The shape of the dendritic AP provides a rough estimate of dendritic electrical properties
It has become possible (at least in theory) for every scientist to begin an experimental project with a simulation of the experiment (Wilson, 2000). Here, a multi-compartmental model (Fig. 1A) was used to test whether the peak latency and the time course of the backpropagating AP in basal dendrites may contain important biophysical clues about the regional electrical properties of these dendrites. Somatic APs were evoked by direct current injections (Fig. 1B-D), and membrane potential waveforms were analysed at two sites: the soma (black trace), and the distal region of a basal dendrite 150 μm from the soma (red trace). Under standard conditions (Ri= 70 Ω cm; Stuart & Spruston, 1998), the AP backpropagates from the soma to a distal segment of the basal dendrite with a peak latency of 0.95 ms (Fig. 1B). A 3-fold increase in Ri (from 70 to 210 Ω cm) caused a dramatic increase in the AP peak latency (Fig. 1C), which could not be totally counterbalanced by a uniform 6-fold increase (from 35 to 210 pS μm−2) in the dendritic Hodgkin-Huxley sodium conductance gNa (Fig. 1D). It can be inferred from computer simulations that the peak latency of a backpropagating AP in basal dendrites is much more sensitive to the specific intracellular resistance than to the density of voltage-gated sodium channels (Fig. 1E), and that a significant increase in the half-width of the backpropagating AP (Fig. 1C) in relatively short basal dendrites is an indication of weak electrical coupling (high specific axial resistance). This modelling study, together with classic work (Goldstein & Rall, 1974), suggests that the AP could be used as an exploration probe. For example, by sending an AP along the basal dendrite and measuring its peak latency and time course en route to and at the distal dendritic segment, we may be able to produce a rough estimate of the dendritic electrical properties.
Voltage imaging of AP backpropagation in apical dendrites
The recently developed voltage-sensitive dye technique was used to monitor the dendritic membrane potential in real cells. Simultaneous optical and electrical measurements were performed on individual neurons in acute brain slices cut from the rat somatosensory area. In our initial effort (Antic et al. 1999), we provided the basic methodology for intracellular dye application and optical recordings from dendrites of individual neurons in brain slices. In the present study, a newly developed fast CCD camera (80 pixels × 80 pixels) replaced the silicon diode array (24 pixels × 24 pixels), which brought substantial improvements in the spatial and temporal resolution (from 600 to 370 μs per whole frame) and, equally importantly, in the sensitivity of the measurements (signal-to-noise ratio). With better signals, experiments were designed to provide a detailed description of AP half-widths and peak latencies along individual dendrites. In a typical experiment, the pyramidal neurons (n= 17) were loaded with the voltage-sensitive dye JPW3028 (Fig. 2A), depolarized to generate a somatic AP, and fluorescent light was measured along the apical dendrite. The optical signal from the soma (Fig. 2B, trace 1) was in good agreement with the whole-cell recording (trace 0), but not with the optical signal from the apical dendrite (trace 2). At a distance of 240 μm from the soma (trace 2), the AP peak latency was 0.56 ms, and the half-width of the backpropagating AP was 135 % of its somatic value (Fig. 1C). These experiments demonstrate that fast voltage-sensitive dye imaging can detect both the peak latency and the broadening of the backpropagating AP in apical dendrites, as previously described (Stuart & Sakmann, 1994).
APs in basal and oblique dendrites
The next set of experiments was carried out with the objective to record membrane potential transients from oblique and basal dendrites of layer V pyramidal cells. The neuron displayed in Fig. 3D was loaded with voltage-sensitive dye and stimulated by somatic current injection to produce a burst of two APs. The optical signal from the somatic region (Fig. 3A, trace 1) captured not only the exact time course of the two APs but also their relative amplitudes. Panels B, C, E and F each consist of the somatic optical signal (trace 1) and four dendritic recordings aligned on a faster time scale. In all neurons examined (n= 25) there was an increase in the peak latency along each dendrite, indicating the direction of propagation from the soma to the periphery. The mean propagation velocity was 0.335, 0.300 and 0.215 m s−1 in apical, oblique and basal dendrites, respectively. Under the present experimental conditions (somatic current injection, in vitro, at room temperature), a failure of the AP to invade a set of dendrites or a particular dendritic region was never observed. In all cases the somatically induced AP invaded every basal and oblique dendrite including second-order branches (general backpropagation). The shapes of the dendritic signals did not show the signs of passive filtering that would have been expected if basal and oblique dendrites were passive and electrotonically distant from the soma (Rall, 1959). In order to improve the accuracy of the measurements, optical signals (Fig. 3G, upper) were subjected to a ‘discrete-to-continuous conversion’ (McClellan et al. 1998), i.e. a smooth continuous-time function was interpolated throughout the sampled points (Fig. 3G, lower).
