INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Rodents can gather spatial information of nearby surroundings by detecting deflections of whiskers. During active exploration mystacial whiskers are rhythmically moved forward and backward at a frequency around 10 Hz (Carvell and Simons 1990; Welker 1964). This behavior, termed whisking, is thought to provide a mechanism for whiskers to touch nearby objects in a controlled manner allowing high sampling rates, which in turn might provide high spatial resolution. Blind rats are thus able to locate small objects by searching the space within whisker reach (Brecht et al. 1997). Furthermore rats are able to discriminate between smooth objects and similar objects with closely spaced 30-µm deep grooves with sensory information obtained during whisking (Carvell and Simons 1990). In awake animals extracellular unit recordings of action potentials in primary somatosensory cortex are synchronized to the whisking frequency (Fee et al. 1997; Nicolelis et al. 1995). Equally controlled stimulation of individual whiskers in anesthetized animals at whisking frequencies evokes cortical activity in response to each stimulus (Simons 1978). Quantitatively, however, the cortical responses to consecutive deflections at whisking frequencies are weaker than to single stimuli (Ahissar et al. 2000; Sheth et al. 1998; Shulz et al. 2000; Simons 1978; review Moore et al. 1999). Since there is little adaptation of responses measured in the primary thalamic nucleus (VPM) (Ahissar et al. 2000; Diamond et al. 1992; Hartings and Simons 1998), the strong reduction in cortical responses during repetitive stimulation is likely to result from short-term plasticity of thalamocortical and intracortical synapses (Abbott et al. 1997; Castro-Alamancos and Connors 1997; Egger et al. 1999; Finnerty et al. 1999; Galarreta and Hestrin 1998; Gil et al. 1998, 1999; Markram and Tsodyks 1996; Markram et al. 1998; Reyes et al. 1998; Reyes and Sakmann 1999; Rozov et al. 2001; Stratford et al. 1996; Tarczy-Hornoch et al. 1999; Thomson 1997; Thomson et al. 1993; Tsodyks and Markram 1997; Varela et al. 1997, 1999). Quantitative phenomenological descriptions of short-term plasticity at neocortical synapses have been able to closely predict responses to trains of stimuli (Abbott et al. 1997; Markram and Tsodyks 1996; Markram et al. 1998; Tsodyks and Markram 1997; Varela et al. 1997, 1999) suggesting that one could begin to attempt to reconstruct the dynamics of in vivo responses in computational simulations of synaptically connected neuronal networks.

Sensory information concerning whisker movements reaches the neocortex primarily from thalamocortical VPM afferents terminating in the barrels of layer 4. The receiving neuronal network in layer 4 thus forms the first level of cortical processing, and a quantitative description of its short-term synaptic plasticity may help to understand the dynamics of neocortical responses to repetitive whisker movements (Moore et al. 1999). This study begins to develop such a description focusing exclusively on the dynamics of transmission between synaptically coupled pairs of excitatory neurons within layer 4 of rat barrel cortex.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Slice preparation

Thalamocortical slices of 300-µm thickness were prepared from halothane-anesthetized Wistar rats (13-15 days old) following the description of Agmon and Connors (1991) with modifications by Feldmeyer et al. (1999). Slices were cut by a vibratome in ice-cold extracellular medium and were subsequently incubated at 35°C for 15-30 min following slicing. The slices were then transferred to room temperature (20-23°C) until required for analysis. Throughout the procedure slices were maintained in extracellular medium containing (in mM) 125 NaCl, 25 NaHCO₃, 25 glucose, 2.5 KCl, 1.25 NaH₂PO₄, 2 CaCl₂, and 1 MgCl₂, bubbled with 95% O₂-5% CO₂.

Whole cell recordings from identified layer 4 neurons

Layer 4 neurons were identified using infrared differential interference contrast microscopy. Excitatory neurons of layer 4 have round somata with ~10 µm diameter and often appear to be clustered. They were electrophysiologically identified by regular action potential firing pattern in response to continuous current injection and broad action potentials (half-widths of over 1 ms). Slices were continuously perfused with extracellular medium bubbled with 95% O₂-5% CO₂. All experiments were performed at 35°C. Whole cell recordings were established using pipettes with resistances of 5 M filled with a solution containing (in mM) 105 potassium gluconate, 30 KCl, 10 HEPES, 10 phosphocreatine, 4 MgATP, and 0.3 Na₃GTP (adjusted to pH 7.3 with KOH). Whole cell electrophysiological measurements were made with Axopatch 200 amplifiers (Axon Instruments, Foster City, CA). Biocytin (2 mg/ml) was routinely included in the intracellular solution to allow the morphology of the neurons to be analyzed. Excitatory neurons were spiny and had initial axonal segments directed toward deeper cortical layers with numerous colaterals projecting locally and up to layer 2/3. The membrane potential of connected neurons was filtered at 2 kHz and digitized at 10 kHz in a sweep-based manner by ITC-16 (Instrutech Corporation, Long Island, NY) under the control of HEKA Pulse software running on a Apple Macintosh computer. Off-line analysis of electrophysiological data was performed using custom-written routines in IgorPro (Wavemetrics, Lake Oswego, OR).

Biocytin staining and reconstruction

Following paraformaldehyde (PFA) fixation, the slices were washed in PBS (0.1 M sodium phosphate, pH 7.2) five times over a period of 2 h. Endogenous peroxidases were then quenched by a 5-min incubation with 1% H₂O₂. The slices were subsequently rinsed in PBS five times over a period of 2 h. Slices were conjugated with avidin-biotinylated horseradish peroxidase following the manufacturers instructions (ABC-Elite; Vector Laboratories). Slices were then washed five times over a period of 2 h with PBS, and subsequently biocytin-stained neurons were visualized under a reaction with 0.5 mg/ml diaminobenzidine and 0.01% H₂O₂. When the neuronal processes were clearly visible, the reaction was stopped by washing with PBS. Finally the slices were mounted on slides using mowiol. Axonal and dendritic processes were subsequently reconstructed using Neurolucida software (Microbrightfield, Colchester, VT).

