Institute of Physiology, University of Bern, Bühlplatz 5, CH-3012 Bern, Switzerland
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Abstract |
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Key Words: BAC firing, calcium spike, cortex, dendrite, gain, pyramidal neuron
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Introduction |
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Subthreshold distal input to the apical tuft of layer 5 neocortical pyramidal neurons is severely attenuated as it spreads towards the cell body (Berger et al., 2001; Williams and Stuart, 2002
) and is shunted by back-propagating action potentials (APs) (Stuart and Häusser, 2001
) so that the site of Na+ AP generation in the axon (Stuart et al., 1997
) is hardly effected by it (although see Cauller and Connors, 1994
). However, suprathreshold input to the apical tuft generates dendritic APs which lead to multiple APs discharging in a burst-like fashion (Schiller et al., 1997
; Larkum and Zhu, 2002
). The probability of reaching threshold for this event is facilitated by the interaction between the back-propagating AP and the distal dendritic excitatory postsynaptic potential (EPSP) which relies on a temporal coincidence of 2030 ms. We refer to this as BAC firing (Larkum et al., 1999
). Another coincidence-dependent phenomenon is the boosting of back-propagating APs by dendritic EPSPs (Stuart and Häusser, 2001
). Under normal circumstances, pyramidal cells are continuously bombarded by inputs (Steriade et al., 2001
) and it is not clear how these timing-dependent mechanisms are influenced by quasi-random fluctuations in membrane potential. Here we investigate this question with noisy, Gaussian-distributed current injections to multiple dendritic sites simultaneously.
Since coincident activation of multiple regions can affect the output of the neuron, it might be expected to modulate the input/output relation (gain) of the neuron. Gain modulation is responsible for a wide range of physiologically relevant behaviors in which different types of information need to be combined (for review see Salinas and Sejnowski, 2001). The underlying computational unit for gain modulation can be realized at the network or single-cell level. It was recently shown on the single-cell level to be dependent on the noise of input conductances (Chance et al., 2002
). We show that BAC firing presents another mechanism for gain modulation, which is based on dendritic Ca2+ conductances. The activation of distal dendritic Ca2+ spikes results in both an increase in gain and the coefficient of variation (CV) of the interspike intervals. In addition, we found that the timing of bursts is correlated with the conjunct input to the distal dendrite and soma within a narrow time window.
The experiments are complemented with a minimal model using two compartments that can fully account for the observed gain modulation and association capabilities of L5 pyramidal neurons. Some of these results have been presented in abstract form (Larkum and Lüscher, 2002).
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Materials and Methods |
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Young adult Wistar rats (P2643, 60171 g; av. P36, 105 g, n = 32) were anaesthetized with Halothane (Eurim-Pharm, Piding, Germany) and decapitated. Parasagittal slices (300 µm thick) of neocortex were prepared (Sigmann Electronik, Hüffenhardt, Germany). Parasagittal slices were prepared in ice-cold extracellular solution containing (in mM): NaCl 125, KCl 2.5, NaH2PO4 1.25, NaHCO3 25, MgCl2 1, dextrose 25, CaCl2 2, at pH 7.4, and transferred to a submersion chamber containing the same solution kept at 37°C for 2030 min. For recordings, the slices were transferred to a smaller chamber mounted under the microscope and perfused constantly with the oxygenated solution warmed to 34°C. Cadmium (25100 µM; Fluka, Buchs, Switzerland) was bath applied. Slices were visualized with a 60x objective (Zeiss, Feldbach, Germany) using infrared differential interference contrast optics.
Electrophysiology
L5 pyramidal cells from the somatosensory cortex were chosen if their apical dendrite could be followed far enough to establish that the dendritic tree was intact. Patch electrodes (510 M for soma and 715 M
for dendrites; borosilicate glass capillaries 2 mm o.d., 1 mm i.d., Hilgenberg, Germany) were made with an electrode puller (Sutter, USA, Model P-97). These were used to make two or three simultaneous whole-cell recordings from different parts of the apical dendrite. One electrode was always placed on the cell soma for recording APs defining the cells output. Electrodes for recording from the proximal compartment were placed 165376 µm from the soma and for the distal compartment 445719 µm from the soma. Pipettes were filled with a solution containing (in mM): potassium gluconate 105, KCl 30, HEPES 10, MgCl2 2, MgATP 2, Na2ATP 2, GTP 0.3, at pH 7.3. In addition, all pipettes contained the fluorescent dye Alexa 568 (Molecular Probes, 10 µM) for visualizing the cells during the experiments and biocytin (0.25%) for reconstruction and positive identification of the cell type. Recordings were made with Axoclamp 2B amplifiers (Axon Instruments, Foster City, USA), digitized at 10kHz with an A/D converter (ITC-18, Instrutech, Port Washington, USA) and acquired on a Macintosh computer using Igor software (Wavemetrics).
