Sensitivity of optical recording

A critical concern of this study was the sensitivity of optical recordings in terms of the signal-to-noise ratio (S/N) at the required spatiotemporal resolution. The best existing sensitivity which allowed optical monitoring of back-propagating action potentials (bAP) from dendritic spines14 was insufficient because EPSP signals would be 5–10 fold smaller in amplitude. The required improvement in sensitivity was accomplished by further increase in the excitation light intensity using a laser at the wavelength that has the best signal, by minimizing photodynamic damage by restricting the excitation light to a small area (18 μm × 18 μm), and by briefly lowering oxygen concentration in the extracellular solution during optical recording (Methods). The sensitivity of optical recording under these conditions is illustrated in Fig. 1. An image of a cortical layer 5 pyramidal neuron situated in the superficial layer of the slice (<30 μm from the surface) and labelled with the voltage-sensitive dye was projected onto a charge-coupled device camera (CCD) for voltage imaging at high magnification so that individual spines could be clearly resolved (Fig. 1b). We selected spines that were isolated from their neighbours both in x–y and in z dimension; the selection was biased against spines with small heads because these were characterized with poor signal-to-noise ratio. The range of distances from the soma along the basal dendrite was 30–120 μm. In a representative experiment shown in Fig. 1, a subthreshold depolarizing transient followed by an action potential were evoked by two current pulses delivered from a somatic patch electrode while optical signals were acquired at a frame rate of 2 kHz from a small segment of a basal dendrite with several spines. Both the subthreshold membrane potential signal and the action potential signal can be clearly resolved in optical recordings from the three spine heads and the parent dendrite with modest signal averaging (temporal average of 16 trials; Fig. 1c). As a rule, the amplitudes of optical signals related to the same electrical event are different when recorded from different neuronal compartments reflecting differences in recording sensitivity due to variability in the surface-to-volume ratio16. Thus, it is necessary to calibrate optical signals on an absolute scale (in mV) to compare signal amplitudes. This was accomplished by normalizing the subthreshold signals to an optical signal from a bAP12,16 which has a known declining amplitude along basal dendrites, as previously determined by patch-pipette recordings12,17. The subthreshold and AP optical signals can also be calibrated using long hyperpolarizing pulses delivered to the soma12,18, which attenuate relatively little as they propagate along dendrites17,19. Both methods of calibration have to be regarded as an approximation due to a known individual variability between neurons and possible inaccuracies in patch-pipette recordings from thin dendrites20. However, we determined that the margin of calibration error is sufficiently small that it does not influence the conclusions of our study (see below). Throughout this study, we used bAP signals as calibration standards because they are substantially shorter compared with steady state hyperpolarizing steps and, thus, less susceptible to slow noise, dye bleaching effects and photodynamic damage. We experimentally confirmed the result previously reported by Palmer and Stuart12 showing that both methods of calibration produce the same results (Supplementary Fig. 1, Methods). In the experiment shown in Fig. 1, the size of the AP measured with an electrode in the soma was 110 mV which corresponds to an average value of 80±10 mV bAP in the basal dendrite at a distance of ∼50 μm from the cell body17 where the spine was located; in all experiments, the bAP amplitude at a distance corresponding to spine position on the basal dendrite was used as a calibration standard. The subthreshold electrical signals that were initiated in the soma are expected to be identical in the three spines and the parent dendrite within the ∼10-μm long dendritic segment shown in Fig. 1. This is because both theory and experiments demonstrated that electrical signals do not attenuate as they propagate from the dendrite into the spines4,12,14. Calibrated subthreshold signals were indeed identical within a fraction of a millivolt as shown in Fig. 1d.

