (Magee, 1999; Berger et al., 2001). In the presence of ZD7288, the differences in the subthreshold and suprathreshold responses between d₁ and d₂ stimulation were eliminated (Fig. 5C,D). These results suggest that the differences in boosting were attributable to a higher density of I_h in the middle segment compared with the proximal segment; the differences in the responses cannot be simply accounted for by the passive filtering properties of the dendrites (Stuart and Spruston, 1998).

Boosting in the distal dendrites

Stimulation of the distal dendrites can trigger Ca²⁺-mediated bursts of APs and plateau potentials (Stuart et al., 1997; Larkum et al., 2001; Oakley et al., 2001; Larkum and Zhu, 2002). To assess the effects of these events on boosting, we recorded from the distal dendrites. As above, one electrode was placed at the soma and a second was placed at d₁. A third electrode (d₃) was placed 400-600 μm from the soma. As observed for d₂ stimulation, EPSCs delivered at low rates to d₁ and d₃ produced comparable depolarization at the soma. At higher EPSC rates, the responses to d₃ stimulation were smaller than the responses to d₁ stimulation (Fig. 6A), although the difference was not as large as that between d₁ and d₂ stimulation (see below). An additional increase in EPSC rate evoked firing (Fig. 6B); a higher EPSC rate was needed to induce firing with d₃ than with d₁ stimulation (Fig. 6C).

Consistent with previous results (Schwindt and Crill, 1999; Williams and Stuart, 1999; Zhu, 2000), d₁ stimulation evoked mostly repetitive, single APs (Fig. 6B, left traces), whereas d₃ stimulation evoked Ca²⁺-mediated complex spikes in the dendrites that resulted in bursts of APs at the soma (Fig. 6B, right traces). The presence of these Ca²⁺-mediated events compensated for the attenuating effects of I_h. Unlike stimulating at d₂, the low firing rates evoked with d₃ stimulation (Fig. 6C, left) were equal to those evoked with d₁ stimulation. At higher EPSC rates, however, there was an abrupt increase in the firing rate evoked with d₃ stimulation. The slopes of the relation for d₃ measured before and after the upward shift in firing rate were not significantly different (p = 0.13; n = 7; paired t test). A plot of the d₃ firing rate versus d₁ firing rate for six cells shows that the increase in d₃ boosting occurred when the firing rate was >10 Hz (Fig. 6C, right).

Summary of boosting along the somatodendritic axis

To document changes in boosting along the somatodendritic axis, the data were pooled as follows. In the experiments described above, three electrodes were placed on the neuron: one at the soma (s) and two at different sites on the dendrite. For comparison, the two dendritic sites are designated as d_A (placed at the proximal dendrite) and d_B (placed further from the soma anywhere from proximal to the distal dendrite). For both subthreshold (n = 15) and suprathreshold responses (n = 17), the percentage of boosting of inputs at the dendrite relative to the soma was calculated [100 × (R_d - R_s)/R_s, where R_d and R_s are the dendritic and somatic responses, respectively, and can either be the average cEPSP or firing rate]. In the subthreshold range (Fig. 7A), when the second electrode (d_B) was placed <300 μm from the soma (diamonds), the percentage of boosting was consistently less than that at d_A. The difference in boosting decreased when d_B was placed at distances >300 μm (triangles). Similar relationships occurred in the suprathreshold range but were more exaggerated as the firing rates evoked at d_B >300 μm tended to exceed those evoked at d_A (Fig. 7B). These trends can be seen more clearly by normalizing (dividing) the percentage of boosting at each dendritic site by the percentage of boosting at d_A (Fig. 7C,D). A polynomial fit through each plot shows a dip in boosting at the middle dendritic segments followed by an increase at more distal sites. In the subthreshold range, the difference in the scaled boosting between middle and distal segments is less apparent than that in the suprathreshold range (Fig. 7C,D), although the differences were significant for both subthreshold and suprathreshold responses (p < 0.05; t test).

