Three-dimensional morphological data of 112 layer V pyramidal cells (PC) from the rat PFC were obtained from the NeuroMorpho database (http://neuromorpho.org) (see Supplementary Tables S1, S2 for morphological features of basal and apical dendritic trees of all 112 pyramidal cells). These neurons were previously reconstructed in the Smith lab from the brains of adult Long-Evans rats at 2–4 months of age (Bergstrom et al., 2008). No data regarding the size, shape and distribution of spines in the estimation of the dendritic surface area were provided. Images of three of these 112 cells are shown in Figure 1. The images of the remaining cells are available at the abovementioned web site.

The digitized cell reconstructions were acquired in SWC format (Ascoli, 1999). All SWC files were checked for any morphological reconstruction inconsistencies before being converted into the HOC format and loaded into the NEURON neural simulator (Hines and Carnevale, 1997).

For all model cells, unless mentioned otherwise, we assumed a uniform membrane resistance of R_m = 30 kΩ cm² in the soma and the axon. In the basal dendrites, the membrane resistance decreased sigmoidally up to half of the somatic value, according to the function Rm(x)=30−151+e10−x5. Similarly, the membrane resistance in the apical dendrites decreased sigmoidally up to half of the somatic value according to the formula Rm(x)=30−151+e300−x50 (Stuart and Spruston, 1998). A uniform intracellular resistivity R_a = 210Ω cm and a specific membrane capacitance (C_m) of 1.2 μF cm⁻² were used in the soma, axon, apical and basal dendrites. The resting membrane potential was set at −66 mV.

Active mechanisms included two types of Hodgkin–Huxley-type Na⁺ currents (transient: I_Naf; persistent I_Nap;), three voltage-dependent K⁺ currents (I_Kdr; I_A; I_D), a fast Ca²⁺ and voltage-dependent K⁺ current, I_fAHP; a slow Ca²⁺-dependent K⁺ current, I_sAHP; a hyperpolarization-activated non-specific cation current (I_h); a low-voltage activated calcium current I_CaT and three types of Ca²⁺- and voltage-dependent calcium currents (I_caN; I_caR; I_caL). In all cells, the conductance of I_Naf was highest in the axon, and increased in the soma and apical dendrites compared to basal dendrites (González-Burgos and Barrionuevo, 2001). The conductance of all three different K⁺ currents was decreased in the apical dendrites compared to the soma (Korngreen and Sakmann, 2000; Schaefer et al., 2007). Both fast and slow AHP currents were present in the soma and much less in the apical dendrites (Lorenzon and Foehring, 1992). The h-current conductance increased sigmoidally, in the apical tree, reaching a maximum value that was10 times greater than the somatic value (Day et al., 2005; Kole et al., 2006). This increase was not implemented in the basal dendrites (Nevian et al., 2007). The mathematical formalism of the pyramidal neuron model used in this study was based on the model of Sidiropoulou and Poirazi (2012) and can be found in the Supporting Online Material (SOM). The parameter values of all active mechanisms are reported in Supplementary Table S3 in the SOM.

Cell “C3_5” (as referred in the NeuroMorpho database) was selected as the control morphology because it was previously used and extensively validated with respect to passive and active membrane properties as well as apical and basal dendritic responses against experimental data by Sidiropoulou and Poirazi (2012) (see Supplementary Figure S1 in Sidiropoulou and Poirazi, 2012 study). To investigate the effects of dendritic tree variability on firing behavior, we kept the soma of cell “C3_5” and varied the apical and basal trees attached to this soma using the 112 PFC layer V PCs previously described in Section “Morphological Data.” Which apical and/or basal tree(s) were attached depended on the specific experiment (see “Results” section for details). The input resistances of all simulated cells were calculated by measuring the steady-state voltage change in response to a 500 ms hyperpolarizing current pulse (0.1 nA). Previous studies (Washington et al., 2000; Krichmar et al., 2002) have shown that dendritic morphology has a strong effect on input resistance. In order to ensure equivalent depolarization in each model cell and eliminate the influence of the input resistance on the electrophysiological response to current injections, the current injections were scaled by the ratio of the cell's input resistance to that of the control cell (cell “C3_5”) multiplied by a constant factor of 0.35 (i.e., the current 0.35 nA), where cell “C3_5” first spiked). Thus, simulations consisted of depolarizing the PFC pyramidal cell model's soma with a normalized injection current, such that the initial instantaneous depolarization was equivalent for all cells, and recording the membrane potential at the soma.