Figure 1: Sensitivity of recording. (a) Voltage-sensitive dye fluorescence image of a neuron; confocal, z-stack projection. Bright rectangle: illuminated recording region. (b) High magnification single frame image focused on the spine inside the red circle obtained with the CCD for voltage imaging. (c) Subthreshold and AP optical signals from colour-coded multiple locations (temporal average of 16 trials; spatial average of pixels within coloured outlines). Black traces: somatic patch electrode recording (upper trace); transmembrane current pulses (lower trace). (d) Optical signals calibrated in terms of membrane potential using bAP signal as calibration standard. The amplitude resolution was improved by additional temporal averaging (the thickness of the grey line is 1 mV; average of 80 trials). The differences in after-depolarization recorded from different locations are not reproducible and likely reflect interaction between slow noise and the exponential subtraction routine used to compensate for dye bleaching. The recording sensitivity shown in c was routinely achieved in all measurements (n=29). Full size image

Linearity and photodynamic damage

Correct interpretation of optical recordings of membrane potential transients depends on two basic requirements: (a) light intensity has to be linearly proportional to membrane potential over the range of signal amplitudes; (b) to allow signal averaging, the electrical response under study has to be stable throughout the experiment indicating the absence of photodynamic damage. We confirmed that both requirements were met (Fig. 2, Methods).

Figure 2: Linearity and photodynamic damage. (a) Superimposed electrical and optical recordings of an evoked bAP. Dye signal (green trace) from dendritic area outlined by green line is linearly related to membrane potential recorded with patch electrode (black trace). (b) The 1st and the 50th 20 ms optical recording trial of the evoked bAP signals from basal dendrite (spatial average of pixels within green outline). Photodynamic damage is small or absent. The small difference in AP size and shape is a common result of preparation rundown. (c) Single frame voltage-sensitive dye fluorescence image of a spine in recording position. Red dot: uncaging location. (d) Individual (grey) and average (black) responses of the first (1–4) and the last (8–12) eEPSP signals evoked by repetitive two-photon uncaging of glutamate as recorded by a somatic patch electrode. (e) Optical recordings of the same eEPSP signals from the outlined area (green line) on the parent dendrite at the base of the spine. Optical signals (green line) are average of four trials. Photodynamic damage is not detectable. Linearity and absence of photodynamic damage has been confirmed in all experiments (n=29). Full size image

Spatial resolution

Another critical parameter is the spatial resolution that can be achieved in wide-field epifluorescence microscopy mode, which has to be adequate to allow recording of spine and dendrite signals separately. To maximize spatial resolution, all measurements were made from spiny basal dendrites in the superficial layer of the slice (Methods). However, because signal contamination due to light scattering depends not only on recording depth but also on other structural and geometrical factors, the extent of light scattering was determined in every experiment. The amount of light scattered from the spine head to the dendrite was estimated by comparing bAP signals from the spine head and from an unstained area equivalent in size to the parent dendrite and at the same distance from the spine (Fig. 3a,b). The amount of light scattered from the dendrite to the spine head was estimated by comparing recordings from the spine head and from an analogous location at the same distance from the dendrite which contained no stained structures (Fig. 3a,b). The summary result from 29 spines analysed in this study (Fig. 3c) indicates that the amount of light scattered from the spine to the dendrite was negligible (3±0.3%; median 3%, range 0.2–6%) as expected from the ratio of membrane surface areas. The amount of light scattered from the dendrite to the spine was 10±0.9% (median 9.7%; range 1–20%). It is possible to estimate whether this amount of scattering will cause significant change in the EPSP signal recorded from the spine head. If one makes an assumption that the amplitude of the true EPSP related fractional signal (ΔF/F) from the spine head is equal to 1 and the one from the dendrite is equal to 0.5 (a hypothetical attenuation across the spine neck of 50%), the recorded optical signal will be composed of 90% of the light carrying the fractional signal from the spine head equal to 1 and 10% of the light carrying the fractional signal from the dendrite equal to 0.5. The recorded composite fractional signal will be 0.95, a 5% error from the true EPSP amplitude of 1 in this example. Even for the extreme (unrealistic) attenuation of EPSP amplitude across the spine neck of 99%, the upper bound for the error would be <10%. It will be shown below that, in our measurements, the actual error due to light scattering has to be much less than 5% and, thus, negligible. This is because the recorded amplitudes of the EPSP signals, even assuming an error of 10%, indicated that the attenuation across the spine neck is ∼10%, considerably less than a hypothetical value of 50% used above.

