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

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. 2A) and a facilitating layer 6 pyramid to layer 5 bitufted interneuron connection (Fig. 2B) are plotted. Although there is scatter, measurements obtained from first, second, and, in Fig. 2A, 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. 3A) and 3 pyramid–interneuron pairs (Fig. 3B) were challenged with ω-Conotoxin GVIA and one pyramid–pyramid connection with ω-Agatoxin IVA. Essentially similar results were obtained in all experiments with presynaptic Ca²⁺ 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 ω-Conotoxin GVIA/ω-Agatoxin 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.

Layer-Specific 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. 6A). This was also true for depressing inputs onto layer 3 multipolar interneurons with narrow APs (width at half-amplitude ≤0.3 ms) (Fig. 6B). 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 same-layer 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.

Applicability of Binomial Model-Based 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 low-frequency single-spike EPSPs and the paired-pulse 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 model-based 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. 45–6), 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 paired-pulse effects. Rather, all methods indicate that paired-pulse 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.

Data Analysis.

Data sets in which first EPSP shape (SI Fig. 8) and amplitude and postsynaptic membrane potential were stable and EPSPs exhibited adequate signal-to-noise ratios were selected. Each EPSP in each sweep was measured, from baseline to peak with cursors (in-house software). To measure short-interval second and subsequent EPSPs, an average of single-spike 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. Single-sweep 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 single-sweep measurements where signal-to-noise ratio was high and CV low, to >300 measurements where signal-to-noise 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 Ca²⁺ Channels.

The presynaptic N-type Ca²⁺ channel blocker, ω-Conotoxin GVIA and the P/Q-type Ca²⁺ channel blocker ω-Agatoxin IVA (Alomone Labs, Jerusalem, Israel) were dissolved in saline and added to the bath to final concentrations of up to 0.1 μM (ω-Agatoxin IVA) and 1 μM (ω-Conotoxin 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 (PSI-Plot, 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}].