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Binomial parameters differ across neocortical layers and with different classes of connections in adult rat and cat neocortex

Edited by Rodolfo R. Llinas, New York University Medical Center, New York, NY, and approved July 12, 2007 (received for review June 19, 2007)
Abstract
Binomial modelbased analysis compared excitatory connections involving different classes of neurons in different neocortical layers. Singlesweep excitatory postsynaptic potentials (EPSPs) from dual intracellular recordings in adult cat and rat slices were measured. For data subsets corresponding to first EPSPs exhibiting different degrees of posttetanic potentiation and second, third etc. EPSPs in trains at different interspike intervals, coefficient of variation (CV), transmission failure rates (F), variance (V), and V/M were plotted against mean EPSP amplitude (M). Curves derived from binomial models in which subsets varied only in p (release probability) were fit and parameters q (quantal amplitude), and n (number of release sites) were estimated. Estimates for q and n were similar for control subsets and subsets recorded during Ca^{2+} channel blockade, only p varied. Estimates from the four methods were powerfully correlated, but when CV, F, V, and V/M were plotted against M, different types of connections occupied different regions of parameter space. Comparisons of linear fits to V/M against M plots and of parameter estimates indicated that these differences were significant. Connections between pyramids in different layers and inputs to different cell classes in the same layer differed markedly. Monte Carlo simulations of more complex models subjected to simple binomial modelbased analysis confirmed the significance of these differences. Binomial models, either simple, in which p and q are identical at all terminals involved, or more complex, in which they differ, adequately describe many neocortical connections, but each class uses different combinations of n, mean p, and mean q.
There are many different types of synaptic connections in neocortex, between neurons of different classes and neurons in different layers. Dual intracellular recordings from pairs of synaptically connected neurons with dyefilling demonstrate striking differences between these classes, particularly their probability of occurrence and dynamic properties (1–9). Most synaptic connections between pyramids and pyramidal inputs onto interneurons with narrow action potentials (APs) display high release probabilities (p) at low firing frequencies and paired pulse and frequencydependent depression. In contrast, excitatory postsynaptic potentials (EPSPs) received by dendritepreferring, more slowly firing cells commonly display a low p and facilitation (2, 10–12).
Few studies, however, have attempted to compare the binomial parameters: n, q, and p, across classes of neocortical connections for clear practical reasons. Traditional analytical methods, e.g., identification of “quantal peaks” in EPSP/excitatory postsynaptic current (EPSC) amplitude distributions, require large data sets with absolute stability and minimal noise (13). Clear quantal peaks allow q to be estimated, but n and p remain unknown. An unambiguous determination of anatomical n requires all close membrane appositions between presynaptic axon and postsynaptic cell to be confirmed as synaptic contacts at the ultrastructural level. This has been successfully achieved in very few studies (4, 14–18), and numbers of connections so studied have been small.
To address this issue analytically, one study compared EPSPs received by layer 4 spiny cells from layer 4 and layer 6 pyramids (19) by plotting the coefficient of variation (CV) of the EPSP against mean EPSP amplitude (M). Measurements obtained fell into two different regions of parameter space, indicating that the underlying parameters may differ (20).
In contrast to the paucity of studies directly assessing or comparing binomial parameters, many have used binomial modelbased analysis to indicate whether a modulatory effect is mediated predominantly pre or postsynaptically (21, 22). Meanvariance analysis in which a parabola is fit to plots of EPSP/C variance against M [Methods, Eq. 2 , (20, 23)] provides estimates of n and q from multiple data subsets between which only p varies (20, 24). A linearized version (Eq. 4 ) can also be used (25). These methods give parameter estimates for individual connections where n and q remain stable throughout and data subsets differ only in p. Limitations associated with applying simple binomial modeldependent analysis are reviewed in ref. 26. Caveats discussed there should be applied to all such analyses.
This study addressed two basic questions: (i) whether binomialbased analytical tools could be used to compare parameters n, p, and q across classes of cortical connections and (ii) whether parameters n, p, and q differ between classes of connections and across cortical layers. Advantage was taken of the dynamic properties of neocortical synapses to generate data subsets that could be predicted to differ primarily in p. Further analysis of applicable models: a simple model in which all contributory terminals display the same p and q (at any one time) and models in which q and/or p vary between terminals is given in supporting information (SI) Text .
