Asymmetric electrotonic coupling between the soma and dendrites alters the bistable firing behaviour of reduced models

The goal of the study was to investigate the influence of asymmetric coupling, between the soma and dendrites, on the nonlinear dynamic behaviour of a two-compartment model. We used a recently published method for generating reduced two-compartment models that retain the asymmetric coupling of anatomically reconstructed motor neurons. The passive input-output relationship of the asymmetrically coupled model was analytically compared to the symmetrically coupled case. Predictions based on the analytic comparison were tested using numerical simulations. The simulations evaluated the nonlinear dynamics of the models as a function of coupling parameters. Analytical results showed that the input resistance at the dendrite of the asymmetric model was directly related to the degree of coupling asymmetry. In contrast, a comparable symmetric model had identical input resistances at both the soma and dendrite regardless of coupling strength. These findings lead to predictions that variations in dendritic excitability, subsequent to changes in input resistance, might change the current threshold and onset timing of the plateau potential generated in the dendrite. Since the plateau potential underlies bistable firing, these results further predicted that asymmetric coupling might alter nonlinear (i.e. bistable) firing patterns. The numerical simulations supported analytical predictions, showing that the fully bistable firing pattern of the asymmetric model depended on the degree of coupling asymmetry and its correlated dendritic excitability. The physiological property of asymmetric coupling plays an important role in generating and stabilizing the bistability of motor neurons by interacting with the excitability of dendritic branches.     

Suppressing the excitability of spinal motoneurons by extracellularly applied electrical fields: insights from computer simulations.

The effect of extracellularly applied electrical fields on neuronal excitability and firing behavior is attributed to the interaction between neuronal morphology and the spatial distribution and level of differential polarization induced by the applied field in different elements of the neuron. The presence of voltage-gated ion channels that mediate persistent inward currents (PICs) on the dendrites of spinal motoneurons enhances the influence of electrical fields on the motoneuronal firing behavior. The goal of the present study was to investigate, with a realistic motoneuron computer model, the effects of extracellularly applied electrical fields on the excitability of spinal motoneurons with the aim of reducing the increased motoneuronal excitability after spinal cord injury (SCI). Our results suggest that electrical fields could suppress the excitability of motoneurons and reduce their firing rate significantly by modulating the magnitude of their dendritic PIC. This effect was achieved at different field directions, intensities, and polarities. The reduction in motoneuronal firing rate resulted from the reduction in the magnitude of the dendritic PIC reaching the soma by the effect of the applied electrical field. This reduction in PIC was attributed to the dendritic field-induced differential polarization and the nonlinear current-voltage relationship of the dendritic PIC-mediating channels. Because of the location of the motoneuronal somata and initial segment with respect to the dendrites, these structures were minimally polarized by the applied field compared with the extended dendrites. In conclusion, electrical fields could be used for suppressing the hyperexcitability of spinal motoneurons after SCI and reducing the level of spasticity.     

Cholinergic modulation of neuronal spike reactions to dendritic and somatic application of excitatory acids

Acetylcholine effects on neuronal firing responses evoked by somatic or dendritic applications of excitatory amino acids were studied in slices of guinea-pig parietal cortex. Excitatory reactions initiated by dendritic activation were enhanced by acetylcholine wherever it was iontophoretically applied: either to soma or dendrites. The effect consisted in shortening spike response latencies and increasing response intensity and duration. The modified responses were recorded within 1-min interval after acetylcholine microinjections at a distance within 300 microns of the soma. Parameters of responses to somatic applications of excitatory amino acids were not significantly changed by acetylcholine. The results suggest that acetylcholine improves dendritic propagation rather than membrane excitability.     

