Passive Dendrites Research Articles

Influence fields: a quantitative framework for representation and analysis of active dendrites

Neuronal dendrites express numerous voltage-gated ion channels (VGICs), typically with spatial gradients in their densities and properties. Dendritic VGICs, their gradients, and their plasticity endow neurons with information processing capabilities that are higher than those of neurons with passive dendrites. Despite this, frameworks that incorporate dendritic VGICs and their plasticity into neurophysiological and learning theory models have been far and few. Here, we develop a generalized quantitative framework to analyze the extent of influence of a spatially localized VGIC conductance on different physiological properties along the entire stretch of a neuron. Employing this framework, we show that the extent of influence of a VGIC conductance is largely independent of the conductance magnitude but is heavily dependent on the specific physiological property and background conductances. Morphologically, our analyses demonstrate that the influences of different VGIC conductances located on an oblique dendrite are confined within that oblique dendrite, thus providing further credence to the postulate that dendritic branches act as independent computational units. Furthermore, distinguishing between active and passive propagation of signals within a neuron, we demonstrate that the influence of a VGIC conductance is spatially confined only when propagation is active. Finally, we reconstruct functional gradients from VGIC conductance gradients using influence fields and demonstrate that the cumulative contribution of VGIC conductances in adjacent compartments plays a critical role in determining physiological properties at a given location. We suggest that our framework provides a quantitative basis for unraveling the roles of dendritic VGICs and their plasticity in neural coding, learning, and homeostasis.

Spatial heterogeneity of passive electrical transfer properties of neuronal dendrites due to their metrical asymmetry

The complex and diverse geometry of neuronal dendrites determines the different morphological types of neurons and influences the generation of complex and diverse discharge patterns at the cell output. The recent finding that each temporal pattern has its spatial signature in the form of a combination of high- and low-depolarization states of asymmetrical dendritic branches with active membrane properties raises the question of the nature of such characteristic spatial heterogeneity of electrical states. To answer this, we consider passive dendrites as a conventional reference case using the known current transfer functions, which we complete by corresponding parametric sensitivity functions. These functions for metrically asymmetrical bifurcations of different sizes, as the simplest elements constituting arborizations of arbitrary geometry, are analyzed under different membrane conductivity conditions related to the intensity of activation of ion channels. Characteristic relationships are obtained on the one hand among the size (branch lengths), metrical asymmetry (difference between sister branches in length and/or diameter), and membrane conductivity, and on the other hand, for the difference between the branches in their current transfer effectiveness as an indicator of their electrical asymmetry (heterogeneity). These relationships (i) allow the introduction of a biophysically based criterion for the electrical distinction between metrically asymmetrical branches, (ii) show how the difference first increases and then decreases with increasing membrane conductivity, and (iii) show that the greatest electrical heterogeneity occurs in a lower or higher range of conductivity, corresponding to larger or smaller bifurcation size. As a consequence, the characteristic low-, medium-, and high-conductance states are derived such that metrically asymmetrical parts of simple and complex trees are electrically distinct when the membrane conductivity lies in the size-related medium range, and indistinct otherwise.

Local unsupervised learning rules for a spiking neural network with dendrite

How could synapse number and position on a dendrite affect neuronal behavior with respect to the decoding of firing rate and temporal pattern? We developed a model of a neuron with a passive dendrite and found that dendritic length and the particular synapse positions directly determine the behavior of the neuron in response to patterns of received inputs. We revealed two distinct types of behavior by simply modifying the position and the number of synapses on the dendrite. In one setting – spatio-temporally sensitive - the neuron responds to a precise spatio-temporal pattern of spikes, but shows little change following an increase in the average frequency of the same input pattern. In the other setting – frequency sensitive - the neuron is insensitive to the precise arrival time of each spike but responds to changes in the average firing rate. This would allow neurons to detect different spatio-temporal patterns.

