Linear to Supralinear Summation of AMPA-Mediated EPSPs in Neocortical Pyramidal Neurons

Jilda S. Nettleton1,3 and William J. Spain1,2,3

 1Veterans Affairs Puget Sound Health Care System, Seattle 98108 and  2Department of Neurology and  3Department of Physiology and Biophysics, University of Washington School of Medicine, Seattle, Washington 98195


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Nettleton, Jilda S. and William J. Spain. Linear to Supralinear Summation of AMPA-Mediated EPSPs in Neocortical Pyramidal Neurons. J. Neurophysiol. 83: 3310-3322, 2000. It has been hypothesized that voltage-sensitive conductances present on the dendrites of neurons can influence summation of excitatory postsynaptic potentials (EPSPs) and hence affect how neurons compile information. Greater than linear summation of EPSPs has been postulated to facilitate coincidence detection by cortical neurons. This study examined whether the summation of subthreshold AMPA-mediated EPSPs generated on layer V neocortical pyramidal neurons in vitro was linear and if any nonlinearities could be attributed to dendritic conductances. Evoked EPSPs (1-12 mV) were recorded somatically by means of intracellular sharp electrodes in the presence of 100 µM amino-5-phosphonopentanoic acid (AP-5) and 3 µM bicuculline. Two independent EPSPs were evoked by a stimulating electrode in layer I and another in layers III-V. The areas of stimulation were isolated from each other by a horizontal cut below layer I. By subtracting the algebraic sum of the individual EPSPs from the evoked response when both EPSPs were evoked simultaneously, we determined that they summed linearly to supralinearly. Supralinear summation was more likely when the soma was hyperpolarized by DC current injection. Summation was predominantly linear when postsynaptic conductances (i.e., Na+ and Ca2+) were blocked with intracellular QX-314. The supralinear summation of EPSPs (without QX-314) decreased as the time between inputs was increased from 0 to 30 ms. To determine the role of dendrites in nonlinear summation, we substituted a current pulse (simulated EPSP) delivered at the soma for either or both of the evoked EPSPs. Simulated EPSPs combined with either an evoked EPSP or another simulated EPSP showed significantly less supralinear summation than two evoked EPSPs, indicating that the dendritic conductances were largely responsible for the observed supralinear summation.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Neurons in cerebral cortex receive a continuous barrage of both excitatory and inhibitory synaptic inputs. There are estimated to be 3,000-10,000 synaptic inputs on a cortical neuron (Peters 1994) of which a considerable fraction may be active at any one time. How does the neuron integrate these individual events into an output firing pattern? According to the Rall model in which the dendrites are assumed to be passive, EPSPs would sum either linearly or sublinearly when there is reduction in the driving force for synaptic conductances (Rall et al. 1967). Dendrites are not passive but instead possess voltage-sensitive conductances that could affect synaptic integration (for review, see Yuste and Tank 1996). Dendrites have been shown to generate regenerative Na+- and Ca2+-dependent potentials (Amitai et al. 1993; Kim and Connors 1993; Llinas and Sugimori 1980; Pockberger 1991; Reuveni et al. 1993; Schiller et al. 1997; Spruston at al. 1995; Stuart and Sakmann 1994; Stuart et al. 1997; Wong et al. 1979). Additionally, dendritic conductances have been shown to modify synaptic currents (Lee and Heckman 1996; Schwindt and Crill 1995, 1997). Pyramidal neurons may have a nonhomogeneous distribution of ionic conductances that could potentially affect how EPSPs at different locations are integrated. Studies in both neocortical and hippocampal pyramidal neurons indicate that there is an uneven distribution of Ca2+ channel types along the apical dendrite (Hell et al. 1993; Johnston et al. 1996; Reuveni et al. 1993; Schiller et al. 1995; Westenbroek et al. 1992; Yuste et al. 1994). There is also evidence that neurons may express uneven distributions of other ion channel types as well (Maletic-Savatic et al. 1995; Sheng et al. 1994; Stuart and Spruston 1998; Westenbroek et al. 1989).

How could these conductances affect integration of subthreshold excitatory postsynaptic potentials (EPSPs)? Evoked subthreshold synaptic potentials can activate Na+ and Ca2+ channels (Magee and Johnston 1995a,b) and cause calcium influx into dendrites (Magee et al. 1995; Markram and Sakmann 1994; Schiller et al. 1997). Na+ and Ca2+ conductances could cause supralinear summation by increasing the size of EPSPs (Gillessen and Alzheimer 1997; Lipowsky et al. 1996). In contrast, dendritically located K+ channels decrease the size of the EPSP in hippocampal pyramidal neurons (Hoffman et al. 1997) and decrease synaptic current in neocortical neurons (Schwindt and Crill 1997). In cultured hippocampal pyramidal neurons, IA causes sublinear summation of synaptic inputs (Cash and Yuste 1998). How EPSPs sum may depend on the relative quantity of Na+, Ca2+, and K+ conductances activated by EPSPs.

Ionic conductances are also time dependent, the relative timing of inputs could have an effect on how much they are able to affect each other. Some modeling studies indicate that layer V neurons could act as coincidence detectors and that only inputs within a millisecond of each other are able to interact with each other to bring the neuron to firing threshold (Konig et al. 1996; Softky and Koch 1993). Other studies propose that neurons operate in an integrate and fire mode (Shadlen and Newsome 1994). The time dependence of excitatory synaptic summation in pyramidal neurons has yet to be measured experimentally.

The goal of this study was to determine if layer V pyramidal neurons sum their synaptic inputs in a linear or nonlinear fashion. We found that subthreshold EPSPs can sum supralinearly in layer V pyramidal neurons due to postsynaptic, QX-314-sensitive conductances, and we determined that dendritic conductances contributed to the supralinear summation. These results give new information about how neurons integrate information. Some of the results have been presented previously in abstract form (Nettleton and Spain 1996).


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Tissue preparation

Slices of sensorimotor cortex were obtained from 24- to 90-day-old Sprague-Dawley rats of either sex as described previously (Cerne and Spain 1997). Briefly, rats were anesthetized with intraperitoneal injections of ketamine and xylazine. Once the animal was areflexive to strong foot pinch, the carotid arteries were cut and sensorimotor cortex was excised. Either 350- or 400-µM coronal slices were cut on a Vibratome and maintained at 33°C in a carbogenated (95% O2 and 5% CO2) Ringer solution containing (in mM) 130 NaCl, 3 KCl, 2 CaCl2, 2 MgCl2, 1.2 NaH2PO4, 26 NaHCO3, and 10 dextrose (pH, 7.4). For recording, slices were transferred to a submerged-type chamber (volume = 0.5 ml) and perfused at 2.5 ml per minute with the carbogenated Ringer solution (34 ± 1°C).

