Cellular Neuroscience

In the barrel cortex of rodents the fi ring of neocortical neurons is sparse with low L5A pyramidal neurons, for instance, respond to whisker stimulation with on average <1AP per stimulus in anesthetized animals, and increase their fi ring rate to ∼5 Hz during whisking episodes (de Kock and Sakmann, 2009); nevertheless, their fi ring patterns are highly irregular and consist of a wide distribution of inter-spike frequencies (<1 to >200 Hz) (Manns et al., 2004; de Kock et al., 2007). The timing, frequency and amplitude of bAPs have strong implications for synaptic and intrinsic plasticity, dendritic electrogenesis, and neuronal output This causal relationship between bAPs and information processing/storage led us to explore: (i) the role of AP timing during physiological activity patterns in dendritic signaling; (ii) the reliance of back-propagation effi cacy on dendrite type and location; (iii) the postnatal development of this form of dendritic signaling; (iv) the regulation of AP back-propagation by active conductances. To address these questions, we used physiological AP patterns previously recorded in L5A pyramidal neurons in the barrel cortex of anesthetized rats (courtesy of de Kock; de Kock et al., 2007); these fi ring patterns were replayed in vitro in the same neuron type and brain area, while measuring Ca 2+ signals along the main apical, apical tuft, and basal dendrites.


INTRODUCTION
In cortical pyramidal neurons, action potentials (APs) are initiated in the axon and back-propagate into their dendritic arbors both in vitro and in vivo (Stuart and Sakmann, 1994;Larkum and Zhu, 2002;Waters et al., 2003;Bereshpolova et al., 2007); APs backpropagate into the basal (Antic, 2003;Kampa and Stuart, 2006;Nevian et al., 2007), oblique (Antic, 2003;Frick et al., 2003), and apical main and tuft dendrites Williams and Stuart, 2000;Larkum and Zhu, 2002). Some of the suggested functional roles of these back-propagating APs (bAPs) are to serve as a feedback signal to the dendrites and to interact with synaptic signals to regulate dendritic plasticity and neuronal AP output (Frick and Johnston, 2005;Waters et al., 2005;Sjöström et al., 2008). Back-propagation is active in cortical pyramidal neurons, but the amplitude of the bAPs gradually decreases with distance from soma. This decline depends on numerous factors such as coincidence with incoming synaptic input Stuart and Hausser, 2001), intrinsic excitability (Bernard and Johnston, 2003;Frick et al., 2004), inhibition (Larkum, 1999), and morphology (Schaefer et al., 2003). Another important factor determining the reliability of back-propagation is the frequency of the AP output (Spruston et al., 1995;Stuart et al., 1997;Larkum, 1999;Williams and Stuart, 2000).
Layer 5A (L5A) pyramidal neurons are a major type of output neurons in neocortical circuits. These neurons differ from L5B pyramidal neurons in many ways, including the morphology of their dendritic arbors, their intra-and sub-cortical connectivity, This work extends previous studies on the frequency dependence of back-propagation in cortical neurons and is, to our knowledge, the fi rst study specifi cally exploring signal propagation in dendrites of L5A pyramidal neurons. Our data indicate that the changes in instantaneous fi ring frequency during physiological AP trains have a crucial role for dendritic voltage and biochemical signaling. These fi ndings may have important implications for the induction of dendritic electrogenesis and plasticity.

CELL IDENTIFICATION AND ELECTROPHYSIOLOGY
The cell layer 5A at the border of whisker-related barrel fi eld of the somatosensory cortex was visualized at low magnifi cation (5×) under bright-fi eld illumination, and layer 5A pyramidal neurons were visualized with infrared gradient contrast microscopy using a Leica upright microscope, fi tted with a 40×/0.8 numerical aperture water-immersion objective. Recording pipettes (4-6 MΩ) were pulled from borosilicate glass and fi lled with (in mM): 135 K-gluconate, 10 HEPES, 10 Phosphocreatine-Na, 4 KCl, 4 ATP-Mg, 0.3 Na-GTP, pH 7.2 (adjusted with KOH). Biocytin (1.5-2.5 mg/ml, Sigma, Munich, Germany) was added to the recording solution for later identifi cation and morphological reconstruction of the neurons. Signals were recorded using an Axon Instrument amplifi er (Axoclamp-2B), low-pass fi ltered at 3 kHz and sampled at 10-50 kHz.

