Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons

Abstract

To investigate the basis of the fluctuating activity present in neocortical neurons in vivo, we have combined computational models with whole-cell recordings using the dynamic-clamp technique. A simplified 'point-conductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic random-walk processes. An advantage of this approach is that all the model parameters can be determined from voltage-clamp experiments. We show that the point-conductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivo-like activity, we injected this point-conductance model into a single-compartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of high-amplitude membrane potential fluctuations, a low-input resistance and irregular spontaneous firing activity. In addition, the point-conductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically.

Fig. 1

Properties of neocortical neurons in the presence of background activity simulated using a detailed biophysical model. (Top) A layer VI pyramidal neuron reconstructed and incorporated in simulations. (A) Membrane potential in the presence of background activity (A1) and at rest (A2). Background activity was simulated by random release events described by weakly correlated Poisson processes of average releasing frequency of 1 Hz and 5 Hz for excitatory and inhibitory synapses, respectively (Destexhe and Paré, 1999). (B) Effect on input resistance. A hyperpolarizing pulse of −0.1 nA was injected at −65 mV in both cases (average of 100 pulses in B1). The presence of background activity (B1) was responsible for about five-fold decrease in input resistance compared to rest (B2). (C) Membrane potential distribution in the presence (C1) and in the absence (C2) of background activity.

Fig. 2

Statistical properties of the conductances underlying background activity in the detailed biophysical model. (A) Time course of the total excitatory (top) and inhibitory (bottom) conductances during synaptic background activity. (B) Distribution of values for each conductance, calculated from A. (C) Power spectral density of each conductance. The insets show the inverse of the power spectral density (1/S(f)) represented against squared frequency (f² ; same scale used).

Fig. 3

Fit of a point-conductance model of background synaptic activity. (A) Power spectral density of the conductances from the biophysical model (top = excitatory, bottom = inhibitory). The continuous lines show the best fits obtained with the stochastic point-conductance model. (B) Distribution of conductance values for the point-conductance model. (C) Time course of the excitatory and inhibitory conductances of the best stochastic model. The same data lengths as in Fig. 2 were used for all analyses.

Fig. 4

Membrane potential and input resistance of the point-conductance model. (A) Membrane potential in the presence (A1) and in the absence (A2) of synaptic background activity represented by two fluctuating conductances. The point-conductance model was inserted in a single compartment with only a leak current (same conductance density as the detailed model). (B) Effect on input resistance (same description and hyperpolarizing pulse as in Fig. 1B). (C) V_m distribution in the presence (C1) and in the absence (C2) of the fluctuating conductances.

Fig. 5

Comparison of point-conductance and detailed biophysical models. (A) Firing rate as a function of the strength of excitation and inhibition. The biophysical model was identical to Fig. 1, while the point-conductance model was inserted in a single-compartment containing the same voltage-dependent currents as the biophysical model. The strength of excitation/inhibition was changed in the detailed model by using different release frequencies for glutamatergic (ν_exc) and GABAergic (ν_inh) synapses, while it was changed in the point-conductance model by varying the average excitatory (g_e0) and inhibitory (g_i0) conductances. g_e0 and g_i0 were varied within the same range of values (relative to the optimal value), compared to ν_exc and ν_inh in the detailed model. (B) Enhanced responsiveness to glutamatergic (AMPA) inputs. Left panel (modified from Hô and Destexhe, 2000): an AMPA-mediated input was simulated in the detailed model, and the cumulated probability of spikes specifically evoked by this input was computed for 1000 trials. The curves show the probabilities obtained when this procedure was repeated for various values of AMPA conductance. Right panel: same paradigm in the point-conductance model. Four conditions are compared, with different values of standard deviation of the V_m (σ_V). In both models, there was a non-null response for subthreshold inputs in the presence of background activity.

Fig. 6

Point-conductance clamp of neurons from rat prefrontal cortex in vitro. (A) Intracellular recording of a prefrontal cortex layer V pyramidal cell in control condition (A2), and injected with the point-conductance model (A1; g_e0 = 0.014 μS, g_i0 = 0.05 μS, σ_e = 0.0058 μS, σ_i = 0.0145 μS, τ_e = 2.7 ms, τ_i = 10.7 ms). The current computed by the point-conductance model, and injected in real time, is depicted in A1, lower trace. The point-conductance clamp depolarized the cell by about 15 mV, and introduced membrane potential fluctuations. (B) Average response of a different cell to a 200-pA hyperpolarizing pulse in control (B2) and in point-conductance clamp (B1) conditions (10 trials; g_e0 = 0.02 μS, g_i0 = 0.1 μS, σ_e = 0.005 μS, σ_i = 0.012 μS, τ_e = 2.7 ms, τ_i = 10.7 ms). The input resistance was decreased by 4.3-fold. (C) Distribution of membrane potential before (C2) and after (C1) the activation of the point-conductance clamp (same cell as in A). The standard deviation of the membrane fluctuations (σ_V) was increased to about 4 mV.

Fig. 7

High variability of spontaneous discharges. The left panels show a 6-s trace of spontaneous activity to illustrate the variability of discharges; the right panels show the CV calculated for periods of >33 s of activity in different conditions and represented against the mean ISI. (A) Detailed biophysical model (same parameter settings as in Fig. 1). The different CV values on the left were obtained by varying excitatory and inhibitory release frequencies (range of 0.5–2.9 Hz and of 4.0–8.0 Hz, respectively). (B) Point-conductance model (identical parameters as in Fig. 5; g_e0 and g_i0 were varied within the range of 0.003–0.035 μS and 0.017–0.145 μS, respectively). (C) Point-conductance clamp in vitro (same parameters as in Fig. 6). The different symbols in the right panel indicate different cells; the different points correspond to variations of the parameters (g_e0 = 0.005–0.0375 μS; g_i0 = 0.025–0.05 μS; σ_e = 0.00025–0.009 μS; σ_i = 0.00025–0.033 μS). All three models gave high CV values.