An operating principle of the cerebral cortex, and a cellular mechanism for attentional trial-and-error pattern learning and useful classification extraction

A feature of the brains of intelligent animals is the ability to learn to respond to an ensemble of active neuronal inputs with a behaviorally appropriate ensemble of active neuronal outputs. Previously, a hypothesis was proposed on how this mechanism is implemented at the cellular level within the neocortical pyramidal neuron: the apical tuft or perisomatic inputs initiate "guess" neuron firings, while the basal dendrites identify input patterns based on excited synaptic clusters, with the cluster excitation strength adjusted based on reward feedback. This simple mechanism allows neurons to learn to classify their inputs in a surprisingly intelligent manner. Here, we revise and extend this hypothesis. We modify synaptic plasticity rules to align with behavioral time scale synaptic plasticity (BTSP) observed in hippocampal area CA1, making the framework more biophysically and behaviorally plausible. The neurons for the guess firings are selected in a voluntary manner via feedback connections to apical tufts in the neocortical layer 1, leading to dendritic Ca2+ spikes with burst firing, which are postulated to be neural correlates of attentional, aware processing. Once learned, the neuronal input classification is executed without voluntary or conscious control, enabling hierarchical incremental learning of classifications that is effective in our inherently classifiable world. In addition to voluntary, we propose that pyramidal neuron burst firing can be involuntary, also initiated via apical tuft inputs, drawing attention toward important cues such as novelty and noxious stimuli. We classify the excitations of neocortical pyramidal neurons into four categories based on their excitation pathway: attentional versus automatic and voluntary/acquired versus involuntary. Additionally, we hypothesize that dendrites within pyramidal neuron minicolumn bundles are coupled via depolarization cross-induction, enabling minicolumn functions such as the creation of powerful hierarchical "hyperneurons" and the internal representation of the external world. We suggest building blocks to extend the microcircuit theory to network-level processing, which, interestingly, yields variants resembling the artificial neural networks currently in use. On a more speculative note, we conjecture that principles of intelligence in universes governed by certain types of physical laws might resemble ours.

Synergies between synaptic and HCN channel plasticity dictates firing rate homeostasis and mutual information transfer in hippocampal model neuron

Homeostasis is a precondition for any physiological system of any living organism. Nonetheless, models of learning and memory that are based on processes of synaptic plasticity are unstable by nature according to Hebbian rules, and it is not fully clear how homeostasis is maintained during these processes. This is where theoretical and computational frameworks can help in gaining a deeper understanding of the various cellular processes that enable homeostasis in the face of plasticity. A previous simplistic single compartmental model with a single synapse showed that maintaining input/output response homeostasis and stable synaptic learning could be enabled by introducing a linear relationship between synaptic plasticity and HCN conductance plasticity. In this study, we aimed to examine whether this approach could be extended to a more morphologically realistic model that entails multiple synapses and gradients of various VGICs. In doing so, we found that a linear relationship between synaptic plasticity and HCN conductance plasticity was able to maintain input/output response homeostasis in our morphologically realistic model, where the slope of the linear relationship was dependent on baseline HCN conductance and synaptic permeability values. An increase in either baseline HCN conductance or synaptic permeability value led to a decrease in the slope of the linear relationship. We further show that in striking contrast to the single compartment model, here linear relationship was insufficient in maintaining stable synaptic learning despite maintaining input/output response homeostasis. Additionally, we showed that homeostasis of input/output response profiles was at the expense of decreasing the mutual information transfer due to the increase in noise entropy, which could not be fully rescued by optimizing the linear relationship between synaptic and HCN conductance plasticity. Finally, we generated a place cell model based on theta oscillations and show that synaptic plasticity disrupts place cell activity. Whereas synaptic plasticity accompanied by HCN conductance plasticity through linear relationship maintains the stability of place cell activity. Our study establishes potential differences between a single compartmental model and a morphologically realistic model.