Efficient fitting of conductance-based model neurons from somatic current clamp

Estimating biologically realistic model neurons from electrophysiological data is a key issue in neuroscience that is central to understanding neuronal function and network behavior. However, directly fitting detailed Hodgkin-Huxley type model neurons to somatic membrane potential data is a notoriously difficult optimization problem that can require hours/days of supercomputing time. Here we extend an efficient technique that indirectly matches neuronal currents derived from somatic membrane potential data to two-compartment model neurons with passive dendrites. In consequence, this approach can fit semi-realistic detailed model neurons in a few minutes. For validation, fits are obtained to model-derived data for various thalamo-cortical neuron types, including fast/regular spiking and bursting neurons. A key aspect of the validation is sensitivity testing to perturbations arising in experimental data, including sampling rates, inadequately estimated membrane dynamics/channel kinetics and intrinsic noise. We find that maximal conductance estimates and the resulting membrane potential fits diverge smoothly and monotonically from near-perfect matches when unperturbed. Curiously, some perturbations have little effect on the error because they are compensated by the fitted maximal conductances. Therefore, the extended current-based technique applies well under moderately inaccurate model assumptions, as required for application to experimental data. Furthermore, the accompanying perturbation analysis gives insights into neuronal homeostasis, whereby tuning intrinsic neuronal properties can compensate changes from development or neurodegeneration.

Mechanisms of Magnetic Stimulation of Central Nervous System Neurons

Transcranial magnetic stimulation (TMS) is a stimulation method in which a magnetic coil generates a magnetic field in an area of interest in the brain. This magnetic field induces an electric field that modulates neuronal activity. The spatial distribution of the induced electric field is determined by the geometry and location of the coil relative to the brain. Although TMS has been used for several decades, the biophysical basis underlying the stimulation of neurons in the central nervous system (CNS) is still unknown. To address this problem we developed a numerical scheme enabling us to combine realistic magnetic stimulation (MS) with compartmental modeling of neurons with arbitrary morphology. The induced electric field for each location in space was combined with standard compartmental modeling software to calculate the membrane current generated by the electromagnetic field for each segment of the neuron. In agreement with previous studies, the simulations suggested that peripheral axons were excited by the spatial gradients of the induced electric field. In both peripheral and central neurons, MS amplitude required for action potential generation was inversely proportional to the square of the diameter of the stimulated compartment. Due to the importance of the fiber's diameter, magnetic stimulation of CNS neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. Passive dendrites affect this process primarily as current sinks, not sources. The simulations predict that neurons with low current threshold are more susceptible to magnetic stimulation. Moreover, they suggest that MS does not directly trigger dendritic regenerative mechanisms. These insights into the mechanism of MS may be relevant for the design of multi-intensity TMS protocols, may facilitate the construction of magnetic stimulators, and may aid the interpretation of results of TMS of the CNS.

Effects of dendritic load on the firing frequency of oscillating neurons

We study the effects of passive dendritic properties on the dynamics of neuronal oscillators. We find that the addition of a passive dendrite can sometimes have counterintuitive effects on firing frequency. Specifically, the addition of a hyperpolarized passive dendritic load can either increase, decrease, or have negligible effects on firing frequency. We use the theory of weak coupling to derive phase equations for "ball-and-stick" model neurons and two-compartment model neurons. We then develop a framework for understanding how the addition of passive dendrites modulates the frequency of neuronal oscillators. We show that the average value of the neuronal oscillator's phase response curves measures the sensitivity of the neuron's firing rate to the dendritic load, including whether the addition of the dendrite causes an increase or decrease in firing frequency. We interpret this finding in terms of to the slope of the neuronal oscillator's frequency-applied current curve. We also show that equivalent results exist for constant and noisy point-source input to the dendrite. We note that the results are not specific to neurons but are applicable to any oscillator subject to a passive load.