Modeling of use-dependent short-term synaptic depression

The phenomenological model used to simulate the excitatory postsynaptic potential (EPSP) amplitudes of responses to repetitive action potentials in presynaptic neurons follows previous descriptions (Abbott et al. 1997; Markram and Tsodyks 1996; Markram et al. 1998; Tsodyks and Markram 1997; Varela et al. 1997, 1999). The starting point is the notion that even after an infinite period of rest an action potential releases only a fraction (here called R₁) of the total releasable resources at any given synaptic connection. The response magnitude after an infinite period of rest in this study is considered equivalent to the amplitude of the response to the first action potential, which in the experiments occurs after a period of 20 s rest. The fraction of releasable resources then refill exponentially with a time constant , in an analogous way to an electrical capacitor being filled with charge following a partial discharge. Thus the fraction of resources relative to that available to the first action potential for release at a time t [given by the variable R(t)] following a first action potential at t = 0 is described by

(1)

The EPSP amplitude in response to a second action potential is thus smaller in magnitude since the releasable fraction of resources is less than unity. The EPSP amplitude is in fact assumed to be directly proportional to the available releasable fraction of resources. Thus the amplitude of the second response is given by

(2)

The paired-pulse ratio (EPSP2/EPSP1) is thus directly equivalent to the function R(t) defined by Eq. 1. Fitting exponential curves of the type presented in Eq. 2 to the recovery time courses from synaptic depression data from individual synaptic connections (Fig. 3) thus provides three constants, which under the current model being considered give a complete description of the short-term dynamics of synaptic transmission: 1) EPSP1, the amplitude of the response to a first action potential, following a long period of rest; 2) R₁, the fraction of resources released by the initial action potential to evoke the response of amplitude EPSP1; this is also equal to the maximal depression at the synaptic connection; 3) , the recovery time constant from depression for that particular synaptic connection. There are many possible physical mechanisms underlying this phenomenological model of which the simplest would make the releasable fraction at any given moment directly proportional to the number of synaptic vesicles docked at active zones (Dobrunz and Stevens 1997).

To test this simple mathematical model further, it was extended to compute responses to trains of action potentials. The nth action potential (AP_n) evokes a response "EPSP_n", whose magnitude is determined by the product of the releasable resources at that time R_n and the connection strength EPSP1

(3)

The fractional amount of released resources is thus R_n * R₁, since EPSP1 is generated by the release of a fraction R₁ of the releasable resources. Thus immediately following this action potential the fractional amount of resources remaining is equal to the amount before the action potential (R_n) minus the released fraction (R_n * R₁). At a time t after this action potential the resources recover with an exponential time course toward full releasable resources. When the next action potential (AP_{n + 1}) arises the available resources are thus described by

(4)

Action potential n + 1 thus evokes a response of amplitude R_n+1 * EPSP1, which as before is determined by the constants EPSP1, R₁, and  and depend on the interstimulus interval t and the previous response through R_n.

Computational modeling of the excitatory neuronal network of a layer 4 barrel

Computational simulation of an excitatory network of 1,000 "integrate-and-fire" neurons was accomplished using IgorPro. This neuronal network was given properties to simulate the excitatory neurons and the synaptic connections within a single layer 4 barrel. The connectivity of the network was derived from previous experimental results (Petersen and Sakmann 2000). The connectivity was chosen in a random manner with each unitary synaptic connection having an EPSP amplitude randomly chosen to match the experimentally obtained distribution (Petersen and Sakmann 2000). Thus stimulation of a single neuron evokes EPSPs in around one-third of the neurons of the network with individual unitary EPSP amplitudes varying from 0.1 mV up to 7 mV when the postsynaptic neuron is at resting membrane potential of 65 mV. The amplitude of evoked EPSPs is scaled linearly with membrane potential with reversal potential at 0 mV. Evoked EPSPs are summated linearly in postsynaptic neurons, and the kinetics of EPSPs are identical in all neurons for all connections (this idealized EPSP was chosen from 1 experiment). To initiate activity, action potentials could be triggered at any time point in any neuron by stimulation controlled by the computer operator. Further evoked action potentials were triggered when the membrane potential crossed a threshold, which was initially set to 45 mV. Once a neuron had fired an action potential, however, the threshold for further activity was increased by adding a decaying exponential function with a time constant of 3 ms to the threshold function. The repeated activation of a neuron evoked EPSPs in target neurons with amplitudes varying depending the short-term dynamics of excitatory synaptic transmission described in the experimental part of this paper. Thus use-dependent short-term depression was incorporated into the model with an exponential recovery time course. For each synaptic connection the recovery time constant and the release-fraction constant determine the behavior of the synapse and were chosen randomly from the experimentally determined values presented in this paper. To model short-term dynamics the time from the last action potential and the amplitude of the response to the last action potential are also used to calculate the response to subsequent action potentials. The model can be downloaded for use on computers running IgorPro software from the following web site: http://sun0.mpimf-heidelberg.mpg.de/~petersen/sensorypathway/barrel/modeling/modelpage.html.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Identification and selection of connected excitatory neurons