Morphological parameters were obtained directly from the three-dimensional neuroanatomical description and included the dendritic size (median diameter, total length, volume, and branch number). The MEP for each apical and basal dendritic tree was also derived. To estimate the median diameter, we first calculated the diameter of each cylindrical section of the dendritic tree (basal or apical) of each cell (112 cells in total) and then took the median value. To estimate the total length we summed the length of all sections of each tree (basal or apical) for all cells. To estimate the branch number, we calculated the branch number of each tree (basal or apical) for all cells.

The volume was estimated using the following equation: (1)V=∑i=1Nπ · Li · (Di/2)2 where for every cylindrical section i of each tree, L_i is the length and D_i is the diameter. We estimated MEP as in Van Elburg and van Ooyen (2010). More specifically, to obtain the MEP of a dendritic tree, we first normalized the length l_i of each terminal, intermediate or root section i with respect to its electrotonic length constants λ_i, yielding a dimensionless electrotonic length Λ_i = l_i/λ_i, in which λ_i was defined as: (2)λi=bi · rm2 · ra where b_i was the radius of dendritic section i, and r_m and r_a were constants denoting the specific membrane resistance and the intracellular resistivity, respectively. The MEP of a dendritic tree with N terminal sections was then given by: (3)MEP=1N∑j=1NPj where P_j was the sum of the electrotonic lengths Λ_i of all dendritic sections in the path from the tip of terminal section j to the soma.

We used two types of active mechanism distributions in the basal dendritic trees of cells: (1) uniform (i.e., the conductance of an active mechanism does not depend on the distance from the soma), and (2) non-uniform (distance dependent) (see Table S3). For each distribution of active mechanisms, the firing behaviors of the model cells were classified into two categories: (1) RS, and (2) IB. A model cell was considered as IB if the interspike interval (ISI) of the first two spikes in its spike train was smaller than 20 ms. Otherwise, the cell was considered as RS. For each firing behavior category (RS or IB), we estimated the median diameter, volume, MEP, branch number, and the total length of the basal or apical tree. A non-parametric statistical Mann–Whitney U-test was performed to test if these features were significantly different between the two categories.

In addition to detecting statistical differences, features such as the diameter, total length, MEP, volume, or branch number were used to classify each model cell as an RS or an IB via the use of a probabilistic Bayesian classifier. Probability distributions for the two categories (“training”) were estimated using 80% of the total number of cells (N_RS + N_IB) and the classifier's classification accuracy was measured on the remaining 20% of cells (“testing”). This procedure was repeated 10 times, using different randomly selected training/test sets of the same size. The performance accuracy reported here was evaluated solely on the 10 test sets, namely the 20% of the samples that were not used for training. The performance reported is the average over the 10 different trials. If the sizes of the RS (N_RS) and IB (N_IB) samples were unequal (e.g., N_RS > N_IB), then we set the size of the larger sample equal to the size of the smaller one, and used the 80% of each sample for training and the remaining 20% for testing. Classification performance was assessed using the sensitivity, specificity and accuracy metrics. Given a two class problem with Negative and Positive examples, sensitivity refers to the percentage of true Positives that are correctly identified, whereas specificity refers to the percentage of true Negatives that are correctly identified as such. Accuracy measures the proportion of true Positives and true Negatives correctly identified. The larger the sensitivity, specificity, and accuracy values, the better the classification.

The simulations were run in the NEURON simulation environment (Hines and Carnevale, 1997) and simulations were executed on a parallel cluster (8 core Intel Xeon processors). Data analysis was performed using MATLAB (The MathWorks Inc., Natick, Massachusetts) and was adapted from the Cuntz et al. (2010) work. The source code of the model is available upon request to the corresponding author at poirazi@imbb.forth.gr. The source code of the original model by Sidiropoulou and Poirazi (2012) can be found on ModelDB (accession number: 144089).