Neural Dynamics in Reconfigurable Silicon

A neuromorphic analog chip is presented that is capable of implementing massively parallel neural computations while retaining the programmability of digital systems. We show measurements from neurons with Hopf bifurcations and integrate and fire neurons, excitatory and inhibitory synapses, passive dendrite cables, coupled spiking neurons, and central pattern generators implemented on the chip. This chip provides a platform for not only simulating detailed neuron dynamics but also uses the same to interface with actual cells in applications such as a dynamic clamp. There are 28 computational analog blocks (CAB), each consisting of ion channels with tunable parameters, synapses, winner-take-all elements, current sources, transconductance amplifiers, and capacitors. There are four other CABs which have programmable bias generators. The programmability is achieved using floating gate transistors with on-chip programming control. The switch matrix for interconnecting the components in CABs also consists of floating-gate transistors. Emphasis is placed on replicating the detailed dynamics of computational neural models. Massive computational area efficiency is obtained by using the reconfigurable interconnect as synaptic weights, resulting in more than 50 000 possible 9-b accurate synapses in 9 mm(2).

Numerical analysis of an active dendrite (HH) using a compact difference scheme

Dendrites are extensions to the neuronal cell body in the brain which are posited in several functions ranging from electrical and chemical compartmentalization to coincident detection. Dendrites vary across cell types but one common feature they share is a branched structure. Passive dendrites do not contain voltage sensitive ion channels thus voltage varies linearly with time. Active dendrites on the other hand have voltage sensitive ion channels which bring about a nonlinearity in the change of voltage with respect to time in these dendrites [1]. The Hodgkin Huxley equations describe the change in voltage with respect to time in an active dendrite. A solution to these equations is normally found using the finite difference scheme [2,3]. Spectral methods have also been used to solve these equations with better accuracy [4]. Here we report the solutions to these equations using the compact difference scheme which gives spectral like resolution but can be more easily used with modifications to the HH equations like nonlinearity, branching and other morphological transforms[5].Widely used in the study of turbulent flow and wave propagation, this is the first time it is being used to study conduction in the brain. Here we discuss its usage in a soma dendrite construct with cylindrical geometry. Different dendritic distributions of voltage gated ion channels are considered. The superior resolving power of the scheme compared to the central difference scheme becomes apparent with increasing complexity of the model.

An Analytic Solution of the Cable Equation Predicts Frequency Preference of a Passive Shunt-End Cylindrical Cable in Response to Extracellular Oscillating Electric Fields

Under physiological and artificial conditions, the dendrites of neurons can be exposed to electric fields. Recent experimental studies suggested that the membrane resistivity of the distal apical dendrites of cortical and hippocampal pyramidal neurons may be significantly lower than that of the proximal dendrites and the soma. To understand the behavior of dendrites in time-varying extracellular electric fields, we analytically solved cable equations for finite cylindrical cables with and without a leak conductance attached to one end by employing the Green's function method. The solution for a cable with a leak at one end for direct-current step electric fields shows a reversal in polarization at the leaky end, as has been previously shown by employing the separation of variables method and Fourier series expansion. The solution for a cable with a leak at one end for alternating-current electric fields reveals that the leaky end shows frequency preference in the response amplitude. Our results predict that a passive dendrite with low resistivity at the distal end would show frequency preference in response to sinusoidal extracellular local field potentials. The Green's function obtained in our study can be used to calculate response for any extracellular electric field.

Accommodation in motoneuron models with passive dendrite: Response to linearly rising currents

The biophysical properties of cat motoneuron (MN) models with passive dendrite and different sizes have been extensively tested. However, the behavior of these models in relation to accommodation has not been tested yet. The experimental data reported have shown that MNs accommodate to a very limited degree, exhibiting, in some extension, breakdown of accommodation phenomenon. One possible explanation for the latter behavior would be the presence of persistent sodium conductance. The accommodation can be evaluated by observing threshold latency (TL) curve and the accommodation coefficient ( I/ I 0) s , obtained from the response to linearly rising currents. The simulation results have showed that the models exhibit breakdown of accommodation phenomenon and much similar accommodation coefficients, despite their type: 1.463, 1.456 and 1.418 to S, FR and FF MN models, respectively. According to these data, all the MN models can be classified as slowly accommodating. Our data suggests that accommodation coefficients cannot be associated to the size or to the type of the MN, and persistent sodium conductance might not be necessary to explain breakdown of accommodation phenomenon in MN soma at all.