Figure 3: Light scattering. (a) Optical signals related to an evoked bAP from a stubby spine head and from an unstained area receiving scattered light. Signals are from areas outlined by corresponding colour lines. The ratio of the spine signal amplitude (red trace) and the amplitude of the signal from an area without spine (blue trace) is a measure of the amount of light scattering from the dendrite to the spine. The ratio of the spine signal amplitude (red trace) and the amplitude of the signal from an unstained area (green trace) at the distance from the spine head equal to the distance of the parent dendrite is a measure of the amount of light scattering from the spine to the dendrite. (b) Same test for a long neck mushroom spine. (c) Scatter plots and mean values for scattered light contribution to dendritic and spine head signals; summary data from n=29 experiments. Standard errors of the mean are smaller than red symbols. Full size image

Selective activation of individual spines

The analysis of EPSP signals from spines requires selective activation of individual synapses to eliminate uncertainties about the source of the signal. A reliable selective activation of one spine/synapse using physiological synaptic stimulation is not presently realizable. While it is possible, although difficult, to insure a reliable repetitive activation of only one individual presynaptic axons, one cannot assume that no more than one synapse is activated12. It is known that practically every presynaptic axon makes more than one functional contact (synapse) with any postsynaptic neuron. Thus, even a minimal stimulation of one presynaptic axon will result, as a rule, in activation of multiple synapses12,21.

To insure that no more than one spine is activated we initially took advantage of micro-iontophoresis of glutamate onto individual spines from a high-resistance sharp electrode as developed in cell culture8. We extended this method to brain slices and confirmed the previously demonstrated spatiotemporal resolution (Fig. 4, Methods). However, micro-iontophoresis suffers from inherently low success rate (∼5%) in experiments that required multiple and reproducible activation of synapses because high-resistance electrodes are notoriously unstable. Thus, in later experiments, we used photolysis of caged glutamate in a diffraction-limited volume based on two-photon light absorption. The firmly established9,10,22 diffraction-limited spatial resolution of two-photon glutamate uncaging was verified in our measurements (Supplementary Fig. 2, Methods). Glutamate release using both iontophoresis and two-photon uncaging was standardized to evoke EPSPs in the soma in the range of 0.2–0.8 mV. These values correspond well to somatic recordings of physiological unitary EPSPs under optically confirmed activation of one individual spine on a neuron21.

Figure 4: Spatiotemporal resolution of glutamate release. (a) A typical release profile with sub micrometre resolution of iontophoresis of a fluorescent dye with molecular weight similar to glutamate. (b) Light intensity as a function of distance from the tip of the sharp electrode. (c,d) An excitatory postsynaptic current of 15 pA recorded from the soma following focal glutamate iontophoresis onto an individual spine head. Repeated iontophoresis produced consistent responses; compare single trial and average of nine trials. Glutamate selectively activated the synapse on the spine head; placing the electrode at the same distance from the dendrite but away from the spine head resulted in no measurable response. This control measurements were carried out in n=19 experiments. (e) Fluorescence image of a spine positioned in close proximity (∼0.5 μm) to the uncaging site. (f) Synaptic current response to iontophoretic release of glutamate (green trace) adjusted to approximate the amplitude and time course of a spontaneous miniature EPSC (black trace). (g) Synaptic current response to two-photon uncaging of glutamate (red trace) adjusted to approximate the amplitude and time course of a spontaneous miniature EPSCs (black trace). The average 10–90% rise time and full width at half height (FWHH) of the spontaneous EPSC recorded in the soma were 1.2±0.1 ms and 5.9±0.4 ms, respectively (n=8). Corresponding values for uncaging-evoked responses were 2.1±0.2 ms and 6.1±0.3 (n=10) while EPSC evoked by iontophoresis where characterized with rise time of 2.9±0.2 ms and FWHH of 12±0.6 ms (n=19). Full size image