STIMULATION PROTOCOLS
Stimulation protocols were designed following previous experiments in which trains of action potentials were recorded juxtasomally from L5A pyramidal neurons in the barrel cortex of anesthetized rats (P25-30) in response to primary whisker stimulation. These data were kindly provided by Dr. C. de Kock (Free University of Amsterdam de Kock et al., 2007). These 500 ms-long traces are comprised of spontaneous action potential output and evoked fi ring (200-ms long whisker stimulation between 145 and 345 ms (for details see de Kock et al., 2007). We tested 10 whisker stimulation episodes from a representative experiment (de Kock, personal communication) containing two to fi ve APs with various ISIs. The absolute time of each action potential during these 500-ms sequences was taken and a replica trace consisting of 3 ms-long current pulses at the respective time points produced (natural fi ring pattern). For illustration purposes and to avoid unnecessary duplication, only sequences that substantially differ from each other are shown in the fi gures. In addition, sequences are arranged in an ascending order of complexity. These natural fi ring patterns were compared to those evoked by the same number of action potentials presented at the mean frequency (mean fi ring pattern). Trains of action potentials at these fi xed frequencies were generated in the same manner using 3 ms-long current injections.

CALCIUM IMAGING
The method used for high-resolution, multi-photon imaging of Ca 2+ fl uorescence was as described previously (Koester et al., 1999). Briefl y, we used femtosecond laser pulses at 870-890 nm from a Ti:Sa-Laser (Mira 900F; Coherent, Santa Clara, CA, USA) pumped by a solid-state laser (Verdi 8W; Coherent), coupled to a galvanometer scanning unit (TCSNT; Leica Microsystems, Mannheim, Germany) that was mounted on an upright microscope (Leica DMLF) equipped with a 40× objective (HCX APO W40x/0.8 NA). Fluorescence was acquired using external non-descanned detectors (photomultiplier tubes, R6357, Hamamatsu Photonics, Herrsching, Germany) behind the objective and the condenser, yielding a high signal collection effi cacy. The Ca 2+ signals were recorded in linescan mode with a temporal resolution of 2.2 ms/line. Recordings of membrane voltage and fl uorescence were analyzed offl ine using commercial software with custom-written algorithms (Igor Pro; WaveMetrics, Lake Oswego, OR, USA). Neurons were fi lled with a combination of the calcium-sensitive dye Oregon Green 488 BAPTA-I (200 µM) or Fluo 5F (200 µM) and the calcium-insensitive dye Alexa 594 (20-50 µM; both dyes from Invitrogen, Carlsbad, CA, USA) added to the intracellular recording solution to visualize the dendritic arbors and measure Ca 2+ signals within. Dyes were allowed to fi ll the neurons for at least 15-20 min before Ca 2+ signals were measured; measurements from the apical tuft region were not taken before at least 45 min after the soma was patched.
Ca 2+ transients are reported as relative changes in OGB-1 fl uorescence and were calculated as ΔF/F (t) = (F(t)−F 0 )/(F 0 −F B ), where F 0 is the baseline fl uorescence, taken within 200 ms before the stimulation and F B is the background fl uorescence, derived from a non-stained background region. Single exponential fi ts to the decay of the fl uorescence transients were made to calculate the peak amplitude, denoted as transient amplitudes. Fluorescence traces are averages of three to fi ve trials and group data are represented as means ± sem. Dendritic length constants L 1/e of calcium profi les were derived by fi tting exponential functions to the profi les, or by taking the value when the profi le had dropped to 1/e. GraphPad software Instat 3 and Prism 4 (GraphPad Software, San Diego, CA, USA) was used for statistical analysis. Statistical signifi cance was calculated using paired t-tests and non-parametric Mann-Whitney U tests.