Parallel processing in active dendrites during periods of intense spiking activity

A neuron's ability to perform parallel computations throughout its dendritic arbor substantially improves its computational capacity. However, during natural patterns of activity, the degree to which computations remain compartmentalized, especially in neurons with active dendritic trees, is not clear. Here, we examine how the direction of moving objects is computed across the bistratified dendritic arbors of ON-OFF direction-selective ganglion cells (DSGCs) in the mouse retina. We find that although local synaptic signals propagate efficiently throughout their dendritic trees, direction-selective computations in one part of the dendritic arbor have little effect on those being made elsewhere. Independent dendritic processing allows DSGCs to compute the direction of moving objects multiple times as they traverse their receptive fields, enabling them to rapidly detect changes in motion direction on a sub-receptive-field basis. These results demonstrate that the parallel processing capacity of neurons can be maintained even during periods of intense synaptic activity.

Spatially dispersed synapses yield sharply-tuned place cell responses through dendritic spike initiation

KEY POINTS

The generation of dendritic spikes and the consequent sharp tuning of neuronal responses are together attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor. Disparate combinations of channel conductances with distinct configurations of randomly dispersed place field synapses concomitantly yield similar sharp tuning profiles and similar functional maps of several intrinsic properties. Targeted synaptic plasticity converts silent cells to place cells for specific place fields in models with disparate channel combinations that receive dispersed synaptic inputs from multiple place field locations. Dispersed localization of iso-feature synapses is a strong candidate for achieving sharp feature selectivity in neurons across sensory-perceptual systems, with several degrees of freedom in relation to synaptic locations. Quantitative evidence for the possibility that degeneracy (i.e. the ability of disparate structural components to yield similar functional outcomes) could act as a broad framework that effectively accomplishes the twin goals of input-feature encoding and homeostasis of intrinsic properties without cross interferences.

ABSTRACT

A prominent hypothesis spanning several sensory-perceptual systems implicates spatially clustered synapses in the generation of dendritic spikes that mediate sharply-tuned neuronal responses to input features. In this conductance-based morphologically-precise computational study, we tested this hypothesis by systematically analysing the impact of distinct synaptic and channel localization profiles on sharpness of spatial tuning in hippocampal pyramidal neurons. We found that the generation of dendritic spikes, the emergence of an excitatory ramp in somatic voltage responses, the expression of several intrinsic somatodendritic functional maps and sharp tuning of place-cell responses were all attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor of models with disparate channel combinations. Strikingly, the generation and propagation of dendritic spikes, reliant on dendritic sodium channels and N-methyl-d-asparate receptors, mediated the sharpness of spatial tuning achieved with dispersed synaptic localization. To ensure that our results were not artefacts of narrow parametric choices, we confirmed these conclusions with independent multiparametric stochastic search algorithms spanning thousands of unique models for each synaptic localization scenario. Next, employing virtual knockout models, we demonstrated a vital role for dendritically expressed voltage-gated ion channels, especially the transient potassium channels, in maintaining sharpness of place-cell tuning. Importantly, we established that synaptic potentiation targeted to afferents from one specific place field was sufficient to impart place field selectivity even when intrinsically disparate neurons received randomly dispersed afferents from multiple place field locations. Our results provide quantitative evidence for disparate combinations of channel and synaptic localization profiles to concomitantly yield similar tuning and similar intrinsic properties.

Dendritic spikes in hippocampal granule cells are necessary for long-term potentiation at the perforant path synapse

Long-term potentiation (LTP) of synaptic responses is essential for hippocampal memory function. Perforant-path (PP) synapses on hippocampal granule cells (GCs) contribute to the formation of associative memories, which are considered the cellular correlates of memory engrams. However, the mechanisms of LTP at these synapses are not well understood. Due to sparse firing activity and the voltage attenuation in their dendrites, it remains unclear how associative LTP at distal synapses occurs. Here, we show that NMDA receptor-dependent LTP can be induced at PP-GC synapses without backpropagating action potentials (bAPs) in acute rat brain slices. Dendritic recordings reveal substantial attenuation of bAPs as well as local dendritic Na⁺ spike generation during PP-GC input. Inhibition of dendritic Na⁺ spikes impairs LTP induction at PP-GC synapse. These data suggest that dendritic spikes may constitute a key cellular mechanism for memory formation in the dentate gyrus.