Stimulus generation
To generate in vivo-like inputs we used the OrnsteinUhlenbeck method (Tuckwell, 1988) to generate noisy currents with a mean (µ), standard deviation (
) and correlation length (
) according to the equation
where I(t) is the injected current and Gt is a random number taken each time step from a Gaussian distribution with mean 0 and standard deviation 1. The correlation length was set to = 3 ms, and the time increment, dt, was the same as the sampling interval, 0.1 ms. We chose relatively long (2 s) and small steps (50100 pA) for the experiments presented here so that the results would be close to steady state. In separate experiments, we examined the effects of injecting shorter steps (data not shown). In these experiments, the gain increased slightly regardless of the site of current injection probably due to the fact that less spike frequency adaptation occurred with shorter steps.
Modelling
The data were reproduced by a two-compartment integrate-and-fire model consisting of a somatic compartment with a transient potassium current to capture the after-hyperpolarization, and a dendritic compartment with a voltage-dependent calcium current (Fig. 7A). The two compartments were linked with an ohmic resistance representing the dendritic shaft. An AP was emitted whenever the somatic membrane potential (VS) exceeded a threshold, which in turn triggered the IAHP. The AP was modelled by clamping VS for 1 ms to 10 mV and resetting it to the somatic resting potential. Details of the model, equations and the parameters can be found in the Appendix.
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Results |
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Threshold for noisy current injection causing AP firing at the soma increased with increasing distance of the injection site from the soma (Fig. 1F, black dot, somatic current injection; blue dots, proximal dendrite; red dots, distal dendrite). As expected, threshold for noisy current was always lower than for DC current injection at all locations (not shown). Current injection at the soma resulted in APs (Fig. 1B) at a similar linear frequency to current (f/I) relationship (Fig. 1C, black dots) to that already reported for L5 pyramidal neurons (Oakley et al., 2001), and produced attenuated back-propagated APs in the dendrite as shown previously (Stuart et al., 1997
).
The gain of the frequency to current relation was assessed by a threshold-linear fit of the non-saturated part of the f/I curve, typically up to 80% of the maximal frequency. This gain was determined for each current injection site. For soma and proximal inputs, the mean gain was 0.046 ± 0.001 AP/s/pA (n = 26) and 0.056 ± 0.013 AP/s/pA (n = 11) respectively (Fig. 1D, black and blue dots). For distal current input, the mean gain was significantly higher (0.082 ± 0.0345 AP/s/pA, n = 17, Fig. 1D, red dot) than for the somatic and proximal compartments. The gain appeared to begin to increase with current injection around 400 µm from the soma and rose as a function of distance from the soma (Fig. 1E). The average increase in gain for distal dendritic current injection was 72%, and 22% for proximal current injection. For the rest of the paper we focus on the comparison between the distal compartment and the soma.
Noisy Distal Dendritic Input Results in a Higher CV than Noisy Somatic Input
Once firing threshold was reached with dendritic current injection, mean spike rate rapidly rose to high values (Fig. 1C, red line; Fig. 2B, triangles). Whereas somatic current injection caused strongly attenuated back-propagating APs (Fig. 2C, expanded time scale, black traces), dendritic current injection caused long-lasting depolarizing dendritic events which were often associated with a burst of somatic APs (Fig. 2D; arrows and expanded time scale). This burst-firing behavior due to dendritic current injection is also reflected in the high CV of the interspike interval (Fig. 2B; inset). When current was injected at the soma, the CV was small and decreased further with increasing current injection. This is consistent with the interpretation that at low currents, the CV is mainly determined by the input current fluctuations (), while at high input currents, CV is mainly determined by the mean (µ) of the input current. For distal current injection the situation was quite different. In this condition, the CV was much higher, particularly near threshold where the CV reached values >1. The APs tended to come in bursts, which are mainly determined by the intrinsic properties of the cell rather than the fluctuations in the input current (Williams and Stuart, 1999
).