A biophysically realistic model of a layer V PFC pyramidal cell was extended to quantitatively investigate the effects of dendritic morphology and distribution of ionic mechanisms (uniform vs. non-uniform) along its basal dendrites on its firing behavior. The model cell was extensively validated in a previous study (Sidiropoulou and Poirazi, 2012) from our group against a wealth of experimental data (Haj-Dahmane and Andrade, 1998, 1999; Fowler et al., 2007; Milojkovic et al., 2007; Nevian et al., 2007; Wang et al., 2008; Sidiropoulou et al., 2009) casting it as a faithful representation of a biologically realistic layer V PFC pyramidal cell. Using this experimentally validated model we systematically varied its basal and apical dendritic trees as well as its ionic mechanism distribution along the basal dendritic trees to parametrically investigate which morphological parameters (diameter, total length, volume, and basal number) and passive properties (MEP) discriminated the cell's firing behavior as an RS or an IB when it was stimulated with a somatic current injection. Our simulation study has quantitatively showed that total length, volume and branch number of the basal dendritic tree are the best morphological parameters to discriminate the cell as an RS or an IB regardless of what is the distribution of ionic mechanisms along the basal trees and irrespectively of the apical tree. Varying combinations of the basal and the apical dendritic tree plexuses and their ionic mechanism distribution produced different cell type percentages indicating that the morphology of apical and basal trees has a strong effect on firing behavior. It should be noted ionic conductance changes are also likely to have an effect on firing patterns. However, the goal of this work was to dissect the effect of morphology from that of biophysics, therefore we chose the use of a model whose ionic mechanisms have been extensively validated against experimental data, to ensure that our analysis is within realistic bounds for these mechanisms. Under such realistic conditions, this work shows in a quantitative manner that specific anatomical features of basal trees in layer V PFC pyramidal neurons are largely determinant of the cells' firing pattern.

The major finding of our simulation study was that the morphological parameters that best discriminated our cells as RS and IB were the total length, volume, and branch number of the basal dendritic tree. This finding was independent of the distribution of ionic mechanisms (uniform vs. non-uniform) along the basal tree (see Table 1 and Figures 2, 4, 5), and insensitive to the use of specific apical trees (Figure 2 and Supplementary Figure S2). The total length of the basal dendritic tree of the RS cells was found to be significantly larger than the total length of the basal dendritic tree of the IB cells. That means that the basal dendritic trees of RS cells are more extensive than the basal trees of IB cells. This result is in line with recent experimental evidence (Chang and Luebke, 2007) and supported by our finding that the branch number in RS model cells is significantly larger than that of IB model cells (Chang and Luebke, 2007). Chang and Luebke (2007) have also reported that the total length and branch number of RS cells in layer V of PFC are greater than that of IB cells in the same layer. On the other hand, another experimental study has shown that IB cells in layer V of the somatosensory neocortex in rats have extensive basal dendritic trees, and their axons tend to ramify in infragranular layers, while RS cells in same layer have smaller dendritic arborizations and their axons ramify to supragranular layers (Chagnac-Amitai and Connors, 1989; Connors and Long, 2004). Yang et al. (1996) showed in layers V-VI of the PFC that RS' proximal, but not basal, dendritic trees bifurcated less profusely than those of IB cells. We think that these variations are region dependent. The basal total length and branch numbers in layer V basal trees of RS pyramidal cells are greater than those of layer V IB pyramidal cells only in the PFC (Chang and Luebke, 2007).

In addition, our simulation study showed that the volume of the basal dendritic trees of RS cells is significantly greater than the volume of IB cells (Figure 4). A larger volume would mean a greater attenuation of the current flowing through the basal tree making the cell less excitable. A larger value of the total length and branch number of the basal tree would also contribute significantly to the reduced cell excitability. In our study, the diameter and the MEP of the basal trees were not the best discriminatory parameters of the cell's firing behavior. This result is contrary to the one reported by Van Elburg and van Ooyen (2010), where MEP was the best discriminatory parameter of the cell's output. One potential explanation for this discrepancy is that dendritic tree size and topological structure was altered without changing the total dendritic length to induce RS or IB firing in that study.