Location-dependent excitatory synaptic interactions in pyramidal neuron dendrites

Neocortical pyramidal neurons (PNs) receive thousands of excitatory synaptic contacts on their basal dendrites. Some act as classical driver inputs while others are thought to modulate PN responses based on sensory or behavioral context, but the biophysical mechanisms that mediate classical-contextual interactions in these dendrites remain poorly understood. We hypothesized that if two excitatory pathways bias their synaptic projections towards proximal vs. distal ends of the basal branches, the very different local spike thresholds and attenuation factors for inputs near and far from the soma might provide the basis for a classical-contextual functional asymmetry. Supporting this possibility, we found both in compartmental models and electrophysiological recordings in brain slices that the responses of basal dendrites to spatially separated inputs are indeed strongly asymmetric. Distal excitation lowers the local spike threshold for more proximal inputs, while having little effect on peak responses at the soma. In contrast, proximal excitation lowers the threshold, but also substantially increases the gain of distally-driven responses. Our findings support the view that PN basal dendrites possess significant analog computing capabilities, and suggest that the diverse forms of nonlinear response modulation seen in the neocortex, including uni-modal, cross-modal, and attentional effects, could depend in part on pathway-specific biases in the spatial distribution of excitatory synaptic contacts onto PN basal dendritic arbors.     

Derivation of cable parameters for a reduced model that retains asymmetric voltage attenuation of reconstructed spinal motor neuron dendrites

Spinal motor neurons have voltage gated ion channels localized in their dendrites that generate plateau potentials. The physical separation of ion channels for spiking from plateau generating channels can result in nonlinear bistable firing patterns. The physical separation and geometry of the dendrites results in asymmetric coupling between dendrites and soma that has not been addressed in reduced models of nonlinear phenomena in motor neurons. We measured voltage attenuation properties of six anatomically reconstructed and type-identified cat spinal motor neurons to characterize asymmetric coupling between the dendrites and soma. We showed that the voltage attenuation at any distance from the soma was direction-dependent and could be described as a function of the input resistance at the soma. An analytical solution for the lumped cable parameters in a two-compartment model was derived based on this finding. This is the first two-compartment modeling approach that directly derived lumped cable parameters from the geometrical and passive electrical properties of anatomically reconstructed neurons.     

DPP6 establishes the A-type K(+) current gradient critical for the regulation of dendritic excitability in CA1 hippocampal neurons

Subthreshold-activating A-type K(+) currents are essential for the proper functioning of the brain, where they act to delay excitation and regulate firing frequency. In CA1 hippocampal pyramidal neuron dendrites, the density of A-type K(+) current increases with distance from the soma, playing an important role in synaptic integration and plasticity. The mechanism underlying this gradient has, however, remained elusive. Here, dendritic recordings from mice lacking the Kv4 transmembrane auxiliary subunit DPP6 revealed that this protein is critical for generating the A-current gradient. Loss of DPP6 led to a decrease in A-type current, specifically in distal dendrites. Decreased current density was accompanied by a depolarizing shift in the voltage dependence of channel activation. Together these changes resulted in hyperexcitable dendrites with enhanced dendritic AP back-propagation, calcium electrogenesis, and induction of synaptic long-term potentiation. Despite enhanced dendritic excitability, firing behavior evoked by somatic current injection was mainly unaffected in DPP6-KO recordings, indicating compartmentalized regulation of neuronal excitability.     

Functional diversity of motoneuron dendrites: by accident or design?

The distribution and geometry of the dendritic trees of spinal motoneurons obey several well-established rules. Some of these rules are based on systematic relationships between quantitative geometrical features (e.g. total dendritic length) and the three-dimensional trajectory followed by dendrites from their origin to their termination. Since dendritic geometry partially determines the transmission of current and voltage signals generated by synapses on the dendritic tree, our goal was to compare the efficacy of signal transmission by dendritic trajectories that followed different directions. To achieve this goal, we constructed detailed compartmental models of the dendritic trees of intracellularly stained neck motoneurons and calculated the electrotonic properties of each soma-to-terminal trajectory. These properties displayed a high degree of variability. To determine if this variability was due, in part, to the orientation (e.g. rostral, rostral-dorsal-lateral) of the trajectory, each trajectory was classified according to its orientation. The attenuation of current and voltage signals en route to the soma were strongly related to trajectory orientation. Trajectories with similar attenuation factors formed functional subunits that were arranged in distinct domains within the ventral horn. The difference in the efficacy of signal transmission between subunits was increased by activation of neighbouring synapses due to trajectory-related differences in non-linear summation. These results indicate that the input-output properties of motoneurons depend on the direction of the path taken by dendrites from their origin at the cell body to their terminals.     