Strings on a Violin: Location Dependence of Frequency Tuning in Active Dendrites

Strings on a violin are tuned to generate distinct sound frequencies in a manner that is firmly dependent on finger location along the fingerboard. Sound frequencies emerging from different violins could be very different based on their architecture, the nature of strings and their tuning. Analogously, active neuronal dendrites, dendrites endowed with active channel conductances, are tuned to distinct input frequencies in a manner that is dependent on the dendritic location of the synaptic inputs. Further, disparate channel expression profiles and differences in morphological characteristics could result in dendrites on different neurons of the same subtype tuned to distinct frequency ranges. Alternately, similar location-dependence along dendritic structures could be achieved through disparate combinations of channel profiles and morphological characteristics, leading to degeneracy in active dendritic spectral tuning. Akin to strings on a violin being tuned to different frequencies than those on a viola or a cello, different neuronal subtypes exhibit distinct channel profiles and disparate morphological characteristics endowing each neuronal subtype with unique location-dependent frequency selectivity. Finally, similar to the tunability of musical instruments to elicit distinct location-dependent sounds, neuronal frequency selectivity and its location-dependence are tunable through activity-dependent plasticity of ion channels and morphology. In this morceau, we explore the origins of neuronal frequency selectivity, and survey the literature on the mechanisms behind the emergence of location-dependence in distinct forms of frequency tuning. As a coda to this composition, we present some future directions for this exciting convergence of biophysical mechanisms that endow a neuron with frequency multiplexing capabilities.

Two-Photon Na+ Imaging Reports Somatically Evoked Action Potentials in Rat Olfactory Bulb Mitral and Granule Cell Neurites

Dendrodendritic synaptic interactions are a hallmark of neuronal processing in the vertebrate olfactory bulb. Many classes of olfactory bulb neurons including the principal mitral cells (MCs) and the axonless granule cells (GCs) dispose of highly efficient propagation of action potentials (AP) within their dendrites, from where they can release transmitter onto each other. So far, backpropagation in GC dendrites has been investigated indirectly via Ca²⁺ imaging. Here, we used two-photon Na⁺ imaging to directly report opening of voltage-gated sodium channels due to AP propagation in both cell types. To this end, neurons in acute slices from juvenile rat bulbs were filled with 1 mM SBFI via whole-cell patch-clamp. Calibration of SBFI signals revealed that a change in fluorescence ΔF/F by 10% corresponded to a Δ[Na⁺]_i of ∼22 mM. We then imaged proximal axon segments of MCs during somatically evoked APs (sAP). While single sAPs were detectable in ∼50% of axons, trains of 20 sAPs at 50 Hz always resulted in substantial ΔF/F of ∼15% (∼33 mM Δ[Na⁺]_i). ΔF/F was significantly larger for 80 Hz vs. 50 Hz trains, and decayed with half-durations τ_1/2 ∼0.6 s for both frequencies. In MC lateral dendrites, AP trains yielded small ΔF/F of ∼3% (∼7 mM Δ[Na⁺]_i). In GC apical dendrites and adjacent spines, single sAPs were not detectable. Trains resulted in an average dendritic ΔF/F of 7% (16 mM Δ[Na⁺]_i) with τ_1/2 ∼1 s, similar for 50 and 80 Hz. Na⁺ transients were indistinguishable between large GC spines and their adjacent dendrites. Cell-wise analysis revealed two classes of GCs with the first showing a decrease in ΔF/F along the dendrite with distance from the soma and the second an increase. These classes clustered with morphological parameters. Simulations of Δ[Na⁺]_i replicated these behaviors via negative and positive gradients in Na⁺ current density, assuming faithful AP backpropagation. Such specializations of dendritic excitability might confer specific temporal processing capabilities to bulbar principal cell-GC subnetworks. In conclusion, we show that Na⁺ imaging provides a valuable tool for characterizing AP invasion of MC axons and GC dendrites and spines.

