| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Department of Physiology, McGill University, Montreal, Quebec, Canada; and 2Biology and Biochemistry, University of Houston, Houston, Texas
Submitted 11 April 2007; accepted in final form 17 September 2007
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
) has led to intensive investigations of dendritic computation (for reviews, see Hausser et al. 2000; London and Hausser 2005; Magee 2000; Migliore and Shepherd 2002; Reyes 2001; Segev and London 2000). Although our knowledge of the electrophysiological properties of dendrites has greatly advanced, previous studies have usually examined neuronal computation by studying how neurons process brief excitatory postsynaptic potentials (EPSPs) or current injections applied to the dendrites (but see Gasparini and Magee 2006; Larkum et al. 2001; Oviedo and Reyes 2002, 2005; Ulrich 2002). Past studies describing the input-output properties of dendrites have produced conflicting results with regard to the linearity or nonlinearity of the integration of synaptic inputs (Cash and Yuste 1999; Larkum et al. 2001; Nettleton and Spain 2000; Tamas et al. 2002; Urban and Barrionuevo 1998; Wei et al. 2001; Williams and Stuart 2002). Synaptic integration may also depend on whether dendrites initiate action potentials (Ariav et al. 2003; Gasparini et al. 2004; Golding and Spruston 1998; Larkum and Zhu 2002; Stuart et al. 1997; Womack and Khodakhah 2004) or on the spatial and temporal patterns of the input (Gasparini and Magee 2006; Hausser and Mel 2003; Magee 1999; Mel 1993; Nevian et al. 2007; Polsky et al. 2004; Schaefer et al. 2003; Williams 2004).
Based on the average background-firing rate of most central neurons, it is unlikely that dendrites receive a "single shock" of only a few isolated EPSPs at any given time. A more realistic scenario is that across the many thousands of synaptic inputs, dendrites receive a constant barrage of excitatory and inhibitory activity that produces a complex time-varying input (Anderson et al. 2000; Borg-Graham et al. 1998; Destexhe and Pare 1999; Destexhe et al. 2003; Ferster and Jagadeesh 1992; Hirsch et al. 1998; Ho and Destexhe 2000). Therefore it is important that we also include this temporal component in our description of the dendrite-to-soma relationship. In this study, we apply system-identification analysis to reveal how the proximal apical dendrites of CA1 hippocampus neurons process a continuous time-varying input. Our first goal was to produce a model that accounted for the signal processing between the proximal apical dendrites and soma.
It has been proposed that dendrite computation includes nonlinearities that modulate the input-output relationship of neurons depending on whether the input is strong enough to initiate dendritic action potentials (Ariav et al. 2003; Gasparini et al. 2004; Golding and Spruston 1998; Hausser et al. 2000; Kamondi et al. 1998; Larkum et al. 2001; Schwindt and Crill 1997; Turner et al. 1991; Williams and Stuart 2002). Although the precise nature of this computational change remains unclear, adaptation and regulation of neuronal gain has been shown to be a prominent component of many forms of neuronal processing (for reviews, see Davis and Bezprozvanny 2001; Salinas and Sejnowski 2001; Salinas and Thier 2000; Turrigiano and Nelson 2000). In addition, information theory dictates, and subsequent experiments have shown, that efficient representation of information requires the nervous system to adapt to the statistical properties of the signals being encoded (e.g., Atick 1992; Barlow 1961; Bialek and Rieke 1992; Fairhall et al. 2001; Hosoya et al. 2005). Therefore a second goal of our study was to determine whether intrinsic channel mechanisms within single neurons contribute to these adaptive processing strategies.
Our results suggest that the dendrite-to-soma input/output relationship is well described by a functional model containing a band-pass filter in the theta frequency range followed by an adapting nonlinear gain-control. In addition, we found that the voltage-dependent current, Ih, contributes to both the frequency response and the gain regulation of the input/output function. A previous abstract of this work has been presented in preliminary form (Cook et al. 2005).
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
Hippocampal slices (300 µm thick) were prepared from male Sprague-Dawley rats (140–197 g, age between 5 and 6 wk) using standard protocols approved by the University of Houston Animal Care and Use Committee (Colbert and Pan 2002). Individual CA1 neurons were visualized with differential interference contrast optics using infrared illumination. Dual simultaneous whole cell patch-clamp recordings were made using two Dagan BVC-700 amplifiers in "bridge" mode, and data were low-pass filtered at 2 kHz (using an external 8-pole Butterworth filter, Krohn-Hite) and acquired at 5 kHz. The normal external recording solution contained (in mM) 125 NaCl, 2.5 KCl, 1.25 NaH2PO4, 25 NaHCO3, 2.0 CaCl2, 1 MgCl2, and 25 dextrose, bubbled with 95% O2-5% CO2 at 
32°C (pH 7.4). The internal pipette solution consisted of (in mM) 140 KMeSO4, 10 HEPES, 1 BAPTA, 0.28 CaCl2, 4.0 Mg2ATP, 0.3 Tris2GTP, 14 phosphocreatine, and 4 NaCl (pH 7.25 with KOH).
Whole cell recording pipettes (somatic, 8 M
; dendritic, 10 M), were pulled from borosilicate glass (Warner). The average capacitance of the dendritic electrodes was 10 pF, measured by fitting a single exponential to a 600-pA current step filtered at 20 kHz and sampled at 50 kHz. Current steps were performed while the electrode was positioned in the bath at approximately the same depth as the target dendrite. Recordings were performed at 30–32°C.
White-noise stimulus
Fifty seconds of Gaussian distributed (0 mean) random current was injected with the dendritic electrode (Fig. 1A). The white-noise stimulus was generated using Matlab and played into the dendrite at 5 kHz. This stochastic stimulus is completely defined by its mean and variance. The average SD of the injected current (Id) was adjusted to be either low (0.3 ± 0.01 nA) or high (1.9 ± 0.3 nA), with the high value set for each neuron individually to just reach the threshold for action potential production. The same noise pattern was injected on every trial (i.e., only the amplitude was varied). Alternating sweeps of low- and high-input variance current were injected for as long as a stable recording configuration could be maintained.
|
All variability is reported as ±SE. Action potentials were identified in MATLAB, checked by eye, and removed by linearly interpolating the somatic voltage (VS) from 1 ms before the action potential peak to either 5 or 10 ms after the peak (both time windows were used and produce equivalent results). Because of the low firing rate, action potentials constituted a very small proportion of the 50 s of data and our analysis produced the same qualitative results when action potentials were included. As our stimulus had a zero mean, our model of the input/output relationship was designed to reproduce the somatic voltage fluctuations around the resting membrane potential. Therefore after action potentials were removed, individual voltage traces were mean subtracted and linearly detrended to remove any slow DC drifts. These slow drifts were usually <1 mV over the 50 s of recording and were as likely to go up as to go down. Traces were then averaged for each input condition. Because the average spectrum of the somatic membrane potential showed very little power above 200 Hz, we digitally low-pass filtered our data at 250 Hz and then resampled at 500 Hz using the Digital Signal Processing Toolbox in MATLAB. This reduced our 50 s of recorded data to 25,000 data points.