A novel targeting signal for proximal clustering of the Kv2.1 K+ channel in hippocampal neurons

The discrete localization of ion channels is a critical determinant of neuronal excitability. We show here that the dendritic K+ channels Kv2.1 and Kv2.2 were differentially targeted in cultured hippocampal neurons. Kv2.1 was found in high-density clusters on the soma and proximal dendrites, while Kv2.2 was uniformly distributed throughout the soma and dendrites. Chimeras revealed a proximal restriction and clustering domain on the cytoplasmic tail of Kv2.1. Truncations and internal deletions revealed a 26-amino acid targeting signal within which four residues were critical for localization. This signal is not related to other known sequences for neuronal and epithelial membrane protein targeting and represents a novel cytoplasmic signal responsible for proximal restriction and clustering.     

Generalized Stein's model for anatomically complex neurons

A neuron with a large dendritic structure is considered. The number of synapses located on the dendrites is substantially higher than on the soma. The synaptic input effect on the neuronal excitability decreases with distance between a synapse ending and the trigger zone. Two areas are distinguished in accordance with the effect of synaptic input--dendritic and somatic. The dendritic area, when compared to the soma, is characterized by much higher intensity of its activation but the amplitudes of synaptically evoked changes of the membrane potential at the trigger zone are in general small. This situation is suitable for a diffusion approximation. However, on the soma, especially in the proximity of the trigger zone, the membrane potential changes are a large fraction of the threshold depolarization. The membrane potential at the trigger zone is modelled by a one-dimensional stochastic process. The diffusion Ornstein-Uhlenbeck process serves as a basis of the model; however, at the moments of somatic synapses activation its voltage changes in jumps. Their sizes represent the amplitudes of the evoked postsynaptic potentials. The unimodal histograms of interspike intervals can be explained by the model. The values of the coefficient of variation greater than one are connected with substantial inhibition.     

Excessive Na+/H+ Exchange in Disruption of Dendritic Na+ and Ca2+ Homeostasis and Mitochondrial Dysfunction following in Vitro Ischemia

Neuronal dendrites are vulnerable to injury under diverse pathological conditions. However, the underlying mechanisms for dendritic Na⁺ overload and the selective dendritic injury remain poorly understood. Our current study demonstrates that activation of NHE-1 (Na⁺/H⁺ exchanger isoform 1) in dendrites presents a major pathway for Na⁺ overload. Neuronal dendrites exhibited higher pH_i regulation rates than soma as a result of a larger surface area/volume ratio. Following a 2-h oxygen glucose deprivation and a 1-h reoxygenation, NHE-1 activity was increased by ∼70–200% in dendrites. This elevation depended on activation of p90 ribosomal S6 kinase. Moreover, stimulation of NHE-1 caused dendritic Na⁺_i accumulation, swelling, and a concurrent loss of Ca²⁺_i homeostasis. The Ca²⁺_i overload in dendrites preceded the changes in soma. Inhibition of NHE-1 or the reverse mode of Na⁺/Ca²⁺ exchange prevented these changes. Mitochondrial membrane potential in dendrites depolarized 40 min earlier than soma following oxygen glucose deprivation/reoxygenation. Blocking NHE-1 activity not only attenuated loss of dendritic mitochondrial membrane potential and mitochondrial Ca²⁺ homeostasis but also preserved dendritic membrane integrity. Taken together, our study demonstrates that NHE-1-mediated Na⁺ entry and subsequent Na⁺/Ca²⁺ exchange activation contribute to the selective dendritic vulnerability to in vitro ischemia.     

