The neocortex is thought to have a modular structure composed of ‘canonical circuits’ performing stereotyped computations (Harris and Shepherd, 2015; Markram et al., 2015; Miller, 2016). Anatomical evidence supports the existence of repeating circuit architectures that display similar general features across species and brain areas (Carlo and Stevens, 2013; Douglas and Martin, 2004; Mountcastle, 1997). It is generally thought that these architectural motifs serve as a physical substrate to perform a small range of specific, canonical computations (Bastos et al., 2012; Braganza and Beck, 2018).

Pyramidal neurons are the main building blocks of these circuit motifs. Across brain areas and species, their biophysical attributes endow them with nonlinear properties that allow them to implement a repertoire of advanced computations at the single cell level (Gidon et al., 2020; London and Häusser, 2005; Spruston, 2008). Layer 5 pyramidal neurons (L5PNs) in particular provide a striking example of how dendritic properties can underlie circuit-level computations in a laminar circuit. Their dendritic nonlinearities enable signal amplification and coincidence detection of inputs – a crucial operation to integrate feedforward and feedback streams that often send projections onto separate dendritic domains. In these cells, a single backpropagating action potential (bAP), when combined with distal synaptic input, can trigger a burst of somatic action potentials. The crucial mechanism underlying this nonlinear phenomenon is the all-or-none dendritic Ca²⁺ plateau (Larkum et al., 1999a; Larkum et al., 1999b).

Morphology and intrinsic properties have a profound influence on neuronal excitability. Dendritic topology and the electrical coupling between the soma and dendrites are thought to be particularly crucial for determining a neuron’s integrative properties (Mainen and Sejnowski, 1996; Schaefer et al., 2003; van Ooyen et al., 2002; Vetter et al., 2001). Recent experimental work has shown that there can be substantial variation in intrinsic properties of L5PNs depending on the location within a cortical area or on the species they are recorded from (Beaulieu-Laroche et al., 2018; Fletcher and Williams, 2019). However, it is often assumed that pyramidal neurons have robust enough properties across cortical areas and brain structures to support similar computations (Bastos et al., 2012; Hawkins et al., 2017; Larkum, 2013; Shipp, 2016). For instance, analogous to L5PNs, hippocampal pyramidal neurons also display dendritic Ca²⁺ APs that support coincidence detection of distal and proximal inputs (Jarsky et al., 2005).

If L5PNs indeed have a common repertoire of operations in support of canonical computations, one would expect the same cell type in adjacent and closely related areas to exhibit the same computational repertoire. Here we have studied the bursting properties of thick-tufted layer 5 pyramidal neurons (ttL5) in mouse primary and medial secondary visual cortices (V1 and V2m). Through systematic and rigorously standardized experiments, we describe fundamentally different operation patterns linked to morphology in the two brain areas. Through computational modelling, we reveal new insights into a biophysical mechanism linking excitability and morphology, which can account for this difference. Our results question the notion of a common operational repertoire in pyramidal neurons and thus of cortical canonical computations more generally.

We made whole-cell patch clamp recordings from ttL5 neurons in V1 and V2m in acutely prepared mouse brain slices. To ensure consistency in cell type, recordings were restricted to L5PNs projecting to the lateral posterior nucleus of thalamus (n = 117), identified using retrograde labelling with cholera toxin subunit B (CTB, Figure 1—figure supplement 1A–E), or to neurons labelled in the Colgalt2-Cre mouse line (n = 12) known to be ttL5 PNs (Groh et al., 2010; Kim et al., 2015). We were thus able to maintain cortical area as the primary variant when comparing V1 and V2m neurons (Figure 1—figure supplement 1F,G).

Thick-tufted layer 5 pyramidal neurons in V2m lack BAC firing

To reproduce the conditions required for triggering BAC firing, we stimulated synaptic inputs near the distal tuft in L1 using an extracellular electrode in conjunction with somatic stimulation through the recording electrode (Figure 1A). To avoid recruiting inhibitory inputs during the extracellular stimulation and create the most favourable conditions to enable BAC firing (Pérez-Garci et al., 2006), we added the competitive GABA_B receptor antagonist CGP52432 (1 µM) to the extracellular solution. Extracellular current pulses in L1 were adjusted to evoke either a subthreshold EPSP or a single action potential at the soma. Somatic injection of a 5 ms depolarizing current pulse through the recording electrode was used to trigger single APs. In V1 neurons, combined stimulation (with the L1 input triggered at the end of the somatic pulse) could evoke a prolonged plateau potential resulting in a burst of 3 APs. Cells were considered to be BAC firing if three or more APs could be evoked following combined somatic and L1 stimulation (each evoking no more than one AP individually). We repeated these experiments in ttL5 neurons located in V2m under the same recording conditions. Upon coincident somatic AP and extracellular L1 stimulation, BAC firing was almost never observed in V2m. In summary, BAC firing was observed in approximately half the recorded V1 neurons (10/21), while neurons in V2m showed an almost total lack of BAC firing (1/18, p = 4.6*10⁻³, Fisher’s exact test, Figure 1B).

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Critical frequency ADP is diminished in V2m ttL5 neurons

To further investigate the prevalence of dendritic nonlinearities in ttL5 neurons across visual cortices, we recorded another hallmark of dendritic Ca²⁺ plateaus: a prominent somatic afterdepolarization (ADP) following a high-frequency train of somatic APs, termed critical frequency ADP or cfADP (Larkum et al., 1999a; Shai et al., 2015). We recorded the somatic membrane potential from ttL5 neurons and evoked three action potentials using 3 ms pulses of somatic current injection at frequencies ranging from 50 Hz to 200 Hz in 10 Hz increments (Figure 1C). In V1 neurons, increasing the AP frequency above a critical frequency typically resulted in a sudden increase in the ADP (Figure 1C, middle). However, when recording in V2m under the same experimental conditions, there was usually no change in ADP, even at firing frequencies as high as 200 Hz (Figure 1C, right). To quantify this effect, we aligned the peaks of the last AP for each frequency and measured the area of the ADP difference between the 50 Hz trace and the higher frequency traces in a 20 ms window (4–24 ms) following the last AP (Figure 1C, inset). This measure of ADP increased sharply above a critical frequency and was often largest around the value of this frequency (Figure 1D). For neurons with a defined critical frequency, the mean values in V1 (112 ± 31 Hz, n = 26) and in V2m neurons (109 ± 26 Hz, n = 11) did not differ significantly (p = 0.82; two-sample t-test; Figure 1E).

Next, we measured the maximal ADP integral value for each cell (Figure 2A), regardless of the presence of a critical frequency. Neurons in V2m had significantly smaller ADP area (V1 mean = 91 ± 50 mV*ms, SD, n = 41; V2m mean = 42 ± 33 mV*ms, SD, n = 49; p = 4.54 * 10⁻⁶, D = 0.52; two-sample Kolmogorov-Smirnov test), reflecting that most of these cells lacked a critical frequency altogether. As there is considerable ambiguity regarding the extracellular Ca²⁺ concentration in vivo (Lopes and Cunha, 2019), we have used both 1.5 and 2 mM CaCl₂ in the artificial cerebrospinal fluid (ACSF). Although some change in the magnitude of Ca²⁺ currents is expected, at the level of maximum ADP integral values there was no statistically significant difference between the two conditions in either V1 or V2m (p = 0.12, D = 0.36 for V1; p = 0.21, D = 0.29 for V2m; two-sample Kolmogorov-Smirnov test; Figure 2—figure supplement 1). Similarly, as there was no significant difference in the maximum ADP integral values across V2m neurons labelled retrogradely or by the Colgalt2-Cre line (p = 0.62, D = 0.24; two-sample Kolmogorov-Smirnov test, Figure 2—figure supplement 2), we pooled these populations. To obtain an unbiased count of cells showing cfADP, we classified the unlabelled maximum ADP values pooled from both V1 and V2m into two groups using k-means clustering with k = 2 (Figure 2A). The percentage of neurons with cfADP, as determined by the classification, was more than three times higher in V1 than in V2m (p = 2.6*10⁻⁵, Fisher’s exact test, Figure 2B).

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To establish parameters which may underlie the difference in dendritic Ca²⁺ electrogenesis between ttL5 neurons in V1 and V2m, we next characterized intrinsic properties of CTB labelled ttL5 neurons recorded during the cfADP experiments from V1 (n = 41) and V2m (n = 49; Figure 2—figure supplement 3A). The distribution of resting membrane potential, input resistance, sag amplitude, and rheobase were similar across the two populations (p > 0.05; two-sample t-test; Figure 2—figure supplement 3D). To capture a wide range of bursting behaviours, we devised a measure we termed the maximal burst ratio (see methods), where a high value represents strong bursting behaviour in a given neuron. In addition, we measured the number of spikes in the burst as well as the magnitude of the AHP immediately following the last spike in the burst. The maximal burst ratio, number of burst spikes, and measured AHP were significantly greater for V1 neurons than for V2m neurons (burst ratio: V1 = 12.9 ± 12.3 vs V2m = 5 ± 3.8, p = 6.1*10⁻⁵; burst spikes: V1 = 3 ± 0.7 vs V2m = 2.3 ± 0.6, p = 6.2*10⁻⁶; burst AHP: V1 = 17.9 ± 7 mV vs V2m = 13.6 ± 3 mV, p = 1.9*10⁻⁴, all two-sample t-tests; Figure 2—figure supplement 3D). Furthermore, neurons categorized as cfADP had significantly higher burst ratios (13.3 ± 11.9, n = 35 vs 5.7 ± 6.3, n = 55; for cfADP and non-cfADP neurons, respectively; p = 1.5*10⁻⁴, two-sample t-test) and more prominent AHP following the burst (17.9 ± 6.9 mV, n = 35 vs 14.1 ± 3.9 mV, n = 55; for cfADP and non-cfADP neurons, respectively; p = 1.6*10⁻³, two-sample t-test).