Intracellular recording

Recordings were performed intracellularly on the presumed somata of layer V pyramidal neurons. Recording electrodes were made from borosilicate glass (OD/ID = 1.0 mm/0.58 mm, Sutter Instruments, Novato, CA) pulled on a Flaming/Brown micropipette puller P-87 (Sutter Instruments) and filled with 2.7 M KCl and 1% biocytin. For some experiments, electrodes also contained 50 mM QX-314 (Alomone Labs or Sigma). Resistance was 25-60 MOmega for all electrodes.

Recording was done in current-clamp using the bridge mode of an AxoClamp amplifier (Axon Instruments, Foster City, CA). Current and membrane potential were low-pass filtered (5 kHz) and recorded on videocassettes using pulse-code modulation (44 kHz) (Neuro-Corder DR-890, Neurodata, New York). All stimulating protocols, data collection, and analyses were computerized using Igor Pro (Wavemetrics, Lake Oswego, Oregon) on a Quadra 800 (Apple Computers, Cupertino, CA) and an ITC16 computer interface (Instrutech, Great Neck, NY) using customized programs. During the experiment, both evoked and simulated EPSPs were digitized at 0.1 ms. Measured values are reported as the means ± SE. Unless otherwise stated, statistical comparisons were performed using a two-tailed Student's t-test with the significance criterion set at P < 0.05. Gaussian curves were fit to histograms using a nonlinear, least-squares fitting routine (Levenberg-Marquardt algorithm).

Evoked and simulated EPSPs

Figure 1 shows the method used to isolate two sites of stimulation so that stimulation at one site did not affect fibers stimulated by the other site. A small piece of razor blade was guided by micromanipulator to make a cut in the slice just below layer I. The cut extended from near the apical dendrite of the recorded neuron to the lateral edge of the slice (Fig. 1A). The distal (Ds) stimulating electrode was placed in layers I-II (above the cut), and the more proximal (Px) stimulating electrode was placed below the cut in lower layer III to upper layer V. The Ds stimulating electrode was placed 200-500 µm from the middle of the distal dendritic tuft. The Px stimulus was 200-500 µm from the main trunk of the apical dendrite and 150-300 µm toward the pia from the recording electrode. Both stimulating electrodes were 150-350 µm lateral from the end of the cut nearest to the apical dendrite. These two sites were chosen because they were far enough apart to prevent one stimulus from affecting the other, yet both would still stimulate inputs to the apical dendrite (Cauller and Connors 1994; Ichinose and Murakoshi 1996; White 1989). In most experiments, fine-point monopolar stainless steel electrodes were used. In a few experiments, concentric bipolar electrodes were used (FHC, Bowdoinham, ME). Each stimulating electrode was separately driven by a constant-current stimulus isolator (Model A365, WPI, Sarasota, FL) using either a 1- or 0.2-ms TTL pulse at a frequency of 0.33 Hz. The current amplitude (range, 1.7-70 µA) was adjusted so that the amplitude of the isolated EPSPs were >= 1 mV but below the amplitude that evoked large regenerative depolarizations when both stimuli were given together. These regenerative events typically had a delayed latency of >= 30-40 ms and were a consequence of having inhibition partially blocked (Chagnac-Amital and Connors 1989) since they did not occur prior to the addition of bicuculline to the bath.



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Fig. 1. Experimental setup used to measure excitatory postsynaptic potential (EPSP) summation. A: composite photomicrograph of fluorescent labeled biocytin-filled layer V pyramidal neuron in a 400-µM-thick slice taken from rat neocortex. ---, where a cut was made in the tissue to isolate 2 stimulation sites (), which are labeled Ds and Px. B: 15 superimposed sweeps of EPSPs evoked from 1-ms stimulating pulses delivered at the Ds, Px, or both (Ds and Px) stimulation sites. Stimulation intensity was 8.5 µA for Ds and 2.8 µA for Px. For the EPSPs labeled Ds and Px, both sites were stimulated simultaneously. Holding potential was -76 mV.

We looked for possible interactions between the two stimulus sites by comparing responses from paired Px and Ds stimuli with responses from paired pulses at one of the stimulus sites. Paired-pulse facilitation and paired-pulse depression result from stimulating the same fibers twice in 50-70 ms (Fisher et al. 1997; Zucker 1989). If the two stimuli in these experiments are stimulating some of the same fibers, then paired-pulse depression or paired-pulse facilitation should be observed when the Px and Ds stimuli are 50-70 ms apart. While in some cases we found paired pulse facilitation for either Px-Px or Ds-Ds paired stimuli, we did not observe any paired pulse facilitation or paired pulse depression when the Px and Ds stimuli were delivered 50-70 ms apart.

Experimental protocols for stimulation were as follows: first the Ds and Px stimuli were given individually 10-15 times each at a rate of 0.33 Hz. The two stimuli were then given together 15-20 times (with the interstimulus delay ranging from 0 to 30 ms). Finally the individual Px and Ds stimuli were again delivered 10-15 times each. Analysis was performed on the averaged 10-20 responses to individual Px, Ds, and simultaneous Px plus Ds evoked EPSPs. For each set of stimulus conditions, we checked for nonstationarity of EPSP size by comparing the integral of the algebraic sum of the EPSPs evoked at the start of each set to the same integral from EPSPs evoked at the end of each set. Data were only used from EPSPs whose summed integral changed by <15%.

To isolate AMPA-mediated EPSPs, slices were perfused continuously with 3 µM bicuculline (to block GABAA-mediated responses) and 100 µM amino-5-phosphonopentanoic acid (AP-5) [to block N-methyl-D-aspartate (NMDA)-mediated responses]. The slices were perfused for >= 20 min before summation experiments were performed. These neurons had little or no GABAB-mediated responses at the low stimulus strengths used in this study (Benardo 1994; van Brederode and Spain 1995). Furthermore, the EPSPs elicited in these experiments were completely blocked by 20-60 µM 6,7-dinitroquinoxaline-2,3-dione (DNQX; Tocris Cookson, St. Louis, MO). Residual EPSPs or inhibitory postsynaptic potentials (IPSPs) were not seen at holding potentials of -69 to -97 mV.