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Input to the dendrite increased the gain but also had a higher threshold. Under more realistic circumstances, large prolonged input is unlikely to arrive exclusively at the distal tuft. To study the effect of simultaneous input distributed over the dendritic tree we combined current injections into the soma and different dendritic sites. To simplify this part of the study we injected steady-state noisy current at one site while injecting noisy staircase current ramps at the other site. We first looked at the effect of fixed, near threshold somatic input on the gain of distal dendritic input. As shown above, if dendritic input was injected alone (with steps of µ = 100 pA from µ = 0 up to 1.1 nA) the AP threshold was reached only with strong current (Fig. 4A; last current step with 1.1 nA, red triangles with open arrow). The somatic f/I relationship is shown in Fig. 4A (black line and filled symbols, labelled s). Injecting 0.25 nA (constant µ) into the soma, which corresponds to a just-subthreshold current for the somatic f/I relationship, and combining it with the staircase current injected into the dendrite significantly reduced the threshold for the dendritic f/I relationship (red arrow, black and red line, labelled s+d). This new f/I curve started with a much reduced gain compared to somatic current injection alone since the passive attenuation of dendritic current and was roughly half of the gain obtained when current was injected into the soma alone. With higher dendritic current a second threshold was crossed (around 0.85 nA), and the gain jumped to a value greater than the somatic gain (from 0.85 to 1.1 nA). During this high-gain range in the combined f/I curve the CV remained high even at an elevated spike rate (Fig. 4B, red symbols). Such an f/I curve with two phases was never seen with current injection into the soma alone.
Figure 4C shows the spike train resulting from the combined current injection (from which the f/I curve in Fig. 4A, s+d, was derived). Looking closely at the somatic and dendritic recordings at an expanded time scale reveals that the underlying cause of the high-gain range and the elevated CV was the activation of dendritic regenerative activity. With combined input (Fig. 4C), the events triggered by a near threshold current (Fig. 4D) were single somatic APs (Fig. 4D1) which resulted in small and short back-propagating dendritic APs. Increasing the distal current continued to elicit such single events until the second, high gain-range of the f/I relationship was crossed where bursts of 24 APs were generated at the soma (Fig. 4E, E1; black traces). The dendritic potentials that were associated with the bursts (Fig. 4E, E1; red traces) were much larger in amplitude and broader than with single back-propagating APs. The change in the gain of the input was therefore most likely due to recruitment of dendritic regenerative activity. At very high dendritic input and simultaneous small somatic input (Fig. 4F), long plateau-like potentials were generated in the dendritic compartment which lead to more or less continuous spiking at high rates at the soma.
Dendritic Input Increases Gain of Somatic Input
By reversing the previous experiment (using constant, subthreshold current input to the distal dendritic compartment with staircase input to the somatic compartment) we tested the modulation of the somatic f/I relationship by dendritic input (Fig. 5). In this case, constant, small subthreshold input to the dendritic compartment shifted the f/I curve (Fig. 5A; filled circles) leftwards to much lower current values (Fig. 5A; open squares and diamonds). This threshold shift was linearly related to the mean current (µ) injected into the dendritic compartment (Fig. 5C). In addition, current injection with constant mean value into the dendritic compartment increased the gain of the somatic f/I curve (Fig. 5A, B). The addition of weak dendritic input combined with somatic input was the most effective regime for causing AP firing. In the example shown in Figure 5, when 250 pA dendritic current was combined with 600 pA somatic current, the firing approximately doubled even though the dendritic input was less than a quarter of the threshold for dendritic current alone (which had a threshold of 1050 pA). This implies that moderate top-down input to the higher layers can significantly increase the output of a cortical column when the layer 5 cells are activated. Note that, in contrast, background activity generating additional somatic input current to layer 5 cells only shifts their f/I relationship to the left, but never increases their gain.