Input integration around the dendritic branches in hippocampal dentate granule cells

Recent studies have shown that the dendrites of several neurons are not simple translators but are crucial facilitators of excitatory postsynaptic potential (EPSP) propagation and summation of synaptic inputs to compensate for inherent voltage attenuation. Granule cells (GCs)are located at the gateway for valuable information arriving at the hippocampus from the entorhinal cortex. However, the underlying mechanisms of information integration along the dendrites of GCs in the hippocampus are still unclear. In this study, we investigated the input integration around dendritic branches of GCs in the rat hippocampus. We applied differential spatiotemporal stimulations to the dendrites using a high-speed glutamate-uncaging laser. Our results showed that when two sites close to and equidistant from a branching point were simultaneously stimulated, a nonlinear summation of EPSPs was observed at the soma. In addition, nonlinear summation (facilitation) depended on the stimulus location and was significantly blocked by the application of a voltage-dependent Ca²⁺ channel antagonist. These findings suggest that the nonlinear summation of EPSPs around the dendritic branches of hippocampal GCs is a result of voltage-dependent Ca²⁺ channel activation and may play a crucial role in the integration of input information.     

Location-dependent effects of inhibition on local spiking in pyramidal neuron dendrites

Cortical computations are critically dependent on interactions between pyramidal neurons (PNs) and a menagerie of inhibitory interneuron types. A key feature distinguishing interneuron types is the spatial distribution of their synaptic contacts onto PNs, but the location-dependent effects of inhibition are mostly unknown, especially under conditions involving active dendritic responses. We studied the effect of somatic vs. dendritic inhibition on local spike generation in basal dendrites of layer 5 PNs both in neocortical slices and in simple and detailed compartmental models, with equivalent results: somatic inhibition divisively suppressed the amplitude of dendritic spikes recorded at the soma while minimally affecting dendritic spike thresholds. In contrast, distal dendritic inhibition raised dendritic spike thresholds while minimally affecting their amplitudes. On-the-path dendritic inhibition modulated both the gain and threshold of dendritic spikes depending on its distance from the spike initiation zone. Our findings suggest that cortical circuits could assign different mixtures of gain vs. threshold inhibition to different neural pathways, and thus tailor their local computations, by managing their relative activation of soma- vs. dendrite-targeting interneurons.     

The retrograde frequency response of passive dendritic trees constrains the nonlinear firing behaviour of a reduced neuron model

Our goal was to investigate how the propagation of alternating signals (i.e. AC), like action potentials, into the dendrites influenced nonlinear firing behaviour of motor neurons using a systematically reduced neuron model. A recently developed reduced modeling approach using only steady-current (i.e. DC) signaling was analytically expanded to retain features of the frequency-response analysis carried out in multicompartment anatomically reconstructed models. Bifurcation analysis of the extended model showed that the typically overlooked parameter of AC amplitude attenuation was positively correlated with the current threshold for the activation of a plateau potential in the dendrite. Within the multiparameter space map of the reduced model the region demonstrating "fully-bistable" firing was bounded by directional DC attenuation values that were negatively correlated to AC attenuation. Based on these results we conclude that analytically derived reduced models of dendritic trees should be fit on DC and AC signaling, as both are important biophysical parameters governing the nonlinear firing behaviour of motor neurons.     

Geometry-induced features of current transfer in neuronal dendrites with tonically activated conductances

The impact of dendritic geometry on somatopetal transfer of the current generated by steady uniform activation of excitatory synaptic conductance distributed over passive, or active (Hodgkin-Huxley type), dendrites was studied in simulated neurons. Such tonic activation was delivered to the uniform dendrite and to the dendrites with symmetric or asymmetric branching with various ratios of branch diameters. Transfer effectiveness of the dendrites with distributed sources was estimated by the core current increment directly related to the total membrane current per unit path length. The effectiveness decreased with increasing path distance from the soma along uniform branches. The primary reason for this was the asymmetry of somatopetal vs somatofugal input core conductance met by synaptic current due to a greater leak conductance at the proximal end of the dendrite. Under these conditions, an increasing somatopetal core current and a corresponding drop of the depolarization membrane potential occurred. The voltage-dependent extrasynaptic conductances, if present, followed this depolarization. Consequently, the driving potential and membrane current densities decreased with increasing path distance from the soma. All path profiles were perturbed at bifurcations, being identical in symmetrical branches and diverging in asymmetrical ones. These perturbations were caused by voltage gradient breaks (abrupt change in the profile slope) occurring at the branching node due to coincident inhomogeneity of the dendritic core cross-section area and its conductance. The gradient was greater on the side of the smaller effective cross-section. Correspondingly, the path profiles of the somatopetal current transfer effectiveness were broken and/or diverged. The dendrites, their paths, and sites which were more effective in the current transfer from distributed sources were also more effective in the transfer from single-site inputs. The effectiveness of the active dendrite depended on the activation-inactivation kinetics of its voltage-gated conductances. In particular, dendrites with the same geometry were less effective with the Hodgkin-Huxley membrane than with the passive membrane, because of the effect of the noninactivating K⁺-conductance associated with the hyperpolarization equilibrium potential. Such electrogeometrical coupling may form a basis for path-dependent input-output conversion in the dendritic neurons, as the output discharge rate is defined by the net current delivered to the soma. Received: 18 December 1997 / Accepted in revised form: 12 June 1998     