In some experiments, simulated EPSPs were created by intracellular current injection, I, as a function of time, t, according to the equation (from Otis et al. 1993)
<IT>I</IT>(<IT>t</IT>)<IT>=</IT><IT>K</IT><IT>∗</IT>(<IT>1−</IT><IT>e</IT><SUP><IT>−</IT><IT>t/t</IT><SUB><IT>1</IT></SUB></SUP>)<SUP><IT>4</IT></SUP><IT>e</IT><SUP><IT>−</IT><IT>t/t</IT><SUB><IT>2</IT></SUB></SUP>
where the amplitude was adjusted by changing K, and the rise and decay of the injected current was altered by changing t1 and t2. The current pulse was adjusted until the time course and amplitude of the evoked voltage response (simulated EPSP) approximated by eye an evoked EPSP in the same neuron. Well-matched simulated EPSPs were then substituted for evoked EPSPs in the experimental protocol.

Histology

After recording, the tissue was fixed using 4% paraformaldehyde in a phosphate buffer solution containing (in mM): 19 NaH2PO4, 83 Na2HPO4, 150 NaCl, and 3 KCl. Once fixed, tissue was either sliced further or left in whole-mount sections. The tissue was processed using a diaminobenzidene reaction to biocytin (Horikawa and Armstrong 1988) or using a fluorescent probe that cross reacts with biocytin. For the fluorescent imaging, neurons were visualized after immersion in 1:100 dilution of Texas Red, Texas RedX or Oregon Green (Molecular Probes, Eugene, OR) for 4-7 days.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The results are based on intracellular recordings from 56 neurons that were recovered histologically and shown to be layer V pyramidal neurons with an intact apical dendrite reaching into layer 1 past the cut (Fig. 1A). For 34 neurons recorded using electrodes containing 2.7 M KCl and biocytin, the mean resting membrane potential was -74 ± 1 mV and mean input resistance was 21 ± 1 MOmega (measured at the end of 5- to 10-mV hyperpolarizing responses evoked by 1-s negative current pulses). All neurons fired action potentials that overshot 0 mV. The 34 neurons were classified as regular spiking neurons (20) or bursting neurons (14, neurons that fired >= 3 action potentials on an initial depolarizing hump) (Connors and Gutnick 1990). No relationship between neuron type and EPSP summation was observed.

Linear to supralinear summation of EPSPs

As shown in Fig. 1, two stimulating sites, one distal (Ds) and the other proximal (Px), were used to evoke EPSPs in layer V pyramidal neurons. To determine if the Ds- and Px-evoked EPSPs summed linearly, the method shown in Fig. 2 was used. The integral of the EPSP generated in response to the simultaneous stimulation at the Px and Ds sites was divided by the integral of the algebraic sum of the individual Px- and Ds-evoked EPSPs to give a summation ratio (SR). In a given neuron, the latency of the Ds-evoked EPSP (4.9 ± 0.2 ms) was always longer than the latency of the Px-evoked EPSP (2.9 ± 0.1 ms), similar to previous observations (Cauller and Connors 1994) (latencies were measured from the stimulus onset to the initial rise of the EPSP). Therefore the integrals began 1 ms after the start of the distal EPSP and were limited to a 15-ms interval in order not to include late polysynaptic events. During late polysynaptic activity, the Ds and Px stimulus might not be isolated from each other because of the possibility of both stimuli acting on common neurons presynaptic to the recorded neuron through polysynaptic connections.



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Fig. 2. Quantification of deviation from linearity of EPSP summation using the summation ratio, SR. The SR was calculated for each set of EPSPs using the equation shown in the figure. The algebraic sum (dashed line ) was calculated as the linear sum of the averaged proximally (Px) evoked EPSP with the averaged distally (Ds) evoked EPSP (the individual average Px- and Ds-evoked EPSPs are shown as thin solid lines). The cell's sum (thick solid line) was the average response evoked by simultaneous stimulation of both the Px and Ds sites. SR was then calculated as the area under the cell's sum divided by the area under the algebraic sum. The area used to calculate SR was limited to the first 15 ms beginning 1 ms after the start of the 2nd EPSP (or the Ds-evoked EPSP when the Ds and Px were evoked simultaneously).

Figure 3C shows the distribution of SR values measured in layer V pyramidal neurons. The mean SR of 1.12 ± 0.02 (n = 74 SR measurements from 23 cells) was significantly >1, the expected SR value of linear summation. There was also a wide range of SR values (0.81-1.73), and the distribution was skewed in the direction of supralinear summation. In some cases in which the SR was greater than linear, there was an inflection in the rising phase of the summed EPSP (arrow in Fig. 3A) suggesting that supralinearity may be due to activation of a regenerative conductance. In these cases, the peak of the summed EPSP was delayed with respect to the peak of the algebraic sum of the Px- and Ds-evoked responses. In other cases where there was supralinear summation, the summed EPSP was a scaled-up version of the algebraic sum (e.g., Figs. 2, 4A, and 8A). A plot of the delay of the peak of the summed EPSP versus SR (Fig. 3C, inset) shows an increase in SR as a function of delay indicating a direct relation between a regenerative process and the amount of supralinear summation.



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Fig. 3. Supralinear summation of EPSPs is due to QX-314-sensitive conductances. A: an example of supralinear summation of EPSPs evoked in a neuron recorded with only KCl in the electrode (control). right-arrow, inflection in the rising phase of the cell's sum of the Px and Ds evoked EPSP. B: a typical example of linear summation of EPSPs evoked in a neuron recorded with an electrode that also contained QX-314 (QX-314). Note that the calculated algebraic sum of the individual Px and Ds evoked EPSPs superimposes perfectly on the EPSP evoked in response to simultaneous stimulation of the Px and Ds sites (cell's sum). C: histogram distribution of all SR values measured from neurons recorded without QX-314. Inset: plot of SR as a function of the time of the peak of the cell's sum of the Px -and Ds-evoked EPSP minus the time of the peak of the algebraic sum (delay of peak). D: histogram distribution of all SR values from neurons filled with QX-314. The histogram was fit to a Gaussian curve (---) and the upper and lower 95% confidence limits were determined (- - -). For both C and D, all SR values were obtained from Px and Ds EPSP whose stimuli were delivered simultaneously. Bin width for both histograms was 0.04 SR units. More than one SR value may be from the same neuron but under different conditions (e.g., holding potential, or stimulus intensity; control: 74 SR values from 23 neurons, QX-314; 34 SR values from 14 neurons). For both the control and QX-314 data, the range of conditions used to gather the data were similar (also see Figs. 4 and 5). For the data shown in Figs. 3-5, the EPSP amplitude ranged from 1.3 to 12.1 mV (control) and 1.2 to 10.4 mV (QX-314). The holding potential ranged from -71 to -91 mV (control) and -67 to -98 mV (QX-314). The nonnormal nature of the control data were not extreme enough to prevent use of a Student's t-test. A Mann-Whitney U test yielded similar results.