The percentages of RS and IB cells in our simulation study varied greatly, depending on the morphology of the apical tree used and the distribution of ionic mechanisms. In the complex model cell case with a uniform mechanism distribution 70% of the cells were RS, 29% were IB and 1% were quiescent. Use of a simpler apical tree reversed these percentages, resulting in 23% RS vs. 76% IB cells (Figure 2). On average however, across all possible apical trees, the percentages of RS and IB cells were 52% and 48%, respectively, for a uniform mechanism distribution. Changing the distribution into a non-uniform only slightly affected these numbers: 46% IB vs. 54% RS cells. Experimental studies (Yang et al., 1996) have reported similar percentages of IB cells in the layer V PFC (64% IB). The percentages of RS cells though were significantly smaller than ours (19% RS cells in Yang et al., 1996). We think this is due to the fact that in our study we only had two classes of cells (RS and IB), whereas in theirs the cells were classified into four types [RS, IB, ROB, and IM (intermediate)]. Also, in the Yang et al. (1996) although the cells studied were from the prelimbic area of the rat PFC as in ours, nevertheless their sample was an under-representative one of PFC neurons projecting to nucleus accumbens (NAc). In fact almost 80% of their PFC → NAc cells were bursting (IB and ROB) ones.

Several extensions to the basic idea deserve further consideration. One such idea is to thoroughly investigate how dendritic morphology affects the somatic firing behavior of a layer V PFC pyramidal cell when the cell's dendritic trees are driven by excitatory synaptic inputs. For example, nonlinear dendritic integration of spatially segregated inputs or spatially clustered synapses may have a much larger impact on the firing behavior of our model cells. Cortical and subcortical excitatory inputs drive PFC pyramidal cell's apical, proximal and basal dendrites, respectively. Each input may convey different information to the pyramidal cell. An experimental study (Schwindt and Crill, 1999) investigated the mechanisms underlying burst and RS evoked by dendritic depolarization in layer V pyramidal neurons in the rat somatosensory cortex. They reported that small dendritic depolarizations evoked spikes consisting of repetitive bursts of action potentials. Larger dendritic depolarizations evoked regular spikes. Burst firing was due to the interplay of Na⁺ and Ca²⁺ spikes. Somatic depolarizations evoked only RS in almost all recorded cells. A recent simulation study investigated the impact of the cell's dendritic morphology on the ping-pong mechanism of burst firing reported earlier, under either somatic current injection or synaptic stimulation of the apical dendritic tree of a layer V pyramidal cell of a cat visual cortex (Van Elburg and van Ooyen, 2010). They reported that burst firing is heavily dependent on the branching structure of the tree. However, none of these studies investigated explicitly the effects of synaptic stimulation of the basal dendritic trees of layer V pyramidal cells on their firing behavior.

Another idea is to investigate the role of basal and apical dendritic inhibition on the firing behavior of PFC pyramidal cells with varying dendritic morphologies. Recent optogenetic studies in the hippocampus have shown that dendritic inhibition can modulate the pyramidal cell somatic output more efficiently than somatic inhibition (Lovett-Barron et al., 2012). Silencing of dendritic inhibition allows NMDA dendritic spikes to turn the PCs from regular spikers to bursters (Lovett-Barron et al., 2012). A recent experimentally based theoretical study (Gidon and Segev, 2012) offered new insights into how dendritic inhibition controls dendritic excitability and affects the firing behavior of a neuron. They showed that distal “off-path” rather than proximal “on-path” inhibition effectively dampens proximal excitable dendritic hotspots, as it operates as a global threshold mechanism that powerfully controls the neuron's output. Varying the morphological parameters (diameter, total length, volume, MEP, etc.) of the dendritic segments at which inhibition impinges onto may uncover a different role of inhibition, perhaps that of a local as opposed to a global threshold setter.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.