Somatosensory barrel cortex was identified in thalamocortical slices viewed under bright-field illumination by the prominent barrel-like structures (Agmon and Connors 1991; Petersen and Sakmann 2000). Whole cell recordings were subsequently established with excitatory neurons lying within the same layer 4 barrel, as judged by the bright-field image (Petersen and Sakmann 2000). Of over 200 dual whole cell recordings, 14 excitatory synaptic connections were found with detectable (>100 µV) unitary EPSPs (uEPSPs), which were stable over the entire period of the experiment. In three of these experiments the neurons were bidirectionally connected (i.e., action potentials evoked in either neuron would elicit uEPSPs). To prevent rundown of responses the trains of presynaptic action potentials were separated by 20-s intervals of rest, making experiments of over 2-h duration necessary to obtain data covering many frequencies of stimulation. Thus it did not prove possible to study both directions of connection and for ease of data analysis, the larger connection was chosen in each case. Biocytin was included in the whole cell recording pipette allowing visualization of the neuronal structure after fixation of slices. In all cases the excitatory neurons recorded from had initial axonal segments directed to deeper layers, which turned into a strong axonal projection within layer 4 and up to layer 2/3 (Lübke et al. 2000). Dendritic arbors were either entirely confined to layer 4 (spiny-stellate cells) or entered layer 2/3 (star-pyramidal cells), and at high magnification spines could be observed. No significant differences were found between recordings from pairs of star-pyramidals, spiny-stellate to star-pyramidals and pairs of spiny-stellates in terms of uEPSP characteristics (as previously reported Feldmeyer et al. 1999) or short-term plasticity. In the example in Fig. 1A, a spiny stellate neuron is bidirectionally coupled to a star-pyramidal neuron, each cell responding with a regular action potential discharge pattern to depolarizing current injection and postsynaptic EPSPs evoked in the other neuron.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Identification of excitatory layer 4 neurons and analysis of unitary excitatory postsynaptic potential (uEPSP) amplitudes. A1: photomicrograph of a synaptically coupled pair of excitatory neurons of layer 4 barrel cortex that were filled with biocytin and stained. A2: reconstruction of the dendritic (black) and axonal (gray) processes of these neurons. Scale bar for A1 and A2, 100 µm. A3: prolonged injection of current into the neurons evoked regular firing patterns characteristic of excitatory neurons. The neurons were bidirectionally coupled, and thus the action potentials in one neuron evoked EPSPs in the other. Scale bar, horizontal 100 ms, vertical 50 mV (action potential trace above) and 5 mV (EPSP trace below). B1: single action potentials in the left neuron were evoked 30 times, and the averaged "ideal" EPSP recorded from the right neuron is shown. B2: a pair of action potentials separated by 50 ms were evoked and EPSPs from a single sweep are shown as the dark trace. The lighter superimposed trace is the best fit of the ideal EPSP according to a least-squares fit. Subtraction of this fitted EPSP (below) leads to a trace with little sign of the initial response suggesting that the fit is good. Subsequent fitting (below) and subtraction (bottom) of the 2nd EPSP with the ideal EPSP suggests that such fitting routine can be reliably used to measure EPSP amplitudes and that little change in EPSP kinetics occurs during repetitive stimulation. Scale bar for B1 and B2, horizontal 20 ms, vertical 50 mV (action potential trace above) and 2 mV (EPSP trace below). C: the amplitudes of EPSPs evoked by pairs of stimuli with filled squares representing the amplitude of EPSP1 and the open circles representing the amplitude of EPSP2.

Quantification of EPSP amplitudes

The analysis of uEPSPs is difficult because spontaneous EPSPs frequently occur that have similar amplitudes and kinetics to the uEPSPs evoked by stimulation of the connected presynaptic neuron. One solution is to average many sweeps knowing that the stimulus locked nature of the evoked EPSP will overwhelm the random spontaneous signals. This approach, however, does not allow the analysis of individual sweeps, which could provide additional information concerning the nature of the synaptic communication. To extract amplitude measurements from single sweeps, an idealized EPSP was first realized by averaging 30 sweeps of the responses to single action potentials aligned to the action potential evoked in the presynpatic neuron (Fig. 1B1). This idealized EPSP was subsequently fitted through a least-squares routine to single sweep data again aligned to the action potential in the presynaptic neuron (Fig. 1B2). The response to the first action potential is subtracted to visualize the error of the fit and to allow fitting to subsequent EPSPs evoked by action potentials in the preysnaptic neuron (Fig. 1B2). Subsequent uEPSPs in general were fitted equally well compared with the first EPSP suggesting that the kinetics of EPSPs is independent of prior activity, at least for the amplitudes of uEPSPs recorded in this study (range 0.1-3 mV). The amplitude of the idealized EPSP fitted to individual sweeps is used throughout this study as the measure of EPSP size and can be plotted in a sweep by sweep manner (Fig. 1C). To prevent the baseline stimulating frequency from interfering with the measurements of short-term plasticity, each sweep is separated by a 20-s interval, as no interactions with plasticity were observed at this stimulating interval. The responses recorded were stable over time showing no rundown over the periods of the experiments that were analyzed.

Synaptic transmission between excitatory layer 4 neurons shows short-term depression

By comparing the responses evoked by the first action potential (EPSP1) to the responses to a second action potential (EPSP2), the paired-pulse short-term plasticity of a given unitary synaptic connection can be determined. When two action potentials are evoked with a 50-ms interval, the second response on average is smaller than the first as shown for the example in Fig. 1B2 for a single sweep and for 30 sweeps in Fig. 1C. This is true for all the connections between excitatory neurons within layer 4 observed in this study. However, the degree of paired-pulse depression varied from connection to connection with paired-pulse ratios ranging from 0.2 to 0.8. One interesting possibility was whether there might be a correlation between the uEPSP amplitude and the magnitude of paired-pulse depression. However, individual experiments with connection strengths varying over an order of magnitude could display similar degrees of paired-pulse depression (Fig. 2, A and B), suggesting that such a correlation would at most be weak. A plot of paired-pulse ratio as a function of uEPSP amplitude confirmed that no correlation existed (paired-pulse ratio = 0.61 ± 0.042 + 0.00061 ± 0.040 * uEPSP amplitude; least-squares fit ± estimated fitting error SD; Fig. 2C).