These results show that under the same conditions and in the same operational ranges V2m ttL5 neurons have similar subthreshold, yet different firing properties compared to V1. Previous research has indicated the length of the apical trunk as a possible factor involved in determining the dendritic integrative capacity of ttL5 neurons in V1 (Fletcher and Williams, 2019). To test this, we reconstructed the apical trunk of 22 V1 and 26 V2m neurons from those recorded. Apical trunk lengths were significantly shorter in V2m than in V1 (V1 mean = 409 ± 64 µm, SD, n = 22 vs V2m mean = 313 ± 65 µm, SD, n = 26; p = 4.26*10⁻⁶, two-sample t-test, Figure 2C). Additionally, there was a correlation between maximum ADP integral values and apical trunk length across the two populations (p = 5.37*10⁻³; F-test). To further test how different aspects of morphology may affect our results, we created full morphological reconstructions of 6 V1 and 7 V2m recorded neurons (Figure 2—figure supplement 4A). Dendritic length and number of branchpoints for the tuft and basal dendrites as well as the number of oblique branches were similar between the two populations. Apical length, convex hull and largest Sholl radius, however, were significantly greater in the V1 neurons (p < 0.005 Bonferroni-corrected two sample t-test, Figure 2—figure supplement 4B,C). While dendritic signals typically attenuate with distance, these results suggest that there may be a counter-intuitive interaction between apical trunk length and dendritic Ca²⁺ electrogenesis in ttL5s – the further bAPs need to travel along the trunk, the more they can trigger Ca²⁺ plateaus.

BAC firing is absent in models of ttL5 neurons with short morphology

To investigate possible mechanisms underlying the dependence of bursting on apical trunk length, we ran numerical simulations in conductance-based compartmental models of ttL5 neurons. We first probed BAC firing in a morphologically detailed model developed by Hay et al., 2011, using the model parameters (biophysical model 3) and morphology (cell #1) favoured for reproducing BAC firing. As in the original paper, BAC firing was triggered by a 0.5 nA EPSC-like injection at the apical bifurcation coupled to a somatic action potential evoked by square-pulse current injection at the soma. Mirroring the responses seen in the subset of strongly bursting ttL5 neurons, coincident stimulation triggered BAC firing in the detailed model (Figure 3A, left). We then applied the same model parameters to an example V2m morphology with a shorter apical dendrite. The high density (‘hot’) Ca²⁺ zone was shortened to 100 µm to reflect the 50% reduction in apical trunk length and repositioned around the new apical branch point (350–450 µm from the soma vs 685–885 µm in the long morphology). Intrinsic properties of this shorter model remained within the physiological range (as well as within the range of V2m recordings; Figure 2—figure supplement 3D). The amplitude of the dendritic current injection in the shorter model (0.217 nA) was chosen to obtain the same EPSP amplitude (~6.2 mV) at the bifurcation in both model cells. With this short morphology from V2m, coincident tuft and somatic stimulation evoked only a single somatic spike and did not trigger a dendritic Ca²⁺ plateau (Figure 3A, right). To explore the sensitivity of Ca²⁺ plateaus to dendritic Ca²⁺ channel density in the long and short neurons, we scaled the total density of Ca²⁺ channels (g_Ca henceforth) to between 0 and 8 times their original quantities, while keeping the ratio of the two Ca²⁺ conductances (high voltage- and low voltage activated; HVA and LVA respectively) constant. The integral of the dendritic voltage at the bifurcation, acting as an indicator of the large and sustained depolarization during a Ca²⁺ plateau, increased proportionally to g_Ca in the long morphology. In the short morphology, however, the voltage integral stayed low across all g_Ca values (Figure 3B), consistent with the absence of Ca²⁺ plateaus. The underlying Ca²⁺ currents, while scaling with g_Ca, were 4 orders of magnitude smaller in the model with short morphology (Figure 3—figure supplement 1A). To explore if Ca²⁺ plateaus were at all possible in the short neuron model, we systematically changed both the dendritic current injection (range: 0.02–0.5 nA, the value used in the long morphology) and the time difference between the somatic and dendritic stimulus (range:± 20 ms). The current injection threshold of dendritic Ca²⁺ electrogenesis showed an asymmetric U-shaped relationship in the long morphology, as expected (Figure 3—figure supplement 1B; Larkum et al., 1999b). In the short morphology, Ca²⁺ plateaus could only be evoked by the largest coincident current injections (0.5 nA, ± 1 ms). While during the largest dendritic injection the evoked dendritic potential was substantially larger than in the long morphology, it resulted in only a small depolarization at the soma and no somatic spike burst was triggered when combined with a somatic spike (Figure 3—figure supplement 1C). Next we tested if the largest coincident dendritic injection (0.5 nA, ± 1 ms) could evoke BAC firing in the short morphology when combined with increased Ca²⁺ conductance. While the dendritic voltage integral scaled similarly to the long morphology, showing active contribution of Ca²⁺ currents (Figure 3—figure supplement 1D), the short neuron model never exhibited BAC firing. To further ensure comparability between the models with long and short morphology, dendritic electrogenesis was probed across a broad range of hot zone sizes (range: 50–200 µm) and different HVA:LVA ratios (range: 100:1 – 1:10). Neither the length of the hot zone (Figure 3—figure supplement 2C,F) nor the HVA:LVA ratio (Figure 3—figure supplement 2D) had a substantial effect on the difference between long and short morphologies in dendritic Ca²⁺ electrogenesis, BAC firing, or on somatic ADP measures (Figure 3—figure supplement 2). These results indicate that, although the size of the Ca²⁺ plateau depends on g_Ca, and to some extent on hot zone length and on the ratio of HVA and LVA channels, these factors alone are not sufficient to enable BAC or critical frequency firing in short neurons.

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Next we set out to explore the effect of altered apical trunk length in isolation from complex interactions found in biological morphologies. Dendritic arbours can be usefully reduced to a small set of equivalent compartments where spatial detail is abstracted away while the essential electrotonic divisions of the neuron are maintained. We selected an existing reduction (Bahl et al., 2012) of the Hay et al., 2011 model for use in all subsequent in silico experiments. While altering apical trunk length in the reduced model, conductances were redistributed with the same decay constant to account for the change in apical length (see Materials and methods). Intrinsic properties remained within the physiological range as well as within the range of V1 and V2m recordings following these changes (Figure 2—figure supplement 3D). As with the morphologically detailed model, the reduced model (with the originally published parameters) displayed BAC firing triggered by coincident tuft and somatic stimulation (Figure 3C, left). Shortening the apical trunk was sufficient to eliminate this response (Figure 3C, right). As with the detailed model, the current injection threshold of dendritic Ca²⁺ electrogenesis at different inter-stimulus intervals showed an asymmetric U-shaped relationship that diminished with shorter trunk lengths (Figure 3—figure supplement 1E).

We explored the dependence of BAC firing on apical trunk length and g_Ca by measuring the time-integral of tuft voltage as an indicator of Ca²⁺ plateau potentials (Figure 3D). The presence of a Ca²⁺ plateau depended strongly on apical trunk length and was only sensitive to g_Ca above a critical length of approximately 350 µm (≅ 0.35 λ). Below this length, no Ca²⁺ plateaus were triggered regardless of how high g_Ca was set to. These experiments show that a reduced model can also reproduce our results, allowing us to explore and dissect the underlying parameters in more detail.

Active propagation enhances voltage in long dendrites

To obtain a better understanding of what causes the length dependence of bursting, we made recordings from the final segment of the apical trunk as well as the tuft using the reduced model of Figure 3C. To recreate the experimental conditions of Figure 1C, we triggered 3 spikes at 100 Hz through somatic current injection. As with coincident bAP and tuft input, increasing the length of the apical trunk facilitated dendritic Ca²⁺ plateau initiation (Figure 4A). Interestingly, the width and peak voltage in the tuft increased steadily with dendritic length (Figure 4B,C), even in the absence of Ca²⁺ conductances (g_Ca = 0). In the presence of voltage-gated Ca²⁺ channels, the increased amplitude of bAPs triggered a large all-or-none Ca²⁺ plateau above a certain threshold length.