Supralinear summation is postsynaptically determined

A goal was to determine if postsynaptic conductances contributed to nonlinear summation of synaptic inputs. Therefore the SR was also determined for a set of neurons filled with QX-314. QX-314, a permanently charged lidocaine derivative, has been shown to internally block several voltage-sensitive conductances: Na+ (Strichartz 1973), some types of K+ (Andreasen and Hablitz 1993), Ca2+ (Talbot and Sayer 1996), and Ih (Perkins and Wong 1995). To allow QX-314 to diffuse into the dendrites, data were gathered after neurons had been penetrated for >40 min (after which the I-V relationship showed no further changes). In the presence of QX-314, neurons ceased firing action potentials, input resistance increased, and the steady-state I-V relation was linearized around resting potential. The mean input resistance for the 23 neurons recorded with QX-314 electrodes was 67 ± 11 MOmega . This was significantly larger than the value obtained from neurons recorded without QX-314 in the electrode (control neurons). The mean resting potential (-69 ± 1 mV) was slightly but significantly more depolarized in QX-314-filled neurons than in control neurons. The range of stimulation intensities used to evoke EPSPs in QX-314 filled neurons was 2.7-7.7 µA for the Px stimulus and 3.6-40 µA for the Ds stimulus. The stimulus amplitudes did not differ significantly from those used in control neurons (Px = 1.7-9.5 µA; Ds = 4-60 µA). The increase in input resistance (with QX-314) would be expected to cause larger EPSPs. However, the range of EPSP sizes evoked in QX-314 versus control neurons were not significantly different. Presumably, the change in input resistance is offset by the block of conductances which amplify the EPSPs (e.g., Deisz et al. 1991). By blocking many of the voltage-sensitive conductances thought to be responsible for nonlinear summation, this method allowed us to determine how these conductances affect EPSP summation. One limitation of these experiments is that they may not account for all nonlinear summation, particularly sublinear summation because QX-314 does not necessarily block all voltage-sensitive conductances completely nor would it block any sublinear summation caused by changes in driving force or synaptic conductance changes.

The distribution of SR values obtained with QX-314 in the recording electrode is shown in Fig. 3D. On average the EPSPs summed linearly with a mean SR of 1.00 ± 0.02 (n = 34, 14 neurons), which was significantly smaller than the SR measured in control neurons. Comparing the distribution of SR values measured in neurons with and without QX-314 revealed other differences. First, the range of SR values measured with QX-314 electrodes was smaller (0.82-1.33). Second, the distribution of SR values from QX-314 filled neurons was well fit by a Gaussian curve with a peak at SR = 0.99 similar to the mean (Fig. 3D). In comparison, the distribution of SR values from control neurons was skewed to the right. Based on the Gaussian fit to the QX-314 data, an upper 95% confidence limit of 1.16 was determined. From the SR values in neurons without QX-314, 23% were above this 95% cutoff limit and were thus considered to show QX-314 sensitive supralinear summation. Figure 3A shows an example of EPSPs with supralinear summation recorded without QX-314, while 3B shows typical EPSP summation from a QX-314-filled neuron. The smaller mean and more restricted range of SR values found in QX-314-filled neurons indicates that QX-314 sensitive conductances are contributing to supralinear summation.

Neurons recorded without QX-314 could not be grouped according to their ability to perform linear or supralinear summation. Instead, a wide range of SR values were obtained for different experimental conditions (i.e., changes in holding potential and/or stimulus strength) within a given neuron. We observed that for neurons with at least three SR measurements, the variation of SR was at least half the variance in SR for all neurons. Additionally, although only 23% of all SR values were >1.16, 35% of all neurons had at least one SR value >1.16. Therefore the most supralinear SR values did not belong to a subset of neurons. Since there did not appear to be a strong neuron-specific effect on SR values, all measurements were pooled for further analysis with some neurons contributing more than one SR value.

Summation ratio dependence on membrane potential and EPSP size

Because the summation of EPSPs is affected by QX-314-sensitive conductances, conditions that change the state of those active conductances (e.g., membrane potential) would be expected to change the amount of summation observed. We therefore measured the relationship between membrane potential and SR. SR increased (e.g., Fig. 4A) in 8 of 10 neurons in which the stimuli were held constant and the holding potential was hyperpolarized from between -71 and -81 mV to between -82 and -97 mV (mean increase = 0.10 ± 0.03 SR units per 10 mV hyperpolarization, range = 0.26 to 0.03 SR units per 10 mV). In one neuron, SR did not change, and in another, SR decreased 0.04 SR units per 10 mV of hyperpolarization. The entire population of SR values is shown graphically in Fig. 4B where SR values are plotted as a function of the membrane holding potential. The data are fit to a linear regression with a slope of -0.09 ± 0.02 SR units per 10 mV, similar to what was found for individual neurons. The slope of the regression is significantly different from zero with an R value of 0.48, indicating that 23% of the variation in SR values can be accounted for by changes in holding potential. Of EPSPs with a holding potential more negative than -84 mV, 42% had SR >1.16, while for more depolarized EPSPs only 10% were in this category.



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Fig. 4. Supralinear summation of EPSPs decreased with membrane depolarization. A: records from a neuron that showed an increase in SR as membrane potential was hyperpolarized from rest (-71 mV) to -92 mV. B: plot of SR as a function of holding potential for control neurons () and QX-314-filled neurons (triangle ). Linear regression revealed a significant decrease of SR with membrane depolarization for control neurons (---; Student's t-test P < 0.001; slope = -0.9 ± 0.2 SR units/10 mV, R = 0.48) but not for neurons recorded with QX-314 (- - -; slope = -0.1 ± 0.1 SR units/10 mV). Two slopes were also significantly different from each other (Student's t-test P < 0.05). Data points are from the same experiments used for the histograms in Fig. 3.

