Dendritic morphology and synaptic nonlinearities enhance functional complexity in human cortical neurons

Significance

What makes human cognition distinctive may begin at the level of single neurons. We introduce the Functional Complexity Index (FCI), a deep-learning-based measure that quantifies the input–output complexity of individual cells. Applying FCI to detailed models of human and rat cortical pyramidal neurons, we uncover a pronounced species gap: human neurons exhibit higher complexity. Mechanistically, this is attributable to expanded dendritic surface and richer branching together with greater density and nonlinearity of NMDA-receptor signaling. Layerwise profiles diverge, with neuron complexity peaking in L2/3 in humans, but in L5 in rats, suggesting different allocations of computation across the cortex. FCI provides a principled bridge from cellular morphology and biophysics to computation and cognition, and a general tool for cross-species comparisons.

Abstract

Humans exhibit unique cognitive abilities within the animal kingdom, but the neural mechanisms driving these advanced capabilities remain poorly understood. Human cortical neurons differ from those of other species, such as rodents, in both their morphological and physiological characteristics. Could the distinct properties of human cortical neurons help explain the superior cognitive capabilities of humans? Understanding this relationship requires a measure to quantify how neuronal properties contribute to the functional complexity of single neurons; yet, such a standardized measure is currently missing. Here, we propose the Functional Complexity Index (FCI), a general, deep-learning-based framework for assessing the input–output complexity of neurons. By comparing the FCI of cortical pyramidal neurons across layers in rats and humans, we identified key morpho-electrical factors that underlie neuronal functional complexity. Human cortical pyramidal neurons are significantly more functionally complex than their rat counterparts, primarily due to differences in dendritic membrane area and branching patterns, as well as in the density and nonlinearity of NMDA-mediated synaptic receptors. These findings reveal the structural and biophysical basis for the enhanced functional properties of human cortical neurons, providing a key step toward understanding the underpinnings of our enhanced cognitive capabilities.

What, fundamentally, endows the mammalian brain with its remarkable computational and cognitive capabilities? Beyond macroscale, network-level factors, such as the large number of computational elements, region-to-region connectivity, and regional specialization (1–3), there is mounting evidence that intrinsic single-neuron properties may also play an important role. At the microscale, human-specific transcriptomic programs (4), human-specific cell types (5), and distinctive morphological and biophysical features of human cortical neurons (6) have all been implicated. Numerous studies have indeed systematically cataloged such distinct properties at the cellular level (6–14). Yet a key question remains unresolved: do these cellular-level differences translate into greater computational power at the level of the single neuron, and thereby shape the capabilities of the systems they compose?

Already Ramon y Cajal noticed that human cortical neurons are particularly large and morphologically complex (15). Over the past two decades, numerous studies have systematically compared the dendritic geometry of human cortical and hippocampal neurons with that of other species, particularly rodents. Human cortical neurons are generally characterized by large dendritic trees with elongated branches, especially the terminal branches of the basal dendrites (10), and extensive arborization (6–9, 11–14, 16). The large and extensive dendritic arborization provides a large surface area for receiving and processing synaptic inputs and supports sampling from a diverse array of inputs. Furthermore, large dendritic extensions may lead to electrical decoupling between dendritic regions that give rise to dendritic compartmentalization, which allows distinct regions of the dendritic tree to operate as semi-independent computational subunits (11, 17–20).

In addition to the morphological distinctions between cortical neurons in rats and humans, several biophysical and synaptic attributes differ across species. Specific membrane properties are one such attribute (11, 21, 22); other attributes include the time-dependent dynamics of the synaptic connection (23, 24) and nonlinear dendritic properties (25). Specifically, recent studies report that the conductance and steepness of the voltage dependence of NMDA receptors are larger in human cortical pyramidal neurons compared to rodents (11, 14). Although Testa-Silva et al. (26) reported a higher threshold for NMDA spike initiation in human L2/3 neurons, their simulations attribute this to morphological factors rather than synaptic properties. Furthermore, independent ultrastructural data show that excitatory postsynaptic densities (PSDs) in the human cortex are approximately 2 to 3 times larger than in rodents (27–29), favoring a greater number of NMDA receptors per synapse in humans. These biophysical properties of human dendrites are likely to enhance their computational capabilities, in particular by increasing the number of independent nonlinear dendritic functional subunits (11, 17, 30–38).

What is critically missing to advance the understanding of how various neuronal characteristics contribute to the functional capabilities of the neuron is a systematic measure that quantifies the functional complexity of neurons, particularly human neurons. Several approaches have been used to systematically assess the computational complexity of single neurons. Poirazi and Mel (32) used simplified conceptual neuron models to show that both the increased nonlinearity of dendritic integration and the sheer number of bifurcation branches increase the neuron’s memory capacity. Eyal et al. (11) showed, using detailed compartmental models, that human L2/3 cortical neurons indeed have a larger number of independent nonlinear dendritic subunits compared to rodents. Ujfalussy et al. (39) captured dendritic computations under in vivo-like conditions using models of increasing complexity and used them to characterize input integration of several neuronal types, though only considering the subthreshold activity of the neuron. Recently, Beniaguev et al. (40) used a deep neural network (DNN) model analogue of a rodent’s L5 cortical neuron to assess the I/O complexity of this neuron, demonstrating the critical role of NMDA-dependent synapses in determining how deep the analogue (twin) DNN is. However, a systematic and quantitative exploration of the influence of the full morphological and biophysical range of the neuron’s properties on its I/O computational complexity is not yet available.

