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¹ Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel² Center for Neural Computation⁶ Department of Neurobiology, The Hebrew University, Jerusalem 91904, Israel³ Institute of Neuroinformatics, University of Zürich and Swiss Federal Institute of Technology (ETH), Winterthurerstrasse 190, CH-8057 Zürich, Switzerland⁴ Division of Neuroscience, John Curtin School of Medical Research⁵ Australian National University Medical School, Canberra, ACT 0200, Australia

	Abstract

Top Abstract Introduction Methods Results Discussion Appendix References

 
Synaptic transmission between pairs of excitatory neurones in layers V (N= 38) or IV (N= 6) of somatosensory cortex was examined in a parasagittal slice preparation obtained from young Wistar rats (14–18 days old). A combined experimental and theoretical approach reveals two characteristics of short-term synaptic depression. Firstly, as well as a release-dependent depression, there is a release-independent component that is evident in smaller postsynaptic responses even following failure to release transmitter. Secondly, recovery from depression is activity dependent and is faster at higher input frequencies. Frequency-dependent recovery is a Ca²⁺-dependent process and does not reflect an underlying augmentation. Frequency-dependent recovery and release-independent depression are correlated, such that at those connections with a large amount of release-independent depression, recovery from depression is faster. In addition, both are more pronounced in experiments performed at physiological temperatures. Simulations demonstrate that these homeostatic properties allow the transfer of rate information at all frequencies, essentially linearizing synaptic responses at high input frequencies.

(Received 13 November 2003; accepted after revision 8 March 2004; first published online 12 March 2004)
Corresponding author C. Stricker: Division of Neuroscience, JCSMR-ANU, GPO Box 334, Canberra, ACT 0200, Australia. Email: christian.stricker{at}anu.edu.au

	Introduction

Top Abstract Introduction Methods Results Discussion Appendix References

 
Information transfer in neural networks is determined by the dynamics of synapses in response to sequences of presynaptic action potentials. Recordings from interconnected neurones reveal that synaptic transmission is indeed dynamic, i.e. synapses in the neocortex typically undergo activity-dependent changes in response to bursts of action potentials (Magleby, 1987; Thomson et al. 1993; Markram et al. 1997; O'Donovan & Rinzel, 1997; Reyes et al. 1998; Tarczy-Hornoch et al. 1998). Specifically, connections between neocortical pyramidal neurones often display a gradual decrease in postsynaptic response, a phenomenon known as synaptic depression.

However, the amplitudes of the postsynaptic response are determined not only by the input pattern, but also by the probabilistic nature of neurotransmitter release, which results in trial-to-trial fluctuations (Kuno, 1964; Jack et al. 1981; Korn et al. 1984). A quantal hypothesis for probabilistic synaptic transmission was developed for the frog neuromuscular junction (Del Castillo & Katz, 1954) and has later been extended to other preparations (reviewed in Redman, 1990). According to this hypothesis, the connection between two neurones is composed of several release sites that always contain at least one vesicle available for release. At the arrival of an action potential, each site releases at most one vesicle with a fixed probability, independent of the release of vesicles from other sites, and from preceding release at the same site (spatial and temporal independence). The postsynaptic response is proportional to the number of vesicles released.

At depressing synapses, it is thought that depletion of the releasable pool of vesicles (‘synaptic resource’) accounts for the reduced postsynaptic response during a burst, i.e. synaptic depression is release dependent. Particularly, in cases of failure to release transmitter during an individual trial, there is no vesicle depletion and therefore no reduction in availability of synaptic resources for subsequent release. This consideration indicates that synapses with low probability of release would be unable to reliably code presynaptic activity because based on vesicle depletion release would occur too infrequently to cause depression. Such a scenario would restrict information transfer related to presynaptic firing rate.

However, there is evidence that synaptic depression can also be release independent (Dobrunz et al. 1997; Thomson & Bannister, 1999; Brody & Yue, 2000; reviewed in Zucker & Regehr, 2002). Release-independent depression (RID) is observed if a decrease in the probability of release occurs even if the second synaptic response is preceded by a transmission failure. In contrast to the scenario above, such a mechanism would allow depression to occur even at synapses with low release probability and therefore would constitute a homeostatic mechanism potentially extending the range of information transfer considerably.

We therefore investigated these questions in a study where experimental observations were combined with the modelling of synaptic dynamics, since at this stage of investigation it is not possible to measure information transfer directly.

To gain a detailed understanding of the factors involved in governing depression and recovery from depression, we recorded from connected excitatory cell pairs in rat somatosensory cortex. This approach allows the delivery of precise presynaptic stimulus patterns and the measurement of the associated postsynaptic responses (EPSCs) under excellent signal-to-noise conditions. We investigated the synaptic dynamics by measuring both the depression caused by a burst of action potentials and the recovery gauged by an action potential delivered with a variable delay after the burst. By carefully quantifying depression, we found that at these connections, there is release-independent as well as release-dependent depression. In addition, at certain connections, recovery from depression is frequency dependent, the rate of which accelerates during periods of increased activity. We show that release-independent depression and frequency-dependent recovery are tightly correlated such that synapses, which significantly depress independently of vesicle depletion, also recover faster from depression under conditions of high frequency firing.

To match these experimental observations, we developed a model, which replicates both the average dynamics of neocortical synaptic transmission, as well as the fluctuations in synaptic release. The two properties of synaptic depression as well as frequency-dependent recovery from depression were incorporated into the model. Release-independent depression was implemented as a decrease in the probability of transmitter release to subsequent action potentials, which is independent of whether release actually occurred. Recovery from depression could be brought about by an activity-dependent decrease of the time constant of recovery from depression. Frequency-dependent recovery from depression has previously been observed at a number of invertebrate and vertebrate synapses (reviewed in Zucker & Regehr, 2002).