In contrast, SR values from neurons recorded with conductances blocked by QX-314 did not vary significantly with holding potential in individual neurons (n = 5). Likewise, for all EPSPs recorded with QX-314 (Fig. 4B), linear regression of SR versus holding potential was not significantly different from zero. The slope of -0.005 ± 0.017 SR units per 10 mV measured for the QX-314-filled neurons was significantly different from the slope measured in control neurons. Therefore we conclude that the increase of SR with increasing hyperpolarization is not simply due to a change in the driving force for AMPA-mediated conductance but results from QX-314-sensitive voltage-dependent conductance.

The amplitude of EPSPs would also be expected to affect the amount of nonlinear summation since larger EPSPs will activate voltage-dependent conductances to a different degree than smaller EPSPs. Unlike holding potential, EPSP amplitude had no clear effect on SR over the range of amplitudes shown in Fig. 5. In individual neurons where the EPSP amplitude was systematically changed, the dependence of SR on EPSP size was variable. In the five cases where the Px stimulus strength was increased systematically while holding potential and Ds stimulus strength were held constant, four showed an increase in SR while one decreased (average: 0.31 ± 0.25 SR units per 10 mV; range: -0.59 to 0.93 SR units per 10 mV). In four cases where Ds stimulus strength was systematically increased, the SR was not significantly changed (average: 0.04 ± 0.07 SR units per 10 mV; range: -0.19 to 0.16 SR units per 10 mV, n = 4).



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Fig. 5. Summation ratio is not dependent on EPSP size. A-C: plots of SR as a function of EPSP amplitude. A: Px-evoked EPSP amplitude; B: Ds-evoked EPSP amplitude; C: algebraic sum of the peak Px- and peak Ds-evoked EPSP amplitudes. In all cases, the fit to a linear regression was not significantly different from zero for neurons recorded without QX-314 (---) or with QX-314 (- - -). For the QX-314 data in A and C, the 1 large SR value is excluded from the regression as it alone altered the significance of the slope. Data points are from the same experiments used for the histograms in Fig. 3.

The relationship between SR and a larger range of EPSP amplitudes is shown in Fig. 5 where all SR values are pooled and plotted as a function of Px amplitude, Ds amplitude, and Px plus Ds amplitudes. For all three plots, linear regression reveals slopes of 0.16 ± 0.009, -0.08 ± 0.008, and 0.01 ± 0.005 SR units per 10 mV, respectively. None of these slopes are significantly different from zero. Since the effect of holding potential could have masked an effect of EPSP size on SR, we also used multiple regression to examine any possible dependence of SR on holding potential and/or EPSP amplitude. Multiple regression analysis revealed that only holding potential had a significant effect on SR in neurons recorded without QX-314.

One limitation of trying to determine the effect of EPSP size on SR was that the EPSP amplitude could only be varied over a narrow range in any one neuron. This was due to inhibition being largely blocked, so small increases in stimulus strength resulted in large polysynaptic potentials (Chagnac-Amitai and Connors 1989) when the two stimuli were given together. Another possible explanation for the surprising lack of dependence of SR on EPSP amplitude is that, while larger EPSPs may activate more Na+ and Ca2+ conductance (which would be expected to lead to an increase in SR), larger EPSPs might increase the relative contribution of voltage-sensitive K+ conductances to synaptic integration. Potassium conductance alone would decrease SR (Cash and Yuste 1998; Margulis and Tang 1998; Urban and Barrionuevo 1998) and counter further increases in SR as a function of depolarization activated inward currents.

Effect of time between EPSPs on summation ratio

Activation of voltage-dependent conductances by EPSPs could either improve coincidence detection (Bernander et al. 1991; Konig et al. 1996; Softky and Koch 1993) or favor temporal summation, depending on the characteristics of the conductance. For example, a conductance with rapid activation and inactivation kinetics could cause supralinear boosting mainly to EPSPs that are nearly coincident. In contrast, a noninactivating inward conductance with slow deactivation kinetics could favor supralinear summation of EPSPs separated in time and thus enhance temporal summation. Therefore to gain insight into how nonlinear summation might influence information processing, we measured SR as a function of the time between the Ds and Px stimuli.

Examples of experiments to determine the effect of a delay between synaptic inputs on SR are shown in Fig. 6A. For the neuron recorded without QX-314, the SR decreased from 1.13 to 1.05 as the time (Delta t) between the Ds and Px stimuli increased from 5 to 30 ms. On the other hand, in a QX-314-filled neuron, the SR was close to linear (1.0) for all Delta t. In nine individual control neurons in which EPSP size and holding potential were held constant while Delta t was increased, six had the largest SR at 0 or 5 ms, one had its peak SR at 10 ms, and two neurons had SR values that were independent of changes in Delta t. Figure 6, B-D, shows the SR distribution histograms for all control and QX-314-filled neurons in which the two inputs were separated by 5, 10, and 30 ms. A majority of summed EPSPs (80%) had the Px EPSP preceding the Ds EPSP. In the remaining, the Ds stimulus was given first. Both groups were analyzed together since no correlation between stimulus order and EPSP summation was observed. Similar to what was observed for Delta t = 0 (e.g., Fig. 3), the distribution of SR's in control neurons were skewed to the right for Delta t's equal to 5 and 10 ms. In the presence of QX-314 and at the same Delta t, the distribution of SR values was relatively normal. For Delta t of 30 ms, the distribution of SR values was close to normal for both groups of neurons. At all Delta t's and for both groups of neurons, measurements were taken over the same range of holding potentials and EPSP sizes. As the time between inputs decreased, the effect of QX-314 on SR values increased, indicating that an active conductance caused the SR to increase in a time-dependent fashion.



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Fig. 6. Supralinear summation depends on the time between inputs. A: records from 2 neurons (left recorded without and right with QX-314) in which the time between Px and Ds stimuli (Delta t) was increased from 5 ms (top) to 10 ms (bottom). In these examples the Px stimulus preceded the Ds stimulus. Holding potential is -75 mV for the control neuron and -70 mV for the neuron with QX-314. B-D: histograms of SR values for Delta t of 5 (B), 10 (C), and 30 ms (D) in control neurons (top) and neurons with QX-314 (bottom). Bin width = 0.04 SR units. As in Fig. 3, the QX-314 histograms are fit to a Gaussian curve (---) and the upper and lower 95% confidence limits were determined (- - -).