View larger version (15K): [in this window] [in a new window]   Fig. 2. Paired-pulse depression is independent of uEPSP magnitude. A: pairs of action potentials were evoked in a presynaptic neuron separated by 50 ms, and the evoked unitary EPSPs were recorded in the postsynaptic neuron. Averaged responses from 3 pairs of neurons are shown with very different connection strengths. Despite the differences in connection amplitude the degree of synaptic depression is very similar. B: the same traces as shown above but now scaled to make the 1st response of equal amplitude. The amplitude of the 2nd response is also very similar in these 3 connections. C: the degree of paired-pulse depression for all pairs of neurons recorded shows no correlation with the unitary EPSP strength.

Time dependence of paired-pulse depression

By varying the interstimulus interval between the first and second action potentials, the time course of the paired-pulse depression was studied. The interstimulus interval was changed from sweep to sweep with each sweep separated by 20 s. Paired-pulse intervals ranged from 10 to 1,000 ms, chosen as the upper limit for the measurements since little paired-pulse depression was observed under this condition. Shorter intervals between the paired pulses evoked stronger depression. The time course of depression was very different between different unitary synaptic connections. In some cases the second EPSP would remain significantly depressed at intervals of 100 ms (Fig. 3A) and longer; but in other cases the recovery would be nearly complete at this time point. For each of the 14 synaptic connections studied, the recovery from depression could be fitted by an exponential function with a single time constant, which ranged from 20 to 1,000 ms averaging 400 ± 256 ms (mean ± SD). Fitting the data with double-exponential functions lead to only small improvements in fitting accuracy through an additional time constant with a small amplitude coefficient, which was either very long (>5 s) (as previously observed Varela et al. 1997, 1999) or very short (~5 ms). Thus throughout this study, single exponential fits are used to describe the recovery from depression for the sake of simplicity. Pooling data from different synaptic connections and then fitting an exponential to the recovery from depression gave a time constant 476 ± 104 ms (least-squares fit ± estimated fitting error SD) with an average maximal depression of 47 ± 4.1% (Fig. 3B). This time constant for recovery from depression is similar to the value of 634 ± 96 ms (Varela et al. 1997, 1999) and 480 ± 40 ms (Finnerty et al. 1999) reported for EPSPs in layer 2/3 pyramidal neurons evoked by extracellular field stimulation; the value of 813 ± 240 ms for connected neighboring layer 5 pyramidal neurons (Markram et al. 1998); and the value of 399 ± 295 ms for layer 5 pyramidal to interneuron synapses (Markram et al. 1998). A trend suggesting that recovery time may be weakly dependent on uEPSP connection amplitude was found (recovery time = 438 ± 105 ms  110 ± 99 ms * uEPSP amplitude), such that stronger connections tended to recover more rapidly from depression (Fig. 3C). No correlation between the time constant and the degree of paired-pulse depression was found (data not shown).

View larger version (16K): [in this window] [in a new window]   Fig. 3. Time course of synaptic depression. A: an example of the time course of synaptic depression with a recovery time constant of 99 ms. B: the pooled data from all connected pairs shows an exponential recovery time constant of around 500 ms.C: the time constant of recovery from depression does not depend strongly on the unitary EPSP strength, although there is a trend for larger amplitude connections to show faster recovery from synaptic depression.

Paired-pulse depression is use dependent

During the analysis of the amplitudes of individual sweeps, it became apparent that the amplitude of the response to the second action potential was correlated to the first response amplitude. For example in Fig. 1C, it is apparent that on the few occasions that the responses to the first action potential are well below normal, the second response in the same sweep is substantially larger than average. To study this in detail the amplitude of responses to the second action potential (EPSP2) as a function of the amplitude of responses to the first action potential (EPSP1) was plotted for every response recorded (2 example experiments are shown in Fig. 4, A and B). Under conditions with strong depression (i.e., short interstimulus intervals), a strong correlation was also apparent between EPSP2 and EPSP1. Thus larger initial responses on average tended to evoke smaller second responses. This is also obvious when the sweeps are separated into two groups, each containing one-half of the responses such that the sweeps with the smallest initial responses are averaged separately from the larger initial responses (Fig. 4, A2 and B2). Smaller initial responses are clearly associated on average with large second responses. Equally consecutive individual sweeps superimposed also give the impression that the second response is larger when the first response is smaller (Fig. 4, A1 and B1). To compare this effect across all experiments, the variability of responses to the first and second action potentials were separately normalized around the mean to the SD. The results from similar interstimulus intervals were pooled, and a significant correlation was observed at 10-ms interstimulus intervals (slope of 0.20 ± 0.063; least-squares fit ± estimated fitting error SD; Fig. 4C) but not at 1,000-ms interstimulus intervals (slope 0.019 ± 0.071; Fig. 4D). The slope of the correlation was thus dependent on the interstimulus interval (Fig. 4E) showing a very similar time dependence to the recovery from synaptic depression. The simplest interpretation of such a depression between excitatory layer 4 neurons is that, if more synaptic vesicles are released by the first action potential, then less will be available for the next action potential until the synaptic refilling processes have returned the synapses to the resting equilibrium state. This form of depression can thus be termed use dependent.