Results
From a larger population, paired recordings were selected for further analysis. Attention focused on longer paired recordings containing multiple data subsets and included 69 connections between excitatory cells, 16 in cat and 53 in rat, and 30 connections from pyramids to interneurons, 13 in cat and 17 in rat. Data subsets from each recording were compared to test whether differences in M resulted primarily from a change in p. If the proportional difference in CV ^{−2} was greater than the proportional difference in M, subsets were accepted as differing primarily in p. In all, 949 data subsets and >50,000 EPSPs measured individually are included here (see SI Figs. 8 and 9).
Plots of CV, F, V, and V/M Against M.
When CV, F, V, or V/M are plotted against M, the binomial model predicts that changes in p alone will shift points along the lines given by Eqs. 1 – 4 (Methods; Fig. 1). Plots were fit with these relations for each connection. For the majority, correlations for fits by Eqs. 1 – 4 were >0.8. In Fig. 2, data obtained from a depressing layer 4 pyramid–pyramid connection (Fig. 2 A) and a facilitating layer 6 pyramid to layer 5 bitufted interneuron connection (Fig. 2 B) are plotted. Although there is scatter, measurements obtained from first, second, and, in Fig. 2 A, third, fourth, and fifth EPSPs in trains can be described by these relationships, and estimates of n and q obtained with the four methods are similar.
Two pyramid–pyramid pairs (Fig. 3 A) and 3 pyramid–interneuron pairs (Fig. 3 B) were challenged with ωConotoxin GVIA and one pyramid–pyramid connection with ωAgatoxin IVA. Essentially similar results were obtained in all experiments with presynaptic Ca^{2+} channel blockers. Data subsets corresponding to first EPSPs expressing different levels of posttetanic potentiation and to second, third, and fourth EPSPs at different interspike intervals were obtained. Control data and test data were plotted and fit separately. Estimates of n and q were similar with all four methods and for control and ωConotoxin GVIA/ωAgatoxin IVA data.
For each parameter estimate, coefficients of variation (CVs) were calculated. For estimates of q, CVs were lower (mean 0.18, 0.24, 0.18, 0.19, P < 0.001 Student's unpaired t test) than CVs for estimates of n (0.45, 0.99, 0.99, 0.39). Correlations between estimates of n and between estimates of q obtained with methods 1, 3, and 4 were strong (correlations >0.92), had slopes close to unity (0.89–1.19), and intercepts close to zero (−0.02–0.6 for n and −0.07–0.06 for q; see SI Fig. 10). Correlations between estimates of n and q obtained with method 2 and those obtained with methods 1, 3, and 4 were less strong (0.7–0.87), but slopes and intercepts were similar.
LayerSpecific Properties of Connections Between Excitatory Cells.
In rat, EPSPs generated by layer 6 corticothalamic pyramids were significantly smaller than those of other pyramid–pyramid connections (P < 0.02, Student's unpaired t test). Layer 3 pyramid–pyramid EPSPs in rat were larger than those in layer 4 (P = 0.01) but similar in size to those in layer 5 and to the outputs of layer 6 corticocortical pyramids (P > 0.29). No significant differences in M were apparent among the populations of cat pyramid–pyramid connections and, as reported (3, 27), no significant differences in M between rat and cat data.
Clear differences in the regions of parameter space occupied by pyramid–pyramid connections in different layers are apparent when CV, F, V, and V/M are plotted against M (Fig. 4). In rat, intralaminar layer 3 and layer 5 connections occupied regions indicative of a higher q than connections within layer 4 or from layer 4 to layer 3. Those in layer 6 occupied intermediate positions. This order is paralleled by the estimates of q for individual connections. In cat, connections from layer 6 pyramids again occupied intermediate regions, but layer 3 pairs appeared to exhibit a smaller q and layer 4 a larger q in this species (Table 1 and Fig. 7).
Connections Made by Different Classes of Layer 6 Pyramids.
Corticocortical pyramidal outputs exhibit depression, whereas those of corticothalamic pyramids facilitate (8, 27). Fig. 5 indicates that this is because the depressing outputs of layer 6 corticocortical pyramids have a higher p at low firing frequencies than facilitating corticothalamic pyramid outputs. The estimates of q obtained with the four methods were similar for these connections (P > 0.9), but estimates of n and p (assuming p = M/nq) for corticocortical outputs were twice those for corticothalamic outputs (P < 0.05, Student's unpaired t test). Here then, are two classes of connections where q is similar but where differences in n and p result in significant differences in M.
Excitatory Inputs onto Interneurons Differ from Those onto Pyramidal Cells.