Since holding potential was shown to affect SR summation at Delta t = 0, we examined the relationship between SR and Delta t for EPSPs with holding potentials positive to -85 mV (depolarized EPSPs) separately from EPSPs with holding potentials equal to or more negative than -85 mV (hyperpolarized EPSPs). Figure 7, A and B, shows plots of the relation of SR to Delta t for all depolarized and hyperpolarized EPSPs, respectively. At hyperpolarized potentials, SR decreased more dramatically with time between inputs than at potentials closer to rest. Such results imply that there is a time-dependent component to supralinear summation that is more pronounced at relatively hyperpolarized holding potentials (i.e., less than or equal to -85 mV).



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Fig. 7. SR depends on both the time between inputs and holding potential. A: plots of mean SR as a function of the time between the Px and Ds stimuli (Delta t) for EPSPs with holding potentials positive to -85 mV. Each point is the mean of 18-43 experiments (, neurons recorded without QX-314, control; open circle , neurons recorded with QX-314). At Delta t = 0, 5, and 10 but not 30 ms, SR was significantly larger in control neurons than in QX-314-filled neurons. B: similar to A but for EPSPs in which the holding potential was less than or euqal to -85 mV. Each point is the mean of 12-31 experiments (, neurons recorded without QX-314; , neurons recorded with QX-314). At Delta t = 0 and Delta t = 5, the SR was significantly larger in control neurons than in QX-314-filled neurons. C: data in A and B are used to calculate the QX-314-blockable component of the SR (Delta SR) for each Delta t. Delta SR is equal to the mean SR measured without QX-314 minus the mean SR measured with QX-314. The plot of Delta SR vs. Delta t from more hyperpolarized EPSPs () was best fit to an exponential function, Ae-Delta t/tau , where the intercept A = 0.16 ± 0.04 SR units, and the time constant tau  = 15 ± 8 ms. The plot of Delta SR vs. Delta t from the more depolarized EPSPs () was best fit to a line with a slope of -0.002 ± 0.001 SR units/ms and y intercept = 0.093 ± 0.020 SR units. All comparisons were done as a 1-way ANOVA, P < 0.05. Error bars represent the SE.

While a QX-314-blockable conductance contributes to a SR >1, there are other possible factors affecting the relationship between SR and time. Factors such as synaptic conductance change, presynaptic interactions between the stimuli, or postsynaptic conductances not blocked or only partially blocked by QX-314 might affect how EPSPs sum in QX-314-filled neurons. Consistent with this idea, we observed that in the presence of QX-314, not all EPSPs summed linearly at all Delta t's. In particular, the mean SR peaked at Delta t = 5 ms for both the hyperpolarized EPSPs and the EPSPs closer to resting membrane potential. Such behavior is consistent with a non-QX-314-blockable component contributing to supralinear summation when the inputs are within 5 ms of each other combined with a reduction in driving force and/or a synaptic conductance change decreasing EPSP summation when the inputs are simultaneous.

To examine only the contribution of the QX-314-blockable conductances to the SR versus Delta t relationship, we plotted the difference in mean SR (Delta SR) between neurons recorded with and without QX-314 as a function of Delta t (Fig. 7C). At both hyperpolarized and resting membrane potentials, there was a clear decrease in Delta SR with Delta t. At membrane potentials more positive than -85 mV, SR decreased linearly (slope = -0.002 ± 0.001 SR units/ms) as the time between inputs increased, until at Delta t = 30 ms, Delta SR was not significantly different from zero. For the hyperpolarized EPSPs, the decrease in Delta SR with time between stimuli was well fit by a single exponential with a time constant of 15 ± 8 ms. These results indicate that there is a QX-314-sensitive, time-dependent component to supralinear summation that is altered by changes in membrane potential.

Dendritic conductances cause supralinear summation of EPSPs

Previous studies indicate that voltage-sensitive conductances on the dendrites play an important role in synaptic integration (for reviews, see Johnston et al. 1996; Yuste and Tank 1996). The hypothesis that dendritic conductances contributed to the supralinear summation that we observed in Fig. 3 was tested by generating simulated EPSPs with current pulses injected through the recording electrode at the soma (see METHODS). The simulated EPSPs were then substituted for one or both of the evoked EPSPs in the experimental protocol shown in Figs. 1 and 2. For all SR values measured from simulated EPSPs, there was no delay between the two stimuli. Figure 8A shows an example of a neuron in which the simulated EPSPs closely approximated the time course and amplitude of the evoked EPSPs. The evoked EPSPs summed supralinearly with an SR of 1.18. When simulated EPSPs were substituted for either the Px, Ds, or both evoked EPSPs, SR values were close to linear (0.99, 1.05, and 1.02, respectively). For 12 neurons in which simulated EPSPs were used, the amount of summation did not depend on whether the simulated EPSPs were substituted for either the Px or Ds or both of the evoked EPSPs. There was no significant difference among the mean SR measured for each of the three groups (simulated Px with evoked Ds: 1.04 ± 0.01, n = 30; evoked Px with simulated Ds: 1.03 ± 0.01, n = 13; both Px and Ds simulated: 1.06 ± 0.02, n = 22). In the same group of neurons, two evoked EPSPs were found to have significantly larger SR: 1.16 ± 0.04, n = 30 (only SR values from EPSPs that were at the same holding potentials as the simulated EPSPs were included in this mean; 1-way ANOVA, P < 0.05 for all group comparisons). Figure 8B compares the SRs from two evoked EPSPs to SRs from well-matched simulated EPSP. In the five cases where the two evoked EPSPs yielded SR values above the QX-314 limit of 1.16, their matched simulated EPSPs yielded SR values close to linear. For the remaining SR measurements, evoked EPSPs yielded larger or equivalent SR values compared with those SR values measured using simulated EPSPs. This demonstrates that although simulated EPSPs created at the soma have SR values >1, the simulated EPSPs are not sufficient to create the same amount of supralinear summation as those obtained from two evoked EPSPs.



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Fig. 8. Nonsomatic conductances contribute to supralinear summation of EPSPs. A: 4 examples from 1 neuron comparing EPSP summation for 2 evoked EPSPs (top left) to EPSP summation for which a simulated EPSP is substituted for: the Px evoked EPSP (top right), the Ds EPSP (bottom left) and both the Px and Ds evoked EPSPs (bottom right). Below each set of voltage traces are the traces of current injected into the soma to generate simulated EPSPs. Simulated EPSPs are shown as thin dotted lines. In all cases, simulated EPSPs give responses that sum close to linear. B: comparison of SR values from summation of evoked EPSPs to summation with their matched simulated EPSPs. To be considered matched, the simulated EPSPs and the evoked EPSPs had to be of similar size, time course and done at the same holding potential. In cases where error bars are shown, 2-5 SR values were measured under similar conditions; however, the size of the simulated EPSP was adjusted to bracket the size of the evoked EPSP or SR values were measured (as in A) where a simulated EPSP was first substituted for one and then for the other (or both) evoked EPSPs. Numbers at the bottom indicate the neuron in which the data were gathered. In 2 neurons, there was more than one group of matched EPSPs. First 3 data points (306.1A-C) are from the same neuron but with different sized EPSPs. In another neuron, 2 data groups were measured at -71 mV (714.2A) and -87 mV (714.2B). The example shown in A corresponds to neuron 714.1 in B.