To address this gap, we employed a modern machine-learning framework inspired by Beniaguev et al. (40). We introduce the Functional Complexity Index (FCI), a measure for quantifying neuronal functional complexity. The FCI enables identification of the factors contributing to a neuron’s computational complexity and allows systematic comparison of input–output complexity across neuronal types. Using this approach, we uncover fundamental differences in the computational capabilities of cortical neurons between humans and rats, as well as across cortical layers, linking morpho-electrical properties to functional complexity.

Results

Fig. 1 summarizes the steps toward defining the complexity of a given biophysically detailed model of a neuron. First, we generated an I/O dataset for the respective biophysical neuron model by driving it with a large set of synaptic inputs over its dendritic tree (Fig. 1 A and B) and collecting both the subthreshold and suprathreshold voltage output at the soma (40). Next, we constructed a fixed, three-layer temporally convolutional neural network (41) with 128 neurons per hidden layer (Fig. 1B and Methods). We selected this specific architecture based on a sensitivity analysis detailed in Discussion (SI Appendix, Fig. S1). We trained this DNN to closely match both the subthreshold and suprathreshold somatic output of the biophysical neuron model for the same synaptic inputs (Fig. 1C, blue trace and Methods). Note that, although the subthreshold membrane potential was utilized during training as a supervisory signal, the complexity assessment is based specifically on spike prediction accuracy, as action potentials are the primary carriers of neuronal communication.

Fig. 1.

Steps in quantifying the functional complexity of neurons. (A) Raster plot of random input spikes activating excitatory (red) and inhibitory (blue) synapses distributed over the dendritic tree of the modeled neuron. (B) Exemplar human layer 2/3 pyramidal neuron (Left) and schematics of a three-layer temporal convolutional network (TCN, Right) that is trained to replicate as closely as possible both the subthreshold (V) and spiking activity (S) of the biophysical model of the cell shown on the Left. (C) Voltage output (black) of the biophysical model of human L2/3 neuron shown above, and the output of the respective TCN (blue, 3 out of 4 spikes are correctly captured by the TCN). (D) Receiver operator characteristic (ROC) curve of spike prediction by a fixed, three-layer TCN (Methods) of the exemplar human layer 2/3 neuron shown in B (green) and of an exemplar rat layer 2/3 neuron shown in D (orange). The area under each of these (green and orange) curves (AUC) indicates the prediction accuracy of the TCN at 1 ms precision; the larger the AUC the better the prediction. (E) FCI (Eq. 1) of the exemplar L2/3 human (green) and rat (orange) cortical pyramidal neurons. The FCI ranges from 0 to 1, where 1 is the most complex neuron. ****P value smaller than 0.0001.

As apparent in Fig. 1C, some of the spikes produced by the biophysical model were captured by the respective DNN, while others were missed. The overall quality of the performance of the TCN is assessed by the Area Under Curve (AUC) of the ROC curve of spike prediction, with 1 ms temporal resolution (Methods). The more complex the neuron model is, the more spikes are missed or falsely predicted by the respective DNN, and the smaller the AUC is. Namely, the more complex the I/O of the neuron, the less accurate the selected fixed DNN is in replicating its I/O properties.

Fig. 1D shows the ROC curves for exemplar human and rat modeled cells: L2/3 cortical pyramidal neurons from human and rat brains (Fig. 1 E, Bottom, rat in orange and human in green). These two biophysical models had identical passive dendritic properties. The synaptic parameters for these two models respectively match experimental data from human and rat (Methods). The primary source of dendritic nonlinearity in these models is NMDAR-mediated synaptic integration; other active dendritic conductances were excluded from both models due to insufficient experimental constraints for human dendrites (Discussion). For each neuron model, we repeated the training and testing processes of the respective DNN three times, with three different random initial conditions (Methods). The AUC is inversely related, in a nonlinear manner, to the complexity of the neurons’ I/O properties. The more complex the I/O is, the smaller the respective AUC ($\mathrm{A}\mathrm{U}\mathrm{C}=1$ corresponds to a perfect fit and lowest complexity). To obtain a measure that monotonically increases with I/O complexity, we defined the FCI as a monotonically decreasing function of the AUC:

$$FCI=\frac{{\text{log}}_{10}\left(\mathrm{1,000}·\left(1-AUC\right)\right)}{{\text{log}}_{10}\left(\mathrm{1,000}·\left(1-0.9\right)\right)}.$$ [1]