Why Neurons Have Thousands of Synapses, a Theory of Sequence Memory in Neocortex

Pyramidal neurons represent the majority of excitatory neurons in the neocortex. Each pyramidal neuron receives input from thousands of excitatory synapses that are segregated onto dendritic branches. The dendrites themselves are segregated into apical, basal, and proximal integration zones, which have different properties. It is a mystery how pyramidal neurons integrate the input from thousands of synapses, what role the different dendrites play in this integration, and what kind of network behavior this enables in cortical tissue. It has been previously proposed that non-linear properties of dendrites enable cortical neurons to recognize multiple independent patterns. In this paper we extend this idea in multiple ways. First we show that a neuron with several thousand synapses segregated on active dendrites can recognize hundreds of independent patterns of cellular activity even in the presence of large amounts of noise and pattern variation. We then propose a neuron model where patterns detected on proximal dendrites lead to action potentials, defining the classic receptive field of the neuron, and patterns detected on basal and apical dendrites act as predictions by slightly depolarizing the neuron without generating an action potential. By this mechanism, a neuron can predict its activation in hundreds of independent contexts. We then present a network model based on neurons with these properties that learns time-based sequences. The network relies on fast local inhibition to preferentially activate neurons that are slightly depolarized. Through simulation we show that the network scales well and operates robustly over a wide range of parameters as long as the network uses a sparse distributed code of cellular activations. We contrast the properties of the new network model with several other neural network models to illustrate the relative capabilities of each. We conclude that pyramidal neurons with thousands of synapses, active dendrites, and multiple integration zones create a robust and powerful sequence memory. Given the prevalence and similarity of excitatory neurons throughout the neocortex and the importance of sequence memory in inference and behavior, we propose that this form of sequence memory may be a universal property of neocortical tissue.

HCN channels enhance spike phase coherence and regulate the phase of spikes and LFPs in the theta-frequency range

What are the implications for the existence of subthreshold ion channels, their localization profiles, and plasticity on local field potentials (LFPs)? Here, we assessed the role of hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels in altering hippocampal theta-frequency LFPs and the associated spike phase. We presented spatiotemporally randomized, balanced theta-modulated excitatory and inhibitory inputs to somatically aligned, morphologically realistic pyramidal neuron models spread across a cylindrical neuropil. We computed LFPs from seven electrode sites and found that the insertion of an experimentally constrained HCN-conductance gradient into these neurons introduced a location-dependent lead in the LFP phase without significantly altering its amplitude. Further, neurons fired action potentials at a specific theta phase of the LFP, and the insertion of HCN channels introduced large lags in this spike phase and a striking enhancement in neuronal spike-phase coherence. Importantly, graded changes in either HCN conductance or its half-maximal activation voltage resulted in graded changes in LFP and spike phases. Our conclusions on the impact of HCN channels on LFPs and spike phase were invariant to changes in neuropil size, to morphological heterogeneity, to excitatory or inhibitory synaptic scaling, and to shifts in the onset phase of inhibitory inputs. Finally, we selectively abolished the inductive lead in the impedance phase introduced by HCN channels without altering neuronal excitability and found that this inductive phase lead contributed significantly to changes in LFP and spike phase. Our results uncover specific roles for HCN channels and their plasticity in phase-coding schemas and in the formation and dynamic reconfiguration of neuronal cell assemblies.

Electrical responses of three classes of granule cells of the olfactory bulb to synaptic inputs in different dendritic locations

This work consists of a computational study of the electrical responses of three classes of granule cells of the olfactory bulb to synaptic activation in different dendritic locations. The constructed models were based on morphologically detailed compartmental reconstructions of three granule cell classes of the olfactory bulb with active dendrites described by Bhalla and Bower (1993, pp. 1948-1965) and dendritic spine distributions described by Woolf et al. (1991, pp. 1837-1854). The computational studies with the model neurons showed that different quantities of spines have to be activated in each dendritic region to induce an action potential, which always was originated in the active terminal dendrites, independently of the location of the stimuli, and the morphology of the dendritic tree. These model predictions might have important computational implications in the context of olfactory bulb circuits.

Development of modified cable models to simulate accurate neuronal active behaviors

In large network and single three-dimensional (3-D) neuron simulations, high computing speed dictates using reduced cable models to simulate neuronal firing behaviors. However, these models are unwarranted under active conditions and lack accurate representation of dendritic active conductances that greatly shape neuronal firing. Here, realistic 3-D (R3D) models (which contain full anatomical details of dendrites) of spinal motoneurons were systematically compared with their reduced single unbranched cable (SUC, which reduces the dendrites to a single electrically equivalent cable) counterpart under passive and active conditions. The SUC models matched the R3D model's passive properties but failed to match key active properties, especially active behaviors originating from dendrites. For instance, persistent inward currents (PIC) hysteresis, frequency-current (FI) relationship secondary range slope, firing hysteresis, plateau potential partial deactivation, staircase currents, synaptic current transfer ratio, and regional FI relationships were not accurately reproduced by the SUC models. The dendritic morphology oversimplification and lack of dendritic active conductances spatial segregation in the SUC models caused significant underestimation of those behaviors. Next, SUC models were modified by adding key branching features in an attempt to restore their active behaviors. The addition of primary dendritic branching only partially restored some active behaviors, whereas the addition of secondary dendritic branching restored most behaviors. Importantly, the proposed modified models successfully replicated the active properties without sacrificing model simplicity, making them attractive candidates for running R3D single neuron and network simulations with accurate firing behaviors. The present results indicate that using reduced models to examine PIC behaviors in spinal motoneurons is unwarranted.