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We found that bAP amplitude in the tuft increased as a function of apical trunk length despite a decreasing bAP amplitude in the distal segment of the trunk (Figure 4B). Conversely, the width of the bAP (measured 2 mV above baseline to capture the long tail in the voltage response without contamination by spiking events) increased in both the tuft and trunk with length (Figure 4C). While waveform broadening is a natural consequence of passive filtering along dendrites, the sustained voltage in the distal trunk required active dendritic propagation. In the reduced model, this active propagation in the apical trunk was mediated primarily by voltage-gated Na⁺ channels. Removing these channels caused a substantial reduction in peak voltage and width of the depolarization in the distal trunk, and importantly also abolished the trend of increasing tuft voltages with longer dendritic trunks (Figure 4D,E). More generally, active propagation caused bAPs to be larger and broader at all distances along a long dendrite compared to the same absolute distances in shorter dendrites (Figure 4—figure supplement 1A,B). Consequently, when comparing the final positions along the trunk, the peak voltage is only marginally smaller in long dendrites despite the larger distance from the soma. This is not the case in a passive dendrite, where voltage attenuation depends almost exclusively on distance and not trunk length (Figure 4—figure supplement 1C), bar the end-effect in the last segment. We next tested how the specific distribution of active conductances affected the results. When all the various conductances were uniformly distributed along the apical trunk, the waveforms did not substantially change, and the enhanced voltage continued to trigger Ca⁺ plateaus only in neurons with long apical trunks (Figure 4—figure supplement 2). We have also tested the specific contribution of the H-current (I_h). Reducing I_h (i.e. g_HCN) either in the tuft alone, or both in the trunk and tuft resulted in a slower increase of tuft depolarization, width and voltage integral with apical trunk length (Figure 4—figure supplement 3A and B). Crucially, tuft peak voltage remained positively correlated with apical trunk length even after the total removal of I_h (i.e. had positive slope), contrary to changes observed with varying the amount of sodium current in the apical trunk (Figure 4—figure supplement 3C). Furthermore, dendritic Ca²⁺ electrogenesis remained dependent on apical trunk length, albeit with the actual threshold length tracking the changes in I_h (Figure 4—figure supplement 3D). It has previously been suggested that axial resistance (R_a) in the apical dendrite may influence the backpropagation efficiency in dendrites and burstiness of ttL5 neurons (Fletcher and Williams, 2019). To test this hypothesis, we measured peak voltage and width in the trunk and tuft for different trunk lengths under different R_a conditions. We found that peak tuft voltage increased with increasing trunk R_a, reaching the highest voltage near the reduced model’s original value, and decreasing again for higher values (Figure 4—figure supplement 4). However, in these simulations both width and voltage integral increased monotonically with trunk length regardless of the specific value of R_a in both the tuft and the last segment of the trunk. This indicates that, although important, R_a is not the primary determinant for generating the length-dependent effect and if R_a indeed correlates with length, these effects may combine to further enhance the tuft voltage in long neurons. These results show that the general phenomenon of enhanced voltage propagation in longer dendrites resulting in amplification of tuft voltage does not depend on any of the particular model parameters above.

While it might seem counterintuitive that peak tuft voltage is increasing when trunk voltage is decreasing with length, we propose that the temporal broadening of the depolarization can at least partially account for this via a passive mechanism. Wider depolarizations allow the tuft compartment to charge to a higher voltage. The rate and peak value of tuft charging depends on the passive properties of the tuft. The peak value of depolarization and the rate of voltage change are proportional to membrane resistance (R_m) and membrane capacitance (C_m), respectively. The product of these two parameters gives the membrane time constant (𝜏) which determines the maximal amplitude reachable over a certain time. To illustrate this, we applied voltage-clamp to the end of the distal segment of the trunk and delivered 30 mV square voltage pulses of increasing width while recording the voltage in the tuft. Due to membrane capacitance, a short (10 ms) voltage step did not fully charge the tuft while a longer, 40 ms voltage step allowed tuft voltage to reach the steady-state value commanded by R_m (Figure 5Ai). To directly test the hypothesis that the relationship between trunk depolarization width and tuft membrane time constant caused the amplitude of the tuft depolarization to increase with length, one could vary R_m by changing g_leak. However, this would affect resting membrane potential and consequently alter voltage-dependent properties in the tuft. In order not to affect other variables in the model, we therefore chose to vary C_m instead (Figure 5Aii). For a given value of depolarization amplitude and width, increasing tuft C_m (and therefore 𝜏) caused a reduction in the tuft peak depolarization (Figure 5B). These simulations show that the tuft time constant and the width of the invading voltage pulse (e.g. bAP) interact to create a higher tuft depolarization with longer apical trunks.

Figure 5

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Overall, it is the combination of increased width and a relatively small reduction in amplitude through active backpropagation that resulted in a trunk voltage integral that increased with trunk length, thereby passing more charge to the adjacent tuft compartment. When active backpropagation was reduced or absent, the trunk integral and resulting tuft voltage decreased with length (Figure 4D,E). The voltage integral in the distal trunk thus seemed to approximately determine the peak tuft voltage. To test this, we applied voltage-clamp to the end of the trunk and injected square steps with a range of integrals obtained through various combinations of width and amplitude (Figure 5C). This revealed a zone above a critical trunk integral for which many different width and depolarization combinations were sufficient to evoke a Ca²⁺ plateau in the tuft (Figure 5D). At the boundary of this Ca²⁺ plateau-evoking zone, iso-integral lines crossed asymmetrically into subthreshold combinations of width and depolarization. These results show that it is the complex interplay of width and amplitude with the tuft time constant that enables dendritic Ca²⁺ electrogenesis.

We made whole-cell patch-clamp recordings from L5PNs in primary and secondary visual cortices of mice. We found that both BAC firing and cfADP were almost entirely absent in the V2m neurons. Moreover, we observed that the propensity for Ca²⁺ electrogenesis was positively correlated with the length of the apical dendrite trunk across all neurons. To investigate the influence of apical trunk length on burstiness, we ran numerical simulations in compartmental biophysical models. Both morphologically detailed and reduced models showed that decreasing the apical trunk length resulted in reduced propensity for dendritic Ca²⁺ electrogenesis. Further simulations revealed that this is due to an interplay between bAP width, amplitude, and tuft impedance that depends critically on the presence of voltage-gated Na⁺ channels in the apical trunk. These results show that the same cell type, in closely related and adjacent cortical areas, and under the same operating conditions can have a very different computational repertoire. Our findings are thus inconsistent with the notion of canonical computations at the single cell level, suggesting they may not exist at the circuit level either.

Contrary to common assumptions, we observed considerable differences in the properties of ttL5 neurons across different brain regions. BAC firing, a dendritic operation, and cfADP, a measure of dendritic excitability, which are both critically dependent on dendritic Ca²⁺ plateaus, were almost completely absent in V2m. One key factor known to control dendritic Ca²⁺ electrogenesis is inhibition (Pérez-Garci et al., 2006). To determine the role of inhibition on the observed differences between V1 and V2m neurons, we pharmacologically blocked GABA_B receptors, thus creating more favourable conditions for BAC firing. To make comparisons rigorous, we have used the same experimental protocols and conditions across all experiments. Furthermore, to exclude bias in selecting ttL5 neurons, we have recorded only from two well-defined groups, identified either by their projection target or genetic label. We found similarly diminished propensity for bursting in both groups of V2m neurons.

The extracellular stimulation used to evoke BAC firing could in principle recruit different polysynaptic circuits in V1 and V2m, which could account for the difference. However, this would not explain the differences measured with the cfADP paradigm using intracellular stimulation only. Another confounding variable affecting excitability could be the Ca²⁺ concentration in the extracellular solution. We have found the same results under different physiologically relevant concentrations. Altogether, these results show that decreased propensity of V2m ttL5 neurons for dendritic Ca²⁺ electrogenesis is a robust phenomenon.

Correlated with the differences in dendritic Ca²⁺ electrogenesis, we found ttL5 neurons in V2m to have significantly shorter apical trunks compared to V1 neurons. This data is consistent with recent structural MRI data showing a thinner cortical mantle in more medial and posterior parts of the cortex (Fletcher and Williams, 2019). Using an existing, prominent biophysical model designed to reproduce ttL5 properties such as BAC firing, we found that the same model applied to a shorter morphology resulted in a loss of BAC firing, independently of Ca²⁺ channel density. This was also true in a reduced ttL5 model with a simplified morphological structure, which allowed for continuous exploration of apical trunk length. We found a sharp cut-off at a length of 0.35 λ (≅ 350 µm in model space), below which no BAC firing could be evoked. We note, however, that the reduced model is based on rat neurons and the apical trunk and oblique dendrites are pooled into the same compartment. It is also worth noting that, as the reduced model does not have a distinct compartment to represent the apical bifurcation, all Ca²⁺ channels are placed in the tuft compartment. Therefore, the numerical values of model length do not translate directly into apical trunk lengths for real mouse neurons.