Electrical coupling across the spine neck

To characterize electrical coupling across the spine neck we monitored evoked subthreshold signals (eEPSP) following brief focal application of glutamate. A representative experiment utilizing micro-iontophoresis is shown in Fig. 5a–e. The tip of the sharp electrode was positioned in close proximity to a spatially isolated spine (Fig. 5a–c) and the iontophoretic current was adjusted so that the eEPSP in the soma (Fig. 5d) was in the range of unitary synaptic events (0.2–0.8 mV). The eEPSP signal was recorded optically from the spine head and from the parent dendrite followed by the recording of the bAP signals from the same locations (Fig. 5d). The EPSP signals were calibrated in mV using the bAP signal as a calibration standard (scaled signals in Fig. 5e). The significance of possible errors in calibrating optical signals is discussed below. From the measured eEPSP spine , eEPSP dendrite and I synapse (recorded separately under voltage clamp in response to a standard glutamate release adjusted to evoke EPSPs in the soma corresponding to somatic recordings of physiological unitary EPSPs) we calculated R neck and Z dendrite (Fig. 5k–m) according to the equations in Fig. 5o applied to the equivalent electrical circuit shown in Supplementary Fig. 3b. The equations in Fig. 5o are derived as time integrals of Ohm’s law applied to a voltage divider representing a spine attached to a dendrite (Supplementary Fig. 3c). This approach integrated synaptic current (I synapse ) over time to arrive at the recorded synaptic charge transfer (Q clamp ) which was subsequently corrected for the error caused by incomplete space clamp. Integrating synaptic current to estimate transferred charge minimizes somatic voltage clamp error23. The significance of this error is discussed below. In the experiment shown in Fig. 5a–e, R neck and Z dendrite , calculated from measured parameters, were 15 and 197 MΩ, respectively. Figure 5f–j shows an example of a similar experiment utilizing two-photon uncaging of glutamate. Again, it is clear that the eEPSP signals in the spine head and in the parent dendrite (Fig. 5i) are similar indicating that R neck is negligible compared with Z dendrite . In this experiment R neck and Z dendrite , calculated from the measured parameters, were 29 and 371 MΩ, respectively. Figure 6 illustrates three additional measurements utilizing two-photon uncaging. The scatter plots of data from n=29/24/22 (spines/cells/animals) experiments showed the mean values of R neck =27±6 MΩ and Z dendrite =275±27 MΩ.

Figure 5: Quantification of R neck and Z dendrite from two representative experimental measurements. (a) Low-magnification fluorescence image of a basal dendrite labelled with a voltage-sensitive dye; z-stack of confocal images. Arrow: recorded spine. (b) High magnification confocal image of the same spine. Tip of iontophoretic electrode (labelled with the fluorescent dye) in the immediate vicinity of spine head. (c) Single frame image of a spine in recording position obtained with CCD for voltage imaging. (d) Traces on left: eEPSP recordings from spine head (red) and parent dendrite (green). Average of 16 trials. Bottom black traces: somatic electrode recording and the uncaging command pulse. Traces on right: bAP signals from same locations. Average of nine trials. (e) Left traces: superimposed eEPSP signals from spine head and parent dendrite calibrated in terms of membrane potential. Right traces: bAP signals corrected for recording sensitivity difference. (f–j) Two-photon uncaging of glutamate. Same information as shown in a–e. Red dot in h: position and approximate size of uncaging light spot. The eEPSP and bAP recordings are average of 8 and 4 trials, respectively. (k) Synaptic current in response to standard focal application of glutamate. Grey area: time integral of synaptic current. (l) Superimposed eEPSP signals from spine head (red) and parent dendrite (green) calibrated in mV. (m) Time integral of synaptic current. (n) Time integral of voltage drop across spine neck. (o) Equations for R neck and Z dendrite calculation. V dendrite —local dendritic membrane potential; V spine —membrane potential of the spine head; I synapse —synaptic current; R neck —electrical resistance of spine neck; Z dendrite —impedance of parent dendrite; Q clamp —total recorded charge transfer; K s-d : distance-dependent adjustment factor for the correction of the somatic voltage clamp error based on experimentally determined dendro-somatic attenuation of synaptic charge transfer23. Full size image

