Modeling a layer 4-to-layer 2/3 module of a single column in rat neocortex: interweaving in vitro and in vivo experimental observations

Abstract

We report a step in constructing an in silico model of a neocortical column, focusing on the synaptic connection between layer 4 (L4) spiny neurons and L2/3 pyramidal cells in rat barrel cortex. It is based first on a detailed morphological and functional characterization of synaptically connected pairs of L4-L2/3 neurons from in vitro recordings and second, on in vivo recordings of voltage responses of L2/3 pyramidal cells to current pulses and to whisker deflection. In vitro data and a detailed compartmental model of L2/3 pyramidal cells enabled us to extract their specific membrane resistivity ( approximately 16,000 ohms x cm(2)) and capacitance ( approximately 0.8 microF/cm(2)) and the spatial distribution of L4-L2/3 synaptic contacts. The average peak conductance per L4 synaptic contact is 0.26 nS for the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid and 0.2 nS for NMDA receptors. The in vivo voltage response for current steps was then used to calibrate the model for in vivo conditions in the Down state. Consequently, the effect of a single whisker deflection was modeled by converging, on average, 350 +/- 20 L4 axons onto the modeled L2/3 pyramidal cell. Based on values of synaptic conductance, the spatial distribution of L4 synapses on L2/3 dendrites, and the average in vivo spiking probability of L4 spiny neurons, the model predicts that the feed-forward L4-L2/3 connection on its own does not fire the L2/3 neuron. With a broader distribution in the number of L4 neurons or with slight synchrony among them, the L2/3 model does spike with low probability.

Fig. 1.

Three reconstructed pyramidal L2/3 pyramidal cells from the barrel cortex. The dendrites of the pyramidal cells are in gray and, in each case, the putative synaptic contacts established with specific presynaptic L4 spiny neurons are marked by blue dots. The input resistance (R_in) and membrane time constant (τ_m) are extracted from experimental transients measured in these cells. The membrane area of the dendritic tree (including spines) is also denoted. (Inset) Voltage trace after a 100-ms current step in the passive model of cell 111200A (green continuous line) superimposed on the averaged and normalized experiment voltage traces measured in this same cell (red dotted line).

Fig. 2.

Extracting synaptic parameters through fitting model to experiments. (A) An experimental average EPSP (n = 39) measured from the postsynaptic L2/3 neuron belonging to pair 111200A (gray line). The dark line is the model fit. (B) Isolated NMDAR-mediated voltage responses at different holding potentials (marked at left) recorded from another L2/3 pyramidal cell (gray lines). The model fits, which were based on morphology and locations of synaptic contacts for 111200A pair, are depicted by dark lines. (C) AMPAR and NMDAR components of the modeled EPSP in A. (D) AMPA- and NMDA-mediated currents under voltage–clamp (at −75 mV) in soma of modeled cell. (E) Space–clamp error in estimating synaptic current. Synaptic contacts were activated at their dendritic sites (blue points in Fig. 1), and voltage–clamp was applied at the soma (−75 mV). The measured synaptic current at the soma for the three cells modeled is shown in gray, and the case without space-clamp error is depicted by the corresponding black lines.

Fig. 3.

EPSP histogram of L4 spiny neurons population converging onto a single L2/3 pyramidal cell. (A) Distribution of 1,575 L4–L2/3 synaptic contacts (from 350 axons) on the dendrites of a L2/3 modeled cell (see Materials and Methods). Each dot may represent more than one synaptic contact. (B) The average amplitude of the resultant 400 EPSPs from each axon is displayed (black squares) superimposed on the average unitary EPSP measured experimentally (gray squares). (C) The average c.v. plotted as a function of the EPSP peak amplitude (model in black, experiments in gray).

Fig. 4.

Sub- and suprathreshold behavior for model compared with experiments. (A) Voltage recording from a L2/3 pyramidal cell recorded in vivo during 300-ms current steps, 100–500 pA (5) in gray compared with model response to the corresponding current step in black. (B) Steady-state V–I relationship shows anomalous rectification. Only Down state periods were analyzed (5) (gray dots). The black line is the second-order polynomial fit to the model I–V curve.

Fig. 5.

Distribution of compound PSP amplitudes after whisker deflection, experiments vs. model. (A) Top trace. Records of 20 responses of a barrel-related L2/3 pyramidal cell to principal whisker deflection (courtesy of M. Brecht). Responses from the Down state are black (middle trace): 20 responses of the model-to-whisker deflection (lower trace). In vivo PSTH of L4 neuron after whisker deflection (n = 25) was used as an input for model (see Materials and Methods). The vertical dashed line denotes time of whisker deflection. (B) Experiments. (C) Model distribution of PSP amplitude from the Down state after whisker deflection.

Fig. 6.

Predicted distribution of the L2/3 compound PSPs when using either the average PSTH or that of individual L4 cells. (A) In vivo PSTH of six L4 neurons after whisker deflection (green) and the average PSTH (blue) (see Materials and Methods). (B) Composite PSP amplitude distribution after whisker deflection predicted by the model based on either individual PSTH shown in A (green histogram, n = 1,000) or the average PSTH (corresponding blue histogram, n = 1,000). Spiking is evoked for PSPs larger than 30 mV (rightmost bar).