We compensated for any filtering of the injected current (Id) by the dendritic electrode. From our measured dendrite electrode capacitance (Ce), we estimated the electrode's capacitive current (IC) using
 | (1) |
 | (2) |
LN model
We described the dendrite-to-soma input/output relationship using an LN model (Fig. 2B). The LN stands for "linear/nonlinear" and the model has the form of a cascade of a linear filter followed by a nonlinear static-gain function (Hunter and Korenberg 1986). The input to the LN model was the time-varying current injection and the output was the somatic membrane potential. The output of the model is expressed mathematically as
 | (3) |
S is the estimated somatic potential. G was defined as two quadratic functions
 | (4) |
|
 | (5) |
We optimized the LN model by minimizing the mean-squared error (MSE) between the model's output, S, and the recorded somatic membrane potential VS using a standard iterative procedure (Hunter and Korenberg 1986). At each iteration, the solution to the linear filter was solved first followed by optimizing the nonlinear gain-function. This procedure was iteratively repeated until the MSE was minimized. Solving for the linear filter was accomplished by expressing the convolution in Eq. 5 as an overdetermined system of linear equations
 | (6) |
In the second step of each iteration, we solved for the nonlinear static gain function. This was accomplished by optimizing the parameters for G that minimized the difference between the output of the linear filter, H * Id, and the observed somatic voltage, VS. Once G was optimized, the inverse for Eq. 3 was calculated as
 | (7) |
The next iteration was then repeated using G–1(S) in place of the observed somatic potential, VS(ti), in Eq. 6.
The amplitude of the linear filter was normalized to insure any change in gain would be expressed by the static-gain function. For our data, we found the MSE usually converged within 20 iterations. The model was optimized separately for the low- and high-variance input conditions.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
). In this study, we directly injected randomly varying current into the dendrites to quantify the temporal and adaptive components of the dendrite-to-soma input/output function. Importantly, the stochastic nature of this type of stimulus permitted us to examine how neurons adapted to the changes in input statistics such as variance.
Simultaneous dual whole cell patch recordings were made along the main apical trunk of CA1 pyramidal neurons in slices (see METHODS). Fifty seconds of zero-mean Gaussian distributed random current (Id) was injected with the dendritic electrode and the resulting change in membrane potential (VS) was measured with the somatic electrode (Fig. 1A). Electrode separation ranged from 55 to 210 µm (median: 145 µm, mean: 125 µm), which roughly corresponds to the proximal 2/3 of stratum radiatum (Ishizuka et al. 1995).
Our random stimulus was defined by two statistics: mean and variance. Although dendritic voltage-dependent channels are no doubt sensitive to the mean of an input, less is known about their sensitivity to fluctuations about the mean. To reveal how the statistics of these fluctuations affected dendritic signal processing, we kept the mean of the injected current at zero and changed the variance on alternate trials between low and high levels.
An example recording in Fig. 1, B and C, illustrates 20 s of the dendritic current injection and the subsequent membrane potential at the soma. The low-variance input produced small voltage fluctuations at the soma, whereas the high-variance input produced large fluctuations that included an irregular train of action potentials. The average SD of the somatic membrane potential across our population of cells was 1.3 ± 0.1 and 5.8 ± 0.4 mV for the low- and high-variance inputs, respectively (n = 15).
Across all our neurons, average firing rates in the high-variance input condition ranged from 0.2 to 2.0 (mean: 0.9) spike/s; these were similar to typical CA1 mean firing rates recorded in vivo (Markus et al. 1995). This suggests that the high-variance input produced overall levels of excitation that the dendrites might reasonably be expected to receive. It is important to emphasize, however, that we do not infer that our continuous-time white-noise current injection was identical to the in vivo synaptic input that CA1 pyramidal cells receive in any specific context.
For example, when we compared the interspike interval distributions of our neurons to that of CA1 neurons recorded from behaving animals on a circular track [in vivo data kindly provided by J. Knierim and D. Yoganarasimha (Yoganarasimha et al. 2006)], we found that on average the in vivo CA1 neurons were more likely to fire in high-frequency bursts. However, the spike statistics of the in vivo recordings were highly variable with long periods of low-frequency firing interspersed with more robust activity. From the in vivo recordings it was possible to identify 50-s epochs, during which the animal actively moved around the track, where the interspike interval distribution (Fig. 1D, - - -) was qualitatively similar to that of our in vitro recorded neurons (—). Thus our random current injection produced a firing pattern that mimicked in vivo activity under at least some conditions.
LN model captures the dendrite-to-soma input/output function
To describe the dendrite-to-soma signal processing, we functionally represented the neuron as a cascade of a linear filter followed by a nonlinear static-gain function as shown in Fig. 2B (Hunter and Korenberg 1986; Korenberg et al. 1988, 1989). This type of functional representation, referred to as a linear/nonlinear model, or LN model for short, has successfully been used to characterized visual processing in the retina (for reviews, see Chichilnisky 2001; Meister and Berry 1999; Wu et al. 2006) as well as the processing of current injected into the soma of neurons (Binder et al. 1999; Bryant and Segundo 1976; Poliakov et al. 1997; Slee et al. 2005).
The LN model is an ideal representation for the dendrite-to-soma input/output function because the linear filter and nonlinear static-gain function, respectively, separate the time-dependent dynamics from any amplitude nonlinearities. However, the most beneficial aspect of the LN model is that it is a functional representation that allows us to discuss the dendrite-to-soma relationship using well-defined signal-processing terms such as temporal filtering and gain control.
As we were primarily interested in understanding the dendrite-to-soma signal processing of the neuron, we did not try to account for the generation of action potentials, which were removed before analysis (see METHODS). However, our results were qualitatively the same (i.e., the dendrite-to-soma input/output filter and gain characteristics did not change) when action potentials were included in the analysis.
We optimized the parameters of the LN model to best reproduce the somatic voltage (VS) for both input-variance conditions separately (see METHODS). Figure 2 provides an example of the optimized LN model to reproduce the dendrite-to-soma input/output relationship of one of our neurons. A portion of the input current and the somatic membrane potential with action potentials removed are shown on an expanded 500-ms time scale in Fig. 2A (black traces). The red and blue traces in Fig. 2A are the LN model's predicted output (S). As this example illustrates, the LN model's predicted output closely matched the recorded somatic potential and only when the voltage scale is expanded by 10 times is any error noticeable (inset). Over the entire 50 s of recording for this particular neuron, the LN model produced a fit that accounted for 97 and 98% of the variance in the somatic membrane potential for the low- and high-variance input conditions, respectively.
The excellent fit demonstrates that the LN model fully captured the input/output function of the somatic voltage in response to a continuous-time random input applied to the dendrite. This result suggests the neuron was stationary (i.e., its properties did not change over the relatively long 50-s recording interval) with inward and outward voltage-gated currents acting in a balanced and predictable fashion. Furthermore, the neuron remained stationary even during the suprathreshold high-variance input condition when action potentials were produced by this cell at an average rate of 0.8 spike/s.