Somato-dendritic Coincidence Detection in the Presence of Noisy Input Currents
To examine the mechanism of increased gain with combined currents we determined the typical current trajectory in the soma and the dendrite at the time of an AP and a dendritic calcium spike. For this analysis, we extracted the current trajectories generating suprathreshold events in the presence of combined noisy input currents at two sites. The somatic current steps ranged from a mean of 50 pA to 1250 pA, while the simultaneously injected dendritic current ranged from a mean of 250 pA to 750 pA. The noise was throughout 300 pA. We looked for transient dendritic depolarizations above 30mV which lasted at least 20 ms with simultaneous somatic and dendritic current injection. During the total injection time of 150 s we counted 229 such events and 2272 APs. On average, these transient dendritic depolarizations triggered 2.2 somatic APs within 15 ms (counted from the first spike after dendritic threshold crossing), yielding an estimated intraburst firing rate of 113 Hz. Using the definition of a burst as at least three APs within 20 ms and less than three APs in the preceding 20 ms period, we counted 238 bursts, almost the same number of transient dendritic depolarizations. We conclude that these dendritic depolarizations typically caused the burst firing of a L5 pyramidal cell in response to noisy, distributed inputs.
To determine the typical voltage trajectories that lead to single APs and bursts we calculated spike-triggered and burst-triggered current averages. They were obtained by superimposing the current traces at the time of an arbitrary AP (defined by the threshold crossing of the somatic membrane potential at 15 mV) and at the time of the first AP within a burst (i.e. after threshold crossing of the dendritic membrane potential at 30mV), respectively (Fig. 6). The spike-triggered average of the somatic current had a much higher peak than the spike-triggered average of the dendritic current (374 pA versus 127 pA; Fig. 6A1, A2). This indicates that, with injections of noisy currents with similar statistics into soma and dendrite simultaneously, an AP was more likely to be correlated to a current fluctuation at the soma than to a current fluctuation in the dendrite. However, when restricting the analysis to the first spike within a burst, the resulting burst-triggered average current was equally strong or even smaller in the soma than in the dendrite (298 pA versus 358 pA; Fig. 6B1,B2), contrasting the case of averaging over all spikes (374 and 127pA; Fig. 6A1,A2). This shows that bursts were typically associated with both, somatic dendritic input currents, while spikes in general are mainly associated with somatic input. Bursts therefore signaled coincident input into the soma and dendrite. The relationship between bursts and coincident inputs is best demonstrated by the correlation coefficients of combined somatic and dendritic current traces centred at the time of an AP (Fig. 6A3), and restricted to the times of the first AP within a burst (Fig. 6B3). Coincident somatic and dendritic input current at this time was roughly three times more correlated with a burst than with a single spike (0.55 versus 0.16). Single spikes tended to signal the presence of input to somatic compartment alone, while bursts tended to signal coincident input to both the somatic and dendritic compartment. The coincidence detection window had a width of roughly 30 ms, as found in the case of single pulse injections into soma and dendrite (Larkum et al., 1999). This indicates that even under conditions of random bombardment of inputs, the same mechanisms and dynamics govern firing as with more stereotypical current injections that lead to BAC firing. We therefore refer to bursts generated under these conditions as BAC bursts.
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Minimal Two-compartment Model for BAC Firing
We constructed a two-compartment integrate-and-fire model with a dendritic calcium current (Fig. 7A, see Methods and Appendix for details) which reproduced the somatic and dendritic voltage traces, and explains the different properties of the somatic and dendritic f/I relationships. The model (Fig. 7B, thick red and blue lines) accurately reproduced the f/I curves for somatic and dendritic current injections (Fig. 7B, red and blue circles), and the somatic and dendritic voltage traces (Fig. 7C1,C2). With the noise level used in the experiment ( = 300pA) the individual spike timings were reliably reproduced (66% within ±2 ms in case purely somatic injections, Fig. 7C1). When the calcium current in the model was removed, the gain of the f/I curve dropped (Fig. 7B, right-most thin red line), as observed in the experiment (Fig.3A). In turn, when the calcium currents in the dendritic compartment were activated by concomitant dendritic background input, the gain of the f/I curve increased (Fig. 7B, left-most thin blue line). A separation of the two classes of inputs (IS, ID) into two compartments is necessary in order to restrict the voltage-dependent interaction of the AP to only one class (ID).