PHYSIOLOGICAL VERSUS MEAN AP PATTERNS -APICAL DENDRITES
First, we investigated the role of AP timing within fi ring patterns in the back-propagation effi cacy along apical dendrites. To do this we triggered 500 ms-long physiological fi ring patterns (de Kock et al., 2007) in L5A pyramidal neurons at P25 and compared them with the corresponding mean fi ring patterns (same number of APs at mean frequency). While frequencies of the mean fi ring patterns were always <20 Hz, physiological fi ring patterns contained instantaneous frequencies of >200 Hz. bAP-evoked Ca 2+ signals were measured at the soma (apical trunk close to soma), 400-500 µm from soma, and in the initial part of the apical tuft (∼650 µm from soma, primary tuft dendrite). For reference, the main branch point (BP) and the tip of the tuft of the L5A apical dendrite at P25 were on average 636 ± 63 µm and 794 ± 88 µm from soma (pia: 845 ± 89 µm, mean ± SD, n = 10), respectively. The diameters of the dendrites were: 2.7 ± 0.6 µm for apical trunk close to soma, 1.3 ± 0.2 µm for apical dendrite ∼400 µm from soma, 1.2 ± 0.1 µm for apical dendrite just before major branch point, 0.9 ± 0.1 µm for primary tuft dendrite; n = 5).
The results from one representative experiment at P25 are illustrated in Figure 1. Five selected sequences of physiological fi ring patterns (out of 10 tested) and the corresponding mean fi ring patterns are shown in Figure 1B, and the resulting Ca 2+ signals are depicted in Figure 1C. A typical fi nding from our experiments was that at the soma/proximal dendrite both physiological and mean fi ring patterns evoked strong Ca 2+ signals -albeit with very different rise times. In sharp contrast, only three out of ten physiological sequences examined (1, 3, and 4; none of the mean fi ring patterns) evoked Ca 2+ transients in the distal half of the apical dendrite (and to some extent even the tuft region beyond the BP). A common feature of these specifi c sequences (also sequence 6) is the occurrence Five (out of ten tested) different physiological fi ring patterns (black traces) and the corresponding mean fi ring patterns (gray traces) triggered in a L5A pyramidal neuron at P25. Frequencies within the AP trains are given above the traces. (C) Ca 2+ transients were measured at the soma, 450 µm from soma, and 650 µm from soma (tuft region) (schematic). Note that only AP sequence 3 back-propagated into the distal dendrite (arrows). Fluorescence changes are given as relative changes in the fl uorescence of the Ca 2+ -indicator OGB-1 (ΔF/F) and are averages of 3-5 traces. (D) Peak amplitudes of Ca 2+ transients (ΔF/F max, normalized) of physiological and mean fi ring sequences are plotted as function of distance from soma. Data were measured at the soma, at 400-500 µm and 600-700 µm from soma, and are given as mean ± sem (n = 9) normalized to the soma values. Dashed line indicates the strongest Ca 2+ signal in the apical dendritic tuft (sequence 3) to emphasize the difference between the physiological and the mean fi ring pattern. of short bursts of two or three APs with short inter-spike intervals (ISIs < 20 ms, f > 50Hz). The other physiological and all mean fi ring patterns, in contrast, are comprised of AP sequences of low frequencies (ISIs ≥ 70 ms, f < 15 Hz). The results from nine similar experiments are summarized in Figure 1D. Here, and throughout the manuscript, sample size always refers to number of branches, which is equal to the number of cells. The amplitude of the Ca 2+ signals at the soma/proximal dendrite was strongly dependent on both the number, and the ISIs of the AP trains. However, the ISIs became progressively more important for determining Ca 2+ signal amplitude with distance from soma. At a distance of 400-500 µm from soma, only AP trains containing high frequency components were capable of eliciting measurable Ca 2+ signals. In this region, the peak amplitudes of the Ca 2+ signals for sequences containing high-frequency components (sequences 1, 3, 6 and 4 (See Figure 2)) dropped to ∼55% (0.554 ± 0.152 ΔF/F, normalized to soma, n = 9), but were signifi cantly larger than those evoked by mean fi ring patterns (0.024 ± 0.008 ΔF/F; n = 9; p = 0.032). Thus, the length constant (L 1/e ) for these fi ring patterns was signifi cantly larger than for the corresponding mean fi ring patterns (L 1/e physiological 553 µm + 42/−33 µm; L 1/e mean 352 µm + 15/−26 µm). The Ca 2+ transients evoked by sequences 3 and 4 (two APs ≥ 100 Hz) were even able to invade the initial part of the apical tuft region beyond the BP (0.397 ± 0.043 ΔF/F normalized to soma). Within the tuft, however, Ca 2+ signals dropped steeply for all fi ring patterns (see below). Interestingly, sequences 1 and 6 contained high-frequency components but failed to elicit Ca 2+ signals in the apical tuft region, perhaps due to their ISI distribution (see Figure 4D).