Figure 2, C and D, illustrates the components of the LN model that were fit to our example cell. For this neuron, the impulse response functions of the linear filters were biphasic (Fig. 2C) and exhibited band-pass characteristics in the 1- to 10-Hz theta range (inset shows the frequency response of the filters). An important observation is that unlike the static-gain function (see following text), the linear filters did not appreciably differ between the low- and high-variance input conditions.
Figure 2D shows the static-gain functions for our example neuron. In these plots, 0 mV corresponds to resting membrane potential. The role of the static-gain function is to transform the output of the linear filter, F, into the membrane potential at the soma, S. Importantly, the static-gain function allows nonlinearities in the amplitude response to be represented in the model. We modeled the static-gain function as a quadratic function of F (see Eq. 4 in METHODS).
The nearly straight-line gain function corresponding to the low-variance input indicates that the neuron was linear for small subthreshold inputs. In contrast, the high-variance input exposed two prominent nonlinearities in the gain function. First, there was an overall reduction in gain as revealed by the reduced slope of the static-gain function at rest (0 mV). Second, there was a gentle compressive nonlinearity at hyperpolarized and depolarized potentials that further attenuated large fluctuations in the input. When the variance of the input increased, the gain of this cell was reduced by 14% at rest and by as much as 40% at depolarized potentials. Thus this neuron changed its gain, but not its temporal filtering characteristics, in response to changes in the variance of the input.
It is important to note that only active dendrites would be expected to exhibit band-pass filtering and nonlinear gain changes. To confirm this point and verify our analysis procedures, we injected the same Gaussian random current into the dendrite of a computer model of a passive neuron. Performing the same analysis produced an LN model with a low-pass filter that exhibited a monophasic impulse response function and a straight-line static-gain function (data not shown). Both the filter and the static-gain function remained the same when the input variance was changed between the low and high conditions.
Summary results of the LN model
We assessed how well the LN model described the input/output relationship of the neurons by comparing the recorded (VS) with the predicted (S) somatic potential. Figure 3A shows the goodness-of-fit of the LN model for our two input conditions for all cells. Across our 15 dual recordings, we found that the LN model described the input/output function equally well for both input conditions (mean R2 of the LN model fits was 0.97). The correlation of the goodness-of-fit between the low- and high-variance input conditions in Fig. 3A is likely due to correlated experimental noise that varied between recording sessions. These results demonstrate that the LN model captured most of the input/output relationship from the dendrite to the soma for all of our cells.
|
The straight line for the average low-variance gain function indicates that the neurons processed small inputs linearly (blue). For the suprathreshold high-variance inputs (red), however, input/output relation exhibited nonlinear behavior with a reduction in gain (i.e., the slope of the static-gain function) at rest that increased for both depolarized, and to a lesser extent, hyperpolarized potentials. Figure 3C shows both static gain functions on the same graph to allow a direct comparison of the slopes.
Adaptation to input variance around the resting membrane potential
Gain control is a fundamental signal processing principle that is observed in many neuronal systems, especially those involved in sensory processing (for reviews, see Salinas and Sejnowski 2001; Salinas and Thier 2000). Both synaptic conductance changes (Chance et al. 2002; Holt and Koch 1997; Kerr and Capogna 2007; Mitchell and Silver 2003; Prescott and De Koninck 2003; Shu et al. 2003) and intrinsic properties of the neuron (Burdakov 2005; Sanchez-Vives et al. 2000) can regulate neuronal gain (Azouz 2005; Higgs et al. 2006; Kim and Rieke 2001). That the gain of the input/output function of our CA1 neurons was sensitive to the input variance delivered directly to the dendrites adds support to the idea that intrinsic nonlinearities, such as voltage- and time-dependent channels, may contribute to the activity-dependent regulation of gain.
Because the scales of the two static-gain functions in Fig. 3C were dramatically different, we re-analyzed the change in gain in another way that would not be biased by gain changes at the extremes of the measured voltages. We fit new static-gain functions over a small limited range of somatic membrane potentials around the resting membrane potential. Figure 4A shows the data from the example cell in Fig. 2 plotted on the same scale (data points corresponding to the high-variance input condition that fall outside this scale were not included in this analysis). Linear fits to each condition in Fig. 4A show a significant change in slope indicating the gain for the high-variance input was reduced over the same somatic potentials as the low-variance input (P < 0.001, bootstrap described in the following text).
|
We applied a bootstrap method to determine if the change in gain for each neuron was significant (Efron and Tibshirani 1993). The analysis in Fig. 4A was repeated 5,000 times for each cell using bootstrap sampling to estimate the variance in the slopes of the linear fits. In 13 of 15 cells, the change in slope (i.e., gain) was significant (P < 0.01, Fig. 4, B and C, open bars and symbols). Thus the dendrite-to-soma input/output function underwent a reduction change in gain when the variance of the input was increased.
As Fig. 4B illustrates, our cells did not always produce the same decrease in gain for the high-variance input. This was because the high-variance input current (Id) was adjusted during each experiment to just produce action potentials and this threshold varied between cells. The advantage, however, of using different input variances between cells was that it allowed us to test if gain changed as a continuous function of input variance. As shown in Fig. 4C, we found that the reduction in gain was moderately correlated with the increase in input variance (R2 = 0.26), suggesting that dendrites adjust their gain in a graded manner. Thus the dendrites performed a sophisticated form of gain control that was based on the variance of the input signal.
Although our white-noise current injection had a zero mean for both the low- and high-variance conditions, it was possible that the mean soma potential varied between the two conditions. Action potentials produced in the high-variance input may have elevated the somatic potential compared with the low-variance condition. To examine this, we calculated the average somatic potential for both input conditions. Our average potential difference [VS(high-variance) –VS(low-variance)] was small and ranged from –4.5 to 1.6 mV (mean: –0.9 mV). Importantly, there was no relationship between the change in mean membrane potential at the soma and the change in gain (R2 = 0.05). Nearly identical results were obtained when we compared the changes in mean potential after spikes were removed. Thus the average somatic potential was not likely a factor in our observed change in gain.
Effects of dendritic location on filtering and gain
The passive cable model of dendrites predicts increased filtering at more distal locations (Rall 1959). We wanted to know how the LN model varied between more proximal and more distal dendritic inputs. Figure 5 illustrates the average filter and gain function for our four most proximal (—) and four most distal recordings (- - -). For clarity, we show only the filter and gain corresponding to the high-variance input condition, however, the results for the low-variance input were similar. The proximal recordings where made between 50 and 60 µm from the soma while the distal where between 160 and 210 µm from the soma.
|
Contribution of Ih to the input/output function
Our results thus far suggest that active channels are contributing to the neuron's frequency response and gain control. To test this, we next blocked Ih, a prominent dendritic voltage-dependent current in CA1 neurons (Lorincz et al. 2002; Magee 1998). Ih has been shown to contribute to the frequency response of cortical pyramidal cells (Ulrich 2002) and affect the nonlinear integrative properties of dendrites in CA1 pyramidal cells (Magee 1999). In addition, removing the contribution of Ih from the neuron's input/output function was an important test of the sensitivity of the LN model.
