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

Abstract

Binomial model-based analysis compared excitatory connections involving different classes of neurons in different neocortical layers. Single-sweep 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 model-based 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.

Fig. 1.

Binomial models in which p is varied (from 0.1 to 0.9 in each case) and where one other parameter, n (Upper) or q (Lower), is varied. Each curve plots values obtained for a single model in which only p varied. CV (A), proportion of F (B), V (C), and V/M (D) are each plotted against M.

Fig. 2.

The four methods of estimating n and q applied to a depressing layer 4 pyramid–pyramid (A) and a facilitating layer 6 pyramid to layer 5 bitufted interneuron connection (B). The curves illustrated were fit to all points including subsets of first EPSPs exhibiting different degrees of posttetanic potentiation and subsets of second, third, fourth and fifth EPSPs at different interspike intervals (see key, Aa). Shown are CV plotted against M (Eq. 1) (Aa and Ba), F plotted against M (Eq. 2) (Ab and Bb), V plotted against M (Eq. 3) (Ac and Bc), and V/M plotted against M (Eq. 4) (Ad and Bd). Estimates obtained for n and q are given as Insets. For these plots r² (coefficient of determination) was 0.85 (Aa), 0.91 (Ab), 0.62 (Ac), 0.60 (Ad), 0.87 (Ba), 0.96 (Bb), 0.65 (Bc), and 0.46 (Bd).

Fig. 3.

A layer 3 depressing pyramid–pyramid connection (A) and a layer 3 depressing pyramid to fast spiking, multipolar interneuron connection (B). These pairs were first recorded under control conditions (filled circles) and then after addition of ω-conotoxin GVIA (open). After addition of this N-type Ca²⁺ channel blocker, EPSPs decreased in M, and F increased. Shown are CV plotted against M (Aa and Ba) and F plotted against M (Ab and Bb). Control and ω-conotoxin GVIA data were fit separately. Estimates for n and q are given as Insets. For these plots, r² (coefficient of determination) was control 0.83, conotoxin 0.92 (Aa); control 0.90, conotoxin 0.95 (Ab); control 0.75, conotoxin 0.93 (Ba); and control 0.85, conotoxin 0.96 (Bb).

Fig. 4.

Comparison of connections between pyramids in different layers and two species, rat (A) and cat (B). Measurements from data subsets like those in Figs. 2 and 3 are plotted. Color codes the layer in which the pre- and postsynaptic neurons lay (key, Bb). Shown are CV plotted against M (Aa and Ba), F against M (Ab and Bb), and V/M against M (Ac and Bc). In rat (Aa–Ac), points from layer 3 (red) and layer 5 pairs (yellow) lie in a region of parameter space indicative of a larger q than those from layer 4 (green). Points from layer 6 (blue) lie between. In cat (Ba–Bc) points from connections involving layer 4 cells (L4–L4, L4–L3, and L5–L4) occupy regions of parameters space indicative of a larger q than connections between layer 3 pyramids, with layer 6 between.

Fig. 5.

Intralaminar connections made by presynaptic corticothalamic pyramids with postsynaptic layer 6 pyramids (filled triangles) compared with intralaminar connections made by presynaptic corticocortical pyramids (open circles). Corticocortical pairs for which only one data set was available are indicated by half-filled circles. CV is plotted against M. The separate regions of parameter space occupied and mean estimates of n and q (Insets) demonstrate that whereas q is similar for both populations (P > 0.5), estimates of n and of p for low-frequency single-spike EPSPs are larger for corticocortical connections than for connections made by corticothalamic axons (P < 0.001).

Fig. 6.

CV plotted against M for pyramidal inputs onto bitufted, dendrite-targeting interneurons (A) and fast spiking, multipolar parvalbumin immunopositive interneurons (B). Filled symbols indicate rat, and open symbols indicate cat data, layers are color coded (key in A). Pyramidal data from Fig. 4 Aa and Ba are shown in gray for comparison. Almost all bitufted and multipolar interneuron data from layer 3 fall outside the parameter space occupied by pyramid–pyramid connections, indicating that these connections display different binomial parameters.

Fig. 7.

Estimates of q obtained by using the four methods plotted against estimates of n. Symbols indicate the method and colors show the type of connection (see keys). (A and B) In rat (A) and cat (B), pyramid–pyramid connections in different layers are compared. (C and D) Pyramidal inputs onto two broad classes of interneurons are compared with pyramid–pyramid connections (gray circles). Open symbols indicate cat and filled symbols indicate rat data. Dotted lines outline populations of connections. (A) In rat, estimates of q for layer 3 pyramid–pyramid connections and for connections between layer 5 pyramids are larger than for connections between layer 4 pyramids, with estimates for layer 6 corticocortical pyramid outputs lying between, this despite a similarly wide range of estimates for n. Estimates of q and n for the outputs of corticothalamic pyramids placed these connections in a distinct region of parameter space corresponding to lower values of n with intermediate values of q. (B) In cat, estimates of q were typically smaller for connections in layer 3 than elsewhere. In C and D, the numbers of connections plotted is small, but the data indicate that for connections from pyramids to interneurons, there may also be differences between layers.