We show that these mechanisms enable a depressing synapse to transmit information about presynaptic firing rates, even at high input frequencies, and results in a synapse that can code rate information at all frequencies.

	Methods

Top Abstract Introduction Methods Results Discussion Appendix References

 
Slice preparation and whole-cell recording

Wistar rats, 14–18 days old, were killed by decapitation and parasagittal cortical slices were prepared as described in Simkus & Stricker (2002). The Department for Veterinary Affairs of the Canton of Zürich, Switzerland, approved the techniques used. Whole-cell recordings were made under visual control using infra-red differential interference contrast (IR-DIC) optics. The artificial cerebrospinal fluid (ACSF) contained (mM): NaCl, 125; KCl, 2.5; NaHCO₃, 25; NaH₂PO₄, 1.25; CaCl₂, 2.0; MgCl₂, 1.0; glucose, 25.0; gassed with 95% O₂ and 5% CO₂, pH 7.4. In most cases, 10 µM bicuculline methiodide was added to block GABA_A-mediated inhibitory transmission. All experiments, except where otherwise stated, were conducted at 36 ± 1°C. The intracellular solution contained (mM): potassium gluconate, 115; KCl, 20; HEPES, 10; phosphocreatine, 10; Mg-ATP, 4; Na-GTP, 0.3; pH 7.2; osmolarity, 305 mosmol l^–1. In a number of experiments, the Ca²⁺ dependence of the mechanisms governing synaptic depression was examined. In these cases the presynaptic neurone was re-patched after the control recording with a pipette, which then contained 0.5–5 mM ethylene glycol-bis (2-aminoethylether)-N,N,N',N'-tetraacetic acid (EGTA). To examine whether Na⁺ current boosting of the postsynaptic response occurred at these connections, the intracellular solution contained 5 mM QX-314 (Alamone Laboratories, Jerusalem, Israel) and the appropriate reduction in potassium gluconate made to maintain iso-osmolarity.

Recordings were obtained between connected pairs of layer V or IV cells. Access resistance was 10.1 ± 2.4 M and was uncompensated. The presynaptic neurone was recorded in current-clamp mode (Axoclamp 2B, Axon Instruments), and action potentials were initiated (Fig. 1B) by injection of rectangular current pulses (5 ms, 0.5–1.5 nA, Fig. 1A). The postsynaptic neurone was held in voltage clamp at –70 mV and excitatory postsynaptic currents (EPSCs) recorded using an Axopatch 200B amplifier (Axon Instruments; Fig. 1C). The choice of postsynaptic voltage clamp was made for the following reason. Firing the cells at stimulus frequencies > 25 Hz would have contaminated the subsequent EPSP amplitudes by the decay phase of the previous responses. In voltage clamp, however, the current decays are markedly faster and allow the measurement of the peak amplitude even at these frequencies. Note that we do not claim to perfectly clamp postsynaptic currents, which is impossible in these distributed structures. The output was amplified (100–500 times) following a sample-and-hold step to ensure that the full resolution of the AD converter could be utilized (custom-built sample-and-hold amplifier integrated with a 8-pole Bessel filter, design JCSMR, ANU, Australia). The signal was filtered at 2 kHz and digitized at 5 kHz using an ITC-18 computer interface (Instrutech Corp, Port Washington, NY, USA). Data were acquired using software developed with IGOR Pro 4.0 (Wavemetrics, OR, USA). Each trial in an experiment involved generating a burst of action potentials (mostly 20) in the presynaptic neurone at a particular frequency (range 3–50 Hz). The frequency during each burst was randomly chosen from a set of a few predetermined frequencies (i.e. 3, 5, 10, 20, 25, 30, 40, 50) to avoid steady-state behaviour. Each burst of action potentials was then followed by a recovery interval (300–1200 ms; also randomized) before a single action potential was evoked to gauge recovery from depression. The trials were repeated every 10–15 s, and 50–900 trials were recorded for each of the frequencies studied (Fig. 1A and B).

View larger version (39K): [in this window] [in a new window]   Figure 1.  Experimental protocol A, sample trials of 20 rectangular current pulse injections (5 ms, 1 nA at 10, 50 and 20 Hz, respectively) applied to the presynaptic neurone with a trial-to-trial interval of 10–15 s. The sequence of trials was randomized for frequency, and the repetitions for each input pattern were between 50 and 900. Recovery was gauged with a delayed current pulse (500 ms in this example). B, single burst of action potentials recorded in the presynaptic neurone in response to a current pulse sequence (A). C, the postsynaptic neurone was held in voltage clamp at –70 mV and excitatory postsynaptic currents (EPSCs) were recorded. For clarity, only sample EPSC trials in response to a burst of action potentials at 10 Hz are shown. In D–E, the analytical procedures are indicated. In D, the analysis starts with sorting trials according to stimulus frequency and delay of the action potential to gauge recovery. E, measuring E1 and E2 in each trial allows determination of the release dependence of depression (RD), construction of the PDFs and comparison of for the 20 trials with the smallest E1 and those with the largest . F, the average of all trials for a particular input pattern are used to determine the total amount of depression, and the characteristics of recovery.

Averages are presented as mean ± 1 S.D., error bars in figures represent ± 1 S.E.M. For statistical comparison, a level of significance of < 0.05 was accepted and the following abbreviations are used: p_r for Pearson's r, p_KS for Kolmogorov-Smirnov, p for ² statistics, p_A for significance calculated based on analysis of covariance (ANCOVA), p_t for Student's t test and p_pt for Student's paired t test.