Figure 6A illustrates 500 ms of the input current (Id, black traces, left) and somatic membrane potential (VS, black traces, right) for a cell where we block Ih by bath applying 20 µM Zd7288. Using the same analysis previously described, we fit the LN model to the data. The predicted somatic membrane potential is shown for both input conditions (S, red and blue in Fig. 6A). As was the case for experiments performed in normal external solution, the LN model fully captured the input/output response for this cell (R2 = 0.95). The average goodness-of-fit for our five cells recorded in Zd7288 (Fig. 7A), however, was slightly lower than those recorded in normal solution.
|
|
The average filters and static-gain functions for our population of neurons recorded in Zd7288 are shown in Fig. 7, B and C (n = 5). Blocking Ih greatly attenuated the band-pass normally present in the 1- to 10-Hz range (Fig. 7B, inset) and altered the static-gain function corresponding to the high-variance input condition (Fig. 7C). Instead of a gain decrease, the lack of Ih produced an average gain increase for the high-variance input condition.
To verify the effect of removing Ih on gain control, we repeated the analysis in Fig. 4 by focusing on the gain change in the neighborhood of the somatic resting membrane potential. Figure 8A shows that eliminating Ih produced an average increase in gain (median: 26%, mean: 28%, P < 0.01, t-test, 
) compared with cells with Ih present (
data are re-plotted from Fig. 4). Unlike the normal condition, there was no systematic relationship between this increase in gain and the increase in input variance (Fig. 8B, 
).
|
re-plotted from Fig. 4). Another possibility, however, is that Zd7288 upset the balance of inward and outward currents, which reduced the stationarity in the dendrite-to-soma input/output function. This second hypothesis is supported by the reduced goodness-of-fit that occurred when Ih was blocked (compare Figs. 3A and 7A). Unfortunately, the low number of cells recorded in Zd7288 makes it difficult to fully distinguish between these two possibilities. Nevertheless, these results suggest Ih plays a prominent role, either by itself or through its interaction with other voltage-dependent channels, in shaping the input/output function of a neuron by contributing to both the frequency response and regulation of the input/output gain. |
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
There is a long history of using white-noise stimuli to quantitatively extract the transfer-function of physiological systems (for reviews, see Marmarelis and Marmarelis 1978; Sakai 1992; Westwick and Kearney 2003) and single neurons (e.g., Jahnsen and Karnup 1994; Moore and Christensen 1985; Wright et al. 1996). In addition to more closely mimicking the highly variable input dendrites are likely to receive in vivo, white-noise also has the advantage of containing all frequencies and temporal correlations. Thus it is a relatively "unbiased" stimulus that is suitable for extracting the input/output properties of the system under study. Although Ulrich (2002) used a sinusoidal "chirp" stimulus to characterize the linear portion of the dendrite-to-soma transfer-function in cortical neurons, to our knowledge a full white-noise characterization has never been applied to the dendrite-to-soma input/output function.
The significance of our observations is supported by the fact that the LN model was able to account for >97% of the variance in the somatic potential in responses to the random current injected at the dendrite. Thus the LN model represents a full description of the neuronal input/output relationship over a wide range of input amplitudes. The excellent fit was not due to over-fitting as the number of data points far exceeded the number of free parameters in the LN model (see METHODS). Given the extreme nonlinearities of voltage-dependent channels, it was surprising to find that a simple functional model captured the input/output function even under large suprathreshold input conditions that produced robust spiking activity.
It should be emphasized that our experiments do not distinguish between the respective contributions of the soma and dendrites to the input/output function. Based on the high density of Ih and other channels in the dendrites of neurons (e.g., Lorincz et al. 2002; Magee 1998) and an abundance of electropysiological data showing that these channels are activated by subthreshold synaptic input (e.g., Magee 1998; Magee and Johnston 1995; Williams and Stuart 2000), it is likely that active voltage-dependent dendritic currents play some role in shaping the input/output relationship of the neuron. However, future experiments will be required to fully quantify the extent to which the dendrites contribute to the filtering and gain control of continuous time-varying input signals.
Theta-frequency band-pass of the dendrite-to-soma linear filter
It is notable that the dendrite-to-soma input/output relationship contained a prominent band-pass in the theta frequency range. Specific cognitive and behavioral states are correlated with theta oscillations in the neuronal activity of the hippocampus. These oscillations occur during active exploration of the environment, during REM sleep and may underlie memory related processes (for reviews, see Buzsaki 2002; Lengyel et al. 2005).
It has been proposed that there is a link between the electrical properties of single neurons and network oscillations in the brain (for review, see Hutcheon and Yarom 2000). Using single-electrode recordings at the soma, studies have demonstrated a band-pass frequency response in variety of central and peripheral neurons (Erchova et al. 2004; Hutcheon et al. 1996; Leung and Yu 1998). In the context of network oscillations, this band-pass feature of the membrane potential is usually referred to as resonance. Importantly, these studies demonstrate that the voltage and time-dependent properties of membrane conductances account for a neuron's resonance. Thus in addition to its role in neuronal oscillations, our results and those of Ulrich (2002) suggest that the resonance of a neuron, as revealed by the dendrite-to-soma linear filter of the LN model, fundamentally affects how dendritic inputs are processed.
The band-pass filtering observed in our experiments agrees with a study on neocortical pyramidal dendrites by Ulrich (2002). The main difference between our approaches is that the sinusoid input used by Ulrich contains strong temporal correlations compared with the flat autocorrelation function of our random stimulus. Although our stimuli were substantially different and the linear filtering and nonlinear gain control were not separated in Ulrich's study, his results also suggest the dendrite-to-soma input/output function of pyramidal neurons contains a prominent band-pass in the theta frequency range.
Ulrich also found that the dendritic band-pass filtering remained relatively constant under sub and super-threshold inputs that varied in amplitude by 20%. We found a similar constancy of filtering using a much larger range of input amplitudes. Thus the constant band-pass filtering may be a general feature of dendritic processing used by pyramidal neurons throughout the brain.