Figure 6: Attenuation ratio eEPSP spine /eEPSP dendrite . (a) The attenuation ratio is directly determined by the ratio of resistances as shown by the equation at the top. Three representative examples of the comparison of eEPSP spine (red) and eEPSP dendrite (green) evoked by two-photon uncaging of glutamate. In each panel, two fluorescent images are shown on left. Upper: z-stack of confocal images. Lower: single frame image of a spine in recording position. Red dot: uncaging location. Lower black traces: somatic patch electrode recordings and timing of uncaging pulse. From top to bottom: averages of 24, 16 and 4 trials. (b) Scatter plot of individual values and the mean R neck . (c) Scatter plot of individual values and the mean Z dendrite . (d) Scatter plot of individual values and the mean ratios R neck /Z dendrite (left scale) and eEPSP spine /eEPSP dendrite (right scale). N=29 in all cases. In c and d s.e.m. is smaller than the red data mark. () Iontophoresis. () 2P uncaging. Full size image

Quantification accuracy

How accurate is our quantification of R neck and Z dendrite ? There are four possible sources of errors that need to be considered: (a) sampling frequency, (b) the S/N ratio, (c) calibration of optical signals in terms of membrane potential and (d) voltage-clamp measurement of unitary synaptic current/transferred charge. The sampling frequency (frame rate) was limited by the available S/N to 2 kHz. The duration of the upstroke of the EPSP (threshold-to-peak) as recorded electrically by others at a sampling rate of 50 KHz is in the range of 1–2 ms (refs 17, 23, 24, 25). In our study, the average 10–90% rise time of optically recorded eEPSPs was 1.2±0.1 ms while the full width at the half height was 5.9±0.4 ms; n=29. Our sampling rate of 2 kHz, although lower than the formally required Nyquist rate, was sufficient for the accurate reconstruction of EPSP waveform because aliasing (sampling artefact which can result in the omission of additional peaks in between data points) can be safely excluded on the basis of additional information available from independent measurements; the general shape of the EPSP is known from dendritic electrical recordings25. These electrical data correspond well with our optical recordings from the parent dendrite.

At the sampling rate of 2 kHz, optical recordings were averaged over 4–16 trials (and rarely up to 25 trials) to reach the S/N of ∼4. The mean S/N in recordings from n=29 spines was 4.3±0.3 (mean±s.e.m.). Due to the larger membrane area, the sensitivity of recordings from the parent dendrites at the base of the spine was significantly higher with the S/N=9.4±2.3. We assumed that the high sensitivity recordings from the parent dendrite are an accurate measure of the true waveform of the eEPSP both in the parent dendrite and in the spine head because the waveform is expected to be practically identical in both compartments. The membrane area of the spine neck and its effective capacitance is extremely small rendering RC filtering across the ∼1 μm long spine neck cable negligible. In addition, regarding the S/N, the calculation of the R neck and Z dendrite is based on the time integral of EPSP signals from spines and dendrites. As illustrated in Fig. 5m,n, integration of the EPSP voltage trace over time acts as a powerful low-pass filter which practically eliminated random high-frequency noise. Thus, we conclude that the quantification of R neck and Z dendrite was based on adequate sensitivity and sampling rate.