Extracting the amplitude of postsynaptic responses

In some cases, the amplitudes were measured manually according to the technique described in Stricker et al. (1996) and an estimate of the baseline noise was obtained (averaged over all experiments _n= 0.9 ± 0.2 pA). In other cases, the response amplitudes in single trials were determined automatically by a custom Matlab routine (MathWorks Inc., Natick, MA, USA). In this case the experimental recordings were low-pass filtered (Gaussian filter with = 0.2 ms) to remove high frequency fluctuations, and the baseline and peak of each synaptic response determined. The detection method was verified by comparing the amplitude of the average EPSC of all trials, with the average of the automatically determined amplitudes.

Since the experiments required a prolonged recording period (> 3 h), the stability of synaptic dynamics was assessed by comparing the mean response for the first and second half of all trials. Only experiments with stable dynamics were used (i.e. where p_t of the normalized averages > 0.05). In some cases, a drift (always run-down) in the average EPSC amplitude was sometimes observed (due to changes in access resistance). In these cases, stationary subsets of data were used for most analyses. However, for modelling, consistent drift in the data (< 50%) was corrected by normalizing the responses according to the slope of the linear regression of the amplitudes over time. To compare recordings under different conditions (e.g. different frequencies of stimulation), the magnitudes were normalized according to the average amplitude of the first EPSC.

Detecting and quantifying release-independent depression

RID is best demonstrated at connections with a low probability of release and a significant number of failures in response to the first action potential. Under conditions of release-dependent depression, the average, and amplitude distribution, of second EPSCs following a failure should equal those of all first EPSCs. To examine such differences in the amplitude distributions, amplitude probability density functions were calculated by kernelling each amplitude with a Gaussian as described in Stricker et al. (1994). Cumulative probability densities were determined, and significant differences tested using Kolmogorov-Smirnov statistics. However, when the initial release probability is high, there are at most few or no trials, where failures in response to the first action potential occur, and adequate statistics cannot be obtained. RID can still be demonstrated in the absence of transmission failures by examining the trials based on the amplitude of the first EPSC (smaller or larger than the mean response). If depression is release dependent, the average amplitude of the second EPSC in those 20 trials with the smallest first EPSC should be larger than that of the 20 trials with the largest first EPSC (; Fig. 1F). This will not hold true for RID, and significant differences were tested using a Student t test. It should be noted that due to the small sample size, the two averages and typically constitute a biased sample and therefore deviations from the predictions of R_D (see below) are likely to be observed.

A further method based on the amplitudes of all first and second EPSCs was devised to quantify the relative contribution of release-dependent and -independent depression. This measure is subsequently called R_D and is proportional to the correlation coefficient between the first and second EPSCs, i.e.

(1)

where E₁ and E₂ are random variables representing the first and second EPSCs. _E1,E2 is the correlation coefficient, and _RDD is the correlation coefficient for pure release-dependent depression (RDD; see Appendix for details). The idea is that if transmitter release is purely release dependent, then E₂ is correlated with E₁ (Matveev & Wang, 2000), In contrast, at a connection with pure RID, no correlation is expected between E₁ and E₂, and therefore R_D equals 0. The measure quantifies the degree of RDD and (for a sufficiently large sample size) holds values between 0 R_D 1, where 0 indicates pure RID and 1 pure RDD.

An illustration of R_D is obtained in a plot of E₂versusE₁ (Waldeck et al. 2000; see Fig. 2B and D). For pure RDD, the slope of the regression line is _RDD and the y-intercept (the average of second responses that follow a failure equals the simple average of all first responses). For pure RID, the slope is 0 by definition and the y-intercept is (the average of all the second responses). R_D is the relative y-intercept normalized by (see eqn (20) in the Appendix).

View larger version (29K): [in this window] [in a new window]   Figure 2.  Release-dependent and -independent components of depression A, a layer V connection expressing prominent release-dependent depression (RDD). EPSCs were recorded in 148 successive trials, in which the presynaptic neurone was stimulated at a frequency of 20 Hz. Left: average (20 trials) depicting the first two EPSCs, in which the first EPSCs were the smallest . Right: average EPSCs, in which the first EPSCs were the largest . Second EPSCs that follow small first EPSCs (left) are significantly larger than second EPSCs that follow large first EPSCs (right). B, plot of second versus first EPSCs for the same connection as in A. Filled circles: experimental data; continuous line: linear regression (r=–0.40, pr < 0.05); dashed lines: theoretical line for pure release-independent depression (RID) (horizontal line) and RDD (oblique line). The y-intercept of the RDD line is the average of first EPSCs and that of the RID line, the average of the second EPSCs . The regression line overlaps the pure RDD line, and the y-intercept of the regression is clearly closer to than . RD= 1.03 ± 0.33, suggesting a strong component of RDD. The open squares indicate and as shown in A. C, a layer IV connection with dominant RID. The response was recorded in 191 successive trials, in which the presynaptic neurone was stimulated at a frequency of 3 Hz. Left, and right, . The amplitudes of the second EPSCs are similar in both cases, largely independent of the first response. D, plot of second versus first EPSCs for the same connection as in C. Filled circles: experimental data; continuous line: linear regression (r=–0.12, pr= 0.09); dashed lines: theoretical line for pure RID (horizontal line) and RDD (oblique line). The y-intercept of the RDD line is the average of first EPSCs and that of the RID line, the average of the second EPSCs . The y-intercept of the regression line is clearly closer to than to , suggesting a strong component of RID. The open squares indicate and as shown in C. E, additional evidence for release-independent depression in a layer IV connection. Probability density functions of the amplitudes of the first EPSC (continuous line, N= 554) and for the second EPSC when the first EPSC was a failure (dashed line, N= 75). The frequency of stimulation was 20 Hz. F, cumulative probability densities for the connection in E. The densities for E1 (continuous line) and E2 following a failure (dashed line) are significantly different (pKS < 0.005). The inset shows the average time course for the first response (continuous black line), the second response, given the first was a transmission failure (dashed line), and all second responses (grey line).