Variation of burst characteristics with input

The bursting behavior evoked with d₃ stimulation contrasted sharply with the predominantly repetitive single APs evoked with somatic, d₁, and d₂ stimulation. This suggests that inputs in the distal dendrites are encoded in a manner that is different from inputs near the soma. To assess the relationship between bursts and stimulus parameters, we documented changes in burst characteristics with the EPSC rate. A typical firing pattern evoked with d₃ stimulation consisted of a burst of two to four high-frequency APs followed by a long interval (Fig. 8A) (see Fig. 10A). Histograms of ISI distribution compiled for a range of EPSC rates (Fig. 8Aii) all show a peak at short ISIs; these correspond to the ISIs of APs in a burst (intraburst intervals). The intervals between the bursts (interburst intervals) were generally longer and are manifested as secondary peaks in the ISI histograms (Fig. 8Aii, bottom histogram). APs were defined to occur in bursts if the ISIs were <20 ms (APs in bursts can also be distinguished on the basis of their timing; see below). With d₃ stimulation, bursting occurred consistently with EPSC rates as high as 1 kHz (Fig. 8Ai,Aii, bottom). In contrast, somatic or d₁ stimulation evoked mainly repetitive APs with only occasional bursts at low EPSC rates (Fig. 8B). Bursting behavior is not restricted to a specific class of layer 5 pyramidal neurons. Both intrinsic bursting (IB) and regular spiking (RS) pyramidal neurons (classified by their responses to current steps delivered at the soma) (Connors et al., 1982; Chagnac-Amitai et al., 1990; Larkman and Mason, 1990; Wang and McCormick, 1993) exhibited bursting preferentially with distal dendritic stimulation. One difference was that bursting was evoked with stimulation at the soma and proximal dendrites in IB cells; but this occurred only at low EPSC rates (Fig. 8B, left plots) (Williams and Stuart, 1999). Therefore, data from both cell types were pooled (Fig. 8B, right).

There were systematic changes in the burst characteristics as the EPSC rate was increased. The intraburst intervals (Figs. 8Ai, 9A) were shortest and the interburst intervals were longest at low EPSC rates (Figs. 8Ai, 9B). At progressively higher EPSC rates, the intraburst intervals increased, reaching maximum values just under 20 ms for an EPSC rate of 1 kHz (Figs. 8Aii, 9A). The interburst intervals, in contrast, decreased (Fig. 9B). In general, the number of spikes in a burst was fairly constant, ranging from two to three APs per burst at all EPSC rates (Fig. 9C). Although the interburst and interspike intervals converged at high EPSC rates, the firing did not simply switch to repetitive firing mode as evidenced by two distinct peaks in the ISI distribution (Fig. 8Aii) and by the timing of the APs.

With increasing EPSC rates, the bursting pattern became more complex, and the timing of the APs became more variable. To accurately document the changes in spiking patterns, we used the C_v2 metric [2|(Δt_{i + 1} -Δt_i)|/(Δt_{i + 1} + Δt_i)], where Δt is the ISI (Holt et al., 1996). Unlike the coefficient of variation (C_v), which gives the variance relative to the mean firing rate, C_v2 provides a measure of variability between pairs of adjacent ISIs during the stimulus and yields several values for a single-spike train. The importance of examining adjacent intervals for the duration of the stimulus is underscored by the fact that many neurons exhibit time-dependent adaptation in firing rate or fire bursts only near the onset of the stimulus. These nonstationary processes as well as the number of spikes within a burst are not readily discernable from ISI histograms or from the C_V metric. Details of the spiking patterns are revealed by plotting C_v2 for pairs of adjacent ISIs against the mean value of those two ISIs and examining the distribution of data points. Hence, neurons firing single action potentials at a regular rate (Δt_{i + 1} =Δt_i) yield ∼0 C_V2 values that are tightly clustered. In contrast, highly variable spikes (large differences in Δt_{i + 1} and Δt_i), as would occur for a poisson process, yield a cloud of C_V2 values ranging from 0 to 2 that spans a wide range of mean ISI values. Changes in the spiking patterns are manifested as changes in the clustering patterns.

At low EPSC rates (Fig. 10Ai, black dots), the repetitive bursts of two to three high-frequency APs resulted in two clusters of C_v2 values. One cluster at mean ISIs of ∼5 ms consisted of C_v2 values <1 and arose from three successive APs that occurred within bursts (the intraburst intervals were each ≤5 ms). Another cluster with high C_v2 values at mean ISIs of ∼150 ms arose from sequences consisting of three APs separated by an interburst (∼300 ms) and an intraburst (∼5 ms) interval. At a higher EPSC rate (Fig. 10Aii), the firing switched to a very stereotyped, repetitive pattern consisting of a burst of two APs separated by a long and fixed interburst interval. The associated C_v2 plot has one cluster at a mean ISI of ∼50 ms. At still higher EPSC rates, the spiking pattern became more irregular as both the interburst and intraburst intervals became more variable. The mean values of two adjacent ISIs were between ∼30 and 40 ms, indicating a relatively constant average firing rate, but the C_v2 values ranged from ∼0 to >1.5 (Fig. 10Aiv). Thus, there is a transition in the firing pattern that depends on the intensity of the stimulus: from regular bursts to more variable spike times. The change in firing patterns with EPSC rate was observed for the entire data set (Fig. 10A, gray dots). The C_v2 values for the firing evoked with stimulation of the soma, d₁, or d₂ were generally <0.5 (n = 30; see below). The ISI histograms at the bottom of Figure 10A show the changes in the distribution of interspike intervals for the same cell highlighted in the C_v2 panels. Note that the histograms do not capture details in the variability of the spike patterns. For example, the histograms in Figure 10, Ai and Aii, are similar, although the bursts consist of three and two spikes, respectively. Similarly, the higher variability of firing in Figure 10, Aiv compared with Aiii (top), is reflected in the spread of C_V2 values (iv, middle), whereas the histograms (bottom) are qualitatively similar.