The FCI increases with complexity, and it is approximately linear in the relevant regime, assuming values close to 0 when the AUC is close to 0.999 (an excellent prediction performance for biophysical neuron models), and values close to 1 when the AUC is close to 0.9 (which indicates poor prediction performance for biophysical neuron models, Methods). For the two exemplar neurons shown in Fig. 1D, the FCI is significantly larger for the human L2/3 pyramidal neuron in comparison with the rat L2/3 pyramidal neuron (0.4294 vs. 0.1877, two-sided t test P = 2.221e-05). To visualize what this difference in complexity scores represents in terms of neuronal output, SI Appendix, Fig. S2 displays representative voltage traces for these two models. In the less complex L2/3 neuron of the rat, the DNN accurately predicts spike timing (high AUC, low FCI). In contrast, the high-complexity human L2/3 neuron exhibits numerous missed and falsely predicted spikes, indicating that the DNN fails to capture the I/O relationship of the respective biophysical model (low AUC, high FCI). The FCI difference between these two exemplar neurons was preserved when using structured spatiotemporal input patterns superimposed on background noise (SI Appendix, Fig. S3) and under biologically realistic nonuniform synaptic placement (SI Appendix, Fig. S4), demonstrating that the FCI is robust to variations in the input protocol.

We next computed the FCI for 24 neuron models: 12 rat pyramidal neurons and 12 human pyramidal neurons spanning all six cortical layers (Fig. 2). We used three exemplar cells for each cortical layer (layer 2/3, layer 4, layer 5, and layer 6). To strictly isolate the contributions of dendritic morphology and species-specific synaptic integration, all biophysical models have identical passive dendritic properties, but the synaptic models were different for humans vs. rats (Methods). The modeled neurons are depicted in Fig. 2 A, Bottom, along with their respective FCI (Top). Human pyramidal neurons attain much higher complexity levels than rat pyramidal neurons (Fig. 2B). The average FCI of all 12 human and 12 rat neurons modeled is 0.3803 and 0.2244, respectively. The difference in the FCI between the two species is highly significant (two-sided t test P = 9.796e-12). Within rat pyramidal neurons, layer 5 pyramidal neurons are significantly more complex than layer 2/3 pyramidal neurons (Fig. 2C, green, two-sided t test P = 0.048). Interestingly, this is not the case in humans, where layer 2/3 pyramidal neurons are significantly more complex both compared to layer 4 (two-sided t test P = 0.013) and layer 5 (two-sided t test P = 0.010) pyramidal neurons (Fig. 2C, orange). It is interesting to note that in the human cortex, layer 2/3 is expanded relative to layer 5 (6), and contains several distinct cell types (5).

Fig. 2.

Human cortical pyramidal neurons display enhanced functional complexity relative to rat cortical pyramidal neurons. (A) Top: FCI scores for all 24 (12 rat in orange and 12 human in green) modeled neurons depicted alongside with their respective morphology (Bottom); Methods and SI Appendix, Table S1 for morphological details. (B) Overall comparison of the FCI between the two species. (C) Comparison of FCI per cortical layer for rat neurons (orange) and human neurons (green). *P value smaller than 0.05, and ****P value smaller than 0.0001.

In summary, Fig. 2 demonstrates that our index for assessing the functional complexity of neurons is sensitive enough to capture variation between cortical pyramidal neurons across cortical layers and across species. This shows that human cortical pyramidal neurons exhibit greater functional complexity than rat cortical pyramidal neurons.

What are the specific factors that contribute to the greater functional complexity of human neurons? To answer this question, we first examined whether morphological properties per se are responsible for the greater complexity of human cortical pyramidal neurons. To that end, we repeated our FCI assessment process, assigning rat type synapses to all morphologies, both human and rat (Methods). Compared to Fig. 2, where we used rat synapses for rat models and human synapses for human models, here the difference between species is less pronounced, although it remains statistically significant, with human neurons exhibiting higher FCI values on average (SI Appendix, Fig. S5, two-sided t test P = 0.022). Crucially, this result demonstrates that the increased functional complexity of human neurons is not solely driven by specific synaptic properties; human morphology alone supports significantly higher FCI than rat morphology. Furthermore, to assess whether the exclusion of active dendritic conductances substantially affects our conclusions, we introduced a full complement of active conductances (Including Na⁺, Ca²⁺, Ih, and others; (42)) into the rat L5 model. Active dendrites significantly increased the FCI, confirming that the framework captures the computational contribution of dendritic nonlinearities beyond NMDA receptors (SI Appendix, Fig. S6). Notably, the human L5 model with only passive dendrites still exhibited a significantly higher FCI than the rat L5 model with active dendrites, underscoring the dominance of morphological factors and NMDAR-mediated nonlinearities in shaping the species gap. Adding Ih alone to the passive-dendrite rat L5 model yielded no significant change in FCI (SI Appendix, Fig. S7). These results imply that particular morphological features make a substantial contribution to the enhanced complexity of human neurons, in addition to the important role of synaptic properties examined later (Fig. 4) and of active dendritic conductances, whose contribution in human neurons remains an open question due to insufficient experimental constraints (Discussion).

Fig. 4.