Extending Cable Theory to Heterogeneous Dendrites

Dendrites may exhibit many types of electrical and morphological heterogeneities at the scale of a few micrometers. Models of neurons, even so-called detailed models, rarely consider such heterogeneities. Small-scale fluctuations in the membrane conductances and the diameter of dendrites are generally disregarded and spines merely incorporated into the dendritic shaft. Using the two-scales method known as homogenization, we establish explicit expressions for the small-scale fluctuations of the membrane voltage, and we derive the cable equation satisfied by the voltage when these fluctuations are averaged out. This allows us to rigorously establish under what conditions a heterogeneous dendrite can be approximated by a homogeneous cable. We consider different distributions of synapses, orderly or random, on a passive dendrite, and we investigate when replacing excitatory and inhibitory synaptic conductances by their local averages leads to a small error in the voltage. This indicates in which regimes the approximations made in compartmental models are justified. We extend these results to active membranes endowed with voltage-dependent conductances or NMDA receptors. Then we examine under which conditions a spiny dendrite behaves as a smooth dendrite. We discover a new regime where this holds true, namely, when the conductance of the spine neck is small compared to the conductance of the synapses impinging on the spine head. Spines can then be taken into account by an effective excitatory current, the capacitance of the dendrite remaining unchanged. In this regime, the synaptic current transmitted from a spine to the dendritic shaft is strongly attenuated by the weak coupling conductance, but the total current they deliver can be quite substantial. These results suggest that pedunculated spines and stubby spines might play complementary roles in synaptic integration. Finally, we analyze how varicosities affect voltage diffusion in dendrites and discuss their impact on the spatiotemporal integration of synaptic input.

Emerging methodologies for the study of hypothalamic gonadotropin-releasing-hormone (GnRH) neurons

Gonadotropin-releasing-hormone (GnRH) neurons form part of a central neural oscillator that controls sexual reproduction through intermittent release of the GnRH peptide. Activity of GnRH neurons, and by extension release of GnRH, has been proposed to reflect intrinsic properties and synaptic input of GnRH neurons. To study GnRH neurons, we used traditional electrophysiology and computational methods. These emerging methodologies enhance the elucidation of processing in GnRH neurons. We used dynamic current-clamping to understand how living GnRH somata process input from glutamate and GABA, two key neurotransmitters in the neuroendocrine hypothalamus. In order to study the impact of synaptic integration in dendrites and neuronal morphology, we have developed full-morphology models of GnRH neurons. Using dynamic clamping, we have demonstrated that small-amplitude glutamatergic currents can drive repetitive firing in GnRH neurons. Furthermore, application of simulated GABAergic synapses with a depolarized reversal potential have revealed two functional subpopulations of GnRH neurons: one population in which GABA chronically depolarizes membrane potential (without inducing action potentials) and a second population in which GABAergic excitation results in slow spiking. Finally, when AMPA-type and GABA-type simulated inputs are applied together, action potentials occur when the AMPA-type conductance occurs during the descending phase of GABAergic excitation and at the nadir of GABAergic inhibition. Compartmental computer models have shown that excitatory synapses at >300 microns from somtata are unable to drive spiking with purely passive dendrites. In models with active dendrites, distal synapses are more efficient at driving spiking than somatic inputs. We then used our models to extend the results from dynamic current clamping at GnRH somata to distribute synaptic inputs along the dendrite. We show that propagation delays for dendritic synapses alter synaptic integration in GnRH neurons by widening the temporal window of interaction for the generation of action potentials. Finally, we have shown that changes in dendrite morphology can modulate the output of GnRH neurons by altering the efficacy of action potential generation in response to after-depolarization potentials (ADPs). Taken together, the methodologies of dynamic current clamping and multi-compartmental modeling can make major contributions to the study of synaptic integration and structure-function relationships in hypothalamic GnRH neurons. Use of these methodological approaches will continue to provide keen insights leading to conceptual advances in our understanding of reproductive hormone secretion in normal and pathological physiology and open the door to understanding whether the mechanisms of pulsatile GnRH release are conserved across species.

Parameter sensitivity of distributed transfer properties of neuronal dendrites: a passive cable approximation

Geometry and membrane properties of the dendrites crucially determine input-output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise.

