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Journal of Physiology (2001), 537.2, pp. 407-420
© Copyright 2001 The Physiological Society
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ABSTRACT |
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-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA) receptors are an important factor determining excitatory synaptic transmission in the brain. Changes in the number (N) or single-channel conductance (
) of functional AMPA receptors may underlie synaptic plasticity, such as long-term potentiation (LTP) and long-term depression (LTD). These parameters have been estimated using non-stationary fluctuation analysis (NSFA).
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were very sensitive to the access resistance of the recording (RA) and the mean open time of AMPA channels. Estimates of were less sensitive to the distance between the electrode and the synaptic site, the electrotonic properties of dendritic structures, recording electrode capacitance and background noise. Estimates of were insensitive to changes in spine morphology, synaptic glutamate concentration and the peak open probability (Po) of AMPA receptors.
by approximately 50-70 %.
vs. changes in N or Po. Neither background noise nor asynchronous activation of multiple synapses prevented reliable discrimination between changes in and changes in either N or Po.
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INTRODUCTION |
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Excitatory synaptic transmission in the CNS is mediated by the release of glutamate from axonal boutons onto specialized dendritic surfaces, typically dendritic spines, expressing glutamate receptors. This process has a host of variables including variations in release kinetics, the concentration of glutamate inside vesicles, the amount of neurotransmitter released from vesicles, the size of dendritic surfaces containing receptors, the shape of dendritic spines, and the number and characteristics of different types of glutamate receptors. Most of these variables have been implicated as a locus of expression of LTP or LTD (Bliss & Collingridge, 1993; Kullmann & Siegelbaum 1995; Malenka & Nicoll 1999; Choi et al. 2000).
Cellular studies of synaptic transmission and LTP and LTD have normally involved electrophysiological recordings from neural somata. This method has the limitation that the sites of interest and the recording site are on different locations of a highly branched dendritic structure. This problem is particularly acute for the study of EPSCs at the Schaffer collateral-commissural synapse onto hippocampal CA1 pyramidal cells, since these neurones have an extensive and highly branched dendritic tree. The development of infrared video microscopy has greatly facilitated recordings from dendrites (Stuart et al. 1993). When this technique is used for recording from CA1 pyramidal cell dendrites and combined with local stimulation, a small number of synaptic contacts can be studied under comparatively good voltage control (Benke et al. 1998; Isaac et al. 1998; Lüthi et al. 1999).
The cerebellar granule cell, which has electrotonic properties that enable high-band-width recording of synaptic currents from the soma, has been used to apply non-stationary fluctuation analysis to determine and N of AMPA-receptor-mediated EPSCs (Traynelis et al. 1993; Silver et al. 1996). To determine whether it may be possible to apply non-stationary fluctuation analysis to highly branched structures, such as CA1 pyramidal neurones, using dendritic recordings, we constructed a multi-compartmental model. Our initial analysis of the model (Benke et al. 1998) showed that the technique could be used to measure relative changes of in neurones providing recording conditions were optimized. Based on this modelling, we used non-stationary fluctuation analysis to estimate changes in before and after the induction of LTP (Benke et al. 1998) and LTD (Lüthi et al. 1999) at CA1 synapses. Here we present a detailed, extended description of the model outlined in Benke et al. (1998).
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METHODS |
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Modelling
The passive electrical properties of a neurone were simulated with a mathematical model (TCABLE) using the formulation of Hines (1984). The neuronal geometry employed a single apical dendrite, up to seven dendritic spines, a soma and a lumped basal dendrite-axon. The model used 25-83 compartments, with seven compartments devoted to each dendritic spine (Holmes & Levy, 1990; Fig. 1). A correction factor of 2.25 was applied to account for the membrane capacitance of spines not explicitly modelled. The model included a whole-cell recording electrode, with access resistance (RA; parameter range, 0.5-60 M
) and pipette capacitance (Cpip, 0-20 pF), attached at variable distances from the spine. Membrane capacitance (Cm, 0.65-1 µF cm-2), membrane resistivity (Rm, 38-154 k cm2) and cytoplasmic resistivity (Ri, 100-294 cm) were varied (Holmes & Levy, 1990; Major et al. 1994; Stuart & Spruston, 1998). All of these values were adjusted to obtain the best fit to experimentally recorded current transients in response to a voltage step (-1 mV).