Dendritic Excitability and Gain Control in Recurrent Cortical Microcircuits

Layer 5 thick tufted pyramidal cells (TTCs) in the neocortex are particularly electrically complex, owing to their highly excitable dendrites. The interplay between dendritic nonlinearities and recurrent cortical microcircuit activity in shaping network response is largely unknown. We simulated detailed conductance-based models of TTCs forming recurrent microcircuits that were interconnected as found experimentally; the network was embedded in a realistic background synaptic activity. TTCs microcircuits significantly amplified brief thalamocortical inputs; this cortical gain was mediated by back-propagation activated N-methyl-d-aspartate depolarizations and dendritic back-propagation-activated Ca²⁺ spike firing, ignited by the coincidence of thalamic-activated somatic spike and local dendritic synaptic inputs, originating from the cortical microcircuit. Surprisingly, dendritic nonlinearities in TTCs microcircuits linearly multiplied thalamic inputs—amplifying them while maintaining input selectivity. Our findings indicate that dendritic nonlinearities are pivotal in controlling the gain and the computational functions of TTCs microcircuits, which serve as a dominant output source for the neocortex.

Active dendrites regulate spectral selectivity in location-dependent spike initiation dynamics of hippocampal model neurons

How does the presence of plastic active dendrites in a pyramidal neuron alter its spike initiation dynamics? To answer this question, we measured the spike-triggered average (STA) from experimentally constrained, conductance-based hippocampal neuronal models of various morphological complexities. We transformed the STA computed from these models to the spectral and the spectrotemporal domains and found that the spike initiation dynamics exhibited temporally localized selectivity to a characteristic frequency. In the presence of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the STA characteristic frequency strongly correlated with the subthreshold resonance frequency in the theta frequency range. Increases in HCN channel density or in input variance increased the STA characteristic frequency and its selectivity strength. In the absence of HCN channels, the STA exhibited weak delta frequency selectivity and the characteristic frequency was related to the repolarization dynamics of the action potentials and the recovery kinetics of sodium channels from inactivation. Comparison of STA obtained with inputs at various dendritic locations revealed that nonspiking and spiking dendrites increased and reduced the spectrotemporal integration window of the STA with increasing distance from the soma as direct consequences of passive filtering and dendritic spike initiation, respectively. Finally, the presence of HCN channels set the STA characteristic frequency in the theta range across the somatodendritic arbor and specific STA measurements were strongly related to equivalent transfer-impedance-related measurements. Our results identify explicit roles for plastic active dendrites in neural coding and strongly recommend a dynamically reconfigurable multi-STA model to characterize location-dependent input feature selectivity in pyramidal neurons.

Mechanisms underlying subunit independence in pyramidal neuron dendrites

Pyramidal neuron (PN) dendrites compartmentalize voltage signals and can generate local spikes, which has led to the proposal that their dendrites act as independent computational subunits within a multilayered processing scheme. However, when a PN is strongly activated, back-propagating action potentials (bAPs) sweeping outward from the soma synchronize dendritic membrane potentials many times per second. How PN dendrites maintain the independence of their voltage-dependent computations, despite these repeated voltage resets, remains unknown. Using a detailed compartmental model of a layer 5 PN, and an improved method for quantifying subunit independence that incorporates a more accurate model of dendritic integration, we first established that the output of each dendrite can be almost perfectly predicted by the intensity and spatial configuration of its own synaptic inputs, and is nearly invariant to the rate of bAP-mediated "cross-talk" from other dendrites over a 100-fold range. Then, through an analysis of conductance, voltage, and current waveforms within the model cell, we identify three biophysical mechanisms that together help make independent dendritic computation possible in a firing neuron, suggesting that a major subtype of neocortical neuron has been optimized for layered, compartmentalized processing under in-vivo-like spiking conditions.