Through our simulations, we identified voltage-gated Na⁺ channels in the apical dendrite as a key factor for reproducing our results. Sodium channels control dendritic excitability by supporting active backpropagation, resulting in reduced attenuation over distance. Combined with a broadening of the bAP proportionally to trunk length (due to capacitive filtering), this caused longer neurons to have larger voltage integrals in the distal trunk, leading to greater charging of the tuft. Indeed, the peak tuft voltage depended on the amount of passive charging it experienced, which was determined by the membrane time constant in the tuft as well as by bAP width and amplitude. We hypothesised that, above a minimal threshold for peak trunk voltage, the primary determinant of peak tuft voltage is the time-averaged voltage in the trunk. Supporting this view, we found that the overall voltage integral was more important for triggering Ca²⁺ plateaus than the particular combination of depolarization width and amplitude.

Aside from dendritic length, our results do not exclude the involvement of other mechanisms to modulate excitability. For example, differences in axial resistance could influence the way voltage propagates along dendrites. While axial resistance indeed had a marked effect on the backpropagation of action potentials in our models, this was independent of trunk length and thus cannot account for our finding. Variations in density and activation properties of other voltage-gated channels may also influence dendritic excitability. It is interesting to note that, in the presence of Na⁺ channels, the bAP in neurons with longer trunks was larger and broader at every distance from the soma. This may be due to a cooperative effect of each trunk section on the sections both up- and downstream, with the voltage at each location decaying slower because of the more depolarised state of the remaining dendrite. Our data thus predicts that bAP width and amplitude measured at the same absolute distance from the soma will be larger in neurons with longer apical trunks. It is worth noting that the models we used lacked NMDA channels. Experimental evidence shows that NMDA spikes can significantly increase the ability of distal tuft input to trigger Ca²⁺ plateaus at the bifurcation. However, when NMDA spikes are triggered directly at the hot zone, they have very little contribution to Ca²⁺ plateaus (Larkum et al., 2009). In addition, the cfADP protocol is independent of synaptically released glutamate, and hence we expect the lack of NMDA channels in the models to have no significant effect on dendritic Ca²⁺ plateaus.

There are a few notable counterexamples to the principle observed here. For example, the human ttL5 neuron was recently shown to have greater compartmentalization and reduced excitability compared to rat neurons despite being substantially longer (Beaulieu-Laroche et al., 2018). This may still be consistent with our predictions, as human ttL5 neurons also had reduced ion channel densities, which we show to be crucial for the length-dependent enhancement. Furthermore, as the boosting effect of a broader depolarization is subject to saturation (when the depolarization is wide enough to fully charge the tuft), we would expect the positive effect of length on tuft voltage to not increase monotonically. Consequently, beyond a certain length the trunk voltage would attenuate to the point where it is no longer sufficient to trigger a Ca²⁺ plateau. On the other end of the spectrum, layer 2/3 pyramidal neurons in rat barrel cortex have shorter apical trunks yet do show cfADP, although they do not exhibit spike bursts during BAC firing (Larkum et al., 2007). It remains to be seen if the length-dependence of dendritic Ca²⁺ electrogenesis generalizes to other species, or across more widespread cortical areas and cell types.

There may be important clinical implications to gaining a better understanding of how variations in cortical thickness, and the resulting changes in neuronal morphology, affect the physiology and computational properties of pyramidal neurons. Indeed, altered cortical thickness has been implicated in several debilitating neurological diseases and mental health conditions. For example, cortical thinning is used as a biomarker for Alzheimer’s disease (Dickerson et al., 2009) and correlates strongly with bipolar disorder (Hanford et al., 2016), while increased cortical thickness is present during development in individuals with autism (Khundrakpam et al., 2017). Interestingly, altered dendritic excitability has also been strongly implicated in several of these diseased conditions (Hall et al., 2015; Nanou and Catterall, 2018; Spratt et al., 2019). We uncovered a possible mechanistic link between cortical thickness and excitability, highlighting a new potential avenue of study for understanding the pathophysiology in these conditions and raising the prospect of identifying intervention targets.

Our findings on dendritic Ca²⁺ electrogenesis in ttL5 neurons have wide-ranging implications for cortical computation. Feedback connectivity between cortical areas tends to target superficial layers while feedforward input favours basal dendrites (Coogan and Burkhalter, 1990; Rockland and Pandya, 1979). BAC firing is believed to play a major role in integrating these two pathways to modulate sensory perception (Bachmann, 2015; Takahashi et al., 2016) and to enable brain-wide learning algorithms that would otherwise be intractable (Guerguiev et al., 2017; Sacramento et al., 2018). This may be even more relevant in higher order cortical areas, which are more likely to process brain-wide feedback to integrate convergent multisensory, motor and cognitive signals (Freedman and Ibos, 2018). However, we show that, at least within the secondary visual cortex, different operations must be implementing the multimodal coincidence detection proposed to underlie various visual phenomena (Bachmann, 2015).

Our findings thus challenge the commonly held notion that the neocortex is composed of canonical circuits performing stereotyped computations on different sets of inputs across the brain. The heterogeneity of operating modes may expand the ability of cortical areas to specialize in the computations that are required for processing their particular set of inputs, at the cost of reduced flexibility in generalizing to other types of input. It may also imply that the nonlinear operations performed through Ca²⁺ plateaus and BAC firing may not be required outside primary sensory cortices, perhaps because in these regions the input hierarchy is less defined. It may therefore be more important to maintain equal weighting between different sensory modalities and rely on other mechanisms to change the weights according to the reliability of each input. With such simple morphological adjustments capable of generating a wide range of possible operations, the brain undoubtedly leverages the array of available computations to improve cognitive processing.

All data, analysis scripts and simulation code is available at https://github.com/ranczlab/Galloni.etal.2020 (copy archived at https://github.com/elifesciences-publications/Galloni.etal.2020).

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Acceptance summary:

This study in mouse elegantly demonstrates that the massive calcium spikes commonly observed in large neocortical layer 5 pyramidal cells critically depends on dendritic trunk length, and are thus a hallmark of specific layer 5 cell types. Of additional interest, the study shows that layer 5 cells have dendritic lengths that vary widely in different cortical areas such that high calcium-dependent dendritic excitability is not ubiquitous feature across neocortex.

Decision letter after peer review:

Thank you for submitting your article "Apical length governs computational diversity of L5 pyramidal neurons" for consideration by eLife. Your article has been reviewed by three peer reviewers, including Brice Bathellier as the Reviewing Editor and Reviewer #1), and the evaluation has been overseen by John Huguenard as the Senior Editor.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission. Please aim to submit the revised version within three months, but we are happy to extend this timeframe if needed, especially regarding the Covid virus crisis.

Summary:

In this study, the authors first show experimentally that L5 neurons in primary vs secondary visual cortex are substantially longer, and that they are more likely to display bursting upon somatic stimulation paired with L1 stimulation. Based on this observation the authors propose that the length of the apical dendritic trunk is key for this phenomenon and show with detailed simulations that trunk length is a critical factor to observe bursting. They finally explain this phenomenon by the combination of active Na⁺ spike backpropagation in the trunk with passive filtering (which increases with length) broadening the spikes and allowing better transfer to the tuft where they trigger a Ca²⁺ spike.

I think the idea that bursting is critically related to dendritic length is interesting (to my knowledge it was not yet proposed but I am not sure), even if it has been shown already that shorter pyramidal cells (e.g. L3) do not have large Ca+ spikes. Especially if this length varies across regions.

The manuscript by Galloni, Laffere and Rancz is an interesting study in which the authors perform experiments (slice electrophysiology) alongside computational modeling, aiming to establish a link between dendritic length and the ability of cortical pyramidal neurons to support calcium plateau potentials and subsequent somatic bursting. They focus on L5 pyramidal cells in two cortical areas, namely V1 and V2m. Their main findings are: (1) PCs in V2m are shorter and less prone to burst than PCs in V1, (2) neuronal excitability is correlated with apical trunk length, (3) shorter model neurons are less prone to burst, (4) apical tuft voltage increases with apical trunk length due to wider bAPs. The authors claim that these findings challenge the notion of canonical computations implemented by cortical neurons, whereby the coincidence of a bAP with dendritic depolarization induced calcium plateau potentials and somatic bursting (Larkum et al., 1999).

While solid evidence against the theory of canonical circuits/computations would be an important finding, I have a number of concerns that dampen my enthusiasm about this work. Specifically, I found that the study suffers from ambiguity in its terminology, makes limited use of computational modeling and presents results that are not sufficiently supported by statistical analysis.

Summary of concerns:

The general approach used by the authors (combination of slice electrophysiology and computational modeling) is particularly well-suited to derive evidence against -or in favor- of the theory of canonical circuits. However, the exploration of the parameter space should be thorough enough so as to not leave any doubts in the reader's mind about the validity of the conclusions. Although the results being presented here are extremely interesting, I cannot find them compelling enough due to a variety of reasons. These fall under three main axes: (1) strength of evidence, as established by the validity of experiments and analysis, as well as the underlying reasoning behind experiments and claims (2) flaws and omissions concerning experimental design (3) issues of clarity in terminology and presentation of results. Corresponding issues are presented below, in descending order of (subjective) importance.