PHYSIOLOGICAL VERSUS MEAN AP PATTERNS -BASAL DENDRITES
In L5A pyramidal neurons, basal dendrites comprise approximately 50% of the total dendritic length (Frick et al., 2008). We therefore examined how well physiological AP output back-propagates into the basal dendrites (Figure 2). Figures 2A,B shows the fi ndings from an individual experiment. Ca 2+ transients in response to physiological fi ring patterns (sequences 1, 3, 4, and 6) and the corresponding mean fi ring patterns were recorded at the soma (basal dendrite close to soma, diameter 1.4 ± 0.2 µm, n = 5), at 75 µm from soma, and at a distal location of 135 µm from soma (diameter at ∼120 µm from soma 0.7 ± 0.1 µm, n = 5; mean length for basal dendrites 162 ± 22 µm, mean ± SD, n = 12, P25). Similarly to the apical dendrites, the amplitude of the Ca 2+ signals at the proximal basal dendrite was a function of both bAP number and ISIs. In contrast, the short ISIs of the physiological fi ring patterns did not substantially promote effective back-propagation into the distal half of the dendrite, resulting in comparable L 1/e (L 1/e physiological 96 + 13/−21 µm, L 1/e mean 92 + 14/−11 µm, average of all seven fi ring sequences, average of all sequences containing at least two APs, n = 6). These experiments demonstrate that the properties of the basal dendrites are very different from those of the apical dendrites.

CRITICAL AP FREQUENCY FOR APICAL DENDRITES
In vivo, L5A pyramidal neurons of the barrel cortex rarely fi re more than two or three APs at higher frequencies -either spontaneously or in response to whisker stimulation (Manns et al., 2004;de Kock et al., 2007). To further examine the critical frequency for effi cient back-propagation within this activity range we therefore induced trains of three APs at fi xed frequencies ranging from 20 to 140 Hz (Figure 3). The results from one experiment are illustrated in Figure 3B, upper panel, in which Ca 2+ signals were measured in the apical dendrite ∼530 µm from soma. The amplitude of the Ca 2+ signal was small at a frequency of 20 Hz (0.12 ΔF/F), but strongly increased with higher frequencies, reaching a maximum at 100 Hz (0.85 ΔF/F). Surprisingly, frequencies above this critical frequency (CF) evoked smaller transients (not shown). The results from 6 similar experiments are summarized in Figure 3B, lower panel. The CF varied from cell to cell, and was on average 91 ± 14 Hz (range 75-140 Hz, n = 6). The reliance on frequency was strongest in the dendritic region 300-400 µm from soma, were the Ca 2+ transients increased substantially when frequencies approached the optimal frequency. In this dendritic region, Ca 2+ transients evoked by AP trains at CF were on average ∼7to 8-fold larger than those evoked by single APs (normalized to somatic values, 1.32 ± 0.17 ΔF/F, n = 6, versus 0.18 ± 0.15 ΔF/F, n = 6; p = 0.0041). In summary, higher frequencies (>40 Hz) were necessary to enable effi cient AP backpropagation into the distal half of the apical dendrite.

LACK OF CRITICAL AP FREQUENCY FOR BASAL DENDRITES
The lack of amplifi cation observed in basal dendrites using physiological AP patterns prompted the question of whether these dendrites possess a critical frequency within the physiological activity range of these neurons. Figure 3C, upper panel, shows the Ca 2+ transients elicited in a basal dendrite ∼51 µm from the soma in response to bursts of three bAPs at varying frequencies. In this example (and confi rmed in 6 experiments), the Ca 2+ signals did not increase as a function of frequency (20-140 Hz; Figure 3C, lower panel). In 3 cells, frequences of up to 225 Hz were tested confi rming the lack of amplifi cation. Thus, Ca 2+ transients of both single bAPs and bAP trains decayed with a similar L 1/e of ∼90-100 µm, indicating that there might not be a CF, at least for short bAP trains, in basal dendrites.

COMPARISON OF APICAL AND BASAL DENDRITES
Our analysis suggests that the dendritic properties determining back-propagation are strikingly different for apical and basal dendrites. Since the length of these dendrite types differs by ∼5-fold (apical ∼800 µm versus basal dendrites ∼160 µm), we compared back-propagation properties as a function of fractional length (Figures 3D,E). Figure 3D shows the normalized Ca 2+ amplitudes evoked by single APs and trains of three APs at 100-Hz along the apical and basal dendrites for six L5A pyramidal neurons. Single bAPs evoked Ca 2+ signals that attenuated more strongly along the fi rst 60-70% of the apical dendrite (L 1/e apical 272 + 26/−19 µm, 0.36 fractional length, n = 6) as compared to basal dendrite (L 1/e basal 92 + 30/−15 µm; 0.55 fractional length; n = 6), but failed to produce Ca 2+ signals in the distal 30% of either dendrite type. Ca 2+ signals evoked by AP trains at 100 Hz were signifi cantly increased in the apical dendrites, but not in the basal dendrites (Figures 3D,E; apical dendrite, signal decay to 1/e of somatic values 596 ± 53 µm, ∼0.85 fractional length; basal dendrite, L 1/e 93 + 25/−18 µm, 0.56 fractional length; n = 6). This analysis strengthens the conclusion that the active properties of basal and apical dendrites are very different.