A software for simulating steady-state properties of passive dendrites based on the cable theory

In this study, a computer software, CableTeo, is introduced for simulating the steady-state electrical properties of passive dendrite based on the cable theory. The cable theory for dendritic neurons addresses to current–voltage relations in a continuous passive dendritic tree. It is briefly summarized that the cable theory related to passive cables and dendrites, which is a useful approximation and an important reference for excitable cases. The proposed software can be used to construct user-defined dendritic tree model. The user can define the model in detail, display the constructed dendritic tree, and examine the basic electrical properties of the dendritic tree using transfer impedance approach. The software addresses to ones who want to run simple simulations of the cable theory without need to any programming language skills or expensive software. It can also be used for educational purposes.

A model of activity-dependent changes in dendritic spine density and spine structure

Recent evidence indicates that the morphology and density of dendritic spines are regulated during synaptic plasticity. See for instance a review by [1]. High-frequency stimuli that induce long-term potentiation (LTP) have been associated with increases in the number and size of spines. In contrast, low-frequency stimuli that induce long-term depression (LTD) are associated with decreases in the number and size of spines. Decreases in spine density also occur due to excitotoxicity associated with very high levels of activity such as during seizures. In this work, we extend previous modeling studies [2] by combining a model for activity-dependent spine density with one for calcium-mediated spine stem restructuring. The model is based on the standard dimensionless cable equation for the changes in membrane potential in a passive dendrite. An additional equation characterizes the activity-dependent changes in spine density along the dendrite. For this continuum model, a typical Hodgkin-Huxley type current balance equation represents the change in membrane potential in an isopotential compartment representing a spine head. Both the cable equation and the current balance equation rely on the spine stem current to represent current flow between the spines and the dendrite. The model also includes equations for activity-dependent changes in the calcium concentration in spines as well as changes in spine stem resistance that depend on the level of calcium in an individual spine. The calcium-mediated changes in spine density and spine stem resistance are based on a conceptual model proposed by Segal et al. [1] where low calcium concentrations lead to spine shrinkage and pruning, an increase in calcium concentration leads to spine elongation and formation of new spines, and significantly higher values cause spine shrinkage and pruning. We use computational studies to investigate the changes in spine density and structure for differing synaptic inputs and demonstrate the effects of these changes on the input-output properties of the dendritic branch. Moderate amounts of high-frequency synaptic activation to dendritic spines cause an increase in spine stem resistance, which is correlated with spine stem elongation. In addition, the spine density increases both inside and outside the input region. The model is formulated so that this LTP-inducing stimulus eventually leads to structural stability. In contrast, a prolonged low-frequency stimulation paradigm that would typically induce LTD results in a decrease in stem resistance (correlated with spine shortening) and an eventual decrease in spine density.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg–Landau equations describing a Turing–Hopf bifurcation with modulation group velocity of O ( 1 ) . Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but also those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin–Feir instabilities.

A model of activity-dependent changes in dendritic spine density and spine structure

Recent evidence indicates that the morphology and density of dendritic spines are regulated during synaptic plasticity. See, for instance, a review by Hayashi and Majewska [9]. In this work, we extend previous modeling studies [27] by combining a model for activity-dependent spine density with one for calcium-mediated spine stem restructuring. The model is based on the standard dimensionless cable equation, which represents the change in the membrane potential in a passive dendrite. Additional equations characterize the change in spine density along the dendrite, the current balance equation for an individual spine head, the change in calcium concentration in the spine head, and the dynamics of spine stem resistance. We use computational studies to investigate the changes in spine density and structure for differing synaptic inputs and demonstrate the effects of these changes on the input-output properties of the dendritic branch. Moderate amounts of high-frequency synaptic activation to dendritic spines result in an increase in spine stem resistance that is correlated with spine stem elongation. In addition, the spine density increases both inside and outside the input region. The model is formulated so that this long-term potentiation-inducing stimulus eventually leads to structural stability. In contrast, a prolonged low-frequency stimulation paradigm that would typically induce long-term depression results in a decrease in stem resistance (correlated with stem shortening) and an eventual decrease in spine density.