Threshold-linear Approximation of the f/I Relations
The different f/I relations can be fitted by a threshold-linear transfer function with gain and threshold depending on the amount of noise, the input location, and the calcium dynamics. For somatic DC current of strength µ the threshold-linear f/µ relation takes the form f = g (µ
), with gain g0 and threshold
. Somatic current fluctuations of amplitude
decrease the threshold by roughly
, but also decrease the gain to some value gs smaller than g (data not shown). The f/µ relation for somatic current injection therefore becomes f = g
(µ +
). With the parameter values g
= 0.05 AP/s/pA and
= 520 pA the f/µ relation of the cell shown in Figure 7 is well fitted (middle line). In a passive dendritic tree the means and fluctuations of dendritically injected currents are scaled by an attenuation factor
, and the slope of the f/µ relation for dendritic current is roughly reduced by
, f = g
(
µ +
). For the experiment shown in Figure 7 with an electrode placed 700 µm from the soma we have
0.4. The effective gain of the f/µ relation is therefore
g
0.02 AP/s/pA, while the effective threshold, (
)/
, roughly increased by 1/
, see Figure 7B, right. Here, the gain reduction due to the attenuation of the mean current (a factor of 0.4) dominated the gain increase due to the reduction of the somatic current fluctuations (a factor of 1.2), so we only consider the former (and therefore identify g = g
). To take into account the dendritic calcium conductances we add a current ßf wich is proportional to the spike frequency f. The proportionality factor ß = ß(µ) is an increasing function of the dendritic mean current µ which saturates for values above 1000pA. The dendritic f/µ relation in the presence of such regenerative dendritic conductances is implicitely given by f=g
(
µ +
+ ßf
), resulting in an increased gain given by
g/(1 ßg). With a maximal value ß = 15 pA/AP/s we obtain a gain of 0.08 AP/s/pA (Fig. 7B, thin red line), which is higher than the gain of the somatic f/µ relation (Fig. 7B, thick red line). When combining somatic and dendritic current inputs, the firing rate is f = g [µS +
µD +
+ ß(µD)f
], with
. Injecting a dendritic current with fixed µD = 750 pA (and
D =
S = 300pA) into the model, we obtain an f/µS relation which is fitted with ß(µD) = 5 pA/AP/s. The slope of this frequency to somatic current relationship is g/[1 ß(µD)g] = 0.07 AP/s/pA (Fig. 7B, thin blue line), which is again higher than the slope for somatic current injection alone (g = 0.05 AP/s/pA; Fig. 7B, thick blue line).
This simple threshold linear approximation of the f/I relationship shows how the mean and the noisy component of the somatic and dendritic currents work together in generating the responses. Roughly, the gain for dendritic input is times smaller and the threshold 1/
times larger than for somatic input without dendritic calcium conductances. Only with dendritic calcium events triggered by the back-propagated AP is the gain for dendritic and somato-dendritic inputs elevated above the gain for purely somatic inputs.
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Discussion |
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Dependence of f/I Relationship on Input Location
One of the new experimental findings of this paper is that the initial slope of the f/I curve increases with the distance of the input from the soma. Current injected at the soma showed an approximately linear relationship to firing. A similar relationship was observed with proximal current injection. Distal current injection caused a much steeper rise in the initial part of the f/I relationship. Using iontophoretic application of glutamate onto the dendrites Oakley et al. (2001) found that firing increase in a step-like manner when threshold was reached, possibly because of the focal nature of the glutamate increase. They conjectured that the jump followed by a plateau is the result of dendritic regenerative activity and not the saturation of glutamate receptors which seems likely in the light of the data we present here. Similarly, the regenerative conductance was found to be Cd2+ sensitive (i.e. a voltage-sensitive calcium conductance) in both studies. Persistent Na+ channels are also known to boost synaptic inputs (Schwindt and Crill, 1995
) in proximal regions (Stuart and Sakmann, 1995
). Activation of this conductance leads to higher firing rates (Oviedo and Reyes, 2002
) which appears to be due to a change in rheobase which shifts the f/I relationship to the left without changing the gain (Crill, 1999
). In the present study, we saw small increases in firing rates for the proximal region corresponding to Oviedo and Reyes (2002
) which could be due to Na+ conductances, however the greatest increase in firing occurred with more distal current injection and blocking Ca2+ channels abolished this increase.
Spike Train Variability
It is well known that the variability (CV) of the interspike interval (ISI) of cortical neurons as observed in vivo during behavior is larger than the CV observed in vitro by noisy current injection or in simulations with stochastic synaptic inputs (Softky and Koch, 1993; but see Van Vreeskijk and Sompolinsky, 1996
). It has been suggested that the CV of the ISI measured in vivo (0.51.0) is influenced by network properties. For example, strongly synchronized input (Softky, 1994
), or the presence of large but nearly balanced excitatory and inhibitory input which is not present in the slice (Shadlen and Newsome, 1994
; Holt et al., 1996
). The corollary is that in the slice preparation, without this network activity, the CV of the ISI reflects the CV of the injected input. Indeed, we consistently found that the CV in layer 5 pyramidal neurons was small (typically CV < 0.5) when using noisy current injected at the soma. However, the same noisy current injected at the dendrite consistently elicited spike trains with CV > 0.5. The presence of high CV was dependent on dendritic calcium conductance since it could be reduced to low values comparable to somatic input with the addition of Cd2+. The high CV in our in vitro experiments was due to the intrinsic properties of the neuron and not the result of network properties.