View larger version (34K): [in this window] [in a new window]   Fig. 4. Use dependence of synaptic depression. A1: 5 consecutive sweeps of EPSPs evoked by pairs of presynaptic action potentials separated by 10 ms. The variability in responses is large, and it is obvious that small initial responses are accompanied by larger secondary EPSPs. A2: separation of all 10-ms paired-pulse sweeps from this experiment into 2 groups depending on the amplitude of the 1st EPSP. The group with small initial EPSPs are accompanied by larger secondary EPSPs compared with those of the other group of responses. A3: plotting the amplitude of the 2nd response as a function of the amplitude of the 1st response demonstrates a clear correlation. A large EPSP1 is on average accompanied by a small EPSP2. The depression can thus be termed use dependent. B1-B3: as above but demonstrating this correlation for a different pair of neurons. C: normalizing each experiment allows an analysis of the pooled data. At short interstimulus intervals that show the greater synaptic depression, the amplitude of the 1st and 2nd EPSPs are also correlated in the pooled data. D: at longer interstimulus intervals where little depression is observed, there is no obvious correlation between the amplitude of EPSP1 and EPSP2. E: the time course of the correlation between the paired responses is very similar to the time course of synaptic depression. The amplitude of evoked responses occurring within ~500 ms of each other are thus directly correlated.

Reduced variability of paired-pulse responses

That larger EPSP2s are on average evoked following smaller EPSP1s could lead to a reduced variability in the summed depolarization evoked by paired-pulse stimulation compared with the variability of responses to single action potentials. Indeed a glance at Fig. 4, A and B, suggest that this is the case. Both the initial responses and the second responses in these examples varied around 1.5 mV (Fig. 4, A1 and B1). The summed depolarization following the second action potential, however, varied less than 1 mV in Fig. 4A1 and less than 0.5 mV in Fig. 4B1. The same effect can be observed in Fig. 4, A2 and B2, where many more sweeps have been averaged separating the large and small initial responses. The difference between the large and small initial responses is larger than the difference between the summed depolarization evoked by the paired pulses. Quantitatively this effect can be judged by the coefficient of variation, which computed across all experiments on average was 0.47 ± 0.077 for EPSP1, 0.78 ± 0.19 for EPSP2, and 0.38 ± 0.059 for the combined depolarization. Although there is considerable variability of response amplitudes to individual action potentials, the response to a high-frequency pair of stimuli is more reliable. Such a phenomenon has been described at facilitating synapses where bursting behavior has been suggested as one mechanism to obtain reliable transmission of information (Lisman 1997). The current observations thus extend the notion of increased reliability of information transfer by bursts to include these depressing synapses.

Phenomenological model for use-dependent synaptic depression

That the short-term synaptic depression between excitatory layer 4 neurons is use dependent and that recovery from depression can be described by an exponential time course suggests a simple mathematical description of neocortical short-term synaptic dynamics as previously published (Abbott et al. 1997; Markram and Tsodyks 1996; Markram et al. 1998; Tsodyks and Markram 1997; Varela et al. 1997, 1999). This model of use-dependent synaptic depression (described in detail in METHODS) requires only three constants for each synaptic connection studied, the uEPSP amplitude (the response to the 1st action potential), the exponential recovery time constant from depression, and the maximal depression (extrapolated from the exponential fit to zero interstimulus interval). These constants are experimentally determined from exponential fits to the data as in Fig. 3. From these constants the response evoked by an action potential can be predicted with the knowledge of the amplitude of the response to the last action potential and when it occurred. The ability to predict response amplitudes based purely on the last response time and amplitude provides a very simple mathematical description of synapses, which could be useful at many levels of description of neuronal networks. It is thus important to test the predictions of such a model.

EPSPs evoked in response to trains of action potentials are well-described by the use-dependent model of depression for a short period of time

Trains of 10 action potentials occurring with intervals between 10 and 200 ms were evoked in presynaptic neurons, and the responses were recorded in the synaptically coupled postsynaptic neurons (Fig. 5). The initial responses evoked by each subsequent action potential decreased in amplitude, but after the first five action potentials the evoked EPSPs changed little in amplitude. The parameters extracted from fitting the exponential function to the recovery from synaptic depression for paired-pulse data from each individual experiment were used to extrapolate the predicted responses according to the use-dependent model. There is close agreement between the response characteristics observed experimentally and that computed by the model (an example of responses evoked by a 10-Hz train of 10 action potentials is shown in Fig. 5A). The mean depression recorded experimentally at various stimulation frequencies is faithfully predicted by the use-dependent model of depression using the values from the exponential fits with a root mean square (rms) error of 4.1% calculated across all response amplitudes (Fig. 5B). Additionally the EPSP amplitude that is reached at a given stimulation frequency after many stimuli can be derived from the model and shows good agreement with the experimental data (Fig. 5C). The model can thus be used to accurately predict the responses to regular trains of presynaptic activity.

View larger version (26K): [in this window] [in a new window]   Fig. 5. Comparison of experimental and simulated EPSPs in response to regular trains of action potentials. A: the postsynaptic response to a regular train of 10 action potentials in the presynaptic neuron evoked with an interstimulus interval of 100 ms (left). The parameters determined from the experimental data of the time course of paired-pulse depression for this pair of connected neurons was used in the phenomenological model to simulate the neuronal response. The model and experiment are in close agreement. B: the normalized amplitude of each EPSP evoked during a train of presynaptic action potentials at either 5, 10, 20, 50, or 100 Hz averaged from all experiments (data points connected by thin lines). The higher the stimulation frequency the greater the depression. The normalized data from all experiments shows close quantitative agreement with the model at each stimulation frequency (thick lines). C: the normalized EPSP amplitude computed for all experiments reached at the end of a train of 10 action potentials (data points) is also well predicted by the model (line) for each stimulation frequency.