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Figure 1. The compartmental model used for non-stationary fluctuation analysis estimates of A, the 25-compartment model. B, the spine with seven compartments, enlarged for detail. The spine head diameter is 0.55 µm and its length is 0.45 µm. The spine shaft diameter is 0.1 µm and its length is 0.68 µm. End-dendritic regions have enlarged diameters to explicitly model fine branches. Variable electrode positions are indicated by the arrows in A. The location of the dendritic spine is marked by the asterisk in A. For distal electrode placement, the distal dendrite was further divided into smaller compartments (not shown). C, equivalent circuit model of the electrode, dendritic segment, spine and synapse with elements of the access resistance (RA) connected to the amplifier command voltage (Vamp), membrane capacitance (Cm), pipette capacitance (Cpip), internal resistivity (Ri) and membrane resistivity (Rm). | ||
AMPA receptor channels (1-160 channels; , 2-40 pS) were modelled with a modification of the macroscopic kinetic scheme of Jonas et al. (1993; Fig. 2A). The mean open time (1/
) was also varied (0.5-5 ms). Stochastic AMPA receptor channel openings were simulated (see Clay & DeFelice, 1983; Wilders & Jongsma, 1993) to respond to a glutamate pulse (0.5-10 mM; 2 µs to 1 ms in duration; 0.4-4.8 ms decay time constant (
decay); Clements et al. 1992; Diamond & Jahr 1995; Fig. 2B). For multisynaptic simulations, individual synaptic activation latency was typically 4 ms with a standard deviation of 0.8 ms (0-0.8 ms, 0 ms indicating no asynchrony; Jonas et al. 1993). The probability of individual synaptic activation (equivalent to the probability of transmitter release, Pr) was typically 0.5 (0.25-1.0). The time-varying concentration dependence of rate variables was solved by a modification of Newton's method (Burden & Faires, 1985). Uniformly distributed random numbers were generated by calls to an internal random number generator after seeding by the system time or a fixed number. Exponentially distributed dwell times were obtained by the logarithmic transformation of uniformly distributed random numbers multiplied by the inverse of the appropriate rate constant(s). Simulated Gaussian noise was obtained by a similar transformation of uniformly distributed random numbers (Press et al. 1986). Gaussian-distributed activation latencies were similarly generated. All code was written in ANSI C and run on either a DEC Alphastation 600 5/333, Intel Pentium II Pro processor at 200 MHz or an AMD K7-550 MHz computer. Simulation of 35 ms of microscopic data with a time step of 10 µs took approximately 25 s using the Pentium II Pro processor for the 25-compartment model.
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Figure 2. Macroscopic AMPA receptor kinetic scheme and simulated excitatory postsynaptic currents (simEPSCs) A, kinetic scheme with rate constants as in Jonas et al. (1993) except | ||
Po was altered (0.3-0.8) by varying the rate constant (3 
103 to 4.24 105). In most simulations, with a mean open time (1/) of 2 ms and of 4.24 103 s-1, Po was 0.53. Modelled activation of these receptors resulted in membrane current detected by the simulated electrode (simEPSC) when this scheme was added to the compartmental model (Fig. 2B). As expected, increasing electrode resistance resulted in a greater voltage-clamp error and filtering of the synaptic current, with peak current attenuation and slowing of the synaptic decay. Gaussian-distributed random noise was added to simEPSCs in some cases. Epochs containing 5-1000 simEPSCs (typically 100) were analysed to obtain estimates of input to the model. In total, over 100 000 simEPSCs were analysed.
The modelling program can be downloaded from:
http://www.bris.ac.uk/synaptic
Analysis
Simulated EPSCs were analysed in the same way as biological data (Benke et al. 1998; Lüthi et al. 1999). Responses were carefully selected for analysis based on the criteria of fast rise times, allowing for the precise alignment of individual responses and a monotonic decay time course. Estimates of the rise and decay times of individual currents were obtained by measuring the 20-80 % rise time and 62 % decay time, respectively (referred to as 'rise time' and 'decay time'). For mean currents, kinetics were calculated using the time constants of exponential fits to the rising and decay phases of the mean simEPSCs (referred to as 'rise' and 'decay'). With the same software as used for experimental data (Benke et al. 1998; Lüthi et al. 1999), simEPSCs were analysed using peak-scaled non-stationary fluctuation analysis (Robinson et al. 1991; Traynelis et al. 1993; De Koninck & Mody, 1994; Silver et al. 1996), a modification of non-stationary fluctuation analysis (Sigworth, 1980), as follows. An ensemble of currents were aligned by their point of maximal rise (estimated numerically by a 5-point formula), and averaged. The average response waveform was scaled to the peak and subtracted from individual responses and squared (Fig. 3A). The variance of the fluctuation around the mean was calculated for 10-100 bins of equal current decrement from the peak of the mean current response until a time equal to 5-6 times decay. The binned variance was plotted vs. the mean current amplitude and the single-channel current was estimated by fitting the data using a least-squares algorithm according to:
2 = iI - I2/N + bl,