Timing of Bursts
The debate about neuronal coding is often reduced to single spike times versus mean frequency (Abeles, 1994). Burst timing offers a third way of encoding both frequency and precision of timing (see also Berger and Lüscher, 2003
). The occurrence of a burst within an irregular train of APs tells a postsynaptic neuron that with high probability a strong transient input was jointly present in the dendritic and somatic compartment within a 30 ms time window. If the postsynaptic neuron can detect the presence of bursts (Williams and Stuart, 1999
) this information may be propagated throughout the network (Snider et al., 1998
). It is interesting to note that both the duration of the burst and the coincidence time window that leads to the burst are approximately of the same duration (
30 ms) which may imply that this level of precision has a special significance in the neocortex. Repetitive somato-dendritic associations leading to bursts may also be important for regulating synaptic plasticity (Pike et al., 1999
; Golding et al., 2002
).
Current Injection versus Dynamic Clamp
To create artificial synaptic input with patch electrodes it is also possible to use the dynamic current clamp technique (Chance et al., 2002). We used the bridge clamp method for this study for technical reasons: for the long recordings made with fine electrodes at multiple dendritic sites, a change in tip resistance has a disproportionate effect on the voltage measured during current injection whereas the magnitude of current injected remains relatively unaffected. Under these conditions, Vm is more robustly determined with bridge clamp and makes comparison between somatic and dendritic current injection possible. Simulations and experiments show that a conductance change in the apical tuft is just as likely to activate calcium regenerativity (Rhodes and Llinás, 2001
; Larkum and Zhu, 2002
). We confirmed this directly with our two-compartment model (see Appendix) by replacing current injection formulation with simulated synaptic conductances in both compartments. The gain modulation produced by simultaneous synaptic activity at the dendritic and somatic compartments was almost unaffected. This implies that the results shown in this paper would be unchanged by the use of the dynamic clamp method. A similar finding was recently reported by another laboratory (Oviedo and Reyes, 2003
). However, if the output frequency is plotted against the frequency of the excitatory input, the gain can be modulated by an additional inhibitory conductance at the dendrite (Prescott and De Koninck, 2003
). This mechanism of gain modulation relies on a coordinate transform of the x-axis without taking active dendritic conductances into account. Top-down inputs have been shown to be predominantly excitatory (Shao and Burkhalter, 1996
) and when activated may lead to a condition in which excitation and inhibition are unbalanced.
Fluctuation-induced Decrease versus Burst-induced Increase of the Gain
Chance et al. (2002) showed that an increase in fluctuations of the input leads to a decrease in gain using noisy conductance changes at the somata of L5 pyramidal neurons. When measuring the gain due to noisy current injected into the dendrite (f/Idend), the resulting fluctuations at the soma are smaller than at the site of injection and this decrease would therefore tend to cause an increase in gain. However, the simultaneous attenuation of mean voltage deflection as it propagates to the soma has a larger and opposite affect on the gain. This can be seen by the fact that the gain is larger with somatic current injection in the absence of Ca2+ spikes. On the other hand, when measuring the modulation of somatic gain (f/Isoma) by steady-state noisy dendritic current, the noise at the dendritic site only serves to increase the total noise at the soma. This increase in noise would decrease the gain as per Chance et al. (2002
). However, we observed an increase in gain under these conditions, indicating that the mechanisms underlying the dendritic boosting of gain outweigh any fluctuation-based decrease.
Recent simulation studies have implied that asynchronous inputs distributed over the dendritic tree should enhance the overall effectiveness of dendritic input (Rudolph and Destexhe, 2003). Under these conditions the probability of dendritic regenerative events was also increased. In the present study, current was localized to a single dendritic point but was still able to recruit dendritic conductances necessary for enhanced output. Thus, it is possible that under in vivo conditions, these mechanisms play an even bigger role in determining output firing.