Conductances near or in the soma may also contribute to supralinear summation. To assess this effect, we compared SRs from summation with simulated EPSPs obtained from neurons recorded without to those recorded with QX-314 electrodes (examples are shown in Fig. 9, A and B, respectively). Figure 9, C and D, shows the distribution of all SR values from control and QX-314-filled neurons, respectively. As seen for evoked EPSPs (Fig. 3), the SR values obtained from control neurons are skewed to the right while the SR values obtained from QX-314-filled neurons have a normal distribution. Since there was no dependence of summation on which EPSP was simulated (or if both were simulated), all SR from simulated EPSPs were pooled. In QX-314-filled neurons, simulated EPSPs combined with an evoked or another simulated EPSP had an average SR value of 0.98 ± 0.01 (n = 20) while in neurons recorded without QX-314, the average SR was significantly larger (1.04 ± 0.01, n = 65; P < 0.02). Thus QX-314-sensitive conductances near or in the soma also affected the degree of linearity of EPSP summation.



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Fig. 9. QX-314 reduces supralinear summation of simulated EPSPs, indicating that somatic conductances also contribute to supralinear summation. Left: examples from 2 neurons in which a simulated EPSP is substituted for the Px stimulus. In A the neuron recorded without QX-314 (control) has a higher SR than the neuron in B which was recorded with QX-314. Below each set of voltage traces are the traces of current injected into the soma to generate the simulated EPSPs. Right: distribution of SR values measured using simulated EPSPs in place of either or both the Px and Ds stimuli for neurons recorded without QX-314 (C, control) and with QX-314 (D). Bin width = 0.02 SR units. As in Fig. 3, the QX-314 histogram is fit to a Gaussian curve (---) and the upper and lower 95% confidence limits were determined (- - -).

Some insight into the relative contribution of somatic versus dendritic conductances can be gained by comparing Fig. 3 with Fig. 9 (note the difference in the horizontal axis scale). In neurons without QX-314, the overall mean SR from two evoked EPSPs (1.12 ± 0.02 ± n = 74) was significantly larger than the mean SR from summation with one or more simulated EPSPs (1.04 ± 0.01, n = 65), demonstrating that dendritic conductances contribute to larger SR values. In contrast, QX-314-filled neurons had a mean SR for evoked EPSPs (0.99 ± 0.01) that was not significantly different from the mean SR for simulated EPSPs (0.98 ± 0.01). Thus QX-314 eliminated both the somatic and dendritic conductances responsible for supralinear summation. Such a difference indicates that a postsynaptic dendritic conductance is responsible for a majority of the supralinear summation observed in these experiments.


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This study provides evidence that voltage-sensitive conductances in dendrites play a role in EPSP summation. Models of passive dendrites predict that synaptic inputs will sum sublinearly if the signal from one input affects the synaptic driving force of other inputs (Rall 1977; Rall et al. 1967) or if synaptic conductance changes cause a reduction in input resistance (Bernander et al. 1991). Early support for the effects of synaptic driving force came from measurements of sublinear EPSP summation in motoneurons (Burke 1967). There is now, however, substantial evidence that many types of neurons contain voltage-sensitive conductances throughout their dendritic trees (for review, see Johnston et al. 1996; Yuste and Tank 1996). Currently there is insufficient characterization of dendritic conductances to make an assumption free empirical model that allows for accurate predictions of how the active properties of pyramidal neuron dendrites will influence the spatial and temporal summation of EPSPs. Recent studies on hippocampal pyramidal neurons that used an approach similar to this study have found linear to sublinear summation (Cash and Yuste, 1998; Urban and Barrionuevo 1998). However, one study found a switch from supralinear to sublinear summation, which depended on the timing of paired pulses of glutamate release at one dendritic location (Margulis and Tang 1998). In contrast, we found that summation of two spatially separated sets of AMPA-mediated synaptic inputs onto layer V neocortical pyramidal neurons is linear to supralinear and that supralinearity is caused by dendritically located postsynaptic conductances. The amount of nonlinear summation is affected by the time interval between inputs and the membrane potential of the postsynaptic neuron.

Supralinear summation is due to postsynaptic mechanisms

When supralinear summation occurred it was primarily due to postsynaptic mechanisms. First, intracellular QX-314 reduced the mean SR to linearity. A presynaptic mechanism for supralinear summation would have been unaffected by intracellular QX-314. Additionally, in QX-314-filled neurons, summation using simulated EPSPs was similar to summation with evoked EPSPs. If presynaptic mechanisms were affecting summation, simulated EPSPs would have had a different mean SR than evoked EPSPs. Finally, paired pulses indicated that the two stimuli were stimulating separate sets of fibers (see METHODS).

Dendritic conductances contribute to supralinear summation

Our results show that the QX-314-sensitive conductances underlying supralinear summation are activated by dendritic events. If the soma region itself contributed to large amounts of supralinear summation, we would expect the SR values measured with simulated EPSPs to be similar to SR values measured with evoked EPSPs. Instead, simulated EPSPs had less supralinear summation compared with evoked EPSPs. The Ds stimulus likely stimulated the distal tuft of the apical dendrite while the Px stimulus likely stimulated more proximal portions of the apical dendrite and/or parts of the basal dendrites due to horizontal cortical pathways (Cauller and Connors 1994; Ichinose and Murakoshi 1996; Thomson and Deuchars 1994; White 1989). The amplitude of an evoked EPSP attenuates as it spreads from the apical dendrite to the soma (Stuart and Sakmann 1995). Also the amplitude of a simulated EPSPs injected at the soma attenuates by approx 80% at a point approx 600 µm distal on the apical dendrite (Stuart and Spruston 1998). Therefore a somatically injected simulated EPSP would not be expected to activate as much dendritic Na+ or Ca2+ conductance as an evoked EPSP that caused the same amount of somatic depolarization as the simulated EPSP.