Detecting and quantifying frequency-dependent recovery from depression

Frequency-dependent recovery (FDR) can be directly observed in the averaged data. It is present when the amplitude of the EPSC after a high frequency burst is greater than that of the EPSC evoked with the same delay following a burst at lower frequency. For the quantification of FDR, we calculated the normalized recovery amplitude (R_rec) for each stimulus frequency as

(2)

where is the mean amplitude of the EPSC induced with a delay (400–600 ms) after the burst (Fig. 1C). is the mean EPSC amplitude in steady state (taken as the average of the last 4 EPSCs in the burst of 20 action potentials). The values will fall between 0 and 1, with a smaller number indicating faster recovery. To quantify the degree of FDR, we calculated the ratio between R_rec at 10 and 20 Hz (R_FDR). R_FDR > 1 indicates FDR, whereas R_FDR= 1 indicates no FDR. It would also be possible to define recovery as 1 –R_rec so that a bigger value indicates faster recovery. R_FDR would then be the ratio between R_rec at 20 and 10 Hz. However, in this case, connections with very little recovery (at an interval of 400–600 ms there was on occasion very little recovery) would have a very small denominator (close to zero) and therefore, R_FDR would be disproportionately large, i.e. in certain instances tend towards infinity. Equally, the measure described above is sensitive to the amount of recovery, and it would not be appropriate to use this measure for long recovery intervals where .

Estimating the initial probability of transmitter release

We attempted to determine the initial release probability for each of the connections used in this study. This is usually done using quantal analysis. However, layer V pairs are not amenable to quantal analysis; the amplitude distributions of first responses are unimodal and overdispersed with more variance than would be expected from a binomial release process (A. Cowan & C. Stricker, unpublished observations). To overcome this problem, we attempted to use the extended moment analysis as described in Courtney (1978), where the probability (p_r, also U₀ in the model) is determined by

(3)

where is the standard deviation of the sample and skew is calculated as follows

(4)

where i is the trial number and N is the total number of trials. The quantal content (m) is

(4)

In cases of overdispersion (too much variance when compared to a classical release process) (²)² becomes the dominant factor in both equations and renders this measure very insensitive. For these reasons, we are unable to provide a measure for release probability per se. However, we resorted to using the skew of the sample as an indication of p_r. For a purely binomial process of transmitter release, a negative skew indicates that p_r > 0.5. Such a distribution has an asymmetric tail extending towards EPSCs of smaller magnitude (remember, however, that since inward currents are measured, the tail extends towards less negative values). A skew of zero corresponds to p_r= 0.5, whereas a positive skew indicates p_r < 0.5 (such a distribution is characterized by an asymmetric tail extending towards large EPSCs). Correlations between the skew and various parameters of synaptic depression suggest a correlation of these parameters with initial release probability.

To examine whether synaptic depression in these connections was a result of a change in p_r, or could be accounted for by other factors (a change in the number of release sites (n) or the quantal size (q), we constructed plots of the inverse of the normalized coefficient of variation squared (CV^–2) versus normalized mean amplitude (as reviewed in Korn & Faber, 1991).

Augmentation

To test if augmentation was present at the connections studied, we used a protocol similar to that described in Stevens & Wesseling (1999). Following a sequence of 100 action potentials at 10 Hz, action potentials were evoked in the presynaptic neurone at a rate of 0.5 Hz for the next 60 s. The amplitudes of the resultant EPSCs were measured and normalized to the final amplitude (i.e. the average value for the last 30 s, as in Stevens & Wesseling, 1999). The time course for the decay of augmentation was then determined by fitting a single exponential to the normalized EPSCs for the first 15 EPSCs following the high frequency burst.

Model

The model implementation is based on the classical quantal hypothesis, to which we add the dynamics of synaptic transmission. These are formalized in previously published deterministic (Tsodyks & Markram, 1997) and probabilistic (Fuhrmann et al. 2002) models, with extensions made to accommodate the experimental findings presented below.

The modelled connection is composed of n release sites each holding at most one vesicle. In response to an action potential, each available vesicle can be released with a constant probability, U_SE. After release, the site can be refilled within each time step dt with the probability dt/_rec, where _rec is the recovery time constant of the refilling process. In contrast to the classical quantal hypothesis, in this model the release sites may be depleted of vesicles, thus no vesicles would be available for transmission.

The processes of transmitter release and recovery from depression can be described by a single differential equation, determining the probability P_v, of vesicle availability at time t,

(6)

(5)

where P_r(t_Ap) is the release probability at each release site at the time of an action potential, t_Ap. It is the product of P_V(t_Ap) and U_SE (see Zucker, 1973; Quastel, 1997). The postsynaptic response is proportional to the number of vesicles released.

Based on the experimental findings, we formalize the mechanism of depression as composed of two components. The first component is release dependent (RDD), which results from the depletion of synaptic resources, as formulated in eqn (5) above. The second component is RID, which is mediated by a decrease in the probability of release to subsequent action potentials, and which is independent of whether release actually occurred. It is formalized by U_SE being a dynamic variable, decreasing with subsequent action potentials in the sequence

(6)

where U₀ is the initial probability of release, U₁ a constant (0 < U₁ < 1) determining the decrease in U_SE per action potential, and _inrec is the recovery time constant of RID. The reason for this choice of implementation is discussed later (Results and Discussion). Thus, between bursts of action potentials (15 s), U_SE increases towards U₀, and when an action potential occurs (t_Ap), it decreases by U₁·U_SE(t_Ap).