The manuscript by Galloni, Laffere and Rancz titled “Apical length governs computational diversity of L5 pyramidal neurons” investigates the biophysical computations performed by layer 5 pyramidal neurons located in primary (V1) and secondary (V2m) visual cortical areas. Here, using patch clamp electrophysiology in vitro, the authors demonstrate that the computations associated with dendritic Ca²⁺ potentials vary substantially, with layer 5 pyramidal neurons in V2 having reduced dendritic excitability and less burst firing. Using modelling, the authors conclude that Na⁺ channel-dependent broadening of backpropagating action potentials underlies the influence of apical length on dendritic excitability. This study is well written and investigates an interesting phenomena which may have implications for all cortical regions. However, overall the manuscript is lacking in detail and surprisingly, there is no discussion in either the Introduction or Discussion regarding their role in the processing of visual information, which may help to put the findings in context.

Essential revisions:

Overall, combining in vivo with in silico experiments is an inspired approach that is unfortunately not seen very often. The authors have made a solid attempt to combine the two and address a very interesting research question. Unfortunately, the work suffers from several issues that detract from its validity, as described below. If these issues are successfully addressed, the work and its findings would make a significant contribution to the field.

1) The validity of the model analysis (statistical and otherwise) is not convincingly documented in several places (see below). This needs to be improved.

a) In subsection “BAC firing is absent in short ttL5 models”, the authors conclude that Ca²⁺ hotspot size does not affect excitability. However, inspection of the relevant figure (Figure 3—figure supplement 2) shows that, when comparing the traces for the 100 μm and 200 μm hotspot sizes, an additional AP is generated in the latter case, and the area under the red trace appears to be greater. This observation seems to contradict the conclusion -although it may be an outlier. The authors should perform statistical testing to support this claim, or if hot spot size plays a significant but small role compared to dendritic length, plot directly the effect of each parameter across physiological range.

Also, in this case, ADP integral measurements are not performed, and no explanation is provided to justify the differences between the two conditions (100 μm / 200 μm Ca²⁺ hotspot size).

b) In subsection “Active propagation enhances voltage in long dendrites”, it is stated that voltage attenuation is independent of trunk length for passive dendrites. However, inspecting the relevant figure (Figure 4—figure supplement 1), the top plot of subfigure c reveals that there seems to be a ~5 mV difference between the curves for the 200 and 300 μm trunk lengths as measured at the 200um mark. To justify the claim that trunk length does not impact voltage attenuation, the authors should use statistical tests to demonstrate the claimed lack of significant differences. Relying on visual inspection is not convincing.

c) In the same section, Ih reduction is stated to have no effect on the trunk length dependence of excitability (measured through bAP voltage, width and integral). However, visual inspection of the figure (Figure 4—figure supplement 3) indicates visible differences (e.g. subfigure b, width plot, tuft Ih change). In addition, prior work by Larkum et al., 2009, appears to be in contradiction with the authors' claim that Ih reduction has no effect on the trunk length dependence of excitability. As such, the claim should be either toned down or additional metrics that quantify the degree of change and deem it statistically significant should be provided.

d) In subsection “Thick-tufted L5 neuron in V2m lack a critical frequency ADP”, a claim is made concerning the properties of ttL5 neurons – but Figure 2—figure supplement 3 only provides a representative trace. A summary statistic or some other indicator that this behavior is found in all (or most) ttL5 PCs should be included.

e) In subsection “Active propagation enhances voltage in long dendrites”, it is stated that "burstiness always increased with trunk length regardless of Ra". However, no data is shown to support this – an additional figure or statistic would be useful.

f) The demonstration made in Figure 5 is not really strong. It would have been probably more convincing to vary Cm in the reduced model in the presence of back propagating APs, to show that it is local filtering of AP waveforms that allow larger spike induced depolarisation in the tuft.

2) The use of computational modeling in this study is sub-optimal. While the authors use both detailed biophysical and reduced models to support their findings, the particular model analysis design suffers from multiple flaws:

a) In general, the authors did not explore the parameter space of their models to check whether the shorter PCs would be able to generate dendritic calcium spikes and drive somatic bursting under different conditions (e.g. different inter-stimulus intervals between somatic and dendritic signals or different stimulus strength etc.). Canonical cortical computations are not synonymous to "all cells act the same" but describe a phenomenon which could be seen in many different cells, not necessarily under the exact same stimulus conditions. Given that the authors use detailed biophysical models, such an exploration is both feasible and necessary. Moreover, any interesting predictions are very easy to test in vitro, and should be tested experimentally by the authors to confirm or refute them.

b) In subsection “BAC firing is absent in short ttL5 models”, the authors state that a reduced model was selected in order to "vary dendritic length across a continuous range of values". However, it is not explained why this was necessary, as the morphology of the detailed cell of Hay et al. could also have been altered in the required manner to produce a cell with an apical trunk of the desired length. The choice to move from a detailed to a reduced model requires additional explanation, particularly when looking for a "mechanistic understanding", which is less likely to be generated by a reduced model (subsection “Active propagation enhances voltage in long dendrites”).

c) The authors report that "increasing the length of the apical trunk facilitated dendritic Ca²⁺ plateau initiation" in a reduced model, without explaining why this happens. Several possibilities exist: is it because the diameter is becoming smaller, therefore impedance is higher? Is it because the effective conductance is higher (more channels, assuming a fixed density)? Is attenuation smaller? There could be many potential explanations and the authors do not explore these possibilities in their model. Such an exploration is necessary.

d) In subsection “BAC firing is absent in short ttL5 models”, the authors describe how they altered the morphology of the detailed cell model, with the new morphology featuring a shorter apical trunk noted as the most relevant change. However, such a drastic change in morphology should have been followed by model validation (as a sanity check) to ensure basic properties remain physiological. This would also partially control for morphological changes unrelated to the length of the apical trunk. Unfortunately, no validation seems to have taken place (Materials and methods).

3) The paper is unfortunately sometimes unclear in its use of terminology, making it hard for the reader to follow all arguments to their conclusion. In addition, figures could be substantially improved, including more information (i.e. statistical) in a more efficient and effective manner. Besides important details listed in the minor points, two major clarity issues should be thoroughly addressed:

a) One of the core conclusions of this work uses a specific definition of "supralinear". In addition, a different definition is used for the same term ("supralinearities") later on (definition in Figure 2). Neither of these definitions are in line with what is commonly understood by "supralinear" in the field (i.e. a response exceeding the linear extrapolation, as seen in e.g. Branco and Hausser, 2011, Figure 1B). A common, consistent definition should be used – or a new term should be coined for the phenomenon being described.

b) The term "excitability" is sometimes used an ambiguous fashion. In paragraph two of subsection “Thick-tufted L5 neurons in V2m lack BAC firing”, "excitability" seems to be derived through the propensity of a neuron to produce bursts. However, in subsection “Thick-tufted L5 neuron in V2m lack a critical frequency ADP”, "excitability" seems to be derived through a metric dependent on the integral of the ADP, not propensity to burst. Furthermore, although the text mentions "excitability", the title of Figure 1 makes claims on bursting alone. Similar to the case in (b), a common, consistent definition should be used – or a new term should be coined for the phenomenon being described.

4) The homogeneity of the experimental data set is a concern. The recordings were performed from two-well-defined groups identified either by their projection target or genetic label. It would have been good if the conclusions could be further strengthened if further analysis was performed on these cell types. Furthermore, it is merely stated that the experiments are performed in two different projection neurons with no detail about the Glt25d2-Cre mice used, and why these particular cells were targeted in the first place. Can the authors please also illustrate which data was obtained under which conditions (ie retrograde labelling VS Glt25d2 mouse; low vs high Ca²⁺ ACSF)

5) In experiments, the supralinearity or its absence is not always thoroughly established. For example, what happens as you increase the intensity of the stimulus in Layer 1? Or the somatic current pulse? Is the response ever “linear” in either V1 or V2m neurons? I think it's important to first establish the linear regime before being able to classify a response as supralinear.

6) Overall, the manuscript is severely lacking in details associated with the findings.

Recordings were performed from layer 5 neurons with V1 and V2m. There are no details in the manuscript regarding how these brain regions were targeted in all the experiments presented. Please provide details in the Materials and methods as well as illustrations of the targeted brain regions. Are there other biophysical properties which are different between the layer 5 neurons in V1 and V2m which may explain the difference in excitability? RMP? Rheobase?

7) The experiments were performed in ACSF with 1.5 or 2 mM CaCl₂. These recordings were pooled together as there was no significant difference between the ADP integral in the different conditions. However, p = 0.122 in V1, and observing the spread of the data points, it appears as though more experiments may indeed separate the data according to ACSF. This is not surprising, considering the authors conclude that V1 has Ca²⁺-dependent supralinearity therefore altering external Ca²⁺ concentration could be expected to alter Ca²⁺-dependent voltage in these cells.