Using the interpolated data, the peak latencies were measured along dendritic branches of 25 neurons (apical N= 17, oblique N= 12 and basal dendrites N= 31; N= number of dendrites) and plotted versus distance from the soma (Fig. 4). In apical dendrites (Fig. 4A) the backpropagation velocity was larger than that measured with dual patch-electrode recordings (Stuart & Sakmann, 1994). The animals used in the present study (3–5 weeks old) were older than those used by Stuart & Sakmann (1994), and this could explain the observed difference on account of the morphological and physiological maturation of pyramidal neurons (Zhu, 2000). Experimental measurements of AP peak latencies in apical (Fig. 4A), oblique (Fig. 4C) and basal (Fig. 4E) dendrites were compared with results from the computer simulation in Fig. 4B, D and F. The model was the same as that used in Fig. 1A. The simulations were carried out using three characteristic values for Ri (70, 150 and 210 Ω cm), while keeping all other parameters fixed. The peak latencies obtained in the model where global Ri was set to 70 Ω cm were closest to the values obtained in the experimental measurements (red lines, Fig. 4B, D and F).
At this point it is necessary to reflect on two problems that could compromise the conclusions of the modelling study. First, the morphology of the model neuron used in Fig. 4B, D and F was borrowed from a 3-week-old Wistar rat (Stuart & Spruston, 1998), while the experimental data shown in Fig. 4A, C and E were collected from 3- to 5-week-old Sprague-Dawley rats. Second, the density of the dendritic sodium conductance (35 pS μm−2) used in the model neuron (Fig. 4) was based on patch electrode measurements along the apical trunk by Stuart & Sakmann (1994). What if the density of voltage-gated sodium channels in basal dendrites was actually higher than that found in the apical trunk? Or, what if the previously reported value was an underestimate of dendritic gNa (for discussion see Rhodes & Llinas, 2001). Both questions were addressed in the new model depicted in Fig. 5.
To eliminate the discrepancy in animal strain and animal age, a layer V pyramidal cell from one of the animals used in our laboratory (Sprague-Dawley, P27) was reconstructed (Fig. 5A and B). The old model (Fig. 4) was then inserted into a new morphology. With identical channel types and densities, the new morphology produced a nearly identical pattern of backpropagation. As previously described, when Ri was set to 70 Ω cm, the AP peak latencies along basal dendrites were closest to experimentally obtained values (not shown).
Next, while preserving the ratio gNa/gK (35/30), higher and higher densities of Hodgkin-Huxley conductances were inserted in the entire dendritic arbor uniformly, and the peak latency was analysed in 13 basal dendrites, 150 μm from the soma (red circles, Fig. 5B). The experimentally measured mean peak latency in basal dendrites at 150 μm from the soma (0.68 ± 0.16 ms; Fig. 5D, horizontal red line) could not have been achieved in neuron models with Ri= 100 Ω cm, even if gNa was set to 350 pS μm−2 (Fig. 5D). This sodium channel density is 10 times higher than that used in recent studies (Mainen & Sejnowski, 1996; Vetter et al. 2001), and it is unlikely that basal dendrites of pyramidal neocortical neurons possess such a large number of sodium channels (Rhodes & Llinas, 2001). Within the plausible range for dendritic gNa (Fig. 5D, turquoise area, 35–120 pS μm−2; Mainen & Sejnowski, 1996; Rhodes & Llinas, 2001), the Ri values that fit experimental measurements of AP peak latency in basal dendrite ‘13’ range between 43 and 60 Ω cm. Basal dendrite ‘13’ has the most favourable geometry (larger diameter and fewer branch points than other basal dendrites) for fast AP propagation, and hence would require the largest Ri to match experimental AP peak latency. All other basal branches (‘1–12’; Fig. 5B) have slower conduction velocities, and require Ri lower than 60 Ω cm to match experimental results within the plausible range for the dendritic gNa (turquoise area).