where 2 is the variance, I is the mean current, N is the number of channels activated at the peak of the mean current, i is the single-channel current and bl is the background variance (Sigworth, 1980). The single-channel conductance, , is then:
= i/V,
where V is the driving force (holding potential, assumed reversal potential of 0 mV). To obtain the most accurate estimate for , different portions of the data were fitted (from 0 to 20, 30, 40, 50 or 100 % of maximum current; Fig. 3B). For simulated records this was typically 50 %. The goodness of fit was assessed by comparing the r2 values obtained from the least-squares algorithm. When comparing experimental manipulations within a given simulated 'experiment', the same fraction of the data was always used for the fit. All of the estimates for which the initial rising phase of the current-variance plot was well-fitted produced very similar values for , as has also been reported previously (Traynelis et al. 1993; Spruston et al. 1995; Benke et al. 1998). Data are expressed as a percentage of the baseline value (i.e. 100 % = no change). The analysis software can be downloaded from http://www.bris.ac.uk/synaptic
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Figure 3. Non-stationary fluctuation analysis of simEPSCs Ai-iii, squared difference currents (top traces) were obtained by subtracting individual simEPSCs (bottom thin traces) from the peak-scaled mean current (bottom thick traces); iv, mean squared difference current (top trace) and mean simEPSC (bottom trace) for the data set. B, variance-mean amplitude plot obtained from 1000 simEPSCs. These data were fitted to | ||
The modelled data were compared to previously published experimental data (Benke et al. 1998; Luthi et al. 1999). In addition some unpublished values were included (T. A. Benke, A. Lüthi, M. J. Palmer, M. A. Wikström & J. T. Isaac). These data were obtained, using the same methods, from rat hippocampal slices in accordance with Home Office guidelines.
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RESULTS |
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A multi-compartmental model was used to compare the effects of different electrical, geometrical and kinetic parameters on estimates of for synaptic AMPA receptors. Estimates of under different conditions were compared to that input to the model and, in some cases, to that obtained by a standard model. The parameters used for the standard model were as follows: = 16 pS, N = 40, mean open time = 2 ms, geometry as in Fig. 1A, proximal distance of the electrode from the spine = 0.5 µm, RA = 20 M, Cpip = 0 pF, Cm = 0.65 µF cm-2, Ri = 290 cm, Rm = 77 k cm2, glutamate pulse length = 2 µs, glutamate pulse decay = 200 µs, glutamate concentration = 10 mM, no added Gaussian noise. A summary of results for the standard model and various manipulations is presented in Table 1.
Effects of the electrical parameters Rm, Cm and Ri
The electrical parameters Rm, Cm and Ri were varied with a fixed RA of 20 or 35 M under otherwise standard kinetic and geometric conditions. Estimates of were obtained for 30 permutations of these parameters and compared to the control estimate of for standard conditions (Cm = 0.65 µF cm-2, Rm = 77 k cm2, Ri = 290 cm). The effects of changes in electrotonic properties on estimates of are shown in Fig. 4. When the recording electrode was very near the synaptic site, for the estimate of to change by more than 20 %, noticeable differences in the membrane response to the voltage step occurred. When the electrode was placed distal (16 µm) to the spine, larger changes in the estimate of occurred for the same change in electrotonic properties. Therefore, in order to minimize the impact of possible changes in electrotonic properties on the estimate of it is desirable to have the recording electrode as close as possible to the synapse.
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Figure 4. Effects of Rm, Cm and Ri on estimates of This graph illustrates the effects of changes in electrotonic parameters on the estimates of | ||
Effects of added Gaussian noise on estimates of
Under standard conditions, increasing levels of Gaussian noise were added to simEPSCs to determine the effect on estimates of . Upon addition of noise, identifiable single-channel transitions were lost (Fig. 5A), even after the addition of only 1 pA root mean square (RMS) noise. As the noise level increased to 2 pA RMS (this corresponds to 2.83 pA peak-to-peak noise), the fit of the data (Fig. 5B) became more error prone, resulting in less accurate estimates of (Fig. 5C). Since AMPA channels have a low , this makes the estimation of by non-stationary fluctuation analysis sensitive to high levels of background noise.
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Figure 5. Effects of Gaussian noise on estimates of A, progressively more Gaussian noise was added to simEPSCs (root mean square values); 0 pA (i), 0.5 pA (ii), 1 pA (iii), 1.5 pA (iv), 2 pA (v) and 2.5 pA (vi). B, current-variance plots obtained from the same ensemble of simEPSCs with increasing noise. C, additional error in estimate of | ||
Electrode distance from synaptic site
Under otherwise standard conditions, moving the recording electrode position away from the synaptic site towards the soma, or distally away from the soma, caused a reduction in the peak amplitude of EPSCs, a slowing of their time course and a reduction in estimated (Fig. 6 and Table 1). However, these changes were small, indicating that estimates of are relatively insensitive to the distance of the recording electrode from the synapse.