8) During coincident input (Figure 1A), was an ADP measured in V1 and not V2 neurons? Otherwise the increased action potentials cannot be labelled as BAC firing as have no proof of calcium-dependence. V2m “usually” did not have a change in ADP. Please quantify. Also, was there a difference in the critical frequency in cells in V1 and V2m (the reported critical frequency is currently combined)?

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your article "Apical length governs computational diversity of layer 5 pyramidal neurons" for consideration by eLife. Your article has been reviewed by one peer reviewer, and the evaluation has been overseen by a Reviewing Editor and John Huguenard as the Senior Editor.

All reviewers agree that the revision has substantially improved the manuscript, however, a few points still need to be adequately addressed. In particular, the authors should make sure they sufficiently explore the parameter realm of single cell models.

Summary:

The authors have successfully addressed the vast majority of my concerns, further increasing the quality of their already impressive work. However, a few points still require clarification, and some experiments need extra support or argumentation in order to be fully convincing.

Revisions:

1) "Propensity for bursting was quantified by measuring the maximal burst ratio for each cell (defined as the largest ratio of consecutive ISIs in any current step), as well as the number of spikes in the burst and the AHP immediately following the last spike in the burst."

The "burst ratio" metric is not a widely-used metric to quantify bursting propensity, and is inadequately explained here (high value = high propensity? Why?). Please explain this better.

2) From rebuttal:

"Regarding the hot zone sizes chosen, 200 µm is the original size in Hay et al., 2011. We scaled this to the ratio of apical trunk length between the long and short morphology to get 100 µm. We added an explanation to lines subsection “BAC firing is absent in models of ttL5 neurons with short morphology”."

"The high density (“hot”) Ca²⁺ channel hotspot zone was shortened to 100 µm to reflect the 50% reduction in apical dendrite length and repositioned around the new apical branch point (350-450 µm from the soma vs 685-885 µm in the long morphology)."

It is assumed here that Ca²⁺ channel hotspot size scales linearly with apical trunk length (assuming that "dendrite" stands in for "trunk" here), which is not necessarily the case. A sub-linear or supra-linear scaling would also need to be checked. The authors appear to have actually done this (new Figure 3—figure supplement 2C/F), but do not refer to it to reinforce their point.

3) "Principled alteration of a continuous morphological parameter, such as apical trunk length, is intractable in complex dendritic morphologies."

Considering the fact that the authors are working with single-cell models, this is an inadequate justification. It is true that excessive parameterization of microcircuit models containing multiple interconnected biophysically accurate and morphologically correct reconstructions rapidly devolves into the realm of computational intractability – however, a single cell can be modeled with much greater ease – even if multiple repetitions (i.e. thousands) are required to attain a substantial sample size. If performing the full series of alterations is practically impossible due to some limitation (e.g. insufficiently powerful hardware), then it would also be adequate to show how, for a limited (but at least somewhat representative) subset of alterations, the key results obtained from a reduced morphology accurately reflect the results produced by a detailed reconstruction.

4) From rebuttal:

"We have now clarified this statement by referring to "the length dependence of Ca²⁺ electrogenesis" instead of excitability in general, and explicitly state the effect on voltage propagation (subsection “Active propagation enhances voltage in long dendrites”, and the corresponding figure legend)."

"Reducing Ih (i.e. gHCN) either in the tuft alone, or both in the trunk and tuft, while affecting voltage propagation, had no effect on the length dependence of Ca²⁺ electrogenesis"

Evidence in support of this claim is shown in Figure 4—figure supplement 3 – however, the claim is insufficiently substantiated. It is true that altering gHCN has an effect on voltage propagation, and as such, the peak voltage is also changed – which explains the change in the y-position of the curves. However, what is not shown is that the change "had no effect on the length dependence of Ca²⁺ electrogenesis" – although a visual inspection shows that all curves appear to exhibit a sudden "jump" in peak voltage (which is the result of Ca²⁺ electrogenesis, as it's absent when Ca²⁺ channels are absent), we cannot rely on mere visual inspection to ascertain whether the length at which this "jump" takes place is the same for every condition. The precise critical length should be reported for each condition, and if there are slight fluctuations, it should be demonstrated that they are not statistically significant (e.g. by repeating the experiment multiple times and taking the average of the critical length plus/minus a standard error, then showing no significant differences via statistical testing).

Essential revisions:

Overall, combining in vivo with in silico experiments is an inspired approach that is unfortunately not seen very often. The authors have made a solid attempt to combine the two and address a very interesting research question. Unfortunately, the work suffers from several issues that detract from its validity, as described below. If these issues are successfully addressed, the work and its findings would make a significant contribution to the field.

1) The validity of the model analysis (statistical and otherwise) is not convincingly documented in several places (see below). This needs to be improved.

a) In subsection “BAC firing is absent in short ttL5 models”, the authors conclude that Ca²⁺ hotspot size does not affect excitability. However, inspection of the relevant figure (Figure 3—figure supplement 2) shows that, when comparing the traces for the 100 μm and 200 μm hotspot sizes, an additional AP is generated in the latter case, and the area under the red trace appears to be greater. This observation seems to contradict the conclusion -although it may be an outlier. The authors should perform statistical testing to support this claim, or if hot spot size plays a significant but small role compared to dendritic length, plot directly the effect of each parameter across physiological range.

Also, in this case, ADP integral measurements are not performed, and no explanation is provided to justify the differences between the two conditions (100 μm / 200 μm Ca²⁺ hotspot size).

We have now carried out comprehensive modeling experiments varying the length of the hot zone in both morphologies between 50 and 200 µm. We have used the voltage integral at the bifurcation and the somatic ADP as output measures for the presence or absence of dendritic Ca²⁺ plateaus. No matter the length of the hot zone, the short morphology never shows Ca²⁺ plateaus, while the long morphology always does (Figure 3—figure supplement 2). The short hot zone does result in one fewer AP, however BAC firing, the target of our inquiry, is still present.

We present these findings in the main text, an extended Figure 3—figure supplement 2. Regarding the hot zone sizes chosen, 200 µm is the original size in Hay et al., 2011. We scaled this to the ratio of apical trunk length between the long and short morphology to get 100 µm. We added an explanation to subsection “BAC firing is absent in models of ttL5 neurons with short morphology”.

b) In subsection “Active propagation enhances voltage in long dendrites”, it is stated that voltage attenuation is independent of trunk length for passive dendrites. However, inspecting the relevant figure (Figure 4—figure supplement 1), the top plot of subfigure c reveals that there seems to be a ~5 mV difference between the curves for the 200 and 300 μm trunk lengths as measured at the 200um mark. To justify the claim that trunk length does not impact voltage attenuation, the authors should use statistical tests to demonstrate the claimed lack of significant differences. Relying on visual inspection is not convincing.

Indeed, there is a slight difference in the last segment due to the end effect. We have now added quantification of the length constant to Figure 4—figure supplement 1 and show statistically that it is independent on dendrite length. We have clarified now this in the Results section and the corresponding figure legend.

c) In the same section, Ih reduction is stated to have no effect on the trunk length dependence of excitability (measured through bAP voltage, width and integral). However, visual inspection of the figure (Figure 4—figure supplement 3) indicates visible differences (e.g. subfigure b, width plot, tuft Ih change). In addition, prior work by Larkum et al., 2009, appears to be in contradiction with the authors' claim that Ih reduction has no effect on the trunk length dependence of excitability. As such, the claim should be either toned down or additional metrics that quantify the degree of change and deem it statistically significant should be provided.

We have now clarified this statement by referring to “the length dependence of Ca²⁺ electrogenesis” instead of excitability in general, and explicitly state the effect on voltage propagation (subsection “BAC firing is absent in models of ttL5 neurons with short morphology” and the corresponding figure legend).

d) In subsection “Thick-tufted L5 neuron in V2m lack a critical frequency ADP”, a claim is made concerning the properties of ttL5 neurons – but Figure 2—figure supplement 3 only provides a representative trace. A summary statistic or some other indicator that this behavior is found in all (or most) ttL5 PCs should be included.

We have now characterized intrinsic properties of V1 and V2m neurons. We present this data in Figure 2—figure supplement 3 and discuss in the main text.

e) In subsection “Active propagation enhances voltage in long dendrites”, it is stated that "burstiness always increased with trunk length regardless of Ra". However, no data is shown to support this – an additional figure or statistic would be useful.

We have clarified this sentence by removing the reference to “burstiness”. We have also changed the layout of Figure 4—figure supplement 4 to show these differences more clearly.

f) The demonstration made in Figure 5 is not really strong. It would have been probably more convincing to vary Cm in the reduced model in the presence of back propagating APs, to show that it is local filtering of AP waveforms that allow larger spike induced depolarisation in the tuft.

The bAP amplitude and width are not independent and are determined by active processes along the apical trunk. We used voltage clamp to decorrelate these properties and explore the distinct contribution of the peak and width of the distal trunk voltage to tuft depolarization. We have added a schematic, changed the layout and updated the title of Figure 5.