Gain control in neural systems
As predicted by information theory, adaptation to the input statistics is a prominent feature of sensory processing at the network and systems level (e.g., Atick 1992; Barlow 1961; Bialek and Rieke 1992; Hosoya et al. 2005; Van Wezel and Britten 2002). For example, there is ample evidence that neuronal responses in the visual system adapt to the variance (also referred to as contrast) of the visual input (e.g., Albrecht et al. 1984; Baccus and Meister 2002; Fairhall et al. 2001; Kim and Rieke 2001; e.g., Maffei et al. 1973; Movshon and Lennie 1979). These mechanisms are generally thought to contribute to the efficient representation of information in the face of changing input statistics. Gain modulation at the circuit level has also been shown to occur throughout the nervous system in a variety of other information processing contexts such as attention (McAdams and Maunsell 1999; Reynolds et al. 2000; Treue and Martinez Trujillo 1999), input normalization (Carandini and Heeger 1994), and gain fields (Salinas and Abbott 1997). It was recently reported that attentional gain changes did not alter the linear transfer function of visual cortical neurons (Cook and Maunsell 2004), which agrees with our current observations that changes in gain occurred with no systematic changes in the temporal filtering of the dendrite-to-soma input/output function.
At first glance, a median 14% reduction in gain of the dendrite-to-soma transfer function observed in our experiments may seem small compared with the relatively large increase in input variance. In vivo studies, however, have shown that small modulations in neuronal activity are correlated with significant changes in behavior. For example, in vivo electrophysiology in non-human primates has demonstrated that attentional state can greatly affect behavioral performance in a visual task while modulating neuronal activity by relatively small amounts of 10–20% (Cook and Maunsell 2002b). In other non-human primate in vivo studies, the correlation between the behavioral choice an animal makes in a task and the corresponding change in neuronal activity is governed by small changes in spike rates of <10% (Britten et al. 1996; Cook and Maunsell 2002a; Dodd et al. 2001; Purushothaman and Bradley 2005; Uka and DeAngelis 2004). Although we do not know the behavioral significance of small modulations in CA1 pyramidal neuron activity, the evidence from in vivo electrophysiology studies suggest even small modulatory effects may carry important behavioral consequences.
Several studies have observed regulation of neuronal gain of signals injected directly into the soma of neurons. These results have suggested that regulation of neuronal gain is due to intrinsic channel mechanisms (Sanchez-Vives et al. 2000), changes in background synaptic activity (Chance et al. 2002; Kerr and Capogna 2007; Mitchell and Silver 2003; Prescott and De Koninck 2003; Rauch et al. 2003; Shu et al. 2003), or an interaction of synaptic input and intrinsic voltage- and time-dependent channel properties (Azouz 2005; Higgs et al. 2006; Kim and Rieke 2001). A recent computer modeling study suggests Ih may contribute to the neuronal gain when combined with other voltage-dependent channels (Burdakov 2005). An intriguing possibility is that control of gain may be possible through diffused modulatory inputs that regulate dendritic plasticity (Magee and Johnston 2005). We should note, however, that our observed gain change is opposite in sign to that recently proposed by Larkum and colleagues (2004), raising the possibility of multiple gain control mechanisms in dendrites of different classes of neurons.
That changing the variance of the input produced a gain change with no change in the filter properties of the input/output function is somewhat surprising given that our high-variance input was large enough to produce action potentials. This is because mechanisms that could potentially modify gain, such as the opening of dendritic voltage-gated conductances, would also be expected to change the temporal filtering properties of the dendrite. Neuronal mechanisms that provide multiplicative changes in gain with no change in the temporal properties have not been easy to resolve and represent an active area of neuroscience investigation (Salinas and Thier 2000).
Functional implications of the LN model
Investigators have been applying system identification methods to characterize the input/output relationship of neuronal systems for many years (e.g., Jones and Palmer 1987; Marmarelis and Marmarelis 1978). Because the LN model separates the temporal and amplitude dependent processing, this functional description provides a satisfying and intuitive picture of input/output function. Describing neuronal processing in precise terms such as filtering and gain control is a distinct advantage because it allows us to draw on the wealth of expertise in the signal processing and information sciences.
Our results suggest that CA1 neurons integrate time-varying inputs in a linear to sublinear fashion that is dependent on the statistics of the input. There are several points to consider when comparing our results with other studies of dendritic integration. First, nonlinear systems often exhibit linear behavior over small input perturbations. Thus dendritic summation may appear linear when explored with small subthreshold EPSPs, or in the case of our study, the low-variance input. A second consideration is that we bypassed the synaptic machinery by using dendritic current injection. Synaptic conductances have nonlinearities that arise from both the reduction in driving force and the voltage dependence of the N-methyl-D-aspartate (NMDA) synaptic conductance.
The third, and potentially most important consideration when comparing the difference between various studies is the state of voltage- and time-dependent channels in the neuron when the synaptic input arrives. Previous studies of dendritic integration usually invoked EPSPs in neurons at rest with no background activity (but see Gasparini and Magee 2006; Larkum et al. 2001; Oviedo and Reyes 2002, 2005). As both depolarization and hyperpolarization produces changes in the activation state of voltage and time-dependent conductances in the dendrite, it is likely that our continuous time-varying input produced a state change in the neuron compared with a quiescent cell at rest. Given that a typical CA1 cell receives thousands of synaptic connections, it is highly unlikely that a neuron is ever in such a quiescent state in vivo.
Several recent studies by Gasparini and colleagues have shown that action potentials initiated in the dendrites produce a supralinear, or expansive nonlinear, effect on synaptic summation (Gasparini and Magee 2006; Gasparini et al. 2004). Because of the random nature of our continuous stimulus, we were unable to clearly determine if our action potentials were initiated in the dendrites during the high-variance input. However, the effect of the high-variance input was the introduction of a compressive nonlinearity, which is opposite to that observed by Gasparini et al. The differences in our results could be explained by the fact their synaptic input was applied to quiescent neurons at rest compared with our continuous-time input. It is also possible that our high-variance input, although strong enough to produce action potentials, was too weak to initiate dendritic action potentials. Another important difference is that our dendritic input was relatively proximal (within the proximal 2/3 of the apical trunk) compared with Gasparini et al. Distal dendrites may be much more active and the effects of very distal inputs on the LN model is the topic for a future study.
That our LN model accounted for much of the input/output function suggests the signal propagation from the proximal apical dendrites to the soma may be highly reliable. A major focus of neuroscience centers on the question of why central neurons produce highly variable patterns of action potentials when recorded in vivo (for review, see Stein et al. 2005). However, single neurons can produce very reliable timing of action potentials in response to fluctuating somatic current injections (Mainen and Sejnowski 1995). Although our experiments did not include enough repeated stimulus presentations to quantitatively assess the reliability of our soma-to-dendrite transfer function, a casual observation of our data suggests there was very little variation of the somatic membrane potential from one repeat to the next. Thus it is possible that signals arriving on the main apical trunk of the dendrites are passed on to the soma with little additive noise.
Contribution of Ih to the input/output function
Although many voltage-dependent conductances play a role in shaping the input/output properties of neurons, our results suggest that Ih may have a primary role in determining the band-pass filter characteristics. Ulrich (2002) also reported that Ih contributes to the band-pass properties in cortical pyramidal neurons while also showing that changes in the DC level of the input altered the linear filtering. It remains to be determined how the DC level of our noise input would affect the components of the LN model.