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Figure 6. Effects of electrode distance from the synapse on estimates of A, mean simEPSCs obtained with successively increasing proximal distance of the electrode from the spine from 0.5 µm (black, electrode at the spine) to 70 µm (brown, electrode on the soma) under otherwise standard conditions. The inset shows corresponding peak scaled currents. B, current-variance plots for the data shown in A. C, the attenuation of the estimated | ||
Peak space-clamp errors were not appreciably different as the electrode position was shifted towards the soma; peak errors of 6.4 mV resulted when the recording electrode was nearest the spine vs. 6.7 mV near the soma and 6.8 mV 46 µm distally. Progressive slowing of the rise time and hence reduction of the estimate of was due to the low-pass filtering effects of the dendrite in addition to that of the electrode. Assuming the rise time of the synaptic response approximates the rise time of the dendrite-electrode filter, the corner frequency is reduced from 1 kHz for dendritic recordings to 330 Hz for somatic recordings (Sakmann & Neher, 1995).
Spine geometry
When the shape of the dendritic spine was altered, the estimate of was relatively unchanged under otherwise standard conditions (Table 1). When the spine head:neck diameter ratio was reduced from 5.5 to 1, the estimate was the same. In this case, however, the peak space-clamp error was reduced from 6.4 mV to 0.8 mV; bloating the spine neck and head diameter to 1 µm reduced the peak space-clamp error only slightly more to 0.5 mV, again leaving the estimate of relatively unchanged. Therefore, the space-clamp errors associated with the dendritic spine geometry have minimal effects on estimates of .
Changes in RA and Cpip
Increases in RA caused a decrease in the peak amplitude and prolonged EPSCs, as expected (Fig. 7A). Estimates of were highly sensitive to variations in RA, resulting in a distortion of current-variance plots (Fig. 7B). Peak variances were reduced to 1 pA2 and less with RA of 40 M and greater. For typical RA values of 20-40 M, underlying values are attenuated by 62-78 % of the input for a mean open time of 2 ms (Fig. 7C). Therefore, for standard conditions, if RA changed during a recording from 20 M to 40 M, the estimated would change from 6.1 pS to 3.5 pS (a reduction of 43 %; Table 1). Thus, a change in recording conditions resulting in a change in RA can significantly alter estimates of . This is due partly to the voltage-clamp error, but mostly to the low-pass filtering effects of the electrode. The peak space-clamp error for an RA of 0.5 M is 6.1 mV, compared to 6.6 mV for an RA of 60 M. Since the estimate of is essentially equivalent to that input to the model when RA is 0.5 M, such space-clamp errors are not a major source of error in estimates of .
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Figure 7. RA affects estimates of A, mean simEPSCs obtained with increasing values of RA from 0.5 M | ||
Capacitance associated with the electrode would also be expected to further filter membrane currents (Major & Evans, 1994). The additional filtering and ultimate attenuation in estimates of , however, was negligible compared to that already contributed by RA. Typical Cpip values under experimental conditions were at most 10 pF (Benke et al. 1998; Lüthi et al. 1999) and this contributes only an additional 1-2 % of attenuation of the estimate of (Fig. 7C).
Receptor mean open time
Under standard conditions, varying the mean open time significantly altered estimates of . Increases in mean open time increased the peak size and noticeably prolonged the time course of mean currents (Fig. 8A). The resulting current-variance plots were each only slightly distorted from the expected parabolic shape, but peak variances were strongly reduced (Fig. 8B). Under standard conditions and with a mean open time of 2 ms, input values were attenuated by approximately 60 %; however, under the same conditions with a mean open time of 3 ms, the underlying was attenuated by approximately 40 % (Fig. 8C). Thus, an increase in the open time by only 1 ms could result in the estimate of increasing to 150 % of control (see Table 1); however, this also results in a noticeable alteration in the time course of mean current. Hence, the mean time course of synaptic currents must remain constant throughout an experiment in order for comparisons of estimated to remain valid.
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Figure 8. Mean open time affects estimates of A, mean simEPSCs obtained with increasing mean open times from 0.5 ms (green) to 4 ms (red). The inset shows peak scaled simEPSCs. B, current- variance plots for the data in A. C, attenuation of the estimated | ||
Synaptic glutamate profile
With super-saturating concentrations of glutamate (10 mM), similar values for mean simEPSC decay (decay), and mean peak simEPSC were obtained with the standard 2 µs and longer 1 ms pulse lengths (Table 1). Increasing the glutamate pulse decay up to 4.8 ms had little effect (data not shown). When lower concentrations of glutamate were used, smaller mean peak current and slightly faster synaptic decays were produced; however, estimates of were unchanged (Table 1). These data are consistent with the kinetic scheme used that involves a small component of desensitization in the closing of AMPA receptor channels.