Calcium-based dendritic excitability and its regulation in the deep cerebellar nuclei

The deep cerebellar nuclei (DCN) convey the final output of the cerebellum and are a major site of activity-dependent plasticity. Here, using patch-clamp recording and two-photon calcium imaging in rat brain slices, we demonstrate that DCN dendrites exhibit three hallmarks of active amplification of electrical signals. First, they produce calcium transients with rise times of tens of milliseconds, comparable in amplitude and duration to calcium spikes in other neurons. Second, calcium signal amplitudes are undiminished along the length of dendrites to the farthest distances from the soma. Third, they can generate calcium signals even in the presence of tetrodotoxin, a sodium channel blocker that abolishes somatic action potential initiation. DCN calcium transients do require the action of T-type calcium channels, a common voltage-gated conductance in excitable dendrites. Dendritic calcium influx was evoked by release from hyperpolarization, peaked within tens of milliseconds, and was observed in both transient- and weak-rebound-firing neurons. In a survey across the DCN, transient-burst rebound firing, which was accompanied by the most rapid calcium flux, was more common in lateral nucleus than in interpositus nucleus and was not seen in medial nucleus. Rebound firing and calcium transients were not present in animals shipped 1-3 days before recording, a condition associated with elevated maternal and pup corticosterone and reduced pup body weight. Rebounds could be restored by the protein kinase C activator phorbol 12-myristate-13-acetate. Thus local calcium-based dendritic excitability supports a stage of presomatic amplification that is under regulation by stress and neuromodulatory influence.

Learning mechanism for column formation in the olfactory bulb

Sensory discrimination requires distributed arrays of processing units. In the olfactory bulb, the processing units for odor discrimination are believed to involve dendrodendritic synaptic interactions between mitral and granule cells. There is increasing anatomical evidence that these cells are organized in columns, and that the columns processing a given odor are arranged in widely distributed arrays. Experimental evidence is lacking on the underlying learning mechanisms for how these columns and arrays are formed. To gain insight into these mechanisms, we have used a simplified realistic circuit model to test the hypothesis that distributed connectivity can self-organize through an activity-dependent dendrodendritic synaptic mechanism. The results point to action potentials propagating in the mitral cell lateral dendrites as playing a critical role in this mechanism. The model predicts that columns emerge from the interaction between the local temporal dynamics of the action potentials and the synapses that they activate during dendritic propagation. The results suggest a novel and robust learning mechanism for the development of distributed processing units in a cortical structure.

Translation-invariant orientation tuning in visual "complex" cells could derive from intradendritic computations

first distinguished "simple" from "complex" cells in visual cortex and proposed a processing hierarchy in which rows of LGN cells are pooled to drive oriented simple cell subunits, which are pooled in turn to drive complex cells. Although parsimonious and highly influential, the pure hierarchical model has since been challenged by results indicating that many complex cells receive excitatory monosynaptic input from LGN cells or do not depend on simple cell input. Alternative accounts of complex cell orientation tuning remain scant, however, and the function of monosynaptic LGN contacts onto complex cell dendrites remains unknown. We have used a biophysically detailed compartmental model to investigate whether nonlinear integration of LGN synaptic inputs within the dendrites of individual pyramidal cells could contribute to complex-cell receptive field structure. We show that an isolated cortical neuron with "active" dendrites, driven only by excitatory inputs from overlapping ON- and OFF-center LGN subfields, can produce clear phase-invariant orientation tuning-a hallmark response characteristic of a complex cell. The tuning is shown to depend critically both on the spatial arrangement of LGN synaptic contacts across the complex cell dendritic tree, established by a Hebbian developmental principle, and on the physiological efficacy of excitatory voltage-dependent dendritic ion channels. We conclude that unoriented LGN inputs to a complex cell could contribute in a significant way to its orientation tuning, acting in concert with oriented inputs to the same cell provided by simple cells or other complex cells. As such, our model provides a novel, experimentally testable hypothesis regarding the basis of orientation tuning in the complex cell population, and more generally underscores the potential importance of nonlinear intradendritic subunit processing in cortical neurophysiology.