There are unavoidable inaccuracies in calibrating optical signals in terms of membrane potential. However, it is possible to determine calibration error limits and establish whether the results and conclusions of the study could be significantly affected. The amplitude of the bAP signals measured electrically from basal dendrites12,17 varied from ∼100 mV at a distance of about 30 μm down to ∼45 mV at a distance of about 120 μm from the soma. Within this range, at any given distance, individual values may vary around the exponential fit to the data by ∼20 mV (ref. 17). Additionally, there are uncertainties about the precision of electrical measurements from thin dendrites which are often ignored. The accuracy of electrical measurements using high-resistance patch electrodes (∼100 MΩ) depends steeply on series resistance and capacitance compensation (which are never perfect). Moreover, patch electrodes introduce additional capacitive load on the dendrite resulting from the capacitance of the pipette that cannot be compensated for (ref. 20). These factors would lead to underestimation of the extent of AP backpropagation. Indeed, voltage-imaging studies showed that the amplitude of bAPs in distal basal dendrite might be larger than what was indicated by electrode measurements26. To take into account these uncertainties, we calibrated EPSP signals for all spines (regardless of the distance from the soma) using both the low-end of the bAP amplitude range (45 mV) and the high-end value of 100 mV. The results showed that the mean R neck values based on low- and high-end bAP amplitudes were 22.5 ±4.8 MΩ and 43.7±9.7 MΩ, respectively. This result sets the upper and lower limits for R neck values indicating that possible errors in calibrating optical signals are too small to influence the conclusions from this study. The mean value of 26.7±6.3 MΩ, obtained by adjusting bAP amplitude as a function of distance from the soma according to the exponential fit to individual data12,17 appears to be the most accurate estimate that can be currently obtained.

Due to incomplete space clamp, the somatic voltage clamp does not report accurate synaptic currents or transferred charge. To minimize these errors, we used the correction factors taken directly from Fig. 3a of Williams and Mitchell23. That figure reports the experimentally determined dendro-somatic attenuation of transferred synaptic charge as a function of distance of the synapse from the recording site (cell body) expressed as a fraction of recovered charge. In every experiment, we used the value of this fraction at the corresponding distance (as determined from the confocal image of the cell) as the correction factor (K s-d ). The range of distances in our experiments was 30–120 μm (Methods) corresponding to a fraction of recovered charge in the range of 75–95%. However, the direct measurements of dendro-somatic attenuation by Williams and Mitchell23 were carried out from primary apical dendrites. Thus, our calculations of the synaptic currents are likely to be underestimates because apical dendritic trunks are characterized by larger diameter and, hence, lower axial resistance compared with basal dendrites. For this reason the charge loss is expected to be larger in basal dendrites. We conclude that our results set the lower limit for current amplitudes at the site of origin which translates into upper bound for calculated spine neck resistance.

It is important to recognize that, in addition to being small, the errors in calibrating optical signals as well as in estimating current amplitudes have no effect on the ratio of resistances because both resistances are equally affected. This is of particular significance because, from the functional point of view, the absolute values of the R neck and Z dendrite are less important than the ratio of resistances which directly determines the attenuation ratio eEPSP spine /eEPSP dendrite (AR) (Fig. 6a; Supplementary Fig. 3). The AR, in turn, determines the effect of a synapse on the membrane potential of a neuron (synaptic weight). It follows from these considerations that AR can be measured directly from optical recordings without any assumptions and with accuracy limited only by the S/N. The scatter plot of the data from 29 experiments indicated mean value for AR=1.10±0.02 (Fig. 6d). In other words, on average, eEPSPs in the spine head are attenuated as they propagate across the spine neck by ∼10% with a significant proportion of spines (∼60%) showing lower attenuation.