Correspondence between various synaptic features and the FCI. (A) Modeled human layer 2/3 pyramidal neuron; the oblique branch receiving excitatory synapses is depicted in red with respective red electrode at left. (B–E) Local dendritic voltage responses in the activated oblique branch of the modeled cells shown in A for different synaptic types; when increasing the numbers of simultaneously activated synapses (from 5 synapses to 400 synapses). (B) Rat synapses were used (orange). (C) Rat synapses with the larger γ factor of human for the NMDA conductance (hybrid A, pink). (D) Human synapses with smaller γ factor of rat (hybrid B, blue). (E) Human synapses were used (green). (F–I) as in B–E but showing the respective soma voltage response. (J) Somatic EPSP amplitude as a function of the number of activated dendritic synapses, for the four cases shown in F–I. (K) FCI distribution for rat morphologies, for the four different synapse types/cases (colors as in B–I, Methods). (L) FCI distribution for human morphologies, given different synapse types. (M) FCI distribution for all (human and rat) 24 morphologies, given different synapse types. *P value smaller than 0.05, and ****P value smaller than 0.0001.

We next extracted 58 different morphological features for the modeled neurons (Methods). In particular, we characterized morphological features related to trunk branches (branches that emerge from the soma and end at a bifurcation) as well as features related to termination branches (branches that start at a bifurcation and end at a dendritic tip), and bifurcation branches (all other branches, i.e., branches that start and end at bifurcations), see Fig. 3A for a graphical demonstration. In order to study which morphological features best predict the FCI, we computed the correlation between the FCI and each of the 58 features measured (Fig. 3 B–E and I). Fig. 3I presents a histogram of the $R^2$ correlation values between the FCI and individual features. It is evident that only a few specific features explain a substantial portion of the FCI’s variance. The single feature best predicting the FCI was the entire area of the dendritic tree (total dendritic area), with $R^2=0.74$ (Fig. 3B). The total length of bifurcating branches (yellow branches in Fig. 3A) achieved an $R^2=0.45$ (Fig. 3C), whereas longest bifurcation branch, which is closely related to the maximal path distance of the tree from soma to tip, achieved an $R^2=0.44$ (Fig. 3D). Surprisingly, the feature reflecting the number of bifurcation branches, achieved a modest $R^2$ of $0.29$ (Fig. 3E).

Fig. 3.

Correspondence between morphological features and the FCI. (A) Human layer 2/3 dendritic tree colored by three dendritic subtrees (trunk, bifurcation, and termination). (B–E) Correlation between single morphological features and FCI; green and orange circles for human and rat neurons respectively. (F) Correlations between FCI with pairs of morphological features (the diagonal refers to the correlation with the single feature). Yellow square highlights the largest correlation. (G) Correlations between FCI and triplets of morphological features. Each pair depicted already incorporates the total dendritic area. (H) FCI correlation with quadruplets of morphological features; each case includes both the total dendritic area and the longest bifurcation branch. (I) Distribution of FCI correlation with single morphological features. (J) Distribution of FCI correlation with a pair of morphological features. (K) Maximal correlation achieved using increasing numbers of morphological features; the cases corresponding to B, F, G, and H are marked above the graph.

Next, we asked what is the minimum number of combined features that most closely predict the FCI. Fig. 3J displays a histogram of the $R^2$ values showing how well pairs of features account for the complexity index. This analysis reveals that pairs of features, when considered together, generally provide a greater explanation of the complexity variance than individual features. Fig. 3F illustrates the $R^2$ values explained by different feature pairs. Notably, the most predictive pairs consistently included total dendritic area. The most predictive pair also included longest bifurcation branch, that together with total dendritic area achieved $R^2$ of 0.81. In Fig. 3G, we correlated the FCI with triplets of features, each including total dendritic area. Again, all triplets best predicting the FCI always included longest bifurcation branch, with the best triplet attaining a value of $R^2=0.85$ (total dendritic area, longest bifurcation branch, and longest trunk branch). Finally, in Fig. 3H, we correlated the FCI with quadruples of features, containing both total dendritic area and longest bifurcation branch. The best predicting quadruple achieved a value of $R^2=0.88$.

Overall, the best third and fourth features were related to either apical or basal trunk branches and terminal branches. Importantly, the coefficients of the third and fourth features were negative, suggesting that the less dendritic length is invested in trunk branches and terminal branches, the more complex the neuron is functionally. In other words, the greater the dendritic length allocated to bifurcation branches, the more functionally complex the neuron becomes (Discussion). Using additional features beyond this core group of four features marginally contributes to the variance explained (Fig. 3K). Notably, the full functional complexity can be entirely explained using a total of 23 features (Fig. 3 K, Top point at Right).

In Fig. 4, we explore the impact of synaptic properties that, as experimental data suggest, contribute to the increased complexity of human pyramidal cells compared to rat pyramidal cells (11, 14). To that end, we repeated our FCI assessment process, only now assigning each morphology with either one of four different synaptic types: rat synapses, human synapses, and two hybrid variants that attempt to disentangle the specific contributions of synaptic conductance of AMPA + NMDA channels, and value of the $\gamma$ factor that reflects the steepness of the NMDA nonlinearity (Eq. 8) in Methods). The hybrid A synaptic type has the rat type synapse parameters (including rat conductance values) together with the larger human $\gamma$ factor, whereas the hybrid B synaptic type has the human type synapse parameters (including human conductance values), together with the smaller rat $\gamma$ factor (Methods and SI Appendix, Table S2).