2) The use of computational modeling in this study is sub-optimal. While the authors use both detailed biophysical and reduced models to support their findings, the particular model analysis design suffers from multiple flaws:

a) In general, the authors did not explore the parameter space of their models to check whether the shorter PCs would be able to generate dendritic calcium spikes and drive somatic bursting under different conditions (e.g. different inter-stimulus intervals between somatic and dendritic signals or different stimulus strength etc.). Canonical cortical computations are not synonymous to "all cells act the same" but describe a phenomenon which could be seen in many different cells, not necessarily under the exact same stimulus conditions. Given that the authors use detailed biophysical models, such an exploration is both feasible and necessary. Moreover, any interesting predictions are very easy to test in vitro, and should be tested experimentally by the authors to confirm or refute them.

We have now explored the effect of a wide range of different inter-stimulus timings and stimulus strengths on dendritic Ca²⁺ electrogenesis in both morphologies and in different lengths of the reduced model. The conclusions remain the same: the short morphology and shorter reduced models fail to produce BAC firing, regardless of the stimulus parameters. This is now included in the main text and in Figure 3—figure supplement 1B and E.

b) In subsection “BAC firing is absent in short ttL5 models”, the authors state that a reduced model was selected in order to "vary dendritic length across a continuous range of values". However, it is not explained why this was necessary, as the morphology of the detailed cell of Hay et al. could also have been altered in the required manner to produce a cell with an apical trunk of the desired length. The choice to move from a detailed to a reduced model requires additional explanation, particularly when looking for a "mechanistic understanding", which is less likely to be generated by a reduced model (subsection “Active propagation enhances voltage in long dendrites”).

We have added a couple of sentences to explain the motivation behind switching to the simplified model (subsection “BAC firing is absent in models of ttL5 neurons with short morphology”).

c) The authors report that "increasing the length of the apical trunk facilitated dendritic Ca²⁺ plateau initiation" in a reduced model, without explaining why this happens. Several possibilities exist: is it because the diameter is becoming smaller, therefore impedance is higher? Is it because the effective conductance is higher (more channels, assuming a fixed density)? Is attenuation smaller? There could be many potential explanations and the authors do not explore these possibilities in their model. Such an exploration is necessary.

We have explored the contribution of Na⁺ channel density, distribution of ion channel along the trunk, HCN channel density as well as axial resistance. In the end, we conclude that it is an interplay between the increase in width and decrease in amplitude of the invading depolarization with increasing apical trunk length what enables Ca²⁺ plateau initiation (Figure 5D).

Regarding the suggested possibilities:

i) By construction the diameter of the apical compartment in the reduced model is kept constant throughout the entire trunk. Furthermore, the diameter of the apical compartment in the model is more difficult to interpret, as it also encompasses the membrane area of oblique dendrites, and it can thus not be directly related to the apical trunk diameter of real neurons.

ii) The density for a subset of channels is not fixed (see Materials and methods); we tested the effect of conductance gradients – thus changing the effective conductance in the last segment – and found no appreciable effect (Figure 4—figure supplements 2 and 3).

iii) Voltage attenuation is indeed smaller with increasing trunk length, but the amplitude in the last segment is still decreasing monotonically with trunk length (Figure 4—figure supplement 1B). Thus, changes in attenuation cannot explain the effect.

d) In subsection “BAC firing is absent in short ttL5 models”, the authors describe how they altered the morphology of the detailed cell model, with the new morphology featuring a shorter apical trunk noted as the most relevant change. However, such a drastic change in morphology should have been followed by model validation (as a sanity check) to ensure basic properties remain physiological. This would also partially control for morphological changes unrelated to the length of the apical trunk. Unfortunately, no validation seems to have taken place (Materials and methods).

We have now carried out the same analysis of intrinsic properties for all model neurons as for the recorded cells. This data is included in Figure 2—figure supplement 3 and shows that basic properties of all models are within the physiological range. We present this now in subsections “Critical frequency ADP is diminished in V2m ttL5 neurons” (detailed model) and “ BAC firing is absent in models of ttL5 neurons with short morphology” (reduced model) in the main text.

3) The paper is unfortunately sometimes unclear in its use of terminology, making it hard for the reader to follow all arguments to their conclusion. In addition, figures could be substantially improved, including more information (i.e. statistical) in a more efficient and effective manner. Besides important details listed in the minor points, two major clarity issues should be thoroughly addressed:

a) One of the core conclusions of this work uses a specific definition of "supralinear". In addition, a different definition is used for the same term ("supralinearities") later on (definition in Figure 2). Neither of these definitions are in line with what is commonly understood by "supralinear" in the field (i.e. a response exceeding the linear extrapolation, as seen in e.g. Branco and Hausser, 2011, Figure 1B). A common, consistent definition should be used – or a new term should be coined for the phenomenon being described.

To reflect exactly the measure used, we have changed the naming of the two groups to “cfADP” and “no cfADP” (instead of no supralinearity) in Figure 2 and Figure 2—figure supplements 1 and 2. We have also changed the relevant text to be in line with the nomenclature used in the field.

b) The term "excitability" is sometimes used an ambiguous fashion. In paragraph two of subsection “Thick-tufted L5 neurons in V2m lack BAC firing”, "excitability" seems to be derived through the propensity of a neuron to produce bursts. However, in subsection “Thick-tufted L5 neuron in V2m lack a critical frequency ADP”, "excitability" seems to be derived through a metric dependent on the integral of the ADP, not propensity to burst. Furthermore, although the text mentions "excitability", the title of Figure 1 makes claims on bursting alone. Similar to the case in (b), a common, consistent definition should be used – or a new term should be coined for the phenomenon being described.

We have now replaced the general term of excitability with more precise ones, like propensity for bursting or dendritic Ca²⁺ electrogenesis. We have however, retained excitability where used in a broad and general term, meaning the ability to respond to input in a regenerative fashion.

4) The homogeneity of the experimental data set is a concern. The recordings were performed from two-well-defined groups identified either by their projection target or genetic label. It would have been good if the conclusions could be further strengthened if further analysis was performed on these cell types. Furthermore, it is merely stated that the experiments are performed in two different projection neurons with no detail about the Glt25d2-Cre mice used, and why these particular cells were targeted in the first place.

The target cell type of our investigation was ttL5, to which both the Glt and the retro-labelled neurons belong. Figure 1—figure supplement 1 shows there is overlap between the two subpopulations, but the extent of this overlap is immaterial as they both belong to the same cell type. We have now clarified that the Glt25d2-cre labelled neurons belong to the ttL5 cell type. An in-depth comparison of Glt and retro-labelled subpopulations is outside of the scope of this paper.

Can the authors please also illustrate which data was obtained under which conditions (ie retrograde labelling VS Glt25d2 mouse; low vs high Ca²⁺ ACSF)

We illustrate the provenance of all low calcium and Glt labelled neurons in Figure 2—figure supplements 1 and 2 and state this now in the respective figure legends.

5) In experiments, the supralinearity or its absence is not always thoroughly established. For example, what happens as you increase the intensity of the stimulus in Layer 1? Or the somatic current pulse? Is the response ever “linear” in either V1 or V2m neurons? I think it's important to first establish the linear regime before being able to classify a response as supralinear.

We acknowledge this use of the term does not follow the convention used in the field, thus we replaced it with “nonlinear” instead. When establishing supralinearity, we have considered the spike output. With this approach, V2m neurons generally responded with 1 spike to the combined stimulus of 1 somatically triggered spike + L1 synaptic input, hence they were termed linear (i.e. 1 + 0 = 1). V1 neurons on the other hand responded with 3 spikes to the combined stimulus of 1 somatically triggered spike + L1 synaptic input, hence they were termed supralinear (1 + 0 ≠ 3).

To address the question of linearity directly at the level of somatic membrane potential, we now carried out additional analysis of our BAC dataset, illustrated in Author response image 1. We have measured the somatic voltage integral in a 50 ms window after the onset of L1 or somatic stimulus. We then compared the integral measured during coincident stimulation to the arithmetic sum of integrals following each stimulus alone for both V1 (top row, n = 21) and V2m (bottom row, n = 18) neurons. To explore both linear and supralinear regimes, the measurements were performed with both low and high L1 stimulus intensities, while somatic stimulation was kept slightly above rheobase in order to consistently evoke exactly one spike. Low L1 stimulus intensities (left column) were tuned to evoke a somatic EPSP of approximately 5 mV in amplitude. In this stimulus regime, all responses summed approximately linearly. High L1 stimulus intensities (right column) were set to evoke no more than one spike at the soma. In this regime, during coincident stimulation a subset of V1 neurons (labelled in red) exhibited BAC firing in the form of larger depolarization and a burst of 3 or more spikes. This is reflected in the voltage integral exceeding the arithmetic sum significantly. The remaining neurons (black) only ever produced at most two spikes, hence were not BAC firing and the voltage integral during coincident stimulus was similar to the arithmetic sum of the two individual stimuli. In V2m, summation was always sublinear, regardless of L1 input intensity.