The precise role of Ih on gain regulation is difficult to reveal because of the contribution of other voltage-dependent currents at depolarized potentials. Ih is clearly a prominent player in the regulation of gain and removing this voltage-dependent current caused the input/output function to go from an average decrease to an average increase in gain with increased input variance (Fig. 8). This suggests a dampening, or shunting, role of Ih in the regulation of the input/output function. That the LN model predicted slightly less of the somatic voltage potential suggests the removal of Ih pushed the input/output relationship of the neuron toward a more nonlinear regime that is less stationary and thus less amenable to a description by a simple functional model.
|
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: E. P. Cook, Dept. of Physiology, McGill University, 3655 Sir William Osler, Montreal, QC H3G 1Y6, Canada (E-mail: erik.cook{at}mcgill.ca)
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
Anderson JS, Lampl I, Gillespie DC, Ferster D. The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290: 1968–1972, 2000.
Ariav G, Polsky A, Schiller J. Submillisecond precision of the input-output transformation function mediated by fast sodium dendritic spikes in basal dendrites of CA1 pyramidal neurons. J Neurosci 23: 7750–7758, 2003.
Atick JJ. Could information theory provide an ecological theory of sensory processing? Network 3: 213–251, 1992.[Web of Science]
Azouz R. Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited. J Neurophysiol 94: 2785–2796, 2005.
Baccus SA, Meister M. Fast and slow contrast adaptation in retinal circuitry. Neuron 36: 909–919, 2002.[CrossRef][Web of Science][Medline]
Barlow HB. Possible principles underlying the transformation of sensory messages. In: Sensory Communication, edited by RosenBlith WA. Cambridge, MA: MIT Press, 1961, p. 217–234.
Bialek W, Rieke F. Reliability and information transmission in spiking neurons. Trends Neurosci 15: 428–434, 1992.[CrossRef][Web of Science][Medline]
Binder MD, Poliakov AV, Powers RK. Functional identification of the input-output transforms of mammalian motoneurones. J Physiol 93: 29–42, 1999.
Borg-Graham LJ, Monier C, Fregnac Y. Visual input evokes transient and strong shunting inhibition in visual cortical neurons. Nature 393: 369–373, 1998.[CrossRef][Medline]
Britten KH, Newsome WT, Shadlen MN, Celebrini S, Movshon JA. A relationship between behavioral choice and the visual responses of neurons in macaque MT. Vis Neurosci 13: 87–100, 1996.[Web of Science][Medline]
Bryant HL, Segundo JP. Spike initiation by transmembrane current: a white-noise analysis. J Physiol 260: 279–314, 1976.
Burdakov D. Gain control by concerted changes in I(A) and I(H) conductances. Neural Comput 17: 991–995, 2005.[CrossRef][Web of Science][Medline]
Buzsaki G. Theta oscillations in the hippocampus. Neuron 33: 325–340, 2002.[CrossRef][Web of Science][Medline]
Carandini M, Heeger DJ. Summation and division by neurons in primate visual cortex. Science 264: 1333–1336, 1994.
Cash S, Yuste R. Linear summation of excitatory inputs by CA1 pyramidal neurons. Neuron 22: 383–394, 1999.[CrossRef][Web of Science][Medline]
Chance FS, Abbott LF, Reyes AD. Gain modulation from background synaptic input. Neuron 35: 773–782, 2002.[CrossRef][Web of Science][Medline]
Chichilnisky EJ. A simple white noise analysis of neuronal light responses. Network 12: 199–213, 2001.[Web of Science][Medline]
Colbert CM, Pan E. Ion channel properties underlying axonal action potential initiation in pyramidal neurons. Nat Neurosci 5: 533–538, 2002.[CrossRef][Web of Science][Medline]
Cook EP, Guest JA, Colbert CM. White-noise analysis of CA1 pyramidal dendrites reveals linear signal processing with boosting of subthreshold inputs. Soc Neurosci Abstr 738.3, 2005.
Cook EP, Maunsell JHR. Dynamics of neuronal responses in macaque MT and VIP during motion detection. Nat Neurosci 5: 985–994, 2002a.[CrossRef][Web of Science][Medline]
Cook EP, Maunsell JHR. Attentional modulation of behavioral performance and neuronal responses in Middle Temporal and Ventral Intraparietal areas of macaque monkey. J Neurosci 22: 1994–2004, 2002b.
Cook EP, Maunsell JH. Attentional modulation of motion integration of individual neurons in the middle temporal visual area. J Neurosci 24: 7964–7977, 2004.
Davis GW, Bezprozvanny I. Maintaining the stability of neural function: a homeostatic hypothesis. Annu Rev Physiol 63: 847–869, 2001.[CrossRef][Web of Science][Medline]
Destexhe A, Pare D. Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81: 1531–1547, 1999.
Destexhe A, Rudolph M, Pare D. The high-conductance state of neocortical neurons in vivo. Nat Rev Neurosci 4: 739–751, 2003.[CrossRef][Web of Science][Medline]
Dodd JV, Krug K, Cumming BG, Parker AJ. Perceptually bistable three-dimensional figures evoke high choice probabilities in cortical area MT. J Neurosci 21: 4809–4821, 2001.
Efron B, Tibshirani R. An Introduction to the Bootstrap. London: Chapman and Hall, 1993.
Erchova I, Kreck G, Heinemann U, Herz AV. Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. J Physiol 560: 89–110, 2004.
Fairhall AL, Lewen GD, Bialek W, de Ruyter Van Steveninck RR. Efficiency and ambiguity in an adaptive neural code. Nature 412: 787–792, 2001.[CrossRef][Medline]
Ferster D, Jagadeesh B. EPSP-IPSP interactions in cat visual cortex studied with in vivo whole-cell patch recording. J Neurosci 12: 1262–1274, 1992.[Abstract]
Gasparini S, Magee JC. State-dependent dendritic computation in hippocampal CA1 pyramidal neurons. J Neurosci 26: 2088–2100, 2006.
Gasparini S, Migliore M, Magee JC. On the initiation and propagation of dendritic spikes in CA1 pyramidal neurons. J Neurosci 24: 11046–11056, 2004.
Golding NL, Spruston N. Dendritic sodium spikes are variable triggers of axonal action potentials in hippocampal CA1 pyramidal neurons. Neuron 21: 1189–1200, 1998.[CrossRef][Web of Science][Medline]
Hausser M, Mel B. Dendrites: bug or feature? Curr Opin Neurobiol 13: 372–383, 2003.[CrossRef][Web of Science][Medline]
Hausser M, Spruston N, Stuart GJ. Diversity and dynamics of dendritic signaling. Science 290: 739–744, 2000.
Higgs MH, Slee SJ, Spain WJ. Diversity of gain modulation by noise in neocortical neurons: regulation by the slow afterhyperpolarization conductance. J Neurosci 26: 8787–8799, 2006.
Hirsch JA, Alonso JM, Reid RC, Martinez LM. Synaptic integration in striate cortical simple cells. J Neurosci 18: 9517–9528, 1998.
Ho N, Destexhe A. Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons. J Neurophysiol 84: 1488–1496, 2000.