Point Input versus Distributed Synapses in a Multi-compartment Neuron
The effect of inputs distributed over the tuft region should be greatest at the nexus of the various tuft branches which corresponds to the major bifurcation of the apical dendrite (Rhodes and Llinás, 2001). This is also the region with the lowest threshold for Ca2+ APs (Larkum and Zhu, 2002
). We used a single dendritic electrode to inject current near this region close to the bifurcation which constitutes the best approximation to distributed input over the tuft. This approach does not preclude effects of interactions of inputs on nearby branches (Poirazi et al., 1993
; Ariav et al., 2003
; Rudolph and Destexhe, 2003
) within either the tuft or the basal dendritic compartments but describes the efficacy of the sum of the synaptic currents and active conductances in these compartments in terms of the input/output relation of the neuron (London et al., 2002
).
Functional Interpretation
BAC firing is a mechanism for associating joint somatic and dendritic input. Somatic and proximal inputs to layer 5 pyramidal cells typically represent bottom-up input from a specific sensory modality, while dendritic inputs typically represent top-down information, for instance from other sensory modalities (Cauller, 1995) or from attention steering centres (Shulman et al., 1999
; Olson et al., 2001
). Our data are compatible with the observation that attention enhances the response of orientation selective cells in a multiplicative way, while the relationship between burst rate and firing rate remains unaffected (McAdams and Maunsell, 1999
). It may be advantageous that this kind of global top-down information modulates the output of a cortical column in a different way than the direct, local bottom-up information does (Körding and König, 2000
; Rolls, 2000
; Siegel et al., 2000
). We showed that BAC firing is precisely such a tool which labels the cortical output depending on whether there is simultaneous top-down and bottom-up input or not.
Several modeling studies have pointed out that neurons can have more than one functional compartment that combine to contribute to their firing properties (Rall, 1964; Poirazi et al., 1993
; Pinsky and Rinzel, 1994
; Mainen and Sejnowski, 1996
). BAC firing provides a mechanism for a L5 pyramidal neuron to make vertical associations of cortical inputs that impinge on two different compartments and operate on two time scales. On the slow time scale, associations are manifested in a high gain and variability of the interspike intervals. On the fast time scale, they are manifested in the timing of the calcium spike-mediated bursts in relation to the times of somatic APs (Larkum et al., 1999
). These two time scales for vertical associations operate simultaneously. A cell can signal top-down input through a high gain, while at the same time coding specific events through the timing of the bursts. Both time scales are dependent on the association of distal and proximal inputs mediated by the back-propagated AP. Hence, it may be more sensible to view layer 5 pyramidal cells as vertical associators rather than coincidence detectors.
Towards a Canonical Layer 5 Pyramidal Cell
From the results shown in this paper a new picture emerges of how the layer 5 pyramidal cell with its distinct morphological features might operate in an in vivo situation (Fig. 8). The back-propagating AP plays a pivotal role in coupling the two-spike initiation zones such that synaptic integration is distributed in time and space. The conspicuously long apical dendrite of the pyramidal neuron and the existence of functionally important inputs at electronically isolated regions has been considered a long-standing enigma (Cauller and Connors, 1994). Indeed, more recently, it has been shown that the existence of Ih in the distal tuft region accentuates the isolation of these inputs (Berger et al., 2001
; Williams and Stuart, 2002
). However, one advantage of this compartmentalization is that integration can occur simultaneously in two separated regions so that subthreshold inputs to the soma and the tuft essentially do not interact. Once APs are elicited in the initial segment (Fig. 8A), the positive feedback mediated by the interaction of these APs with dendritic calcium currents (Fig. 8B) completely changes the relative importance of inputs to the cell. Above the association threshold, the frequency and timing of the neuronal output is dominated by distal inputs. A simple integrate-and-fire model cannot account for these cellular properties. A model with two compartments, each having its own spike initiation mechanism, is necessary and sufficient to capture this complex phenomenology.
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Appendix |
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The simulation results shown in Figure 7 of the main text were obtained by a two-compartment integrate-and-fire model consisting of a somatic compartment with a transient potassium current and a dendritic compartment with a voltage-dependent calcium current. The two compartments are electrically coupled with a transfer resistance of RT = 65 M. The compartments have a total membrane resistance of RS = 50 M
and RD = 43 M
, and a total capacitance of CS = 0.26 nF and CD = 0.12 nF, respectively. The compartments also have different resting membrane potentials, Vrest,S = 70 mV and Vrest,D = 60mV, due to action of the hyperpolarization activated unspecific cation current, Ih, located in the dendrite (Berger et al., 2001
). The subthreshold dynamics of somatic membrane potential VS is given by
and the dynamics of the dendritic membrane potential VD is given by
Here, Iinject,S/D represents the current injected into the somatic and distal dendritic compartment, respectively.