To summarize, the coincident stimulation only resulted in supralinear summation when BAC firing was evoked in V1. In all other cases summation was either linear or sublinear. We note however that the somatic voltage integral is a convoluted measure affected by different AHP and ADP magnitudes as well as the number of spikes. We thus decided not to include this figure as supplementary material.

Author response image 1

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6) Overall, the manuscript is severely lacking in details associated with the findings.

Recordings were performed from layer 5 neurons with V1 and V2m. There are no details in the manuscript regarding how these brain regions were targeted in all the experiments presented. Please provide details in the Materials and methods as well as illustrations of the targeted brain regions.

Brain areas were targeted based on stereotaxic coordinates for V1 and V2m found in the Franklin and Paxinos, 2007 brain atlas, as described in the Materials and methods section. In addition, we have now substantially expanded Figure 1—figure supplement 1 to show the location of all cells recorded in the cfADP experiments, which represents the bulk of our recordings. Currently we can’t determine the exact location of the cells from the BAC firing experiments due to the Covid-19 lockdown, but the very same targeting approach was used.

Are there other biophysical properties which are different between the layer 5 neurons in V1 and V2m which may explain the difference in excitability? RMP? Rheobase?

This question is answered in major point 1d.

7) The experiments were performed in ACSF with 1.5 or 2 mM CaCl₂. These recordings were pooled together as there was no significant difference between the ADP integral in the different conditions. However, p = 0.122 in V1, and observing the spread of the data points, it appears as though more experiments may indeed separate the data according to ACSF. This is not surprising, considering the authors conclude that V1 has Ca²⁺-dependent supralinearity therefore altering external Ca²⁺ concentration could be expected to alter Ca²⁺-dependent voltage in these cells.

Our statement relates purely to the technical ability to pool these two datasets and we do not deny the quantitative role extracellular Ca²⁺ concentration plays in the magnitude of Ca²⁺ currents. To clarify this, we have reworded the corresponding part and added the exact p values together with the test statistics to the main text. Furthermore, both the magnitude and the similarity of sample sizes across conditions and brain areas further supports the validity of pooling.

8) During coincident input (Figure 1A), was an ADP measured in V1 and not V2 neurons? Otherwise the increased action potentials cannot be labelled as BAC firing as have no proof of calcium-dependence.

We have now carried out the measurements requested and quantified the somatic voltage integral (see response to major point 5). In BAC firing (i.e. bursting) neurons this complex ADP measure shows supralinear summation, but we decided not to add this data to the supplementary material for the following reasons:

The relationship between the timing of the last somatic spike in the burst and the termination of the Ca²⁺ plateau is much more complex than in the cfADP experiments, hence an ADP is a misleading measure and is not directly comparable to the cfADP. Furthermore, the output measure for the experiments in Figure 1A was the nonlinear spike output to coincident stimulation (see response to major point 5) and not the ADP.

V2m “usually” did not have a change in ADP. Please quantify.

ADP values are quantified as shown in Figure 1C and plotted in Figure 2A.

Also, was there a difference in the critical frequency in cells in V1 and V2m (the reported critical frequency is currently combined)?

We updated the text and Figure 1E to display critical frequency data separately for V1 and V2m neurons.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Revisions:

1) "Propensity for bursting was quantified by measuring the maximal burst ratio for each cell (defined as the largest ratio of consecutive ISIs in any current step), as well as the number of spikes in the burst and the AHP immediately following the last spike in the burst."

The "burst ratio" metric is not a widely-used metric to quantify bursting propensity, and is inadequately explained here (high value = high propensity? Why?). Please explain this better.

We thank the reviewer for pointing out that the explanation here was too brief. We devised this novel metric to capture the widest range of bursting behaviours. We have updated paragraph three of subsection “Critical frequency ADP is diminished in V2m ttL5 neurons” and subsection “Data acquisition and analysis”.

2) From rebuttal:

"Regarding the hot zone sizes chosen, 200 µm is the original size in Hay et al., 2011. We scaled this to the ratio of apical trunk length between the long and short morphology to get 100 µm. We added an explanation to lines subsection “BAC firing is absent in models of ttL5 neurons with short morphology”."

"The high density (“hot”) Ca²⁺ channel hotspot zone was shortened to 100 µm to reflect the 50% reduction in apical dendrite length and repositioned around the new apical branch point (350-450 µm from the soma vs 685-885 µm in the long morphology)."

It is assumed here that Ca²⁺ channel hotspot size scales linearly with apical trunk length (assuming that "dendrite" stands in for "trunk" here), which is not necessarily the case. A sub-linear or supra-linear scaling would also need to be checked. The authors appear to have actually done this (new Figure 3—figure supplement 2C/F), but do not refer to it to reinforce their point.

We have indeed tested both sub- and supra-linear scaling of hot zone size and we agree with the reviewer that these are important controls worthy of highlighting. We now refer to them directly and replaced “dendrite” with “trunk”.

3) "Principled alteration of a continuous morphological parameter, such as apical trunk length, is intractable in complex dendritic morphologies."

Considering the fact that the authors are working with single-cell models, this is an inadequate justification. It is true that excessive parameterization of microcircuit models containing multiple interconnected biophysically accurate and morphologically correct reconstructions rapidly devolves into the realm of computational intractability – however, a single cell can be modeled with much greater ease – even if multiple repetitions (i.e. thousands) are required to attain a substantial sample size. If performing the full series of alterations is practically impossible due to some limitation (e.g. insufficiently powerful hardware), then it would also be adequate to show how, for a limited (but at least somewhat representative) subset of alterations, the key results obtained from a reduced morphology accurately reflect the results produced by a detailed reconstruction.

We apologize for having been inaccurate with our phrasing and thank the reviewer for helping us make our reasoning clearer. The reviewer correctly points out that we do not face computational intractability in this instance. Instead, this is a conceptual question in our view. The morphologically detailed model runs on a real biological morphology, which inherently has a variety of co-dependent factors (such the positions of oblique dendrites) that are also known to influence bursting behaviour. While it is indeed possible to arbitrarily alter the morphology, either manually or through generative models such as the TREES toolbox, such a chimera of biological and artificial morphology would make it difficult to interpret the result and may show behaviour that is misleading. It is for this reason that we made the explicit decision when designing our study to focus this investigation on the reduced model, where such morphological alterations are less ambiguous.

We accept that this may be a conceptual point where our opinions differ. We hope to have made our reasoning clearer by rephrasing the relevant sentences.

4) From rebuttal:

"We have now clarified this statement by referring to "the length dependence of Ca²⁺ electrogenesis" instead of excitability in general, and explicitly state the effect on voltage propagation (subsection “Active propagation enhances voltage in long dendrites”, and the corresponding figure legend)."

"Reducing Ih (i.e. gHCN) either in the tuft alone, or both in the trunk and tuft, while affecting voltage propagation, had no effect on the length dependence of Ca²⁺ electrogenesis"

Evidence in support of this claim is shown in Figure 4—figure supplement 3 – however, the claim is insufficiently substantiated. It is true that altering gHCN has an effect on voltage propagation, and as such, the peak voltage is also changed – which explains the change in the y-position of the curves. However, what is not shown is that the change "had no effect on the length dependence of Ca²⁺ electrogenesis" – although a visual inspection shows that all curves appear to exhibit a sudden "jump" in peak voltage (which is the result of Ca²⁺ electrogenesis, as it's absent when Ca²⁺ channels are absent), we cannot rely on mere visual inspection to ascertain whether the length at which this "jump" takes place is the same for every condition. The precise critical length should be reported for each condition, and if there are slight fluctuations, it should be demonstrated that they are not statistically significant (e.g. by repeating the experiment multiple times and taking the average of the critical length plus/minus a standard error, then showing no significant differences via statistical testing).

Our original focus was on determining which conductance is critical to the length dependence, i.e. to the general finding that peak tuft voltage increases with trunk length. As we show, gNa is critical to this length dependence, while gHCN appear to only have a minor modulatory role. We paid less attention to modulatory effects.

We have carried out extra modelling to elaborate the modulatory effect of gHCN. We have now quantified the effect of gHCN on both the voltage propagation and critical (threshold) length. Please note that while gHCN does affect the nominal threshold length somewhat, our main finding, namely that there is length dependence of Ca²⁺ electrogenesis, persists even at zero I_h.

The results of this analysis are now shown in Figure 4—figure supplement 3 CD. We have extended the relevant text in subsection “Active propagation enhances voltage in long dendrites”. As the analysis of threshold length required finer granularity simulations, we have also updated Figure 4B-E as well as Figure 4—figure supplement 3 AB.

Author details

1. Alessandro R Galloni

   1. The Francis Crick Institute, London, United Kingdom
   2. University College London, London, United Kingdom

   Contribution

   Conceptualization, Formal analysis, Investigation, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9602-4274

2. Aeron Laffere

   1. The Francis Crick Institute, London, United Kingdom
   2. Birkbeck College, University of London, London, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Numerical modeling

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8307-0079

3. Ede Rancz

   The Francis Crick Institute, London, United Kingdom

   Contribution

   Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   ede.rancz@crick.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7951-1385

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