Modeling and simulation for three-dimensional signal propagation in passive dendrites

This paper presents a three-dimensional model for neuronal signal processing in passive dendritic branches. The approach is based on Maxwell’s equations, in particular, on the equation of continuity for the electric flux. The quantities of interest are the electric potentials in the intra- and extracellular domain as well as the membrane voltage. The model is given by an integral Laplace equation with a source term that models the current through the membrane. We give results based on the numerical solution of the three-dimensional model, and we compare the model with the well known one-dimensional cable equation. One of the features of the new model is that it directly accounts for the possibility to include detailed measured geometry of dendritic branches into a three-dimensional numerical simulation. As a result, we are able to show for the first time that there is a significant impact of the extracellular domain into the solution of neuronal signal propagation in passive dendrites.

Quantification of the factors that influence discharge correlation in model motor neurons.

The purpose of this study was to quantify the influence of intrinsic properties, active dendritic conductances, and background excitation and inhibition on measures of discharge correlation in the time and frequency domains with known levels and patterns of common synaptic input. The study involved a computer simulation of a population of neurons with a range of input resistances (0.54-3.7 MOmega) and surface areas (407,000-712,000 microm(2)). The neurons were simulated with no, moderate, or high levels of active dendritic conductances and were activated with either excitatory input only or excitatory and inhibitory inputs. The patterns of common input, either branched common input or common modulation, were tested with 0, 30, 60, and 90% common input. The results confirm previous findings of an exponential relation between the level of common input and indexes of synchronization; only when the common input comprised >/=60% of the total excitatory input was there a significant effect on discharge correlation. Synchronization was greatest in models that had passive dendrites. Active dendritic conductances caused the discharge rate of the neuron to saturate and decreased motor-unit synchronization. However, the addition of 10% background inhibitory input increased synchronization in these models. In contrast, common rhythmic modulation of inputs at 24 Hz usually decreased synchronization. Significant coherence at the modulated frequency occurred in the commonly modulated neurons when >/=60% of the inputs were modulated. Furthermore, active dendritic conductances decreased coherence. Branched common input caused high levels of coherence across a broad spectrum and when combined with active dendritic conductances caused significant frequency peaks in the 30- to 50-Hz band. In conclusion, the level of inhibitory input and active dendritic conductances interact with the amount of common input to determine time- and frequency-domain discharge correlation.

High I(h) channel density in the distal apical dendrite of layer V pyramidal cells increases bidirectional attenuation of EPSPs.

Despite the wealth of recent research on active signal propagation along the dendrites of layer V neocortical pyramidal neurons, there is still little known regarding the traffic of subthreshold synaptic signals. We present a study using three simultaneous whole cell recordings on the apical dendrites of these cells in acute rat brain slices to examine the spread and attenuation of spontaneous excitatory postsynaptic potentials (sEPSPs). Equal current injections at each of a pair of sites separated by approximately 500 microm on the apical dendrite resulted in equal voltage transients at the other site ("reciprocity"), thus disclosing linear behavior of the neuron. The mean apparent "length constants" of the apical dendrite were 273 and 446 microm for somatopetal and somatofugal sEPSPs, respectively. Trains of artificial EPSPs did not show temporal summation. Blockade of the hyperpolarization-activated cation current (I(h)) resulted in less attenuation by 17% for somatopetal and by 47% for somatofugal sEPSPs. A pronounced location-dependent temporal summation of EPSP trains was seen. The subcellular distribution and biophysical properties of I(h) were studied in cell-attached patches. Within less than approximately 400 microm of the soma, a low density of approximately 3 pA/microm(2) was found, which increased to approximately 40 pA/microm(2) in the apical distal dendrite. I(h) showed activation and deactivation kinetics with time constants faster than 40 ms and half-maximal activation at -95 mV. These findings suggest that integration of synaptic input to the apical tuft and the basal dendrites occurs spatially independently. This is due to a high I(h) channel density in the apical tuft that increases the electrotonic distance between these two compartments in comparison to a passive dendrite.