In order to investigate the impact of the NMDA receptor nonlinearity across various synaptic types, we progressively activated an increasing number of synapses along an oblique dendritic branch of a representative human layer 2/3 neuron model (Fig. 4A). The resulting local dendritic and soma responses are illustrated in Fig. 4 B–E and F–I, respectively. Comparing the curves in Fig. 4 B and C to those in Fig. 4 D and E, it is evident that the NMDA-based response in the later cases is more pronounced.

This is summarized in Fig. 4J which depicts the peak somatic voltage as a function of the number of activated synapses on a single oblique branch of a human L2/3 model shown in Fig. 4A, for each of the 4 synapse types used. The rat and hybrid A type synapses exhibited linear responses with fewer than 50 simultaneous synaptic activations (inset shows that NMDA saturation for these synapse types occurs only at ~250 activated synapses). However, with the same number of 50 activated synapses, both human and hybrid B type synapses demonstrated a significant nonlinear increase in somatic voltage response, which results from the generation of highly nonlinear NMDA spike in the activated dendrite. Notably, the human synapse type exhibited a critical transition to steep nonlinearity around the activation of 35 synapses, shifting from sublinear to supralinear summation of synaptic inputs.

Indeed, models with human type synapses were significantly functionally more complex than models with rat type synapses, across rat morphologies (Fig. 4K), across human morphologies (Fig. 4L) and across all morphologies combined (Fig. 4M). However, models with either hybrid A or hybrid B synaptic types were only slightly more complex than models with rat synaptic types. These findings are consistent with the results shown in Fig. 4J, highlighting the impact of the more nonlinear NMDA receptors on the functional complexity of human neurons under these specific biophysical assumptions.

We conclude that, if human NMDA receptor–mediated conductance is indeed larger and exhibits steeper nonlinearities, as modeled here, these properties further amplify the difference in functional complexity between the two species.

Discussion

Since the seminal work of Rall (43–45), detailed biophysical models of single neurons have been developed across brain regions and species (11, 14, 42, 46, 47), capturing the substantial morphological and physiological diversity of cortical neurons. Yet a key gap remains: the lack of a systematic, quantitative measure that links this diversity to the complexity of their input/output (I/O) relationships, enabling comparisons across neuron types, layers, and species, and bridging single-neuron computation to network function.

This gap is particularly critical in the context of human evolution: although human cortical neurons exhibit distinct structural and biophysical properties compared to those of rodents, it remains unclear whether these differences confer greater computational power at the level of the single neuron. To address this, we developed the FCI, a deep learning-based framework for quantifying neuronal I/O complexity. Using this approach, we show that human cortical pyramidal neurons are significantly more functionally complex than their rat counterparts; a difference that arises primarily from morphological features and is further amplified by nonlinear synaptic dynamics.

The FCI measure developed here is based on how well a fixed-sized DNN can approximate the I/O transformation of a detailed biophysical neuron model. Unlike previous approaches based on abstract neuronal models or subthreshold dynamics (32, 39), the FCI directly captures both suprathreshold and subthreshold behavior and provides a scalable framework for comparing neurons across cell types and species. This approach builds on our recent work using DNNs to approximate neuronal I/O functions (40) and aligns with emerging concepts in machine learning across diverse fields, including statistical learning theory, physics, and atmospheric sciences, where the “learnability” of a system by a constrained neural network serves as a proxy for its intrinsic complexity (48–53).

The FCI is a robust measure that enables a systematic comparison of neurons, revealing how their morphology and biophysics shape their functional complexity. However, this measure faces several challenges, notably the computational cost of generating large I/O datasets from the biophysical model and training the respective neural networks, especially when varying biophysical parameters and morphology of neurons. Additionally, the use of output normalization (Methods) focuses the analysis on a particular regime of the model’s I/O space. Moreover, the FCI depends on specific hyperparameters and DNN architecture: overly expressive architectures may compress complexity differences, whereas underexpressive ones may inflate them. Careful architecture selection is therefore crucial to ensure a meaningful dynamic range.

To address these issues, we used a three-layer temporally convolutional network (TCN), an architecture shown to successfully approximate biophysically detailed neuron models (40). Our sensitivity analysis across depths 1 through 9 (SI Appendix, Fig. S1A) confirmed that the L2/3 species (human vs. rat) difference in complexity is consistently present across all tested depths. We selected depth 3 because it avoids both the floor effect of overly shallow networks, which fail to learn basic integration properties, and the ceiling effect of deeper networks, where performance saturates and compresses FCI differences, while also being the most computationally parsimonious architecture within this stable regime. Furthermore, we validated the robustness of our approach by testing a broad set of exemplar neurons (rat and human, layers 2/3, 4, 5, and 6) with varying network depths (depths 2 through 7) and found that complexity rankings remained consistent (SI Appendix, Fig. S1B). Beyond architecture choice, the FCI was also robust to variations in the input protocol, including structured spatiotemporal input patterns [SI Appendix, Fig. S3, (39)] and biologically realistic nonuniform synaptic placement [SI Appendix, Fig. S4, (54)].

Our analysis identifies dendritic morphology as a key determinant of neuronal complexity. Human cortical pyramidal neurons exhibit larger dendritic surface area, greater dendritic extent, and more elaborate branching patterns, all of which correlate strongly with increased FCI. These features likely enhance compartmentalization of dendritic processing, enabling semi-independent integration across dendritic subregions and thereby increasing computational capacity (11, 17–20, 55, 56). Notably, our results suggest that complexity is not determined solely by the number of branches, but rather by the interaction between dendritic size and branching structure, extending earlier work on dendritic subunits (11, 32).