The result shown in Fig. 5D is based on two assumptions: (1) the specific membrane capacitance (Cm) in neocortical pyramidal neurons is 1 μF cm−2; (2) the density of spines, the membrane potential in spine heads and the spine stem currents are distributed variables with continuous rather than discrete spatial arguments (Baer & Rinzel, 1991), and the effect of dendritic spines on membrane area can be simulated by decreasing Rm and increasing Cm by a factor of 2 (Stuart & Spruston, 1998). What if the ‘spine factor’ of 2 is an overestimate of the effective contribution of spine heads to the dendritic capacitance? That is, high-resistance spine necks may prevent the full charging of spine heads during fast membrane potential transients. In order to address this possibility, the spine factor was varied between 1.5, 1.75 and 2. Each spine factor was explored within the plausible range for the dendritic gNa (35–120 pS μm−2). The analysis was done for the fastest (‘13’) and slowest dendrite (‘10’, Fig. 5B). The results in Fig. 6A show that under any possible combination of three parameters (dendritic geometry, dendritic gNa and spine factor) the experimental data could not be matched in the model with Ri values above 87 Ω cm (yellow circle, Fig. 6A).
In the above modelling, the increase in the dendritic gNa was accompanied by a proportional increase in dendritic gK; i.e. the gK/gNa ratio of 30/35, established originally by Mainen & Sejnowski (1996), was preserved in every simulation. In the next set of simulations different gK/gNa ratios were tested. The spine factor was set to 1.5 to allow for higher Ri estimates, and the gK/gNa ratio was varied between 0.2, 1.0 and 2.0 (Fig. 6B). The results show that under any possible combination of three parameters (dendritic geometry, dendritic gNa and gK/gNa ratio) the experimental data could not be matched in the model with Ri values above 95 Ω cm (orange circle, Fig. 6B). Thus even after a radical cut in dendritic membrane capacitance from 2 to 1.5 μF cm−2, combined with an increase in the dendritic Rm from 12 500 to 16 666 Ω cm2, and a radical increase in gK/gNa ratio up to 2.0 (Fig. 6B), Ri values required to match the experimental data were lower than the popular neurocomputational range of 150–250 Ω cm (Anderson et al. 1999; Destexhe & Pare, 1999; Archie & Mel, 2000; Durstewitz et al. 2000; Rhodes & Llinas, 2001; Vetter et al. 2001).
Calcium electrogenesis in basal dendrites
The experimental measurements of the AP peak latency and half-width, together with the computer simulation, suggest that distal basal segments experience a substantial depolarization during the somatic spike (Fig. 5C). Is this depolarization large enough to open high voltage-activated calcium channels? Using intracellularly applied calcium-sensitive dye fura-2, Schiller et al. (1995) addressed this question in the most proximal parts of the basal dendrites, less than 80 μm from the cell body. Basal dendrites, however, typically extend up to 250 μm in pyramidal layer V neurons (see Fig. 5). In addition, it is still unknown whether a single AP reliably invades the entire basal bush or fails at particular branch points, so that some distal dendritic segments experience less depolarization than others, and hence less (or zero) calcium influx. The next set of experiments was designed to determine whether a single AP could trigger calcium influx at distal dendritic regions, at distances larger than 150 μm from the soma. In single sweeps calcium signals were sampled simultaneously from all basal dendrites in the visual field; typically three to four basal branches. Particular attention was paid to dendritic segments beyond the branch point (see also ‘Supplementary material’). In the representative example shown in Fig. 7, the pyramidal cell was loaded with the calcium-sensitive dye Calcium Green-1 and a single AP (Fig. 7C, trace 0) was evoked by brief somatic current injection. Optical recordings of intracellular free calcium concentration were performed simultaneously along four basal branches. Four ROI were selected from two basal dendrites for display (traces 1–4). In repeated trials, single APs regularly evoked calcium transients in every basal branch examined. The same result was obtained from 20 basal dendrites in eight neurons (5 neurons at 23 °C, 3 neurons at 32–34 °C). These data indicate that backpropagating APs depolarize the distal tips of basal dendrites (up to 200 μm from the centre of the soma) sufficiently to open voltage-gated calcium channels and trigger the surge of calcium ions into the dendritic cytosol. AP propagation failures were never observed in these experiments. On the contrary, the amplitudes of calcium signals were very similar between different basal dendrites in the visual field (Fig. 7C), thus rejecting the hypothesis that some dendritic segments experience significantly larger voltage transients than others. Moreover, each somatic AP in a 20 Hz train (n= 3) was associated with a distinguishable calcium transient in distal dendrites (Fig. 7D), further supporting the hypothesis that the dendritic membrane potential swing, caused by the backpropagating spike, is both strong and swift.