The Subcellular Distribution of T-Type Ca2+ Channels in Interneurons of the Lateral Geniculate Nucleus

Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca²⁺-spikes and possibly by backpropagating action potentials. Ca²⁺-spikes in INs are predominantly mediated by T-type Ca²⁺-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.     

Noradrenergic enhancement of Ca2+ responses of basal dendrites in layer 5 pyramidal neurons of the prefrontal cortex

Although the excitatory effects of noradrenaline have been thoroughly studied in the central nervous system, there is relatively little known about the adrenergic effects on Ca2+ dynamics of dendrites. In the present study, we imaged basal dendrites of layer 5 pyramidal neurons in the prefrontal cortex using two-photon microscopy. In our experiments noradrenaline, applied in the bath, enhanced excitability of layer 5 pyramidal neurons. The number of evoked action potentials following current injection to the soma increased by 44.7% on average. In the basal dendrites and spines the evoked Ca2+ responses were also markedly enhanced. Noradrenaline-induced effects could be blocked by the beta-adrenergic blocker propranolol. Our data, that activation of the noradrenergic system increases excitability of layer 5 pyramidal neurons via beta-adrenergic receptors and enhances Ca2+ signaling in basal dendrites, suggest a cellular site of action for noradrenaline to improve the integrative capabilities of dendrites.     

Differentiation of Apical and Basal Dendrites in Pyramidal Cells and Granule Cells in Dissociated Hippocampal Cultures

Hippocampal pyramidal cells and dentate granule cells develop morphologically distinct dendritic arbors, yet also share some common features. Both cell types form a long apical dendrite which extends from the apex of the cell soma, while short basal dendrites are developed only in pyramidal cells. Using quantitative morphometric analyses of mouse hippocampal cultures, we evaluated the differences in dendritic arborization patterns between pyramidal and granule cells. Furthermore, we observed and described the final apical dendrite determination during dendritic polarization by time-lapse imaging. Pyramidal and granule cells in culture exhibited similar dendritic patterns with a single principal dendrite and several minor dendrites so that the cell types were not readily distinguished by appearance. While basal dendrites in granule cells are normally degraded by adulthood in vivo, cultured granule cells retained their minor dendrites. Asymmetric growth of a single principal dendrite harboring the Golgi was observed in both cell types soon after the onset of dendritic growth. Time-lapse imaging revealed that up until the second week in culture, final principal dendrite designation was not stabilized, but was frequently replaced by other minor dendrites. Before dendritic polarity was stabilized, the Golgi moved dynamically within the soma and was repeatedly repositioned at newly emerging principal dendrites. Our results suggest that polarized growth of the apical dendrite is regulated by cell intrinsic programs, while regression of basal dendrites requires cue(s) from the extracellular environment in the dentate gyrus. The apical dendrite designation is determined from among multiple growing dendrites of young developing neurons.     