In addition to morphology, synaptic properties further shape neuronal I/O complexity. In our models, we assumed that maximal NMDA conductance in human synapses is approximately threefold higher than in rats, consistent with evidence that human excitatory synapses exhibit larger spine heads and 2 to 3 times larger PSDs (27–29, 57, 58), likely reflecting increased numbers of NMDA receptors (11, 14). We also assumed a steeper NMDA voltage dependence (γ factor) in humans, following Eyal et al. (11) (SI Appendix, Table S2). Notably, Testa-Silva et al. (26) reported a reduced capacity to evoke NMDA spikes in human neurons compared to rodents; however, their analysis suggests that this difference arises primarily from morphological factors rather than synaptic properties.

We therefore conclude that the relevant synaptic effect is not a simple increase in human EPSP amplitude per se, but rather the promotion of nonlinear synaptic integration. Specifically, the stronger voltage-dependent NMDA conductance, together with the steeper NMDA voltage dependence, enables stronger combinatorial nonlinear interactions among coactive excitatory synapses in human neurons, resulting in more complex I/O transformations and higher FCI (Fig. 4), consistent with prior work linking synaptic nonlinearity to computational capacity (30, 31, 36, 40, 59–62).

From an evolutionary perspective, our results suggest that increased single-neuron complexity may coevolve with network architecture. In humans, we find that layer 2/3 pyramidal neurons exhibit higher functional complexity than neurons in other layers, in contrast to rats where layer 5 neurons dominate. Interestingly, this shift parallels the expansion of layer 2/3 in the human cortex (6) and may reflect an increased role for these neurons in cortical computation, potentially associated with specialized functional properties (5).

Although our models excluded active dendritic conductances due to limited experimental constraints, particularly in human dendrites, supplementary simulations incorporating Na⁺, Ca²⁺, and Ih conductances into the rat L5 model significantly increased FCI, confirming that the framework captures dendritic nonlinear contributions beyond NMDA-dependent mechanisms (SI Appendix, Fig. S6). Notably, the human L5 model with passive dendrites still exhibited higher FCI than the rat model with active dendrites, underscoring the dominant role of morphology and NMDA-mediated nonlinearities in the species difference. Adding Ih alone had no significant effect (SI Appendix, Fig. S7), although it may contribute indirectly in the full nonlinear model. Despite reported differences in ion channel properties in human neurons (25, 63), a comprehensive characterization of dendritic conductances is still lacking, leaving open the question of whether active conductances exert even stronger effects on FCI in human neurons.

Beyond these methodological considerations, several biological directions warrant further investigation, including the role of abundant dendritic spines in shaping the I/O transformation in human cortical neurons (57, 64, 65), their unique axonal excitability (66), and local connectivity patterns (8, 67–69). Extending our framework to additional neuronal types (e.g., CA1/CA3 pyramidal neurons, cerebellar Purkinje cells) and species, including nonhuman primates, will also be important.

Applying the FCI framework in vivo requires datasets that link synaptic inputs to somatic output with high temporal resolution. Large-scale efforts such as MICrONS (70) and OpenScope (71), combining calcium imaging, spine-level measurements, and connectomics, provide promising testbeds. Training DNNs on such data could enable direct estimation of neuronal I/O complexity in vivo, separating computational signal from biological noise. Complementary approaches, such as whole-cell voltage imaging, may further capture single-neuron complexity under naturalistic conditions.

Methods

Neuron Morphologies.

Morphologies of 24 3D-reconstructed cortical pyramidal neurons were used in this study, 12 rat pyramidal cells and 12 human pyramidal cells. Three neurons were modeled from each of the following layers: layer 2/3, layer 4, layer 5, layer 6. Rat neurons were taken from (42, 46, 72) and human neurons from (9, 47); we confirm that these human samples were fully deidentified prior to their use in this study. To consider the variability in the reconstruction quality, the diameters of all morphologies were edited such that no diameter would be smaller than 0.3 μm. A complete description of the morphologies used is provided in SI Appendix, Table S1.

Neuron Models.

We constructed a detailed biophysical model (44) for each morphology. All models have specific membrane capacitance Cm = 1 µF/cm², specific axial resistance $R_a=150 \mathrm{\Omega }cm$ and specific membrane resistance $R_m=20,000 \mathrm{\Omega }{\mathrm{cm}}^2$. All models were equipped with spike-generating voltage-dependent Na⁺ and K⁺ ion channels in the soma and axon. Channel kinetics were as in Hay et at. (42). The maximal conductance of the active channels of all models was fit to match the experimental F-I curve as in Hay et al. (42). The maximal conductance of the active channels in the soma and axon of all morphologies were normalized by the electrical load that the dendritic tree imposes on the soma (${\rho }_{\mathit{soma}}$) and on the axon (${\rho }_{\mathit{axon}}$), using the rho scaling method (73). By this, the conductance of each somatic or axonal active channel for each morphology was set as follows:

$$\begin{array}{c}{\overline{g}}_{morph,soma}={\overline{g}}_{hay,soma}·\frac{{\rho }_{morph,soma}}{{\rho }_{hay,soma}},{\overline{g}}_{morph,axon}={\overline{g}}_{hay,soma}·\frac{{\rho }_{morph,axon}}{{\rho }_{hay,axon}},\hfill \end{array}$$ [2]

where $\rho$ is the dendrite-to-soma or dendrite-to-axon conductance ratio defined as:

$${\rho }_{morph,soma}=\frac{g_{in,dendrite}}{g_{in,soma}},{\rho }_{morph,axon}=\frac{g_{in,dendrite}}{g_{in,axon}}.$$ [3]

Synapse Models.