Holt GR, Koch C. Shunting inhibition does not have a divisive effect on firing rates. Neural Comput 9: 1001–1013, 1997.[CrossRef][Web of Science][Medline]
Hosoya T, Baccus SA, Meister M. Dynamic predictive coding by the retina. Nature 436: 71–77, 2005.[CrossRef][Medline]
Hunter IW, Korenberg MJ. The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol Cybern 55: 135–144, 1986.[Web of Science][Medline]
Hutcheon B, Miura RM, Puil E. Subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76: 683–697, 1996.
Hutcheon B, Yarom Y. Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci 23: 216–222, 2000.[CrossRef][Web of Science][Medline]
Ishizuka N, Cowan WM, Amaral DG. A quantitative analysis of the dendritic organization of pyramidal cells in the rat hippocampus. J Comp Neurol 362: 17–45, 1995.[CrossRef][Web of Science][Medline]
Jahnsen H, Karnup S. A spectral analysis of the integration of artificial synaptic potentials in mammalian central neurons. Brain Res 666: 9–20, 1994.[CrossRef][Web of Science][Medline]
Johnston D, Magee JC, Colbert CM, Cristie BR. Active properties of neuronal dendrites. Annu Rev Neurosci 19: 165–186, 1996.[CrossRef][Web of Science][Medline]
Jones JP, Palmer LA. The two-dimensional spatial structure of simple receptive fields in cat striate cortex. J Neurophysiol 58: 1187–1211, 1987.
Kamondi A, Acsady L, Buzsaki G. Dendritic spikes are enhanced by cooperative network activity in the intact hippocampus. J Neurosci 18: 3919–3928, 1998.
Kerr AM, Capogna M. Unitary IPSPs enhance hilar mossy cell gain in the rat hippocampus. J Physiol 578: 451–470, 2007.
Kim KJ, Rieke F. Temporal contrast adaptation in the input and output signals of salamander retinal ganglion cells. J Neurosci 21: 287–299, 2001.
Korenberg MJ, French AS, Voo SK. White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches. Biol Cybern 58: 313–320, 1988.[CrossRef][Web of Science][Medline]
Korenberg MJ, Sakai HM, Naka K. Dissection of the neuron network in the catfish inner retina. III. Interpretation of spike kernels. J Neurophysiol 61: 1110–1120, 1989.
Larkum ME, Senn W, Luscher HR. Top-down dendritic input increases the gain of layer 5 pyramidal neurons. Cereb Cortex 14: 1059–1070, 2004.
Larkum ME, Zhu JJ. Signaling of layer 1 and whisker-evoked Ca2+ and Na+ action potentials in distal and terminal dendrites of rat neocortical pyramidal neurons in vitro and in vivo. J Neurosci 22: 6991–7005, 2002.
Larkum ME, Zhu JJ, Sakmann B. Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons. J Physiol 533: 447–466, 2001.
Lengyel M, Huhn Z, Erdi P. Computational theories on the function of theta oscillations. Biol Cybern 92: 393–408, 2005.[CrossRef][Web of Science][Medline]
Leung LS, Yu HW. Theta-frequency resonance in hippocampal CA1 neurons in vitro demonstrated by sinusoidal current injection. J Neurophysiol 79: 1592–1596, 1998.
London M, Hausser M. Dendritic computation. Annu Rev Neurosci 28: 503–532, 2005.[CrossRef][Web of Science][Medline]
Lorincz A, Notomi T, Tamas G, Shigemoto R, Nusser Z. Polarized and compartment-dependent distribution of HCN1 in pyramidal cell dendrites. Nat Neurosci 5: 1185–1193, 2002.[CrossRef][Web of Science][Medline]
Maffei L, Fiorentini A, Bisti S. Neural correlate of perceptual adaptation to gratings. Science 182: 1036–1038, 1973.
Magee JC. Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal CA1 pyramidal neurons. J Neurosci 18: 7613–7624, 1998.
Magee JC. Dendritic lh normalizes temporal summation in hippocampal CA1 neurons. Nat Neurosci 2: 508–514, 1999.[CrossRef][Web of Science][Medline]
Magee JC. Dendritic integration of excitatory synaptic input. Nat Rev Neurosci 1: 181–190, 2000.[CrossRef][Web of Science][Medline]
Magee JC, Johnston D. Synaptic activation of voltage-gated channels in the dendrites of hippocampal pyramidal neurons. Science 268: 301–304, 1995.
Magee JC, Johnston D. Plasticity of dendritic function. Curr Opin Neurobiol 15: 334–342, 2005.[CrossRef][Web of Science][Medline]
Mainen ZF, Sejnowski TJ. Reliability of spike timing in neocortical neurons. Science 268: 1503–1506, 1995.
Markus EJ, Qin YL, Leonard B, Skaggs WE, McNaughton BL, Barnes CA. Interactions between location and task affect the spatial and directional firing of hippocampal neurons. J Neurosci 15: 7079–7094, 1995.[Abstract]
Marmarelis PZ, Marmarelis VZ. Analysis of Physiological Systems: The White Noise Approach. New York: Plenum, 1978.
McAdams CJ, Maunsell JHR. Effects of attention on orientation-tuning functions of single neurons in macaque cortical area V4. J Neurosci 19: 431–441, 1999.
Meister M, Berry MJ Jr. The neural code of the retina. Neuron 22: 435–450, 1999.[CrossRef][Web of Science][Medline]
Mel BW. Synaptic integration in an excitable dendritic tree. J Neurophysiol 70: 1086–1101, 1993.
Migliore M, Shepherd GM. Emerging rules for the distributions of active dendritic conductances. Nat Rev Neurosci 3: 362–370, 2002.[CrossRef][Web of Science][Medline]
Mitchell SJ, Silver RA. Shunting inhibition modulates neuronal gain during synaptic excitation. Neuron 38: 433–445, 2003.[CrossRef][Web of Science][Medline]
Moore LE, Christensen BN. White noise analysis of cable properties of neuroblastoma cells and lamprey central neurons. J Neurophysiol 53: 636–651, 1985.
Movshon JA, Lennie P. Pattern-selective adaptation in visual cortical neurones. Nature 278: 850–852, 1979.[CrossRef][Medline]
Nettleton JS, Spain WJ. Linear to supralinear summation of AMPA-mediated EPSPs in neocortical pyramidal neurons. J Neurophysiol 83: 3310–3322, 2000.
Nevian T, Larkum ME, Polsky A, Schiller J. Properties of basal dendrites of layer 5 pyramidal neurons: a direct patch-clamp recording study. Nat Neurosci 10: 206–214, 2007.[CrossRef][Web of Science][Medline]
Oviedo H, Reyes AD. Boosting of neuronal firing evoked with asynchronous and synchronous inputs to the dendrite. Nat Neurosci 5: 261–266, 2002.[CrossRef][Web of Science][Medline]
Oviedo H, Reyes AD. Variation of input-output properties along the somatodendritic axis of pyramidal neurons. J Neurosci 25: 4985–4995, 2005.