Comparison of the predictions of the model with experimental data
The model predicts that the estimates of decay and are very sensitive to RA. To estimate the extent that RA affected estimates of decay under our experimental conditions, we performed a post hoc correlation analysis of dendritic recordings from 91 neurones (Benke et al. 1998; Lüthi et al. 1999; authors' unpublished data). Linear extrapolation of the correlation between decay and RA suggests that, in the absence of the filtering imposed by the RA, the mean value of decay would be 3.1 ms (y-intercept of the linear regression analysis in Fig. 9A). This value is identical to the prediction of the model for a mean open time of 2 ms, which yielded a decay of 3.1 ms. The discrepancy in the model between the value for mean open time and that of decay is due to the kinetic scheme employed, which incorporates multiple desensitized states.
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Figure 9. Correlation analysis of experimentally measured values of RA with estimates of A, plot of estimated | ||
To estimate the extent that RA affected estimates of under our experimental conditions, we performed a similar post hoc correlation analysis of these 91 neurones (Fig. 9B). The standard model agreed well with the experimental data over the range that stable recordings could be obtained (20-65 M) and suggested that the value of , with no RA, is likely to exceed 16 pS. We can conclude, therefore, that the value of , as measured by non-stationary fluctuation analysis of dendritic recordings, is greatly underestimated.
Distinguishing changes in from changes in N or Po
Using the standard model, increasing results in a markedly different parabola compared to increasing N (Fig. 10A). As expected, when N increased (quadrupled in this case), the initial slope of the parabola remained the same (since was unchanged). This is in contrast to a doubling of , which resulted in a noticeable change in the initial slope of the parabola. The linear 1:1 relationship between change in input and change in estimated was consistent over a range of values of RA, Ri and electrode separation from the synapse (Fig. 10B). Under standard conditions, increases in input (2-40 pS) resulted in an almost linear increase in simEPSC mean amplitude (Fig. 10C, red circles). This is in contrast to changes in either N, or rate constants affecting Po that affect simEPSC mean amplitude in the absence of changes in (green symbols; Fig. 10C). Similar findings were also obtained in the presence of realistic levels of added Gaussian noise, with the recording electrode up to 26 µm distal or proximal to the synapse (Fig. 10D). In this case, 2.5 pA peak-to-peak Gaussian noise was added, which is similar to that observed experimentally (Benke et al. 1998; Lüthi et al. 1999).
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Figure 10. Non-stationary fluctuation analysis distinguishes changes in N and the peak open probability (Po) from changes in A, peak-scaled NSFA of 500 simEPSCs (under otherwise standard conditions) resulting from different input N or | ||
A multisynaptic model
In order to address the interaction of multiple synapses, including the asynchrony of release between synapses, on estimates of , a more complex model was employed. This model has seven synapses on spines with increasing separation, spaced along a 52 µm segment of dendrite, and 2.5 pA (peak-to-peak) added Gaussian noise (Fig. 11A). The recording electrode (RA = 35 M) was kept at the same place in the centre of this arrangement. Other properties were as in the 'standard' model. The asynchrony of release was addressed by randomizing the inter-synaptic latency. The randomized mean latency was set to 4 ms with a standard deviation of 0.8 ms (Jonas et al. 1993). For a given ensemble of simEPSCs, between 0 and 6 of the synapses were set as non-releasing (i.e. probability of transmitter release (Pr) = 0). When releasing, each synapse had a fixed Pr of either 0.25 or 0.5. This generates EPSCs of a range of sizes, many produced by multiple releases. Some of these will be composed of multiple asynchronous EPSCs, therefore some traces contained obvious asynchrony, resulting in slower rise times or even double peaks (blue traces; Fig. 11B). This asynchrony was sometimes observed in the experimental EPSCs (Benke et al. 1998; Lüthi et al. 1999), and these EPSCs were always discarded. After elimination of simEPSCs exhibiting asynchrony, mean currents (black trace; Fig. 11B) and current-variance plots were obtained. The time course of mean simEPSCs (rise and decay, Fig. 11E) for the activation of all, or some, of the seven synapses were very similar and independent of mean simEPSC peak amplitude.
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Figure 11. Effects of asynchronous release from multiple synapses on estimates of A, the original model was expanded to 83 compartments with 7 dendritic spines (1-7, modelled as in Fig. 1B) with asynchronous synaptic activation (as detailed in the text) and 2.5 pA peak-to-peak added Gaussian noise. B, with all synapses releasing (Pr = 0.5 at each synapse), four example traces are shown: synaptic failure (green), asynchronous responses (blue) and fast monophasic traces (red). Only traces such as the red traces were used for analysis to give the mean simEPSC (black trace). C, the range of parameters tested. Syn refers to the numbering of the active synapses (1-7). D, plot of estimated | ||
Using this more realistic model, changes in could still be readily distinguished from other alterations that affected simEPSC amplitude (Fig. 11D). Thus, altering simEPSC amplitude by changing the number of active synapses, Pr or N at each synapse did not significantly alter the estimate of . In contrast, altering the input resulted in both a greater simEPSC amplitude and a larger estimate of .