For each neuron model, one excitatory AMPA + NMDA-based synapse and one inhibitory GABA_A-based synapse were placed on every $1\mu m$ dendritic length. The synaptic current was modeled as:

$$I_{\mathit{syn}}=g_{\mathit{syn}}\left(t,V\right)·(V-E_{\mathit{syn}}),$$ [4]

where $E_{\mathit{syn}}$ is the reversal potential for the synaptic current and $g_{\mathit{syn}}$ is the synaptic conductance modeled using two-state kinetic scheme:

$$\begin{array}{c}{g}_{\mathit{syn}}\left(t,V\right)=B·\overline{g}·N·(\text{exp}(-t/{\tau }_d)-\text{exp}(-t/{\tau }_r)).\hfill \end{array}$$ [5]

Here $\overline{g}$ is the peak conductance and $N$ is a normalization factor given by:

$$N=\frac{1}{\text{exp}(-t_{\mathit{peak}}/{\tau }_d)-\text{exp}(-t_{\mathit{peak}}/{\tau }_r))},$$ [6]

where $t_{\mathit{peak}}$, time to peak of the conductance, is

$$t_{\mathit{peak}}=\frac{{\tau }_{\mathit{rise}}·{\tau }_{\mathit{decay}}}{{\tau }_{\mathit{decay}}-{\tau }_{\mathit{rise}}}·\text{log}(\frac{{\tau }_{\mathit{decay}}}{{\tau }_{\mathit{rise}}}).$$ [7]

Where τ_rise and τ_decay are the rise time and decay time constants. For AMPA and GABA_A conductances, $B$ = 1 (voltage-independent conductance).

For the voltage-dependent NMDA conductance B was defined as in Jahr and Stevens (74):

$$B=\frac{1}{1+\text{exp}\left(-\gamma ·V\right)·\left[M{g}^{2+}\right]·n}.$$ [8]

$[M{g}^{2+}$] was set to $1\mathrm{m}\mathrm{M}$, n was 1/3.57 mM. The kinetics (synaptic rise and decay time constants, etc.) and conductances of rat excitatory synapses were taken from Markram et al. (46), whereas those of human excitatory synapses were taken from Eyal et al. (11). Hybrid A excitatory synapses combined rat AMPA/NMDA conductance values with the human NMDA γ factor; hybrid B excitatory synapses combined human AMPA/NMDA conductance values with the rat NMDA γ factor. The kinetics and conductances of inhibitory GABA_A synapses were taken from Markram et al. (46) and kept identical across all conditions. A full description of the synaptic properties is provided in SI Appendix, Table S2.

Normalizing for the Input Firing Rates.

In order to avoid the possible confounding effect of the different firing rates of different models on the FCI, we carefully selected the rate of the input excitatory (E) as well as inhibitory (I) synapses such that the average output firing rate of all models will be 1 sp/s. For each model, we chose 10 valid input E/I firing rate combinations that resulted in an average output firing rate that is within 0.01 sp/s around the chosen 1 sp/s mark. Every valid input firing rate combination spans a range of 0.1 sp/s difference in firing rate both in excitation and in inhibition (for example, a valid input firing rate combination of a specific model might be 1 to 1.1 sp/s in excitation and 2 to 2.1 sp/s in inhibition, which amounts to an average output firing rate of 1.005 sp/s). To find valid input firing rate combinations, we exhaustively searched the input firing rate space between 0 sp/s to 20 sp/s in both excitation and inhibition (SI Appendix, Fig. S8). The resulting ratios of inhibitory to excitatory conductance changes (ΔG_i: ΔG_e) fell within the balanced in vivo regime reported by Haider et al. (75).

Simulations and Resulting Datasets.

In order to fit DNN models per simulated neuron, we followed the study of Beniaguev et al. (40). First, we generated a simulation dataset for each modeled neuron. In each simulation, the modeled neuron was stimulated by random excitatory and inhibitory synaptic input (one synapse per $1 \mathrm{\mu }\mathrm{m}$ dendritic length) distributed randomly over the dendritic surface of the modeled neuron for a duration of 10 s. As explained above, in each simulation we used an input regime that results in an output firing rate of ~1 sp/s. Each presynaptic spike train was sampled from a Poisson process with a smoothed piecewise constant instantaneous firing rate. The Gaussian smoothing sigma, as well as the time window of constant rate before smoothing, were independently resampled for each 10 s simulation from the range of 10 ms to 1,000 ms. This was the case, as opposed to choosing a constant firing rate, to create additional temporal variations in the data, in order to increase the applicability of the results to a wide range of potential input regimes. This stochastic input paradigm follows system identification principles: random inputs act as a broad-spectrum probe that stimulates the neuron across a wide range of its input space, enabling a comprehensive mapping of its multidimensional transfer function. Control simulations using structured spatiotemporal inputs superimposed on background noise (39) confirmed that the resulting FCI values are not dependent on the specific input statistics (SI Appendix, Fig. S3). For each neuron model, we created a dataset consisting of 12,000 train simulations of 10 s each, equivalent to ~1.4 d of neural data (see below). Simulations were performed using NEURON software (76) and were run in parallel on a CPU cluster.