To account for FDR, we suggest that _inrec itself is activity dependent. Its dynamics evolve according to

(7)

where ₀ is the initial value of the recovery time constant for RID, ₁ is a constant determining the step-like decrease in _inrec per action potential (0 < ₁ < 1), and _inrec is the relaxation time constant of _inrec. Similar to the idea above, between bursts of action potentials, _inrec increases towards ₀.

The mean synaptic response can be calculated as

(8)

where A_SE=nqis the maximal response produced when all the sites release their vesicles. Note that even though a uni-vesicular hypothesis is implied here, the formalism does not preclude multivesicular release, because A_SE is simply a scaling factor and as such has no biological meaning. The variable R(t) is the fraction of vesicles available at time t and is calculated according to the following equation, which is analogous to eqn (5):

(9)

In order to study the functional implications of RID and FDR (see Fig. 13), we explore the total postsynaptic current (I_syn) produced by the activity of a population of K= 1500 presynaptic neurones, connected to the target neurone by uniform synapses, since the discharge frequency of a neurone is proportional to the total postsynaptic current (Granit et al. 1966); i.e.

(10)

View larger version (24K): [in this window] [in a new window]   Figure 13.  Functional implications of FDR Simulated net postsynaptic current (Isyn, calculated according to eqn (10)) generated by a population of 1500 presynaptic neurones, firing randomly (Poisson) and undergoing synchronous transitions (indicated by arrows) from a low firing rate to a higher firing rate. Left: transition from 5 to 50 Hz. Right: transition from 30 to 50 Hz. A, model with pure RDD and no FDR. At low firing rates (left), the connections can code both a transition (by a transient increase in response), and average firing rate (by the mean current). At high firing rates (right), the connections cannot code the firing rates, as the input current does not change. However, it can still code (with the transient response) a change in rate. Model parameters: U0= 0.4, U1= 0, rec= 500 ms, 0= 1000 ms, 1= 0.2, inrec= 2000 ms and ASE=–200 pA. B, model with pure RID and FDR. At low firing rates (left) the synapses can code both a transition (by a complex transient), and the firing rate. At high firing rates (right), the synapses retain their ability to code firing rates. Model parameters: U0= 0.4, U1= 0.2, rec= 5 ms, 0= 1000 ms, 1= 0.2, inrec= 2000 ms and ASE=–200 pA.

There are seven parameters (A_SE, _rec, U₀, U₁, ₀, ₁, and _inrec) in these equations, which determine the dynamics of transmission. While A_SE is a scaling parameter, and the ratio between U₀ and U₁ is determined by , there are five free parameters remaining. The fitting of the model to the data is done in two steps. First, we choose the few parameter sets (approx. 50) which can best describe the dynamics of the EPSCs, and which are in the biologically plausible range. This is done by minimizing the sum of squared errors between the mean experimental and predicted responses to bursts of action potentials for each stimulus condition (eqn (9)). Second, the fit is chosen which also best describes the relation between experimental and .

	Results

Top Abstract Introduction Methods Results Discussion Appendix References

 
The properties of synaptic depression were examined in 38 pairs of pyramidal neurones in layer V of the somatosensory cortex. In layer IV, four pairs between star pyramidal cells, one spiny stellate–star pyramid connection, and a star pyramid–spiny stellate connection were also examined. We included layer IV cells since these showed largely the same characteristics as in layer V and because in some of them, we were able to identify a significant number of transmission failures. All connections reported here failed to show any sign of facilitation at any frequency between 5 and 50 Hz, i.e. the average amplitudes of the first few EPSCs in the sequence were smaller than the preceding ones. The recordings were a subset of the connections recorded (80%; 20% of connections showed a facilitatory response). For neurones in layer V, the average resting membrane potential was –62.5 ± 4.0 mV, the action potential height 95.2 ± 8.7 mV, half-width 1.2 ± 0.3 ms and input resistance was 92.2 ± 30.1 M. The EPSCs averaged –38.2 ± 30.1 pA, had a rise time (10–90%) of 1.2 ± 0.3 ms and a half-width of 6.4 ± 1.7 ms. The CV was 0.4 ± 0.2 and the skew of the amplitude distribution –0.3 ± 0.6. Paired-pulse depression was 0.45 ± 0.15 (range: 0.35–0.77).

Release dependence of synaptic depression

Release-dependent depression (RDD) was identified at some of the connections. At these connections, as depicted for example in Fig. 2A, (the average amplitude of E₂ for the 20 trials where E₁ was the smallest, see ‘Detecting and quantifying release-independent depression’ above) was significantly larger than (average E₂ for 20 traces where E₁ was the largest, Fig. 2A), indicating that there was some degree of release-dependent depression. In Fig. 2B, the second EPSC amplitude (E₂) is plotted as a function of the first (E₁). For guidance, the theoretical lines of pure RDD (oblique dashed line; for details see Appendix) and pure RID (horizontal dashed line) are depicted. It can be seen that the regression line for the data (continuous line) and the one for RDD (oblique dashed) are almost identical. The normalized factor indicating release dependence (R_D, eqn (20)) was 1.03 ± 0.33, suggesting that depression at this connection was dominated by RDD. ANCOVA verified that the regression line is not significantly different from pure RDD (p_A= 0.43 for RDD; p_A < 0.05 for RID).

