Fig 1.
Single neuron recordings and model fitting.
(A) Example of the initial (upper curve) and steady-state (lower curve) input-output relation (f-I curve) of a single neuron. Black and gray curves show experimental data, red and blue curves indicate the simpAdEx model fits. (B) Voltage trace from a slice recording of a prefrontal cortical layer 5 pyramidal cell (black) and from the corresponding model cell (red) in response to the same fluctuating input current. The same neuron model and parameters as in Panel A were used [15]. (C) Examples of parameter distributions obtained from fitting model neurons to electrophysiologically recorded cells. Histograms (black) and derived parameter distributions used for network specification (red) illustrating parameters with an approximately Gaussian (gL, left), Gamma (τw, middle), and exponential distributional form (b, right).
Table 1.
Neuron parameters.
Fig 2.
Anatomical and synaptic properties.
(A) Laminar structure of a single network column. Arrow widths represent relative strength of connections (black: excitatory, gray: inhibitory), i.e. the product of connection probability and synaptic peak conductance. (B) Left panel: Distribution of three different short-term plasticity types over different combinations of pre- and postsynaptic neuron types. Arrows from or to one of the shaded blocks (rather than from or to a single neuron type) denote connection types that are identical for all excitatory (PC) or inhibitory (IN) neurons. Where all three types are drawn, they are randomly distributed over all synapses between these two neuron types according to the probabilities given in the figure. Right panel: Illustration of the postsynaptic potential in response to a series of presynaptic spikes for three types of short-term synaptic plasticity for excitatory (E1 to E3) and inhibitory synapses (I1 to I3).
Table 2.
Cell numbers.
Table 3.
Synaptic parameters.
Fig 3.
Spiking statistics of simulated PFC model networks.
(A) Comparison of relative frequency histograms for three different spike time statistics between recordings from an in vivo experiment (gray, see text for details) and from the simulation with input currents Iex = 250 pA, Iinh = 200 pA (black). The shaded region represents the mean ± the SEM at each point of the experimental distribution. (B) Raster plot of the spike times over the last six seconds of the simulation. The two layers (L2/3 and L5) are separated by a black line, pyramidal cells (PC) are in black, interneurons (IN) in gray. (C) Auto-correlation function of the inter-spike intervals of the experimental recordings (gray) and the network simulations (black).
Fig 4.
Comparison of simulated membrane and local field potentials with experiments.
(A) Estimated distribution of the standard deviation of the membrane potential from anaesthetized rats (gray) and simulated neurons (black) with non-zero firing rates. (B) Power spectrum of the local field potential obtained from experiments (gray) and simulations (black). The dotted lines illustrate the three power laws. The shaded region represents the mean ± the SEM at each point of the experimental distribution, as in Fig 3.
Fig 5.
Propagation of transient input.
(A) Raster plot of the spike times in the network in response to an external input (gray line) to 10% of the L2/3 pyramidal cells. The input currents are Iex = 250 pA, Iinh = 200 pA. (B) Same as Panel A, but with a stronger (higher rate) external stimulus (see text for details). (C) Same as Panel A, but with neuron parameter variability reduced by 80% (standard deviation set to 20% of its original value). (D) Number of spikes in response to the input as a function of neuron parameter variability. Each data point is the mean ± SEM over a number of repetitions.
Fig 6.
Dependence of network behavior on the magnitude of synaptic background inputs.
(A) Maximum of the Kolmogorov-Smirnov test statistic (DKS) comparing the experimental and respective simulated distributions for the mean ISI, CV, and cross-correlation as a function of input currents into excitatory (Iex) and inhibitory (Iinh) neurons in layer 2/3. DKS values within the blackly delineated area have p values larger than 0.05 for each of the three tests. The insets show the three individual DKS values as a function of one of these input currents alone (for Iinh = 200 pA in the left and Iex = 400 pA in the lower inset, indicated by the white dotted lines). DKS values above 0.4 (green lines) correspond to significant (p = 0.05) deviations from experiments in the given distribution. The red asterisk indicates the parameter set used for the simulations presented in the previous figures. (B) Fraction of neurons emitting at least 10 spikes during a 30 sec simulation period for the same currents used in Panel A. The blackly delineated area was copied from Panel A and superimposed on the current graph. (C) Ratio of the number of spiking pyramidal cells between layers 5 and 2/3 as a function of the input current ratio into pyramidal cells in layers 2/3 and 5. Each data point represents the mean ± SEM over three different ratios of input currents into interneurons in layers 2/3 and 5 and a number of and
values.
Fig 7.
Scaling of total synaptic input current with network size.
(A) Synaptic input current as a function of the number of columns. Shown are the averaged values over different neuron densities (mean ± SEM) as a function of column number for the inputs into L2/3 pyramidal cells (solid blue), L2/3 interneurons (solid red), L5 pyramidal cells (dotted blue) and L5 interneurons (dotted red). The region of currents which yield in vivo-like behavior (cf. black region in Fig 6A, DKS < 0.4) is marked in blue for Iex and in red for Iinh. (B) Same as in A, but synaptic input as a function of total cell density, averaged over column numbers ≥ 5. The dotted horizontal lines show the upper and lower bound of densities found in anatomical studies.
Fig 8.
Effect of synaptic parameter changes on network activity.
(A) Maximum of the Kolmorov-Smirnov test statistics (DKS) comparing the three experimental and simulated distributions (black) and standard deviation of the simulated membrane potential (gray) for different GABAA reversal potentials. Each data point is the mean ± SEM over several values of input currents. The black line denotes the DKS limit of 0.4 above which differences become significant (p ≤ 0.05), and the gray line marks the average of the experimentally observed standard deviations (cf. Fig 4A). (B) DKS values as a function of percent change in overall synaptic peak conductances between pyramidal cells (E) and interneurons (I). The dotted line denotes the critical DKS value of 0.4 (see above). (C) DKS values for different values of the standard deviation of the synaptic peak conductances using either the original log-normal distribution (gray curve) or a Gaussian distribution with the same mean and standard deviation (black curve). As above, the dotted line marks the critical DKS value of 0.4. In all figures, each data point shows the mean ± SEM over the DKS values for a number of different input currents.
Table 4.
Short-term synaptic plasticity.