THE APICAL TUFT REGION AS A SEPARATE DENDRITIC ZONE
Our previous results indicate that fi ring patterns containing highfrequency components (e.g. physiological sequences 3 and 4) can reach the apical tuft, but that the Ca 2+ signals drop off steeply within the tuft. We set out to investigate back-propagation into the tuft in more detail (Figure 4). Figure 4A shows the tuft region and measurements of the Ca 2+ signals produced by three bAPs at 100 Hz just before the BP (position 1), and at two dendritic sites within the tuft.  attenuation resulted in a small L 1/e (∼30 µm starting from position 1, Figure 4B, n = 5) that was ∼3-fold and ∼20-fold smaller when compared to the basal dendrite (L 1/e < 100 µm) and the main apical dendrite (L 1/e ∼600 µm), respectively. Next, we addressed the question of whether the Ca 2+ transients in the tuft depend on the number of bAPs or the AP timing within the bursts. Figure 4C demonstrates that increasing the number of APs within the highfrequency train enhanced the Ca 2+ infl ux within the apical tuft. To probe the reliance of the Ca 2+ signals on the AP timing, a regular 3 AP-sequence at 100 Hz was compared with those, were the 2nd AP was shifted ±5 ms ( Figure 4D). Sequences containing equal ISIs or a shorter ISI (5 ms) followed by the longer one (15 ms) resulted in a comparable Ca 2+ infl ux, whereas the reverse order produced a reduced Ca 2+ signal. These data suggest that both the number of APs and the distribution of ISIs within a fi ring pattern are important factors for the regulation of back-propagation effi cacy.

MATURATION OF BACK-PROPAGATION DURING POSTNATAL DEVELOPMENT
Does the back-propagation effi cacy in L5A dendrites change during the postnatal period between P14 and P25? To address this question, physiological and mean fi ring patterns were triggered in L5A pyramidal neurons at P14 and the evoked Ca 2+ transients were measured along the apical and basal dendrites (Figures 5, 6 and 7C). Similar to P25 dendrites, fi ring patterns containing highfrequency components substantially improved back-propagation effi cacy into the distal half of apical dendrites (Figures 5 and 6), but not basal dendrites (Figure 6). Figure 7 compares several aspects of back-propagation along the apical dendrite for the two age groups P14 and P25. The CF of AP bursts to induce signifi cant amplifi cation of the Ca 2+ signals increased signifi cantly from 55 ± 9 Hz (CF P14 , range 40-75 Hz, n = 6, P14) to 91 ± 13 Hz (CF P25 , range 75-140 Hz, n = 6; p = 0.036, P25) ( Figure 7A). We also compared the Ca 2+ profi le for single APs, short AP trains, and for physiological AP patterns along the apical dendrite (Figures 7B,C). Single APs back-propagated more effi ciently at P14 compared to P25, whereas the profi le for trains of three APs at the respective CFs (CF P25 and CF P14 ) was more complex. For these AP trains, back-propagation was more effi cient along the fi rst half of the dendrite at P25 than at P14, while the reverse was true for the distal half of the dendrite ( Figure 7B). Physiological fi ring patterns containing two APs at ∼CF P25 backpropagated more effi ciently at P25 (Figure 7C). The Ca 2+ profi le for the physiological fi ring sequence 1 (three APs at high frequencies)

FIGURE 5 | Backpropagation of physiological fi ring patterns into the apical dendrites at P14. (A)
Five (out of ten tested) different natural fi ring patterns (black traces) and the corresponding mean fi ring patterns (gray traces) were evoked by somatic current injection in a layer 5A pyramidal neuron at P14. Frequencies within the AP trains are given above and the sequence numbers below the traces. (B) Ca 2+ transients elicited by these AP sequences were measured at the soma, 450 µm from soma, and 650 µm from soma (tuft region) across the apical dendritic arbor (see schematic). Note that only AP sequences containing high-frequency components (arrows) back-propagate into the distal half of the apical dendritic arbor. Fluorescence changes are given as relative changes in the fl uorescence of the Ca 2+ -indicator OGB-1 (ΔF/F) and are averages of 3-5 traces. (C) Peak amplitudes of Ca 2+ transients (ΔF/F Max , normalized) of natural and mean fi ring sequences are plotted as function of distance from soma. Data were measured at the soma, at a region 400 to 500 µm from soma, and at a region 600 to 700 µm from soma, and are given as mean ± sem (n = 9) normalized to the soma values. Dashed line indicates the strongest Ca 2+ signal that could be evoked in the apical dendritic tuft (sequence 1) to emphasize the difference between the natural and the mean fi ring pattern. matched the profi le for trains of three APs at high frequencies, i.e. the Ca 2+ signals produced in the distal dendrite were larger for P14 than P25.
Single bAPs and low-frequency (20 Hz) bursts of three bAPs produced little or no Ca 2+ signal 300-400 µm from soma, preventing us from examining Ca 2+ channel contribution. Thus, only the effects of blockers on BK Ca channels and A-type K + channels were quantifi ed.