In contrast, at some connections, synaptic depression was found to be highly release independent (Fig. 2C and D). This was deduced from the facts that, at these synapses, and were not significantly different from each other (Fig. 2C) and that R_D was close to zero. In Fig. 2D, the linear regression analysis confirms that depression in this example is largely release independent. It is evident that the y-intercept of the regression line is indeed closer to than to . R_D was small (0.21 ± 0.14), and ANCOVA confirms that depression at this connection is significantly different from pure RDD (p_A < 0.0005), but not from pure RID (p_A= 0.45).

Additional evidence for the existence of RID is depicted in a layer IV connection in Fig. 2E and F, where the amplitude distribution of the first EPSCs, and that of the second EPSCs, given that the preceding EPSC was a failure, are shown (Fig. 2E). In Fig. 2F, the cumulative probabilities of the two distributions are significantly different (p_KS < 1e^–9). The average synaptic response that follows a failure is also smaller than , but slightly bigger than (inset).

Our results indicate that most of the recorded connections exhibit at least some degree of RID. This can be inferred from the results of ANCOVA, where six of the layer V connections and five of the layer IV connections showed pure RID. Sixteen layer V connections were significantly different from both RID and RDD, indicating that they express both forms of depression, whereas three of the layer V connections were not significantly different from either pure RID or RDD. One layer IV connection (star pyramid–star pyramid), and seven layer V connections were highly release dependent, i.e. not significantly different from RDD but significantly different from RID. The remaining six layer V pairs were used in other experimental protocols (augmentation, recovery times, see below). The mean value of R_D was 0.45 ± 0.35.

We investigated whether the existence of some degree of release-independent depression in most connections could be an artefact of our recording conditions. We do not believe this is the case for a number of reasons. Firstly, the degree of release dependence remained stable throughout long recording periods. For example, in Fig. 3, a plot of E₂versusE₁ for the first and last hour of a 4 h recording period is shown, during which the degree of release dependence remained unchanged (R_D= 0.45 ± 0.15 in Fig. 3A, 0.53 ± 0.22 in Fig. 3B, p_t= 0.7).

View larger version (13K): [in this window] [in a new window]   Figure 3.  The properties of synaptic depression are stable A, plot of second versus first EPSCs for a layer V pair for the first hour of a prolonged recording period. RD= 0.45 ± 0.15 (N= 228, r=–0.42, pr < 0.05). B, plot of second versus first EPSCs for the same connection after 3 h of recording. The RD of 0.53 ± 0.22 (N= 238, r=–0.38, pr < 0.05) is not different (pt= 0.7) from that in A and in both cases the linear regression line is significantly different from a horizontal line. The open squares indicate and .

Since in most of our experiments we included bicuculline in the ACSF to block GABA_A-mediated transmission, and bicuculline has been shown to block Ca²⁺-dependent K⁺ channels (see for example Debarbieux et al. 1998), we investigated whether RID was still observed in the absence of bicuculline. In 15 experiments, R_D corresponded to 0.54 ± 0.35, which was not significantly different from when the ACSF contained bicuculline (p_t= 0.3).

A process that resulted in a positive correlation between E₁ and E₂ could potentially counterbalance the negative correlation of release-dependent depression, and result in an apparent lack of correlation. Such a process could include active postsynaptic boosting (Stuart & Sakmann, 1995) in imperfectly voltage-clamped neurones. Such a process would preferentially affect the largest E₁. However, subsets of data with only large or small E₁ resulted in the same R_D value as the complete data sets (p_pt > 0.5, data not shown). As a further test for this possibility we examined connections under control recording conditions and then after re-patching the postsynaptic neurone with an intracellular solution containing 5 mM QX-314. In four experiments, the presence of postsynaptic QX-314 did not change R_D(control: 0.48 ± 0.22; QX-314: 0.42 ± 0.10, p_pt= 0.6) or E₀/E₁(control: 0.71 ± 0.15; QX-314: 0.65 ± 0.11, p_pt= 0.5, data not shown).

We also examined whether RID was an artefact of the analysis technique, for example, whether quantal variance or the noise variance could mask a correlation between E₁ and E₂. However, we found that there was no correlation between the connections with a large CV and the expression of RID. In fact, there was the opposite correlation between large CV and the expression of RDD, as might be expected for connections with a higher initial release probability (see below, p_r= 0.002, data not shown). There was no correlation between the noise variance and R_D (p_r= 0.6).

The site of expression

Depression could be a result of a change in release probability (P_r, eqn (5)), a change in the number of release sites (n), a change in quantal size (q), or a combination of these factors. To determine the mechanism of depression, a CV^–2 analysis was performed since depression resulting from changes in either n or q will be indicated by data points significantly above the 45 deg line (dashed lines in Fig. 4A and B), whereas changes in p_r alone are observed as data points on or below this line (for details see Korn & Faber, 1991). The plots of this analysis are illustrated in Fig. 4 for two types of connections, namely those which showed a high degree of RDD (R_D > 0.65; Fig. 4A) and those, where the depression was predominantly RID (R_D < 0.35; Fig. 4B). In both cases, the points followed the 45 deg line, thus suggesting that the most likely cause for depression in both cases is a change in the probability of release.

View larger version (13K): [in this window] [in a new window]   Figure 4.  Synaptic depression results from a change in release probability A, plot of normalized CV–2versus normalized mean amplitude for those neurones with RD > 0.65 (i.e. dominated by release-dependent depression). The points represent the average data for the first 3 and the last (20th) EPSCs. Open circles: 10 Hz burst; filled squares: 20 Hz burst; filled circles: 50 Hz burst. For guidance are labelled for the 20 Hz burst. B, plot of normalized CV–2versus normalized mean amplitude for those neurones with RD < 0.35 (i.e. dominated by release-independent depression). Note that the dispersion of the data points is less than in A due to the fact that the EPSC during the sequence converges to a steady-state of similar amplitude for all frequencies of stimulation.