The change in the distribution of C_v2 values with EPSC rates was not observed with stimulation of proximal dendrites (Fig. 10B) (n = 7). At low EPSC rates (0.4 kHz), d₁ stimulation evoked mainly low-frequency (∼10 Hz), repetitive, single APs. The C_v2 values were generally <0.5 except for a few points that were attributable to occasional bursts at the start of the train. In contrast, the C_v2 values for d₃ stimulation were in three clusters. One cluster (Fig. 10B, a) consisted of C_v2 values for sequences of three high-frequency APs that occurred in bursts. A second cluster (Fig. 10B, b) was from sequences of three APs separated by a long interval (interburst) and a short interval (intraburst). A third cluster (Fig. 10B, c) was from sequences of three single APs that did not occur in bursts. Stimulation of d₁ at high EPSC rates (0.96 kHz) increased the firing frequency of the neuron to ∼20 Hz; the mean ISI pair values shifted leftward with only a slight increase in C_v2 values (Fig. 10B, right). For d₃ stimulation, there was one cluster, but the range of C_v2 values ranged from ∼0 to >1.5. This indicates that the bursting pattern evoked with d₃ stimulation persisted for a relatively large range of EPSC rates and firing frequencies and remained distinct from the repetitive APs evoked with d₁ stimulation.

Current clamp versus dynamic clamp

The algorithm for calculating the input barrage sums the individual EPSCs linearly. Injecting these inputs into the cell under current clamp mimics the condition in which synaptic inputs from electrotonically and spatially distant branches converge at a common site (e.g., at the dendritic recording sites). Injecting the barrage under dynamic clamp simulates the case in which inputs are close to each other on the same branch. Under this condition, mutual shunting leads to sublinear summation (Rall, 1964). The fact that boosting occurred under both current-clamp and dynamic-clamp conditions suggests that the findings of this study can be generalized to a wide range of synaptic input configurations.

I_h-mediated decrease in boosting

In the subthreshold range, the decrease in boosting observed at middle dendritic sites was likely a result of I_h. Because I_h has a reversal potential of -47 mV, it maintains the resting potential at a more depolarized level and decreases the input resistance of the cell. With depolarization, I_h deactivates within 20 to 100 ms (Berger et al., 2001) so that when the input barrage is injected, the resultant depolarization peaks but then decreases to a lower steady-state level (Fig. 2). The attenuating effects were greater at the middle dendritic segment, because the density of I_h increases with distance from the soma (Williams and Stuart, 2000; Berger et al., 2001). In the distal dendrite, the attenuating effects of I_h were partially counteracted by the presence of Ca²⁺ conductances (Figs. 6, 7). These Ca²⁺ conductances can be activated by single EPSPs and by subthreshold tonic depolarization (Schiller et al., 1997).

Similarly, boosting in the suprathreshold range dipped in the middle dendritic segments. During tonic repetitive firing, the associated depolarization deactivates I_h, thereby reducing the net excitatory drive (Spain et al., 1987; Magee, 1999). Again, this effect is enhanced in middle dendritic sites because of the higher density of I_h, although boosting is not completely eliminated.

In the proximal dendrite, I_h does not substantially reduce boosting of firing rate (compared with the soma). Previously, we showed that selectively blocking Na⁺ channels in the proximal dendrite (<200 μm) with tetrodotoxin caused the dendritically evoked firing to become equal, rather than dip below, to the somatically evoked firing (Oviedo and Reyes, 2002). This is consistent with the density of I_h being approximately equal in the soma and proximal dendrite (Berger et al., 2001).

Boosting in the distal dendrites was greatly magnified at high EPSC rates most likely because there was sufficient depolarization to trigger Ca²⁺ plateau potentials (Oakley et al., 2001; Larkum et al., 2004). The contribution of these Ca²⁺ plateau potentials is additive, shown by the upward shift in firing rate without an accompanying change in the slope of the input-output curve (Fig. 6C).