However, it is unlikely that such regular activity patterns should arise physiologically, and it is thus important to test whether responses to irregular trains are also well predicted by the model. Two different irregular spike trains composed of arbitrarily spaced action potentials were therefore tested. The evoked responses were then compared with the predictions determined by the computational model. In general the experimental and the modeled responses had a similar overall pattern (Fig. 6, A and B). Quantitatively the predicted EPSP amplitude has a rms error of approximately 0.1 mV measured across all experiments, which only increases a little during the stimulus train (Fig. 6C). The fractional rms error (normalized to the amplitude of each EPSP), however, increased significantly during the stimulus train from an initial error of 7.8% for the first three responses to 23.6% for the last three responses in the 10-stimulus train. The increase in error during the stimulus train is thus caused by the decrease in the amplitude of later EPSPs giving rise to larger fractional errors. Part of the differences between experiment and model are undoubtedly due to genuine complexity of short-term dynamics of synaptic transmission that are not accounted for by the simple model presented here. Further error is also unquestionably generated by response variability and spontaneous EPSPs, which are difficult to average out when the response amplitude becomes very small. To quantify the contribution of experimental error due to the limited number of sweeps that were averaged, the responses were divided into two groups of odd and even numbered sweeps. An rms error of 17.8% is found by comparing these two groups of responses to identical irregular spike trains. To compute these sampling errors the sweeps were divided into two groups (each group containing 1/2 of the total number of sweeps used to compute the simulation errors), but these errors will decrease with the square root of sample number. The sampling errors might then account for approximately one-half of the error estimated in the modeling (estimated sampling rms error is 13.6%; simulation rms error is 21.3% across all responses). The error involved in predicting the responses to irregular trains is thus estimated to be under 15% for a 10-action potential train occurring over a 500-ms duration.

View larger version (28K): [in this window] [in a new window]   Fig. 6. Comparison of experimental and simulated EPSPs in response to irregular trains of action potentials. A: responses to an irregular train of 10 action potentials evokes an irregular train of EPSPs of varying amplitudes. The use-dependent model with experimentally determined parameters from the time course of paired-pulse depression for this pair of connected neurons is able to simulate the experimental data. B: as above but applying a different irregular train to the same pair of connected neurons. C: the root mean square (rms) error of the predicted response amplitude computed across all experiments is relatively constant at around 0.1 mV during the train of action potentials. D: the fractional rms error computed for all experiments increases during the train of action potentials since the response amplitude decreases but the error remains constant.

These errors then give an estimate of the reliability with which the simple phenomenological model of synaptic depression can be used to predict responses to any sequence of presynaptic stimulation. The model is good for short periods of time involving a small number of stimuli, but errors gradually increase over time and with larger numbers of stimuli.

Modeling of the short-term dynamics of the excitatory layer 4 neuronal network

By extending the use-dependent model of synaptic depression from individual pairs of excitatory layer 4 neurons to a larger framework of many interconnected neurons, one can make the initial steps toward a complete computational simulation of how a single barrel might respond dynamically to stimulation. Since quantitative experimental data are limited to excitatory neurons, the neuronal network presented here does not include inhibitory neurons, which are likely to play an important role in neocortical function and dynamics. The neuronal network should thus be considered as a first building block on which quantitative data can be added as further experimental measurements are made. The connectivity of rat layer 4 barrel cortex has been closely examined (Feldmeyer et al. 1999; Petersen and Sakmann 2000). Each excitatory layer 4 neuron is connected to roughly one-third of the other layer 4 excitatory neurons within the same barrel. There are very few connections to neighboring layer 4 barrels, which suggests that each layer 4 barrel functions as an independent processing unit at least as a first-order approximation (Petersen and Sakmann 2000, 2001). To consider the network activity of layer 4 barrel cortex, our attention can thus be limited to a single barrel. A small-diameter barrel contains on the order of 1,000 interconnected excitatory neurons, which in the present model are connected in a random fashion following the experimentally observed distribution of connection amplitudes (Petersen and Sakmann 2000). Testing the behavior of this model and modifications of it may help our understanding of how large numbers of neurons interact, which becomes particularly important for consideration of responses measured in the intact animal.

The model was constructed as described in METHODS and can be downloaded to run within the environment of IgorPro from http://sun0.mpimf-heidelberg.mpg.de/~petersen/sensory-pathway/barrel/modeling/modelpage.html. Most of the key parameters were determined experimentally. Thus the distribution of unitary connection strengths (Fig. 7A) was derived in a previous study (Petersen and Sakmann 2000), and this study documents the distribution of parameters describing short-term depression R₁ (Fig. 7B) and  (Fig. 7C). To simplify the construction of the model, all EPSPs are given the same EPSP kinetics taken from an individual experiment (Fig. 7D) and are summated linearly until the threshold for action potential initiation is reached (Fig. 7E). The threshold for action potential initiation is set to 45 mV, but after the initiation of an action potential an additional refractory threshold is added to prevent the inevitable generation of multiple spikes (Fig. 7F). This refractory threshold was arbitrarily assigned an exponential function with decay time of 3 ms. Changing the threshold function to a step function preventing action potential generation for 5 ms had only a small effect on simulated responses, and thus the arbitrary nature of this function does not appear to strongly affect the simulation.

View larger version (30K): [in this window] [in a new window]   Fig. 7. A neuronal network model of the excitatory synaptic interactions within a layer 4 barrel. A: the experimentally determined distribution of unitary EPSP strengths (Petersen and Sakmann 2000) used in the dynamical simulation of the excitatory neuronal network of a layer 4 barrel. B: the experimentally determined distribution of the maximal releasable fraction R1 used in the simulation. C: the experimentally determined distribution of the time constant of synaptic depression used in the simulation. D: an experimentally recorded EPSP waveform used in the simulation. E: a simple example of the output of a simulation. Either 1, 2, or 3 presynaptic neurons are stimulated each evoking an EPSP in a single postsynaptic neuron. The responses are added linearly until an action potential is initiated at the threshold of 45 mV. F: following an action potential in a given neuron, there is a refractory period during which it is more difficult to initiate further action potentials. This is modeled by adding the refractory threshold waveform shown here to the action potential threshold, which is otherwise at rest set to 45 mV. G1: simulated responses evoked in 2 cells by stimulation of 10 presynaptic neurons with 100-ms interstimulus interval. G2: the simulated responses from cell B, but now with 25 active presynaptic neurons. H1: the simulated responses with the same initial 10 presynaptic neurons but now stimulated at 10-ms intervals. H2: the responses in cell B evoked by the 25 active presynaptic neurons as before but now with 10-ms interstimulus intervals.