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Properties of RID and RDD

Dependence on initial release probability.  It appears that the type of synaptic depression (RID or RDD) is dependent on the initial release probability of the synapses. Firstly, there is a negative correlation between the values of R_D and the skew of the amplitude distribution (Fig. 5A, r=–0.54, p_r < 0.005 Courtney, 1978). Since a negative skew indicates a high initial release probability (U₀ > 0.5), this correlation is suggestive that RDD is more prominent for connections with a high initial probability. At the same time, we observed that the degree of paired-pulse depression is inversely correlated with skew (Fig. 5B, r= 0.55, p_r < 0.005). Since a high initial release probability is expected to result in a large depression of the second pulse, this finding is consistent with the above observation and, thereby, serves as an internal check for consistency of using skew as an indirect measure of initial release probability. Secondly, for the same data set, R_D is correlated with the ratio (r =–0.41, p_r= 0.02, data not shown). Taken together, these correlations suggest that strongly depressing synapses (which have a relatively high initial probability of release, i.e. U₀ > 0.5) are more likely to express more RDD. Conversely, pure RID is most likely to be observed at synapses with low initial release probability and weak depression.

View larger version (25K): [in this window] [in a new window]   Figure 5.  Features of RDD and RID A, the release dependence of depression (RD) is correlated with release probability. Here the skew of the amplitude distribution is used as a coarse indicator of release probabilities. The continuous line indicates the linear regression (r=–0.54, pr < 0.005). B, the amount of depression is also correlated with the skew of the amplitude distributions. The continuous line indicates the linear regression (r= 0.55, pr < 0.005). C, temperature dependence. The response of a layer V connection maintained at 30°C to the first two action potentials in a sequence. Stimulation frequency was 10 Hz. E2 is plotted as a function of E1 for each trial. Continuous line: linear regression of the data. Dashed lines: theoretical line for pure RID (horizontal line) and pure RDD (oblique line). The connection displays a strong component of RDD (RD= 0.88 ± 0.11). The open squares indicate and . D, same connection as in C, but at 36°C, showing a strong component of RID (RD= 0.02 ± 0.11). The open squares indicate and .

Ca²⁺ dependence of depression.  To investigate the Ca²⁺ dependence of synaptic depression, we re-patched the presynaptic neurone with electrodes containing the calcium buffer EGTA at increasing concentrations (0.5–5 mM, N= 5 for each concentration; Ohana & Sakmann, 1998; Rozov et al. 2001). In the presence of EGTA, the average EPSC amplitude decreased in comparison to the control recordings (77 ± 8% of control after re-patching the presynaptic neurone with intracellular solution containing 5 mM EGTA). The amount of depression tended to increase, on average (Fig. 6A); however, the effect was variable with depression increasing at some and decreasing at other connections (thus the increase in the variance in Fig. 6A). R_D, however, consistently decreased at EGTA concentrations 1 mM (Fig. 6B). Using 1 mM EGTA, R_D was 0.15 ± 0.18 (p_pt= 0.02; the control R_D for the same 5 neurones was 0.41 ± 0.22). This finding is consistent with the correlation between R_D and skew (i.e. U₀), since EGTA is expected to decrease the initial release probability.

View larger version (7K): [in this window] [in a new window]   Figure 6.  The effect of buffering presynaptic Ca2+on synaptic depression A, the amount of depression plotted as a function of EGTA concentration. With increasing concentration of EGTA, depression increases on average but this effect is variable; in some examples depression was reduced (note the increase in the error). B, plot of RD as a function of EGTA concentration. With increasing concentration, the release dependence of depression decreases.

Frequency-dependent recovery from depression (FDR)

In this section, we present another phenomenon observed at the recorded connections. It relates to the mean EPSCs of a connection, evoked after a recovery interval and averaged over many repetitions of the same input pattern (Fig. 1C). In previous studies, the steady-state response at high frequencies was shown to decrease in a manner inversely proportional to frequency (Abbott et al. 1997; Tsodyks & Markram, 1997). Indeed, some connections (Fig. 7A and B) exhibited such an inverse relationship. However, at other connections (Fig. 7C and D) the steady-state response at higher stimulus rates is frequency independent. This convergence to a similar steady state occurred for rates 10 Hz. For example in Fig. 7C, the magnitude of the steady-state response of a layer V connection is similar at 10 and 20 Hz. The convergence during steady-state to a constant value is shown in Fig. 7D.

View larger version (22K): [in this window] [in a new window]   Figure 7.  Connections with and without apparent frequency-dependent recovery (FDR) A, a layer V connection with no apparent FDR. The average response (N= 40) to action potentials triggered at three different frequencies (5, 10 and 20 Hz). In all cases, a further action potential was triggered 500 ms after the burst. The amplitudes of the steady-state response and the recovery EPSC are smaller, with increasing input frequency. B, of the connection in (A) is plotted as a function of frequency. There is no convergence to a steady-state of similar amplitude at different frequencies. The dashed line indicates the change proportional to 1/f. C, a layer V connection with FDR. The average response (N= 100) recorded at 5, 10 and 20 Hz. In all cases, a further action potential was triggered 600 ms after the burst. is the same at 10 and 20 Hz, but is larger when the preceding burst was 20 Hz. D, of the connection in C. There is convergence to a similar at frequencies = 10 Hz. Dashed line indicates the analytically computed value of for high input frequencies.