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DISCUSSION |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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A multi-compartmental neuronal model, incorporating a range of electrotonic properties, a kinetic scheme for AMPA receptor channels and a simulated patch electrode, was used to simulate the EPSCs resulting from the synaptic activation of AMPA channels. Non-stationary fluctuation analysis of the simulated EPSCs was used to investigate the feasibility of estimating from structures resembling CA1 pyramidal neurones, using dendritic recording. Estimates of were most sensitive to RA and mean open time. Provided that these parameters and electrotonic properties remain constant, the model predicts that non-stationary fluctuation analysis can be used to reliably detect changes in . Therefore, it is possible to separate changes in synaptic conductance into their elementary components: N/Po, mean open time and . The simulations presented support experimental results (Benke et al. 1998) showing that LTP involves changes in of AMPA receptors. More generally, the model can be used to explore how changes in and other parameters may influence synaptic function.
Effects of RA and mean open time: comparison of modelling and experimental data
In the present study, the effects of RA were investigated for values between 0.5 and 60 M. Over this range, the attenuation of estimated varied between 0 and 80 %. In experimental studies we found that to be able to maintain stable dendritic recordings, of the sort required to study LTP, experimentally determined values of RA were usually between 20 and 50 M, with a mean value of 34 ± 1 M (Benke et al. 1998). Modelling using a value for RA of 35 M resulted in an attenuation of of approximately 70 %. However, the level of attenuation was greatly affected by the value for mean open time. This calculation was based on the standard model that incorporates a mean open time of 2 ms, which is similar to the predominant mean open time of 2.1 ms for AMPA receptor channels measured from outside-out patches obtained from CA1 dendrites (Spruston et al. 1995). This value resulted in a decay of 3.1 ms (the slowing of the synaptic current being due to desensitization), which was identical to the extrapolated value for our experimentally determined decay with an RA value of 0 M. This decay value of 3.1 ms is also very similar to the weighted AMPA receptor 'deactivation time constant', obtained from outside-out patches from CA1 dendrites of 13- to 15-day-old rats (Spruston et al. 1995). In that study, was estimated to be 10.2 pS using non-stationary fluctuation analysis. Compared to this value, our mean experimental value of of 5.4 pS suggests an attenuation of 47 %. However, the model predicts that the level of attenuation is significantly greater. Therefore, in the absence of additional practical methods of characterizing the cable filter (Häusser & Roth, 1997; Kleppe & Robinson, 1999), there is considerable uncertainty regarding the precise amount of attenuation of .
Since estimates of are very sensitive to RA and mean open time, it is important that these parameters remain constant during recordings. In the model, significant alterations in RA or mean open time were accompanied by noticeable changes in the mean decay of EPSCs or the passive membrane response to current injection.
Effects of passive membrane properties
Alterations in membrane properties (Rm, Ri and Cm) sufficient to alter estimates of were also usually associated with readily detectable changes in the response to the voltage step. However, such changes were more difficult to detect, particularly with respect to changes in Rm, if the electrode was separated from the synaptic site. This emphasizes the importance of minimizing the separation between the electrode and the synaptic conductance and hence the advantage of dendritic vs. somatic whole-cell recording. The passive membrane parameters used for the standard model are within the range of previously published values (Major et al. 1993, 1994; Jonas et al. 1993; Traub et al. 1994) and based on fits to our own measurements of current responses to voltage steps. However, had the values of Rm, Ri and Cm been set differently, but within the range of published values, more filtering of EPSCs could have occurred (e.g. if Cm had been higher and Rm had been higher), but this would not have affected the overall conclusions.
Provided that RA, mean open time and passive properties remain stable, relative estimates of are valid. These predictions are borne out experimentally (Benke et al. 1998; Lüthi et al. 1999). Other predictions of the model have also been verified experimentally, for example altering EPSC amplitude by changing N, by paired-pulse facilitation or addition of sub-saturating concentrations of an AMPA receptor antagonist, does not affect the estimate of (Benke et al. 1998).
Limitations and future enhancements of the model
The standard model presented here is the one that we used initially to test the feasibility of applying NSFA to dendritically recorded EPSCs in hippocampal CA1 neurones. Although the model provides realistic estimates of rise, decay and generated from single-channel data, it is reasonable to assume that the model could be made more accurate by incorporating more realistic geometry. In the model, AMPA channels have a single conductance state, whereas native channels are known to have multiple conductance states (Cull-Candy & Usowicz, 1987; Jahr & Stevens, 1987; Swanson et al. 1997) that are sensitive to L-glutamate concentration (Rosenmund et al. 1998). The model could be further expanded to incorporate these possibilities.