The potassium current has the form IAHP(t) = gAHP (EK VS)exp(t/
K), with a maximal conductance of gAHP = 4 nS, a reversal potential of EK=90 mV, and a decay time constant of
K = 80 ms (cf. blue lines in the lowest traces in Fig. 7C). The dendritic calcium current has the form ICa = gCamh(ECa VD), with a maximal conductance gCa = 70 nS. The activation and inactivation variables, m and h, are characterized by first-order kinetics with time constants
m = 15 ms and
h = 80 ms, half activations m1/2 = 9 mV and h1/2 = 21 mV, and slopes sm = 1/2 mV1 and sh = 1/2 mV1 of their steady-state functions m
and h
, respectively.
Whenever the somatic membrane potential (VS) exceeds a threshold ( = 47 mV) an AP is emitted which in turn activates IAHP. The different AP-activated AHP currents are added linearly, as would be expected from a calcium-activated potassium current. The AP is modelled by clamping VS for 1 ms to 10 mV and resetting it to 52 mV. To mimic the back-propagated AP, the dendritic membrane potential (VD) is artificially elevated by 10 mV, 3 ms after the crossing somatic threshold. To reproduce the saturation of the f/I curves with strong input currents, an additional AP-triggered rectification would be required.
Current Clamp versus Dynamic Clamp
To check whether the dendritic gain modulation is dependent on the use of normal or dynamic current clamp, we repeated the experiments in the two-compartment model using conductances imitating excitatory and inhibitory synaptic inputs. Somatic and dendritic AMPA and GABAA conductances were mimicked by rectified OrnsteinUhlenbeck processes with a correlation length of 3 ms. The reversal potentials of the AMPA and GABA receptors were set to 0 and 65 mV, respectively. The mean and variance of the inhibitory somatic and dendritic conductances were fixed to half the mean and variance of the corresponding excitatory conductances. We then increased the mean somatic conductances according to a step protocol with step durations of 2 s and step sizes adjusted to cover the range of mean currents used in the experiment. The variance of the conductances was set such that the variance of the total synaptic currents matched the variance of the injected currents in the original model. We plotted the firing rates against the mean total somatic current generated by the excitatory and inhibitory conductance fluctuations, both with and without dendritic conductance modulation (Fig. A1, dashed lines). These two curves are well approximating the two original f/I curves shown in Figure 7B left, obtained by simulating direct current injection (with dendritic mean current of 0 and 750 pA, respectively). The relative gain increase due to the additional dendritic drive is similar for normal and dynamic current clamp: with normal current clamp the gain increases by a factor of 1.5 (from 4.5 Hz/100pA to 6.8 Hz/100 pA), and with dynamic clamp it increases by a factor of 1.48 (from 4.8 Hz/100pA to 7.3 Hz/100 pA). We conclude that the dendritic gain modulation is independent of whether the current is directly injected or if a conductance change is simulated with dynamic current clamp.
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Because balanced noisy input to the soma lowers the gain of the f/I curve (Chance et al., 2002), one may wonder how the additional dendritic noise affects the gain. In fact, the dendritic noise propagates to the soma (with some attenuation factor of roughly 0.4 as shown by Berger et al., 2001
) where it decreases the gain of the f/I curve. Since in the experiment we not only increased the mean of the dendritic input (from 0 to 750 pA) but also the amplitude of the noise (from 0 to 300 pA, see Fig. 5), the increased noise is effectively counteracting the gain increase produced by the dendritic calcium spikes. If we had only increased the mean of the dendritic input, while leaving the amplitude of the dendritic noise constant (both at 300 pA), the gain of the f/I curve would have increased even more. Again, this effect is independent of whether the somatic current was generated by current or dynamic clamp.
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The authors declare that they have no competing financial interests.
Address correspondence to Dr Matthew Larkum, Institute of Physiology, University of Bern, Bühlplatz 5, CH-3012 Bern, Switzerland. Email: larkum{at}pyl.unibe.ch.
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References |
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