FIGURE 6 | Comparison between apical and basal dendrites at P14. (A)
Reconstruction of a L5A pyramidal neuron at P14. Trains of three APs were evoked by current injections into the soma and calcium measurements were taken at the soma and at three different distances along either the apical dendrite or the basal dendrite (indicated by the symbols and ranges). (B) Apical dendrites, upper panel. Ca 2+ transients (ΔF/F) evoked by trains of three APs at different fi xed frequencies measured at the main apical dendrite close to the major branch point (548 µm from soma, see arrow) in a P14 L5A pyramidal neuron. Frequencies ranged from 20 Hz to 100 Hz. Note that the maximal response was evoked at 50 Hz. Lower panel. Peak amplitudes of Ca 2+ transients (n = 6) evoked by trains of three APs at different frequencies are normalized to the somatic values and plotted as function of distance from soma. For comparison, Ca 2+ transients evoked by single APs (dashed line) are also shown. Average values are mean ± sem. Note that the frequency is becoming increasingly important at distances from soma more distal than 300 µm, and that signals drop off steeply beyond the major branch point within the apical tuft. (C) Basal dendrites, upper panel. Ca 2+ transients (ΔF/F) evoked by trains of three APs at different fi xed frequencies measured at the basal dendrite ∼50 µm from soma in a P14 L5A pyramidal neuron. Frequencies ranged from 20 to 100 Hz. Lower panel. Peak ΔF/ F Ca 2+ signals evoked by single APs and short trains of three APs at different fi xed frequencies ranging from 20 to 140 Hz are normalized and plotted against distance from soma along the basal dendrites (n = 6). Note that there is no signifi cant difference in the effi cacy of back-propagation within this frequency range. (D,E) Comparison of apical versus basal dendrites. (D) Peak Ca 2+ signals elicited by single APs and trains of three APs at 50 Hz were normalized and plotted as function of distance from soma. Distances along the basal and apical dendrites were normalized with respect to the total length of the dendrites to enable comparison of back-propagation effi cacy across different dendrite compartments. Note the signifi cant differences in back-propagation for apical and basal dendrites. (E) Differences in frequency-dependence are compared for a normalized distance of ∼70% along the basal (80-100 µm) and apical (400-500 µm) dendrites. Ca 2+ signals evoked by trains of three APs at different frequencies were normalized to the 20-Hz train. Note the steep amplifi cation in Ca 2+ infl ux at the apical dendrite with increasing frequency. Dashed lines indicate the CF-ranges from 40-75 Hz at P14 and 75-125 Hz at P25 (corresponding to 1/6 and 5/6 of cumulative probability).
(B) Normalized (to soma) peak ΔF/F Ca 2+ signals evoked by single APs and bursts of three APs at the respective CF at P14 (60-75 Hz) and P25 (100-125 Hz) as function of normalized distance from soma (mean ± sem, n = 6 for each age group). (C) Normalized peak ΔF/F Ca 2+ signals of physiological fi ring patterns (sequences 1, 3, 4, and 6) as function of distance from soma for P14 and P25 L5A pyramidal neurons (mean ± sem, n = 9 for each age group).

DISCUSSION
Our major conclusion is that the temporal composition of physiological fi ring patterns consisting of variable instantaneous frequencies determines back-propagation effi cacy of the apical dendritic arbor. Specifi cally, we found that even two APs at CF signifi cantly increase the amplitude of Ca 2+ infl ux into the distal half (excluding the tuft region) of L5A apical dendrites. This CF shifted during early postnatal maturation from ∼55 Hz at P15 to ∼90 Hz at P25. In contrast, mean fi ring patterns with frequencies of <20 Hz back-propagated inefficiently into the distal apical dendrites. Furthermore, we show that the rules governing back-propagation are dendrite type-specifi c, in that there was no comparable amplifi cation in back-propagation observed for the basal dendrites or the tuft region of the apical arbor. We also examined the role of various voltage-gated ion channels in regulating back-propagation during these different activity regimes. To our knowledge, this is the fi rst study investigating the active properties of L5A pyramidal neuron dendrites, and our data further underline the importance of studying neuronal properties in a manner that refl ects the activity of the specifi c cell type under investigation.