Analysis of the model indicates that the convergence of EPSCs to a steady-state value at high input frequencies requires that depression is strongly dominated by one of the two forms of depression (RDD or RID), which recovers in a frequency-dependent manner (see below). Since most connections exhibit some degree of RID, we investigated whether FDR was associated with release-dependent or -independent depression (Fig. 8). For this purpose, we used R_FDR (see Methods) to estimate the relative degree of FDR in all the recorded connections. We found that the expression of FDR was negatively correlated with R_D, indicating that connections with prominent RID also exhibited more FDR (r=–0.51, p_r= 0.005). Such a relationship can also be inferred from Fig. 4A and B, where the amplitude of the 20th EPSC following different frequencies of stimulation is distributed over a wider range along the diagonal for those neurones with R_D 0.65 (Fig. 4A, see left-most symbols for each frequency) than for those with R_D 0.35 (Fig. 4B).

View larger version (8K): [in this window] [in a new window]   Figure 8.  Correlation between RFDR and RD The ratio of the normalized recovery amplitude following a burst at 10 and 20 Hz (RFDR) is plotted against RD(determined at 20 Hz) of layer V connections (filled circles) and 3 layer IV connections (open squares). There was a significant correlation between the two parameters as indicated by the linear regression for layer V connections (r=–0.51, pr < 0.005).

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View larger version (22K): [in this window] [in a new window]   Figure 9.  Modelling FDR The magnitudes of EPSCs of a layer V pyramidal–pyramidal connection expressing FDR (same as in Fig. 7C and D) at three frequencies of stimulation (5, 10 and 20 Hz) with the recovery EPSC (open circle) are shown with fits of two alternative models. A, simple model with no FDR (inrec constant; with pure RID). The experimental EPSC amplitudes (filled circles) and the modelled one (line) are plotted as a function of the number in the sequence. In all cases the last EPSC is the response to gauge recovery . Model parameters: U0= 0.1, U1= 0.4, rec= 1 ms, 0= 700 ms, 1= 0, inrec= 300 ms and ASE=–1130 pA. B, full model with FDR (inrec activity dependent; again with pure RID). Model parameters: U0= 0.4, U1= 0.4, rec= 1 ms, 0= 2000 ms, 1= 0.4, inrec= 500 ms and ASE=–282 pA. Dashed horizontal line indicates no response. C, steady-state response as a function of frequency for models with both RDD and RID for various values of rec (continuous lines). Dashed lines represent the analytically calculated relation between and input frequency (f), expected at high input frequencies (1/f). Model parameters: U0= 0.3, U1= 0.1, 0= 1800 ms, 1= 0.5, inrec= 1800 ms and ASE=–100 pA, rec= 200, 300, 400, 500, 600 ms. D, of a connection with pure RID and FDR. (continuous line) of the connection converges to an analytically calculated constant value at high input frequencies (dashed line). Model parameters: U0= 0.4, U1= 0.4, rec= 0 ms, 0= 2000 ms, 1= 0.4, inrec= 500 ms and ASE=–62 pA.

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Further experimental evidence for FDR is provided in Fig. 10, where the normalized recovery amplitude is plotted against the delay before the final action potential for a connection where there was no increase in recovery rate with increasing frequency (Fig. 10A; note that 1 –R_rec is plotted so that recovery increases with time), and for an alternative example, where there was strong FDR (Fig. 10B). In every case, the data points were adequately fitted by a single exponential (p < 0.05). The apparent recovery time constants (_a) for frequencies of 10, 20 and 50 Hz were not significantly different for the first example (580–660 ms). However, _a increased approximately 4-fold over this frequency range for the connection with FDR (Fig. 10B; from 1240 ± 184 ms at 10 Hz to 321 ± 112 ms at 50 Hz).

View larger version (14K): [in this window] [in a new window]   Figure 10.  Time course of recovery from depression A, a connection showing no FDR. The time constant for recovery following a burst at 10 Hz (580 ± 78 ms, open circles) is not significantly different from that at 20 Hz (654 ± 81 ms, filled squares) or at 50 Hz (609 ± 73 ms, filled circles). B, a connection showing prominent FDR. The time constant for recovery following a burst at 10 Hz (1243 ± 184 ms, open circles) is significantly slower than that at 20 Hz (525 ± 76 ms, filled squares) and that at 50 Hz (321 ± 112 ms, filled circles). Note that 1 –Rrec (where Rrec is recovery amplitude) is plotted here so that recovery increases with time and the time constant of recovery is more easily demonstrated.

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_a

Since two processes seem to participate in the overall recovery from depression, we needed to find evidence that FDR was not caused by a process associated with eliciting a series of 20 action potentials at an intermediate frequency. Augmentation (Zengel et al. 1980; Stevens & Wesseling, 1999) is such a mechanism, which could superimpose on the depression and thereby mimic FDR. Despite the fact that we chose a subset of neurones that showed no signs of facilitation within the first few action potentials, we investigated whether augmentation was still present. When the presynaptic burst of action potentials was increased to 100 pulses at 10 Hz, we could discern a small amount of augmentation. This was maximally 40% greater than the initial EPSC amplitude (Fig. 11A) and decayed with a _Aug of 10.9 ± 5.3 s, which is much longer than _a at the same frequency (0.76 ± 0.15 s; p_t < 0.0002). In order to further corroborate that augmentation was not causing an apparent FDR, we checked the differential sensitivity to Ca²⁺ buffering by EGTA. Surprisingly, in our study presynaptic EGTA at a concentration of 5 mM did not affect augmentation (Fig. 11B). Under this condition, _Aug was 7.3 ± 2.4 s, which was not different from that with the control intracellular solution (N= 5, p_pt= 0.2). However, the inability of EGTA to block augmentation was significantly different from the effect on FDR, which was abolished at this concentration (see below).

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