The role of voltage-sensitive channels in spines

The conceptual model used for R neck calculation (Supplementary Fig. 3) is valid only if voltage-sensitive channels in the parent dendrite do not contribute significantly to eEPSP dendrite amplitude. We used a pharmacological test to measure this contribution (which is currently unsettled12,27,28). The eEPSP amplitudes were measured under control conditions and in the presence of a cocktail of pharmacological agents that selectively block NMDA receptors as well as Na2+ and Ca2+ voltage-sensitive channels (Fig. 7, Methods). In these measurements, it was sufficient to monitor eEPSP signals from a small section (∼20 μm in length; Fig. 7) of the dendrite at the base of the spine. These signals provide accurate information about changes in the synaptic current and eEPSP amplitude while the recording from the relatively large dendritic membrane area relaxes the requirement for signal averaging. The summary result from n=7/6/6 experiments (spines/cells/animals) showed that the pharmacological block of voltage-sensitive channels did not reduce the amplitude of the eEPSP (eEPSP control /eEPSP blockers =1.006±0.05; P<0.01; Student’s t-test). These data argue that the contribution of voltage-sensitive channels to unitary eEPSPs was not significant.

Figure 7: A representative example of the effect of channel blockers on eEPSP amplitude. Left panel: fluorescence image of a section of basal dendrite with one spine in focus; uncaging location indicated by red dot. Right panel: top traces: optical recordings of the eEPSP dendrite signals from outlined dendritic area (green) evoked under control conditions and in the presence of a cocktail of channel blockers (1 μM TTX, 100 μM AP-5, 10 μM nimodipine, 100 μM NiCl 2 ). Average of 4 trials. No effect of channel blockers detected. Middle traces: somatic electrode recordings of eEPSP. Bottom traces: timing of the uncaging pulse. Full size image

Computational modelling

To establish how our experimental results correspond to widely accepted electrical behaviour of dendritic cables we constructed a multicompartmental model of a layer 5 pyramidal neuron with typical passive dendritic cable properties (Methods) and experimentally determined dendritic diameters from live neurons (Supplementary Fig. 4). The model predicts the amplitude and the time course of EPSP spine , EPSP dendrite and AR=1+R neck /Z dendrite (refs 3, 4, 5, 6) for a given I synapse , according to Ohm’s law and Kirchhoff’s current law for spines at different locations (Fig. 8; Supplementary Fig. 3). In a series of simulations, the position of a typical spine (neck length 1 μm; diameter 0.17 μm)7 attached to a parent dendrite was moved across the entire dendritic arbour. The EPSP spine , EPSP dendrite , Z dendrite and AR were calculated for every location after the spine was activated with a conductance change synapse model adjusted to mimic a unitary EPSC21. The colour-coded display of the results illustrates spatial distribution of the four parameters mentioned above (Fig. 8b). Because the calculated Z dendrite was much larger than R neck in most parts of the dendritic tree (a fact that is not universally appreciated29), the AR was close to unity (between 1 and 1.1) in these distal regions (Fig. 8b, right-most model result). For a typical basal dendrite the model predicted a ratio of 1.5, 1.3 and <1.1 at distances of 20, 30 and >60 μm from the soma. This modelling prediction corresponds well to the range of recorded values shown in Fig. 6d. The exception from this rule was the proximal primary dendritic trunk characterized by large diameter and a very low Z dendrite , comparable to the value of R neck of the standard spine (∼30 MΩ). The AR in these proximal regions varied between 1.5 and 3 indicating that the EPSP in these spines was up to 3 times larger than in the dendrites at the base of the spine. However, larger attenuation in these spines is based on low Z dendrite , not on large R neck . Thus, the overall input impedance of a proximal spine (Z spine =R neck +Z dendrite ) is low and, consequently, the peak amplitude of EPSPs produced in these spines is expected to be low. Patch-clamp recordings from basal dendrites confirmed this expectation (Nevian et al.17). Notably, these proximal dendritic compartments are largely devoid of spines30. Another consequence of much larger Z dendrite relative to R neck over most of the dendritic tree was that the spatial distribution of EPSP spine amplitudes was highly non-uniform and similar to the spatial distribution of both Z dendrite and EPSP dendrite amplitudes (Fig. 8b, left three model results). This result shows that, in the model, Z dendrite is the main determinant of the EPSP amplitude in both compartments (spine and dendrite) while the effect of R neck is small and limited to proximal parts of the primary apical dendrite. Our experimental measurements are in full agreement with these modelling predictions.