Processes of excitation in the dendrites and in the soma of single isolated sensory nerve cells of the lobster and crayfish

The stretch receptor organs of Alexandrowicz in lobster and crayfish possess sensory neurons which have their cell bodies in the periphery. The cell bodies send dendrites into a fine nearby muscle strand and at the opposite pole they give rise to an axon running to the central nervous system. Mechanisms of excitation between dendrites, cell soma, and axon have been studied in completely isolated receptor structures with the cell components under visual observation. Two sensory neuron types were investigated, those which adapt rapidly to stretch, the fast cells, and those which adapt slowly, the slow cells. 1. Potentials recorded from the cell body of the neurons with intracellular leads gave resting potentials of 70 to 80 mv. and action potentials which in fresh preparations exceeded the resting potentials by about 10 to 20 mv. In some experiments chymotrypsin or trypsin was used to make cell impalement easier. They did not appreciably alter resting or action potentials. 2. It has been shown that normally excitation starts in the distal portion of dendrites which are depolarized by stretch deformation. The changed potential within the dendritic terminals can persist for the duration of stretch and is called the generator potential. Secondarily, by electrotonic spread, the generator potential reduces the resting potential of the nearby cell soma. This excitation spread between dendrites and soma is seen best during subthreshold excitation by relatively small stretches of normal cells. It is also seen during the whole range of receptor stretch in neurons in which nerve conduction has been blocked by an anesthetic. The electrotonic changes in the cells are graded, reflecting the magnitude and rate of rise of stretch, and presumably the changing levels of the generator potential. Thus in the present neurons the resting potential and the excitability level of the cell soma can be set and controlled over a wide range by local events within the dendrites. 3. Whenever stretch reduces the resting membrane potential, measured in the relaxed state in the cell body, by 8 to 12 mv. in slow cells and by 17 to 22 mv. in fast cells, conducted impulses are initiated. It is thought that in slow cells conducted impulses are initiated in the dendrites while in fast cells they arise in the cell body or near to it. In fresh preparations the speed of stretch does not appreciably influence the membrane threshold for discharges, while during developing fatigue the firing level is higher when extension is gradual. 4. Some of the specific neuron characteristics are: Fast receptor cells have a relatively high threshold to stretch. During prolonged stretch the depolarization of the cell soma is not well maintained, presumably due to a decline in the generator potential, resulting in cessation of discharges in less than a minute. This appears to be the basis of the relatively rapid adaptation. A residual subthreshold depolarization can persist for many minutes of stretch. Slow cells which resemble the sensory fibers of vertebrate spindles are excited by weak stretch. Their discharge rate remains remarkably constant for long periods. It is concluded that, once threshold excitation is reached, the generator potential within slow cell dendrites is well maintained for the duration of stretch. Possible reasons for differences in discharge properties between fast and slow cells are discussed. 5. If stretch of receptor cells is gradually continued above threshold, the discharge frequency first increases over a considerable range without an appreciable change in the firing level for discharges. Beyond that range the membrane threshold for conducted responses of the cell soma rises, the impulses become smaller, and partial conduction in the soma-axon boundary region occurs. At a critical depolarization level which may be maintained for many minutes, all conduction ceases. These overstretch phenomena are reversible and resemble cathodal block. 6. The following general scheme of excitation is proposed: stretch deformation of dendritic terminals → generator potential → electrotonic spread toward the cell soma (prepotential) → dendrite-soma impulse → axon impulse. 7. Following release of stretch a transient hyperpolarization of slow receptor cells was seen. This off effect is influenced by the speed of relaxation. 8. Membrane potential changes recorded in the cell bodies serve as very sensitive detectors of activity within the receptor muscle bundles, indicating the extent and time course of contractile events.     

Distance-dependent differences in synapse number and AMPA receptor expression in hippocampal CA1 pyramidal neurons

The ability of synapses throughout the dendritic tree to influence neuronal output is crucial for information processing in the brain. Synaptic potentials attenuate dramatically, however, as they propagate along dendrites toward the soma. To examine whether excitatory axospinous synapses on CA1 pyramidal neurons compensate for their distance from the soma to counteract such dendritic filtering, we evaluated axospinous synapse number and receptor expression in three progressively distal regions: proximal and distal stratum radiatum (SR), and stratum lacunosum-moleculare (SLM). We found that the proportion of perforated synapses increases as a function of distance from the soma and that their AMPAR, but not NMDAR, expression is highest in distal SR and lowest in SLM. Computational models of pyramidal neurons derived from these results suggest that they arise from the compartment-specific use of conductance scaling in SR and dendritic spikes in SLM to minimize the influence of distance on synaptic efficacy.