Poliakov AV, Powers RK, Binder MD. Functional identification of the input-output transforms of motoneurons in the rat and cat. J Physiol 504: 401–424, 1997.
Polsky A, Mel BW, Schiller J. Computational subunits in thin dendrites of pyramidal cells. Nat Neurosci 7: 621–627, 2004.[CrossRef][Web of Science][Medline]
Prescott SA, De Koninck Y. Gain control of firing rate by shunting inhibition: roles of synaptic noise and dendritic saturation. Proc Natl Acad Sci USA 100: 2076–2081, 2003.
Purushothaman G, Bradley DC. Neural population code for fine perceptual decisions in area MT. Nat Neurosci 8: 99–106, 2005.[CrossRef][Web of Science][Medline]
Rall W. Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol 1: 491–527, 1959.[CrossRef][Web of Science][Medline]
Rauch A, La Camera G, Luscher HR, Senn W, Fusi S. Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents. J Neurophysiol 90: 1598–1612, 2003.
Reyes A. Influence of dendritic conductances on the input-output properties of neurons. Annu Rev Neurosci 24: 653–675, 2001.[CrossRef][Web of Science][Medline]
Reynolds JH, Pasternak T, Desimone R. Attention increases sensitivity of V4 neurons. Neuron 26: 703–714, 2000.[CrossRef][Web of Science][Medline]
Sakai HM. White-noise analysis in neurophysiology. Physiol Rev 72: 491–505, 1992.
Salinas E, Abbott LF. Invariant visual responses from attentional gain fields. J Neurophysiol 77: 3267–3272, 1997.
Salinas E, Sejnowski TJ. Gain modulation in the central nervous system: where behavior, neurophysiology, and computation meet. Neuroscientist 7: 430–440, 2001.
Salinas E, Thier P. Gain modulation: a major computational principle of the central nervous system. Neuron 27: 15–21, 2000.[CrossRef][Medline]
Sanchez-Vives MV, Nowak LG, McCormick DA. Membrane mechanisms underlying contrast adaptation in cat area 17 in vivo. J Neurosci 20: 4267–4285, 2000.
Schaefer AT, Larkum ME, Sakmann B, Roth A. Coincidence detection in pyramidal neurons is tuned by their dendritic branching pattern. J Neurophysiol 89: 3143–3154, 2003.
Schwindt PC, Crill WE. Local and propagated dendritic action potentials evoked by glutamate iontophoresis on rat neocortical pyramidal neurons. J Neurophysiol 77: 2466–2483, 1997.
Segev I, London M. Untangling dendrites with quantitative models. Science 290: 744–750, 2000.
Shu Y, Hasenstaub A, Badoual M, Bal T, McCormick DA. Barrages of synaptic activity control the gain and sensitivity of cortical neurons. J Neurosci 23: 10388–10401, 2003.
Slee SJ, Higgs MH, Fairhall AL, Spain WJ. Two-dimensional time coding in the auditory brain stem. J Neurosci 25: 9978–9988, 2005.
Stein RB, Gossen ER, Jones KE. Neuronal variability: noise or part of the signal? Nat Rev Neurosci 6: 389–397, 2005.[Web of Science][Medline]
Stuart G, Schiller J, Sakmann B. Action potential initiation and propagation in rat neocortical pyramidal neurons. J Physiol 505: 617–632, 1997.
Tamas G, Szabadics J, Somogyi P. Cell type- and subcellular position-dependent summation of unitary postsynaptic potentials in neocortical neurons. J Neurosci 22: 740–747, 2002.
Treue S, Martinez Trujillo JC. Feature-based attention influences motion processing gain in macaque visual cortex. Nature 399: 575–579, 1999.[CrossRef][Medline]
Turner RW, Meyers DE, Richardson TL, Barker JL. The site for initiation of action potential discharge over the somatodendritic axis of rat hippocampal CA1 pyramidal neurons. J Neurosci 11: 2270–2280, 1991.[Abstract]
Turrigiano GG, Nelson SB. Hebb and homeostasis in neuronal plasticity. Curr Opin Neurobiol 10: 358–364, 2000.[CrossRef][Web of Science][Medline]
Uka T, DeAngelis GC. Contribution of area MT to stereoscopic depth perception: choice-related response modulations reflect task strategy. Neuron 42: 297–310, 2004.[CrossRef][Web of Science][Medline]
Ulrich D. Dendritic resonance in rat neocortical pyramidal cells. J Neurophysiol 87: 2753–2759, 2002.
Urban NN, Barrionuevo G. Active summation of excitatory postsynaptic potentials in hippocampal CA3 pyramidal neurons. Proc Natl Acad Sci USA 95: 11450–11455, 1998.
Van Wezel RJ, Britten KH. Motion adaptation in area MT. J Neurophysiol 88: 3469–3476, 2002.
Wei DS, Mei YA, Bagal A, Kao JP, Thompson SM, Tang CM. Compartmentalized and binary behavior of terminal dendrites in hippocampal pyramidal neurons. Science 293: 2272–2275, 2001.
Westwick DT Kearney RE. Identification of Nonlinear Physiological Systems. Piscataway: IEEE Press, 2003.
Williams SR. Spatial compartmentalization and functional impact of conductance in pyramidal neurons. Nat Neurosci 7: 961–967, 2004.[CrossRef][Web of Science][Medline]
Williams SR, Stuart GJ. Site independence of EPSP time course is mediated by dendritic I(h) in neocortical pyramidal neurons. J Neurophysiol 83: 3177–3182, 2000.
Williams SR, Stuart GJ. Dependence of EPSP efficacy on synapse location in neocortical pyramidal neurons. Science 295: 1907–1910, 2002.
Womack MD, Khodakhah K. Dendritic control of spontaneous bursting in cerebellar Purkinje cells. J Neurosci 24: 3511–3521, 2004.
Wright WN, Bardakjian BL, Valiante TA, Perez-Velazquez JL, Carlen PL. White noise approach for estimating the passive electrical properties of neurons. J Neurophysiol 76: 3442–3450, 1996.
Wu MC, David SV, Gallant JL. Complete functional characterization of sensory neurons by system identification. Annu Rev Neurosci 29: 477–505, 2006.[CrossRef][Web of Science][Medline]
Yoganarasimha D, Yu X, Knierim JJ. Head direction cell representations maintain internal coherence during conflicting proximal and distal cue rotations: comparison with hippocampal place cells. J Neurosci 26: 622–631, 2006.
This article has been cited by other articles:
|
|
 |
|
  P. J. Sjostrom, E. A. Rancz, A. Roth, and M. Hausser Dendritic Excitability and Synaptic Plasticity Physiol Rev, April 1, 2008; 88(2): 769 - 840. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
60 µm, —) and distal (electrode separation 
160 µm, - - -) dendritic current injections. Each is an average of 4 experiments, and data are shown for only the high-variance input. Error bars are SE.