Concluding remarks
The model presented here can be used to test the effects of manipulating a number of parameters that are relevant for a molecular understanding of synaptic transmission and plasticity. Therefore, this model could be used to reduce the number of experimental investigations required to establish the molecular basis of synaptic mechanisms in the CNS.
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REFERENCES |
|---|
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
|---|
| BENKE, T. A., LÜTHI, A., ISAAC, J. T. R. & COLLINGRIDGE, G. L. (1998). Modulation of AMPA receptor unitary conductance by synaptic activity. Nature 395, 793-797 | |
| BLISS, T. & COLLINGRIDGE, G. (1993). A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361, 31-39 | [Medline] |
| BURDEN, R. L. & FAIRES, J. D. (1985). Interpolation and polynomial approximation. In Numerical Analysis, pp. 78-135. PWS, Boston | |
| CHOI, S., KLINGAUF, J. & TSIEN, R. W. (2000). Postfusional regulation of cleft glutamate concentration during LTP at 'silent synapses'. Nature Neuroscience 3, 330-336 | [Medline] |
| CLAY, J. R. & DEFELICE, L. J. (1983). Relationship between membrane excitability and single channel open-close kinetics. Biophysical Journal 42, 151-157 | [Abstract] |
| CLEMENTS, J. D., LESTER, R. A. J., TONG, G., JAHR, C. E. & WESTBROOK, G. L. (1992). The time course of glutamate in the synaptic cleft. Science 258, 1498-1501 | |
| CULL-CANDY, S. G. & USOWICZ, M. M. (1987). Multiple-conductance channels activated by excitatory amino acids in cerebellar neurons. Nature 325, 525-528 | [Medline] |
| DE KONINCK, Y. & MODY, I. (1994). Noise analysis of miniature IPSCs in adult rat brain slices: Properties and modulation of synaptic GABAA receptor channels. Journal of Neurophysiology 71, 1318-1335 | [Medline] |
| DIAMOND, J. S. & JAHR, C. E. (1995). Asynchronous release of synaptic vesicles determines the time course of the AMPA receptor-mediated EPSC. Neuron 15, 1097-1107 | [Medline] |
| HAUSSER, M. & ROTH, A. (1997). Estimating the time course of excitatory synaptic conductance in neocortical pyramidal cells using a novel voltage jump method. Journal of Neuroscience 17, 7606-7625 | [Abstract/Full Text] |
| HINES, M. L. (1984). Efficient computation of branched nerve equations. International Journal of Bio-Medical Computing 15, 69-76 | [Medline] |
| HOLMES, W. R. & LEVY, W. B. (1990). Insights into associative long-term potentiation from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. Journal of Neurophysiology 63, 1148-1168 | [Medline] |
| ISAAC, J. T. R., LÜTHI, A., PALMER, M. J., ANDERSON, W. W., BENKE, T. A. & COLLINGRIDGE, G. L. (1998). An investigation of the expression mechanism of LTP of AMPA receptor-mediated synaptic transmission at hippocampal CA1 synapses using failures analysis and dendritic recording. Neuropharmacology 37, 1399-1410 | [Medline] |
| JAHR, C. E. & STEVENS, C. F. (1987). Glutamate activates multiple single channel conductances in hippocampal neurons. Nature 325, 522-525 | [Medline] |
| JONAS, P., MAJOR, G. & SAKMANN, B. (1993). Quantal components of unitary EPSCs at the mossy fibre synapse on CA3 pyramidal cells of rat hippocampus. Journal of Physiology 472, 615-663 | [Abstract] |
| KLEPPE, I. C. & ROBINSON, H. P. C. (1999). Determining the activation time course of synaptic AMPA receptors from openings of colocalized receptors. Biophysical Journal 77, 1418-1427 | [Abstract/Full Text] |
| KULLMAN, D. M. & SIEGELBAUM, S. A. (1995). The site of expression of NMDA receptor-dependent LTP: new fuel for old fire. Neuron 15, 997-1002 | [Medline] |
| LÜTHI, A., CHITTAJALLU, R., DUPRAT, F., PALMER, M. J., BENKE, T. A., KIDD, F. L., HENLEY, J. M., ISAAC, J. T. R. & COLLINGRIDGE, G. L. (1999). Hippocampal LTD expression involves a pool of AMPARs regulated by the NSF-GluR2 interaction. Neuron 24, 389-399 | [Medline] |
| MAJOR, G. & EVANS, J. D. (1994). Solutions for transients in arbitrarily branching cables: IV. Nonuniform electrical parameters. Biophysical Journal 66, 615-634 | [Abstract] |