In plots of CV against M (Fig. 6) and F, V, and V/M against M (data not shown), points for facilitating inputs onto bitufted interneurons with broad APs (width at half amplitude >0.3 ms) and adapting or burst firing characteristics occupied regions of parameter space that were largely separate from connections onto pyramids (Fig. 6 A). This was also true for depressing inputs onto layer 3 multipolar interneurons with narrow APs (width at halfamplitude ≤0.3 ms) (Fig. 6 B). Mean estimates of q for all pyramid–pyramid connections were smaller than for pyramid–interneuron connections (P < 0.01, Student's unpaired t test). Mean estimates of p for depressing inputs onto fast spiking interneurons were similar to those for pyramid–pyramid connections, but for facilitating inputs onto bitufted interneurons, estimates of p were significantly lower (P < 0.01, Table 1).
That further differences in n might appear with larger samples is indicated by comparison of the slopes of linear fits to V/M against M plots of population data in which points that could not be used for parameter estimates (because data subsets were too few or too consistent in M) could be included. The outcome paralleled conclusions drawn from parameter estimates but suggested additional differences because 13:22 comparisons of pyramid–pyramid connections in rat and 5:9 in cat and the majority of samelayer comparisons between pyramid–pyramid and pyramid–interneuron connections resulted in rejection of the hypothesis that the two populations fell on the same line at the 95–99% confidence level.
Discussion
Binomial modelbased methods have been less widely used for estimating n, p, and q than to assess the site responsible for a change in M. Only one previous study in adult cat neocortex compared connections this way (19). Larger numbers of connections and data subsets and a wider range of connection classes were available here.
Applicability of Binomial ModelBased Analysis.
Strong correlations for fits of data from single connections with Eqs. 1 – 4 and correlations between parameter estimates obtained with these four methods indicate that binomial models describe well the type of data analyzed. The parameter estimates and ranges summarized here could therefore be useful in models of cortical circuitry.
With methods 1–3, estimates of q demonstrated lower CVs than estimates of n, suggesting that q is more accurately estimated, whereas method 4 may be the most applicable to estimating n. Indeed, Fig. 1 indicates that the separation between model curves 1–3 is minimal for large differences in n unless p is high. The negative correlation between estimated p for lowfrequency singlespike EPSPs and the pairedpulse ratio (correlation > 0.80, SI Fig. 11), indicates that the estimates of n and q obtained provide a useful comparison. To determine whether more complex binomial models might equally apply and whether the conclusions drawn here would be confounded if q and p differed between synapses involved in a connection, data subsets from Monte Carlo simulations of a simple and five complex models were analyzed (SI Figs. 12–15 and Discussion). In brief, data from complex models could not be distinguished from data from simple models with similar n, mean p, and mean q. Although it is possible therefore that the synapses constituting individual connections do not conform to a simple model, i.e., q and p may not be not identical, simple modelbased analysis does provide useful estimates of n, mean q, and mean p and useful comparisons.
Differences Between Populations of Pyramid–Pyramid Connections.
The principle outcome was the differences in the regions of parameter space occupied by different classes of connections, whether CV, F, V, or V/M was plotted against M (Figs. 4 , 5–6), or estimated mean q was plotted against estimated n (Fig. 7). More sophisticated methods will be required to distinguish whether these differences result from the number and type of receptor, synapse location and/or dendritic properties and filtering. In rat, intralaminar layer 4 pyramid–pyramid connections stood out, exhibiting a lower mean q than connections in other layers despite a similarly wide range for estimated n. In cat, intralaminar layer 4 pyramid–pyramid connections appear to exhibit a larger mean q and a narrow range of smaller values of n with the relatively smaller number of data sets available. With the exception of layer 4, cat connections appear to involve a larger number of smaller quanta than rat connections, possibly reflecting the larger volume available for making connections in cat neocortex. Layer 6 corticothalamic pyramid outputs also stood out. Although estimated mean q was similar to that in other layers, n and p were particularly low, the low p correlating with these being the only pyramid–pyramid connections consistently described as facilitating in neocortex (6, 27, 28).
Differences Between Pyramid–Pyramid and Pyramid–Interneuron Connections.
The larger values of mean q at pyramid–interneuron compared with pyramid–pyramid connections explain the larger CVs of pyramid–interneuron EPSPs often described, but not explicitly explored before e.g., (2, 6, 11, 14). This may result from the shorter electrotonic lengths of interneuronal dendrites and/or different numbers and types of receptors. The binomial models described in SI Text are not, however, applicable to all connections. Some facilitating connections onto bitufted interneurons do not exhibit the relationship between CV ^{−2} and M that indicates a change in p for pairedpulse effects. Rather, all methods indicate that pairedpulse potentiation is due to an increase in q. Moreover, for some of these connections, estimates of n were lower than anatomical n. An economical explanation is nonindependent release from groups of terminals served by single axonal branches that fail on occasions to transmit an AP. The analysis recognizes the activation of all terminals served by a branch as a unitary or quantal event whose amplitude increases as p increases (see also ref. 26), resulting in the appearance of a smaller n and a larger, but not invariant, q.