Another consideration is that in these experiments, which utilized sharp electrodes, the input resistance of layer V pyramidal neurons was 22 ± 2 MOmega , while whole cell recording from the same aged rats with patch electrodes yielded an input resistance of 77 ± 5 MOmega (from Cerne and Spain 1997) (temperature = 33 ± 1° C). The 3.5-fold difference in input resistance is indicative of a somatic shunt resulting from the use of sharp electrodes (Spruston and Johnston 1992). Due to this shunt, somatic conductances may contribute less to EPSP summation than they would normally. Thus under the experimental conditions employed in this study, only the supralinear summation in the dendrites was readily apparent, while the somatic component was minimal.

What conductances underlie supralinear summation?

A QX-314-sensitive conductance underlies the cases of supralinear summation. QX-314 blocks several conductances (Na+, Ca2+, Ih, and K+ conductances) (Andreasen and Hablitz 1993; Issac and Wheal 1993; Nuñez and Buño 1992; Perkins and Wong 1995; Stafstorm et al. 1985; Talbot and Sayer 1996). Ih and most K+ conductances would be expected to cause attenuation of EPSPs and sublinear summation (Cash and Yuste 1998; Hoffman et al. 1997; Magee 1998; Margulis and Tang 1998; Schwindt and Crill 1997; Stuart and Spruston 1998; Urban and Barrionuevo 1998; but see Wessel et al. 1999). We found summation to be linear to supralinear with a direct relation between the amount of supralinear summation and the appearance of a regenerative component to the summed EPSPs (Fig. 3A and inset in C). Furthermore hyperpolarization of membrane potential increased supralinear summation. Membrane hyperpolarization will remove inactivation of both T-type Ca2+ and Na+ conductances. Also both types of conductances have been shown to be activated in dendrites by subthreshold EPSPs (Magee and Johnston 1995b; Magee et al. 1995; Schiller et al. 1997; Stuart et al. 1997). Therefore a regenerative Na+ and/or Ca2+ conductance is the likely mechanism underlying supralinear summation.

The cases of supralinear summation that did not show a clear regenerative hump might represent activation of dendritically located persistent Na+ current (Schwindt and Crill 1995). Alternatively, a small regenerative response generated distally might have been smoothed by dendritic filtering.

If activation of dendritic Na and/or Ca conductance caused supralinear summation, then why didn't larger EPSPs cause more supralinearity? One explanation is that the larger EPSPs, while activating more Na+ and Ca2+ conductances, will also activate K+ conductances that will counteract the boosting effects from Na+ and Ca2+ conductances. Additionally, in our experiments there is not necessarily a proportional relationship between EPSP size measured at the soma and EPSP size in the dendrites since we do not know the location along the dendrites of the synapses we activated and the location likely varied in different neurons. Indeed there was a suggestion that, for the more proximal evoked EPSPs, the larger ones resulted in a larger SR (SR increased in 4 of the 5 neurons where we systematically increased the strength of the Px stimulus). However, the relation of SR to EPSP size did not reach significance for the whole population of neurons (Fig. 5A).

Inwardly rectifying K+ current (GIRK) was recently found to cause supralinear summation of EPSPs in a leach neuron (Wessel et al. 1999). GIRK is present in the dendrites of neocortical pyramidal neurons (Takigawa and Alzheimer 1999). GIRK would be expected to cause more supralinear summation of EPSPs as membrane potential becomes hyperpolarized. Therefore GIRK might also have contributed to the supralinear summation that we observed. It is unknown if GIRK is completely blocked by QX-314. A residual GIRK may account for summation not becoming sublinear in QX-314-filled neurons.

Functional implications

What implications do our results have for information coding by neocortical neurons? On average, EPSP summation was only slightly greater than linear. However, any model of synaptic integration must take into account three results. First, we observed a wide range of SR values (from linear to supralinear) that did not depend on differences in the properties of individual neurons. Second, most of the supralinear summation occurred during synaptic events separated by <= 5 ms. Finally, supralinear summation was unlikely unless the EPSPs were preceded by membrane hyperpolarization.

Do the conditions that favored supralinear summation ever occur normally? Based on dual recordings from pyramidal neurons with patch-pipettes, hyperpolarizing the soma by 15 mV (e.g., from -70 to -85 mV) would cause the membrane potential of the apical dendrite (at approx 500 µm from the soma---a distance corresponding to halfway between the Ds- and Px-stimulating electrodes) to hyperpolarize by approximately equal to -4 mV (e.g., from -70 to -74 mV) (Stuart and Spruston 1998). Therefore 4 mV below resting potential represents the maximum dendritic hyperpolarization (at 500 µm) in our experiments. Periods of membrane hyperpolarization to approximately equal to -75 mV lasting several hundred milliseconds are frequently observed during in vivo recordings from neocortex (Stern et al. 1997).

Supralinear summation of nearby inputs might favor coincidence detection if the boosting is due to conductances with a rapid time course (e.g., <= 1 ms) (Softky 1994). Alternatively, longer-lasting supralinear summation would favor temporal integration. The cases of supralinear summation we observed were associated with a regenerative response originating in the dendrite, but supralinear summation occurred even when the two stimuli were separated by 5 ms. Thus events occurring within an approx 5-ms time span would be temporally integrated and seen as coincident compared with events separated by longer time intervals that summed linearly. Taken together, our results suggest that supralinear summation of EPSPs would likely cause synchronization and an initial boost to excitatory input after a period of inhibition. However within a few milliseconds of depolarizing activity, EPSPs would switch to linear summation. If linear summation results from separated synapses, the supralinear summation must result from closer synapses. But only linear summation is expected during sustained depolarization. Thus during continuous activity in the neocortical neurons it may be reasonable to ignore the spatial location of synaptic inputs when considering their relative influence on each other.


    ACKNOWLEDGMENTS

We thank J.F.M van Brederode for helpful suggestions during the experiments, M. D. Binder and P. C. Schwindt for comments on the manuscript, R. Lee for technical assistance, and K. Bumsted, A. Hendrickson, and A. Erickson for assistance with histological procedures.

This work was supported by a VA Merit Review and National Institutes of Health Grant DC-02254 and Training Grant GM-07108.


    FOOTNOTES

Address for reprint requests: W. Spain, Neurology (127), VA Puget Sound Health Care System, 1660 S. Columbian Way, Seattle, WA 98108.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 29 July 1999; accepted in final form 18 February 2000.


    REFERENCES
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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