VALIDITY OF STUDYING BACK-PROPAGATION IN VITRO
Neocortical brain slices exhibit a lower synaptic background activity than that occurring in vivo. In spite of this, several studies demonstrate that the amplitude of bAPs in L2/3 and L5B pyramidal neurons is similar in vivo and in vitro (Helmchen et al., 1999;Larkum and Zhu, 2002;Waters et al., 2003;Bereshpolova et al., 2007;Bar-Yehuda and Korngreen, 2008). Together, this work supports the idea that bAPs are a robust and reliable property of pyramidal neurons during different states of network activity.

EFFECTIVE BACK-PROPAGATION INTO THE APICAL DENDRITES DURING PHYSIOLOGICAL AP PATTERNS
We show that, in L5A pyramidal neurons, low-frequency (≤20 Hz) AP fi ring fails to effi ciently invade the distal half of the apical dendritic arbor. In contrast, effi cient back-propagation is evoked by physiological or regular AP patterns containing higher frequencies, particularly at the CF (Figures 1, 3 and 5-7). Since bAPs are important in a variety of neuronal processes (including STDP; Magee and Johnston, 1997;Markram et al., 1997;Dan and Poo, 2006), the induction of intrinsic plasticity; Frick et al., 2004 and local synaptic integration;Larkum et al., 1999;Stuart and Hausser, 2001), effi cient back-propagation during physiological fi ring patterns will also determine the rules for information processing and storage (Frick and Johnston, 2005;Dan and Poo, 2006;Sjöström et al., 2008).

COMPARISON BETWEEN APICAL, BASAL, AND TUFT DENDRITES
In contrast to the main apical dendrites, neither physiological fi ring patterns nor short high frequency bursts of APs are able to enhance back-propagation into the 5A basal dendrites. As a result, the degree of attenuation (L 1/e ) for high-frequency AP bursts is approximately 6-fold higher for basal compared to apical dendrites ( Figure 3D). In the apical tuft, in contrast to the main apical and basal dendrites, no Ca 2+ infl ux is produced by low frequency fi ring (Figures 1, 3 and 5).
Even physiological AP patterns/regular AP trains containing CF components produce only small Ca 2+ transients that drop steeply beyond the BP (L 1/e ∼30 µm for three APs at 100 Hz, Figure 4). Differences in back-propagation properties between main apical, apical tuft, and basal dendrites may refl ect differences in the expression levels and/or types of voltage-dependent conductances, and in the dendritic morphology.

Back-propagation in basal dendrites
In contrast to L5A, Ca 2+ transients evoked by single bAPs do not attenuate along the basal dendrites of L5B pyramidal neurons (Kampa and Stuart, 2006;Nevian et al., 2007), and regenerative  Ca 2+ infl ux may or may not be recruited by high-frequent AP activity in these neurons (Kampa and Stuart, 2006;Nevian et al., 2007). In L5A pyramidal neurons, we did not observe a signifi cant increase in the Ca 2+ transients of basal dendrites within the physiological activity range (Manns et al., 2004;Frick et al., 2007;de Kock and Sakmann, 2009) for these neurons.

Back-propagation into the distal tuft
Similar to the results obtained for L2/3 neurons (Waters et al., 2003), but in contrast to those from L5B Larkum, 1999), single APs and short low-frequency AP patterns failed to produce Ca 2+ signals in the tuft beyond the major BP. High-frequency AP patterns, on the other hand, evoked small Ca 2+ signals within the tuft (similar to L2/3 pyramidal neurons for comparable AP numbers) (Waters et al., 2003). These signals, however, were strongly attenuated along the primary tuft dendrites with L 1/e of ∼30 µm from major BP (three APs at 100 Hz). This attenuation was much more pronounced than that observed in the primary tuft dendrites of L5B pyramidal neurons (Larkum, 1999), and more similar to that recorded in the higher-order tuft branches in these neurons (Helmchen et al., 1999;Larkum and Zhu, 2002). One explanation for these fi ndings is that the primary tuft dendrites of L5A pyramidal neurons contain a lower density of active conductances, resulting in a more passive membrane and an increase in the threshold for dendritic electrogenesis. It is possible that Ca 2+ spikes in the tuft dendrites can be evoked by the coincidence of bAPs and synaptic input, thereby increasing the gain of these neurons.