In conclusion, simple and complex binomial models appear to describe well many intracortical excitatory connections, and different classes of connections use different combinations of n, mean p, and mean q to achieve the range of synaptic strengths that they display.
Materials and Methods
Dual intracellular recordings with biocytin labeling were made from synaptically connected neurons in slices of young adult rat somatosensory and visual cortex and in cat visual cortex as described (29, 30). Some unpublished experiments are reported (e.g., experiments with presynaptic Ca^{2+} channel blockers). However, data sets from which parameters such as average connectivity ratios, mean EPSP amplitude, and time course, have been published were also reanalyzed. All procedures complied with U.K. Home Office regulations for animal use. For details of slice preparation and recordings see SI Text .
Data Analysis.
Data sets in which first EPSP shape (SI Fig. 8) and amplitude and postsynaptic membrane potential were stable and EPSPs exhibited adequate signaltonoise ratios were selected. Each EPSP in each sweep was measured, from baseline to peak with cursors (inhouse software). To measure shortinterval second and subsequent EPSPs, an average of singlespike EPSPs was scaled to match the amplitude of the first EPSP in each sweep and the second EPSP measured from its peak to the appropriate point on the decay of the scaled first EPSP average (SI Fig. 9).
Data Subset Selection.
Where posttetanic potentiation was apparent, first EPSPs were sorted into subsets according to the number and frequency of spikes in the preceding spike train. Singlesweep second, third, etc., EPSP amplitudes were plotted against interspike interval and smoothed [running average of 10–20 points (for details and examples, see refs. 7–9)]. Data subsets were selected according to a narrow range of interspike intervals over which the smoothed second EPSP was stable. Between 1 and 110 such subsets were obtained from each paired recording. Subsets varied in size from 30 singlesweep measurements where signaltonoise ratio was high and CV low, to >300 measurements where signaltonoise ratios were low and CV was large, or where smaller data subsets from the same measurements did not differ significantly. M, V, V/M, SD, CV, and F were calculated for each data subset.
Blockade of Presynaptic Ca^{2+} Channels.
The presynaptic Ntype Ca^{2+} channel blocker, ωConotoxin GVIA and the P/Qtype Ca^{2+} channel blocker ωAgatoxin IVA (Alomone Labs, Jerusalem, Israel) were dissolved in saline and added to the bath to final concentrations of up to 0.1 μM (ωAgatoxin IVA) and 1 μM (ωConotoxin GVIA) (31, 32). BSA was added before toxin to occlude nonspecific binding sites. Effects of these toxins reached equilibrium after 20–30 min.
Analysis.
Relationships among CV, F, V, V/M, and M were tested by fitting curves (PSIPlot, Poly Software International, Pearl River, NY). In plots of CV against M, the simple binomial model predicts:
Because the binomial expansion predicts that the probability of no release occurring: and because: F is given by In plots of V against M, the binomial model predicts that A linear version of this relationship can also be used where CV is the coefficient of variation of the EPSP amplitude, V the variance, M the mean EPSP amplitude, n the number of release sites, q the quantal amplitude, p the release probability and F the proportion of failures of transmission [P _{k = 0}].
Acknowledgments
We thank Dr Thomas Wennekers and Prof. Mike Denhan (University of Plymouth, Plymouth, U.K.) for making the COLAMN cluster available for the Monte Carlo simulations. This work was supported by the Medical Research Council (U.K.), the Engineering and Physical Sciences Research Council (U.K.) through the COLAMN project, and Novartis Pharma (Basel, Switzerland).
Footnotes
 *To whom correspondence should be addressed. Email: alex.thomson{at}pharmacy.ac.uk

Author contributions: D.C.W. and A.M.T. designed research; A.M.T. performed research; A.B., D.C.W., and A.M.T. analyzed data; and A.M.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0705661104/DC1.
 Abbreviations:
 n,
 number of release sites;
 p,
 release probability;
 q,
 quantal amplitude;
 M,
 mean EPSP amplitude;
 V,
 variance;
 CV,
 coefficient of variation;
 EPSP,
 excitatory postsynaptic potential;
 EPSC,
 excitatory postsynaptic current;
 F,
 proportion of transmission failures;
 AP,
 action potential.

Freely available online through the PNAS open access option.
 © 2007 by The National Academy of Sciences of the USA
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