| MAJOR, G., EVANS, J. D. & JACK, J. J. B. (1993). Solution for transients in arbitrarily branching cables: I. Nonuniform electrical parameters. Biophysical Journal 65, 423-449 | [Abstract] |
| MAJOR, G., LARKMAN, A. U., JONAS, P., SAKMANN, B. & JACK, J. J. B. (1994). Detailed passive cable models of whole-cell recorded CA3 pyramidal neurons in rat hippocampal slices. Journal of Neuroscience 14, 4613-4638 | [Abstract] |
| MALENKA, R. C. & NICOLL, R. A. (1999). Long-term potentiation - a decade of progress? Science 285, 1870-1874 | |
| PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A. & VETTERLING, W. T. (1986). Random numbers. In Numerical Recipes, pp. 191-202. Cambridge University Press, Cambridge | |
| ROBINSON, H. P. C., SAHARA, Y. & KAWAI, N. (1991). Nonstationary fluctuation analysis and direct resolution of single channel currents at postsynaptic sites. Biophysical Journal 59, 295-304 | [Abstract] |
| ROSENMUND, C., STERN-BACH, Y. & STEVENS, C. F. (1998). The tetrameric structure of a glutamate receptor channel. Science 280, 1596-1599 | |
| SAKMANN, B. & NEHER, E. (1995). Single-Channel Recording, 2nd edn, p. 487. Plenum, NY | |
| SIGWORTH, F. J. (1980). The variance of sodium current fluctuations at the node of Ranvier. Journal of Physiology 307, 97-129 | [Medline] |
| SILVER, R. A., CULL-CANDY, S. G. & TAKAHASHI, T. (1996). Non-NMDA glutamate receptor occupancy and open probability at a rat cerebellar synapse with single and multiple release sites. Journal of Physiology 494, 231-250 | [Abstract] |
| SPRUSTON, N., JONAS, P. & SAKMANN, B. (1995). Dendritic glutamate receptor channels in rat hippocampal CA3 and CA1 pyramidal neurons. Journal of Physiology 482, 325-352 | [Abstract] |
| STUART, G. J., DODT, H.-U. & SAKMANN, B. (1993). Patch-clamp recordings from the soma and dendrites of neurons in brain slices using infrared video microscopy. Pflügers Archiv 423, 511-518 | [Medline] |
| STUART, G. & SPRUSTON, N. (1998). Determinants of voltage attenuation in neocortical pyramidal neuron dendrites. Journal of Neuroscience 18, 3501-3510 | [Abstract/Full Text] |
| SWANSON, G. T., KAMBOJ, S. K. & CULL-CANDY, S. G. (1997). Single-channel properties of recombinant AMPA receptors depend on RNA editing, splice variation, and subunit composition. Journal of Neuroscience 17, 58-69 | [Abstract/Full Text] |
| TRAUB, R. D., JEFFERYS, J. G. R., MILES, R., WHITTINGTON, M. A. & TOTH, K. (1994). A branching dendritic model of a rodent CA3 pyramidal neurone. Journal of Physiology 481, 79-95 | [Abstract] |
| TRAYNELIS, S. F., SILVER, R. A. & CULL-CANDY, S. G. (1993). Estimated conductance of glutamate receptor channels activated during EPSCs at the cerebellar mossy fiber-granule cell synapse. Neuron 11, 279-289 | [Medline] |
| WILDERS, R. & JONGSMA, H. J. (1993). Beating irregularity of single pacemaker cells isolated from rabbit sinoatrial node. Biophysical Journal 65, 2601-2613 | [Abstract] |
Acknowledgements
This work was supported by the MRC (G.L.C.), NIH (T.A.B.), the Swiss National Science Foundation (A.L.), and the Wellcome Trust (J.T.R.I., W.W.A.). M.A.W. is a research fellow supported by The Swedish Foundation for International Cooperation in Research and Higher Education (STINT). The Dec Alpha computer was funded by a grant from the Dr Hadwen Trust for Humane Research (T.A.B., W.W.A.). TCABLE and the non-stationary fluctuation analysis programs can be downloaded from the MRC Centre for Synaptic Plasticity website: http://www.bris.ac.uk/synaptic
Corresponding author
T. A. Benke: Cain Foundation Laboratories, Department of Pediatric Neurology, Baylor College of Medicine, Houston, TX 77030, USA.
Email: tb024948{at}bcm.tmc.edu
Authors' present addresses
M. J. Palmer: Vollum Institute, OHSU L-474, 3181 SW Sam Jackson Park Road, Portland, OR 97201, USA.
A. Lüthi: Department of Pharmacology/Neurobiology, Biozentrum University of Basel, CH-4054 Basel, Switzerland.
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