Stimulus-dependent changes in bursting

In addition to quantitative changes in firing rate along the somatodendritic axis, there were also prominent changes in the pattern of APs. In contrast to the soma and proximal dendritic sites, stimulation of distal dendrites evoked bursts. This bursting behavior has been documented both in vitro (Amitai et al., 1993; Kim and Connors, 1993; Markram and Sakmann, 1994; Yuste et al., 1994; Williams and Stuart, 1999) and in vivo (Larkum and Zhu, 2002). We found that burst characteristics changed systematically with the EPSC rate. The increase in excitatory drive decreased the intervals between bursts but increased the intervals of APs within a burst. The latter is probably attributable to the accumulation of Ca²⁺ and an increase in the activation of Ca²⁺-dependent K⁺ conductances (Yuste et al., 1994; Sah and Bekkers, 1996; Schiller et al., 1997; Schwindt and Crill, 1997; Helmchen et al., 1999). These Ca²⁺-dependent K⁺ conductances have been implicated in regulating burst dynamics (Pinsky and Rinzel, 1994).

The changes in burst characteristics translated into an increase in the variability of firing. At low EPSC rates, the firing consisted mostly of repetitive bursts of two to three APs. At higher EPSC rates, the firing switched to bursts interspersed with single spikes, leading to more irregular firing. This indicates that although the highly irregular firing of cortical neurons can arise from synchronous synaptic drive (Softky and Koch, 1993; Stevens and Zador, 1998), Ca²⁺-mediated events in the distal dendrites may also contribute substantially to spike variability. A similar conclusion was reached by Larkum et al. (2004) with white noise current injection.

Burst characteristics (interburst intervals, intraburst intervals, and AP variability) changed systematically with EPSC rates. All three parameters did not saturate for EPSC rates as high as 1 kHz; at this input rate, the neuron can sustain tonic firing at frequencies ranging from 25 to 30 Hz for at least 1 s. In the soma and proximal dendrites, the relationship between uncorrelated input and output can be described by a linear or sigmoidal function (Oviedo and Reyes, 2002). A similar relationship exists in the distal dendrite if the timing of APs is ignored and only the average firing rate is considered (Fig. 6C). However, bursting and repetitive APs are likely to have different effects on the postsynaptic target of the pyramidal neuron particularly because the majority of EPSPs evoked in target neurons exhibit depression or facilitation (Markram et al., 1998; Reyes et al., 1998; Reyes and Sakmann, 1999). Because the development and recovery from depression or facilitation depends on the intervals between APs, any change in the intervals between burst, intervals of APs within the burst, and the variability of the firing will lead to different amplitude EPSPs in the target neurons (Lisman, 1997; Tsodyks and Markram, 1997). In this view, four regularly spaced action potentials would have a different effect on the target cells than two action potentials occurring in two bursts (Lisman, 1997; Williams and Stuart, 1999). Thus, the information transmitted to target neurons by distal dendritic input may be fundamentally different from that transmitted by inputs near the soma even when the average firing rate of the pyramidal neuron is the same in both cases.

For simplicity, we used asynchronous inputs to drive the neurons. However, in vivo recordings reveal a wide range of synaptic input time courses. Because ionic conductances are time dependent, their activation states, and hence the evoked firing, are likely to change with the time course of inputs (Reyes, 2001). Additional experiments are needed to determine how, for example, synchronous inputs (Oviedo and Reyes, 2002) affect the bursting characteristics.

Functional significance

The apical dendrites of layer 5 pyramidal neurons can span nearly all of the cortical layers. The afferents from different classes of presynaptic cells are not scattered randomly throughout the dendritic tree but tend to be clustered on specific branches (Bernardo et al., 1990a,b; Ito, 1992; Gottlieb and Keller, 1997; Dodt et al., 2003; Thomson and Bannister, 2003). The finding that boosting and firing patterns vary along the somatodendritic axis has several implications. First, inputs from different classes of presynaptic cells are boosted differentially. Afferents from other cortical areas and from layers 2/3 that terminate in the distal apical dendrite would be weighted more than afferents that terminate in layer 4, near the middle dendritic segments. At the very least, greater boosting would partially compensate for the relatively smaller somatic EPSPs evoked with stimulation of distal dendrites (Williams and Stuart, 2002). Second, the different densities of active conductances would impart filtering characteristics to inputs at each dendritic segment. For example, the relatively slow kinetics of I_h deactivation would mean that tonic inputs would be preferentially attenuated over transient or synchronous inputs. Finally, qualitatively different firing patterns may provide a means of uniquely encoding inputs that occur in the distal dendrites. In this scenario, bursts would provide a “tag” for cortico-cortical signals, for example, that are processed in the distal dendrite.