Recently, patch electrode measurements from apical dendrites have shown that the activation of the voltage-gated calcium channels by backpropagating APs causes a substantial broadening of the dendritic spike, sometimes manifested with a characteristic calcium shoulder on the falling phase of the electrical signal (Stuart et al. 1997; Larkum et al. 2001). Thus one might expect a calcium-dependent plateau in the distal tips of basal dendrites, because these branches experience a 6-fold higher calcium transient than the distal regions of the apical trunk or soma during an AP (Schiller et al. 1995). However, AP-associated voltage-sensitive dye signals from basal dendrites were very similar in shape to somatic optical signals. In the present study, the great majority of optical measurements were performed at distances less than 180 μm from the cell body (79 basal dendrites in 24 pyramidal neurons). In this group of experiments (Fig. 8A) AP half-width in the dendritic segment never exceeded 125 % of the somatic half-width. A considerably smaller number of recordings (7 dendrites in 5 neurons) were done at distances larger than 180 μm. Among these, two different dendritic responses were observed. In the first group (5 dendrites in 3 neurons) there was no significant change in the shape of the AP (Fig. 8B). In the second group (2 dendrites in 2 neurons) an obvious broadening of the AP (half-width increase larger than 25 %) was detected ∼200 μm from the soma (Fig. 8C). However, none of the AP-associated dendritic signals in the present study, regardless of the distance from the cell body, showed any signs of a calcium shoulder.
In order to investigate whether basal and oblique dendrites exhibit activity-dependent backpropagation as observed in the apical trunks of hippocampal (Spruston et al. 1995) and neocortical pyramidal neurons (Stuart et al. 1997), glutamate iontophoresis was used to evoke somatic bursts of APs. The results from two representative cells are displayed in Fig. 9A and B. As part of a standard experimental routine, and for the purpose of electrophysiological identification, a burst of APs was evoked by direct current injection during the dye-loading protocol (Fig. 9A1 bottom, trace 0). The patch electrode was then carefully pulled out and the neuron was left at room temperature for 3 h. Following the incubation period the bath temperature was increased to 29 °C and a glutamate-filled sharp glass electrode was advanced into the brain slice and positioned in the vicinity of the oblique dendrite as indicated by the schematic drawing. A brief glutamate pulse (20 ms) produced a burst, which lasted 480 ms and consisted of 11 APs (Fig. 9A3). Optical signals (traces 1–5) obtained from three different basal branches (as indicated in Fig. 9A2) appeared to have constant amplitudes throughout the bursting episode. In the second example (Fig. 9B1), the basal dendrite of interest was positioned near the centre of the recorded area. Following a 2 h incubation period the bath temperature was increased to 33 °C. The first glutamate pulse delivered in the basal area triggered a 200 ms long burst of APs (Fig. 9B2). A stronger iontophoretic pulse (Fig. 9B3) evoked a long-lasting burst, which consisted of more than 20 APs firing at approximately 40 Hz. Voltage imaging failed to detect frequency-dependent amplitude modulation in basal dendrites (up to 180 μm, n= 7 neurons, 18 basal dendrites) and oblique dendritic regions (up to 220 μm from the soma, n= 2 neurons, 3 oblique dendrites). In basal dendritic segments 150 μm from the cell body, the mean and standard deviation of the ratio of the amplitude of the fifth spike to the first spike in a train (30–40 Hz) was 92.5 ± 11.3 %. The experimental data suggest that the backpropagation of APs in basal and proximal-oblique dendrites of pyramidal layer V neurons is not dynamically regulated at firing rates of up to 40 Hz.