Fitting DNNs to the I/O of Neuron Models.

We followed Beniaguev et al. (40) to train DNNs based on the neuron model simulation datasets. The DNN was fed as an input with the same presynaptic spike as the biophysical model did. The respective DNN was expected to produce voltage output that matches as closely as possible both the subthreshold and the spiking activity at the soma. In this study, we predefined a fixed-size TCN with 3 layers and a width of 128 units per layer for all neuron models (40, 41) with 3 different random initializations per modeled neuron. Each network was trained for approximately 4 d of neural data, corresponding to roughly 3 full epochs over the entire training dataset. The resulting computational cost to fit the DNNs and estimate the FCI for a single neuron model was approximately 8.7 single GPU days. Consequently, the total number of single GPU years needed to fit all DNNs and estimate all FCIs throughout the entire study was ∼2.3 y.

Sensitivity Analysis and Architecture Selection.

To validate our choice of DNN architecture, we performed two types of sensitivity analyses (SI Appendix, Fig. S1). First, to assess the dynamic range and potential saturation of the FCI, we trained networks of varying depths (1, 2, 3, 5, 7, and 9 layers) on two representative models (Rat L2/3 and Human L2/3). This revealed that performance improvements plateau beyond 3-5 layers (SI Appendix, Fig. S1A). Second, to ensure that our comparative results were not artifacts of a specific depth, we reevaluated eight exemplar models (spanning all layers and both species) using 2-layer, 3-layer, and 7-layer networks. This confirmed that the relative complexity ranking is robust to architectural changes (SI Appendix, Fig. S1B).

DNN Performance.

We divided our 12,000 simulations to a training set of 10,000 simulations, a validation set of 1,000 simulations and a test set of 1,000 simulations. We fitted all DNN models on the training set and calculated the DNN performance on the unseen test set. The validation set was used for modeling decisions, hyperparameter tuning, and snapshot selection during the training process (early stopping). The DNN’s task was the binary classification task of predicting whether the neuron emitted a spike in all 1 ms time points. While the network was trained on both subthreshold and suprathreshold voltage data to ensure robust internal representations (40), the final evaluation measure was restricted to spike prediction. We prioritized this measure because the timing of action potentials represents the fundamental output code transmitted to downstream neurons. This was evaluated using the ROC of binary spike prediction. The performance was finally quantified using the AUC of the ROC. Additional details are found in Beniaguev et al. (40).

FCI.

We defined the FCI of a neuron model as inversely proportional to the performance of its respective DNN (Fig. 1 and Eq. 1). Specifically, the performance of the DNN model was quantified using the AUC measure. We found that typical values of AUC of such models ranged between 0.9 to 0.999 (40). In other words, an $AUC=0.9$ indicates a very poor performance of the DNN. Therefore, the $\mathit{FCI}$ of such cases was set to 1 (Eq. 1). For a great performance where the $AUC=0.999$, the FCI was set to $0$ (see SI Appendix, Fig. S9 for the full relationship between the FCI and the AUC).

Morphological Features.

We used NeuroM (77) to calculate the values of various morphological features for each of our modeled morphologies. The following features were considered: total dendritic length, total dendritic area, number of forking points, number of bifurcation points (a forking point of exactly two branches), number of leaves, max Radial distance, max branch order, mean sibling ratio, sum/mean/longest bifurcation branches, sum/mean/longest terminal branches, and sum/mean/longest trunk branches. Each of these features was calculated separately for the basal and the apical trees of each morphology. Additionally, we used three features related to the entropy of the topological representation of the dendritic tree (78), namely, the sum/mean/max entropy of the morphology. In total, we had 58 morphological features.

Correlation Between Morphological Features and Complexity.

To predict the value of the FCI from the neuron’s morphological features, we used linear regression to fit the following equation:

$$FCI(m)={\displaystyle \sum _{i=1}^n}{\alpha }_i{f}_i(m)+\beta ,$$ [9]

where $f_i(m)$ is the $i$-th feature computed for a given morphology, $m$. ${\alpha }_i$ is the fitted coefficient for the $i$-th feature; $\beta$ is a fitting bias and $n$ is the number of features used for fitting. In this study, we computed (Eq. 9) with $n$ ranging from $1$ to $4$.

Given a linear regression curve, we calculate the $R^2$ to quantify how well this curve fits the data. The results for different numbers of features ($n$) are provided in Fig. 3. In Fig. 3 F–H, the yellow square indicates the highest correlation.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Morphologies and neuron models data have been deposited on GitHub (79). All other data are included in the manuscript and/or SI Appendix.