The model can be used to simulate the effects of stimulating sets of neurons at given times. Examples of the responses generated by a regular 10-Hz train of stimuli delivered to 10 neurons within the network are shown in Fig. 7G1. Cell A in this example shows weak responses with strong depression, whereas cell B shows much larger responses that only depress slightly. These differences are due to the random wiring of the neuronal network both in terms of connection amplitudes and short-term plasticity. With the stimulation of only 10 randomly chosen excitatory neurons, no further action potentials are generated in this network. When 25 neurons are stimulated cell B responds to each stimulus with an action potential resulting from summated EPSPs (Fig. 7G2), whereas none are observed in cell A (not shown). Figure 7H shows responses for the same subsets of neurons stimulated as before but at 100 Hz. Under these conditions when 25 neurons are stimulated (Fig. 7H2), there are stimuli that fail to evoke an action potential in cell B. Since the modeled neuronal network does not include inhibitory synaptic transmission, even a single stimulation of more than around 30 neurons typically leads to explosive excitation of all neurons in the network within 50 ms of the stimuli.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Synaptic transmission between pairs of excitatory layer 4 neurons exhibits a pronounced short-term depression. This plasticity can be closely reproduced by a simple use-dependent model allowing the computational simulation of a dynamic excitatory layer 4 neuronal network.

Determinants of short-term depression within the excitatory layer 4 neuronal network

Whereas different classes of neocortical GABAergic interneurons can receive facilitating or depressing excitatory input from an individual pyramidal neuron in a well-defined target-cell specific manner (Markram et al. 1998; Reyes et al. 1998), synaptic transmission between neocortical layer 4 neurons is always depressing. This is most likely related to the high release probability reported at these excitatory layer 4 to layer 4 synaptic connections (Feldmeyer et al. 1999; Stratford et al. 1996; Tarczy-Hornoch et al. 1999). However, the maximal degree of depression and the recovery time varied substantially between different connections but did not appear to be strongly correlated to each other or to the strength of the synaptic connection. The independence of these experimentally determined parameters maximizes the ability of these synaptic connections to respond differentially to distinct patterns of activity. Equally the lack of correlation of these values suggests that they may be regulated independently and might result from physically separable mechanisms.

One possible way of regulating the short-term plasticity in an activity-dependent manner is through presynaptic long-term plasticity. Excitatory connections within layer 4 barrel cortex have been shown to exhibit a presynaptic form of long-term depression (LTD), which is engaged during strong correlated activity of presynaptic and postsynaptic neurons (Egger et al. 1999). At younger developmental ages than those studied by Egger et al. (1999), layer 4 excitatory connections may also exhibit long-term potentiation as observed with thalamocortical inputs (Crair and Malenka 1995). The presynaptic components of long-term plasticities are likely to modulate short-term plasticity in the layer 4 excitatory neuronal network. That stronger unitary connections are weakly correlated to more rapid recovery from depression (Fig. 3C) might suggest that changing the recovery time constants form a possible mechanism to increase the strength of a synaptic connection between neurons. For example, shorter recovery time constants could occur by faster delivery of vesicles to the releasable pool, which in turn could lead to larger releasable pools increasing the synaptic efficacy. That the correlation is rather weak may well suggest that other processes during development are important for determining the short-term dynamics. That short-term plasticity in fact is changed by activity in vivo at excitatory synaptic connections between neurons of layer 4 and layer 2/3 and within layer 2/3 was recently demonstrated by deprivation of sensory input by whisker trimming (Finnerty et al. 1999). How such deprivation of sensory input might alter the dynamics of the excitatory layer 4 neuronal network will be of great interest and will provide important insight into the activity-dependent determinants of short-term synaptic plasticity.

Physiological significance of the short-term depression in the excitatory neuronal network of layer 4 barrel cortex