AP FIRING PATTERNS AND DENDRITIC ELECTROGENESIS
The variability in AP timing of physiological activity patterns could convey important information, refl ecting the precise integration of spatio-temporal patterns of synaptic inputs; alternatively, this irregularity may refl ect noise and information could be represented by mean fi ring rates recorded over hundreds of milliseconds (Mainen et al., 1995;Shadlen and Newsome, 1995;Nowak et al., 1997;Stevens and Zador, 1998;Ahissar et al., 2000;Panzeri et al., 2001). Our study shows that the effi cacy of AP back-propagation along L5A apical dendrites strongly correlates with the distribution of instantaneous ISIs during physiological activity patterns. These data lend support to the idea that the temporal structure of physiological fi ring patterns may contain important information for dendritic signaling and plasticity (Williams and Stuart, 2000). Short bursts of action potentials in physiological spike trains have been suggested to transmit signifi cant informational content (reviewed in Lisman, 1997).

ION CHANNELS REGULATING AP BACK-PROPAGATION
It was hitherto unknown which active conductances shape AP back-propagation in L5A pyramidal neurons. In L5B pyramidal neurons, low-voltage (T-type) and high-voltage (L-and N-type) Ca 2+ channels, A-type K + channels, and BK Ca channels are present in the apical dendrites (Migliore and Shepherd, 2002;Benhassine and Berger, 2005). We found that low-and high-voltage Ca 2+ channels (T-/R-, L-, and others) are activated in the apical dendrites of L5A neurons during regimes of high frequency AP activity. Our results also demonstrate that A-type K + channels strongly dampen den-dritic excitability, both during low-and high-frequent AP activity, in agreement with fi ndings from hippocampal CA1 pyramidal neurons (e.g. Hoffman et al., 1997;Frick et al., 2003). BK Ca channels and A-type K + channels signifi cantly dampened the highfrequency bAP burst-evoked Ca 2+ signals. In contrast to A-type K + channels, however, BK Ca channels were not signifi cantly activated by single bAPs or low-frequency bAP bursts. This is consistent with a recent study showing that BK Ca channels increase the threshold for dendritic electrogenesis (Benhassine and Berger, 2009), but that their activation requires a large Ca 2+ infl ux (Benhassine and Berger, 2005). Our results are a fi rst step in determining the source of Ca 2+ signals, and the ion channels that dampen dendritic excitability in the dendrites of L5A pyramidal neurons.

DEVELOPMENTAL CHANGE IN AP BACK-PROPAGATION
Our results show that the profi le of AP-associated Ca 2+ signals along the apical dendrites changes during postnatal development.
For the apical dendrites, the attenuation of Ca 2+ signals evoked by single APs and low-frequency (≤20 Hz) AP trains increased with age. Physiological AP patterns containing high-frequency components (mostly two APs, e.g. sequences 3,4, and 6), however, propagated more effi ciently towards the distal dendrite at P25 compared with P14. Ca 2+ signals evoked by trains of three APs at fi xed frequencies suggest that at P25 the largest amplifi cation occurs in more proximal dendritic regions (∼300 µm) when compared with P14 (∼500 µm). In contrast to most physiological AP patterns, but similar to sequence 1 (three APs at high frequencies), these signals attenuated more strongly within the distal half of the dendrite than at P14. This suggests that at P14 an additional AP has a larger amplifying effect on back-propagation than at P25. We also observed an increase in the CF from ∼55 to ∼90 Hz between P14 and P25 days of postnatal development. For the basal dendrites, AP-Ca 2+ signal attenuation was more pronounced at P14 than at P25, and no amplifi cation was observed for the activity patterns tested at both ages. The most plausible explanation for these changes in dendritic excitability during development is a change in the expression levels of active conductances in the dendrites (Hamill et al., 1991;Zhu, 2000;Atkinson and Williams, 2009). In summary, we conclude that the active dendritic properties of L5A pyramidal neurons strongly depend on the age and the type of dendrite -setting up largely different rules for information processing and plasticity in the main apical, apical tuft, and basal dendrites, respectively. Accordingly, these different dendritic arbors will have branch specifi c rules for the propagation of physiologically occurring action potential output and for its coupling with synaptic input. In this way, these different rules could improve the storage and processing capabilities of L5A pyramidal neurons. Lastly, our study supports the idea that the different role L5A and L5B pyramidal neurons play within the neocortical circuitry is established by their distinct morphological, connectivity, and now dendritic criteria.