Sensory stimulation of whiskers may occur many times per second giving rise to high-frequency firing of action potentials in neocortical neurons. Information concerning whisker movement from the thalamus is relayed to barrel cortex neurons primarily in layer 4, which respond to whisker deflections with shorter latency and more action potentials than neurons in the other layers. Excitatory neurons within a layer 4 barrel are strongly connected, and it is likely that the initial cortical processing of whisker information occurs within a single layer 4 barrel. The short-term dynamics of the excitatory neuronal network are thus likely to be of importance in determining the response properties of the neocortex under physiological conditions. That synaptic transmission between excitatory neurons of layer 4 show short-term depression suggests that the layer 4 network responds best to isolated stimuli separated by over a second and that repetitive high-frequency stimulation would result in sensory desensitization. It therefore seems somewhat paradoxical that rodents should deliberately induce high-frequency whisker movement during active exploration. One possibility is that the depression of synaptic transmission evoked by high-frequency stimulation of whisking engages the neuronal network in a state more suitable for detecting the subtle changes of whisker movement as it encounters an object. During whisking one might assume that information concerning the immediate surroundings of the rodent head is conveyed not so much by the regular pattern of neuronal activity engaged by the whisking itself, but rather by disturbances from this pattern. So if a whisker encounters an object, the deviation from the expected whisking induced pattern is of the greatest significance. The detection of such disturbances from a regular pattern of activity may in fact be enhanced by an excitatory neuronal network with short-term synaptic depression as illustrated by the neuronal network simulation presented in Fig. 8. Rhythmical whisking activity is simulated by triggering action potentials in a set of 25 neurons at 100-ms intervals. In the neuronal network with short-term depression, the responses to subsequent whisks initially decrease rapidly, but after a few whisks the responses change little. Without short-term depression each whisk evokes the same response (Fig. 8A). If an object is struck by a whisker, then the whisker will become deflected earlier and in a different manner to that expected from the whisking-induced movements. This different movement of the whisker is likely to evoke responses in a different set of trigeminal sensory neurons since they are highly direction and stimulus selective. In the neocortex one might then suppose that a different subset of neurons within the network are stimulated by the encounter with an object. In the simulation, this is described as action potentials in a different set of 25 neurons to those activated by whisking. This is clearly an extreme case, since overlapping subsets of neurons are likely to be activated physiologically during a whisking encounter with an object. In a network without short-term depression, this evokes a similar amount of activity to that evoked by a normal whisking cycle. However, in a network with depression, the responses to each whisking cycle are depressed, whereas the response to hitting an object is not depressed. The difference in responses between a whisking cycle without hitting an object compared with a cycle where an object is encountered is thus greatly enhanced in a neuronal network based on short-term depression. In 10 such simulations a normal whisk in the middle of a whisking episode evoked action potentials in 2 neurons in a network with short-term depression, whereas 102 neurons were activated without depression. When an object was struck, 82 neurons were activated in the network with depression, whereas 120 were activated without depression. Under these conditions the network with depression thus shows a 40-fold increase in responsiveness on hitting an object, whereas without depression only a 1.2-fold increase in responsiveness is obtained. The precise quantitation for the increased activity associated with whiskers encountering unexpected objects will vary depending on the assumptions of the simulation. In particular the larger the overlap between the subset of neurons activated by whisks with and without an object, the smaller will be the advantage of networks invoking short-term depression. Nonetheless, the general principals involved should ensure that the qualitative answer is always the same. Short-term depression may thus be of significance to desensitize the neuronal network to regular rhythmical activity induced by whisking, while enhancing the detection of the unexpected deflection of a whisker evoked by hitting an object during whisking.

View larger version (28K): [in this window] [in a new window]   Fig. 8. Short-term depression may be physiologically important in detecting an object in the whisking space. A: the average responses across the entire population of simulated excitatory neurons is compared with an identical network lacking depression. Whisking is simulated as evoked action potentials in 25 neurons occurring regularly at 100-ms intervals. In the network without depression identical responses are evoked in each whisking cycle (top left panel, top trace, subthreshold membrane potential changes averaged across all neurons in the network and bar graph below is the quantification of the total number evoked action potentials). The network with depression shows a large response at the onset of whisking but responses to subsequent whisks are depressed (bottom left panel). The encounter of an object on the 6th whisking cycle is simulated by evoking action potentials in a different set of 25 neurons (right panels). In both networks the striking of an object by the whisker evokes activity. However, the difference in activity compared with whisking cycles where no object is hit is much more striking in the more physiological network including short-term synaptic depression. Vertical scale bar 10 mV for EPSPs (top traces) or 5 action potentials (bottom bar graphs); horizontal scale bar 200 ms. B: the results of similar simulations in 10 randomly generated networks suggest that the detection of a whisker striking an object is much easier in a network with short-term synaptic depression. Whereas the average response to a whisking cycle is only enhanced a little by striking an object in a network without depression, a strong increase in response is detected by a network with depression. Vertical scale bar 10 mV for EPSPs (top traces) or 4 action potentials (bottom bar graphs); horizontal scale bar 10 ms.

Extending the neuronal network model

For any model it is important to compare the predictions of the model with experimental data. One simple comparison that could be made is between the average simulated and experimentally observed responses to trains of stimuli evoked by extracellular stimulation. Voltage-sensitive dye imaging of responses to extracellular stimulation electrodes placed within a layer 4 barrel appear to measure mainly subthreshold postsynaptic depolarization of the local excitatory neuronal network (Petersen and Sakmann 2001). During a 10-Hz train of such stimuli, voltage-sensitive dye responses within a layer 4 barrel depress to 54 ± 7% (n = 13) of the initial response (Petersen and Sakmann 2001). The predicted amplitude of the simulated responses evoked at the end of a train of 10 stimuli delivered at 10 Hz of 25 neurons averaged across all neurons in the network was depressed to 52 ± 2% (n = 10) of the first EPSP amplitude. This is thus a quantitative indication that the dynamics of the neuronal network in vitro might be closely simulated with this computational model. However, to be able to make quantitative comparisons of in vivo physiological data with simulations, the simple excitatory neuronal network presented here should be extended as quantitative data becomes available. Neurons of layer 4 receive very little excitatory input from layer 2/3 or layer 5, but they receive a strong excitation from thalamic VPM neurons and weaker excitation from layer 6 neurons (Gil et al. 1999; Stratford et al. 1996; Tarczy-Hornoch et al. 1999). These studies have also begun to characterize the short-term plasticity of these synaptic connections showing a depressing thalamic input and a facilitating layer 6 input; however, the published data do not allow quantitative modeling. The short-term dynamics of the excitatory synapses of layer 4 may also be modified during development as reported for synaptic transmission between pyramidal neurons (Reyes and Sakmann 1999), although voltage-sensitive dye imaging of short-term plasticity of layer 4 responses in postnatal day 28 rats (C. Petersen, unpublished data) did not show significant differences compared with those recorded at postnatal day 14 (Petersen and Sakmann 2001). The role of different functional classes of inhibitory neurons (Beierlein et al. 2000; Galarreta and Hestrin 1998, 1999; Gibson et al. 1999; Gupta et al. 2000; Markram et al. 1998; Porter et al. 2001; Reyes et al. 1998) in controlling the behavior of the layer 4 neuronal network will also be of enormous interest to incorporate in more sophisticated models. The current model, although limited, provides insight into the dynamics of the excitatory layer 4 neuronal network suggesting a role for short-term plasticity in suppressing rhythmic whisking from generating cortical excitation and enhancing object detection.