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Commentary: Orientation tuning of input conductance, excitation, and inhibition in cat primary visual cortex

A number of papers reported data on estimation of excitatory and inhibitory synaptic conductances as input signals into principal neurons of the primary visual cortex (Anderson et al., 2000; Monier et al., 2003, 2008; Priebe and Ferster, 2005). Authors emphasize that they observed the counterphase of excitation and inhibition in simple cells and associate the observations with the push-pull mechanism (Troyer et al. 1998; Fregnac and Bathellier, 2015). However, the procedure of the estimation might occur incorrect and derived conclusions might be controversial, because of using too strong assumption that synaptic conductances are voltage-independent. The role of this assumption has been studied by Monier et al. (2008). It is wrong in presence of NMDA-receptor mediated component, which makes current significantly nonlinear due to magnesium block of the channels. In order to reduce this effect, the recordings are done in the voltage range where the NMDA voltage-current relationship is close to linear. Below we reconsider this issue and demonstrate in simulations how the estimation errors may lead to a doubtful conclusion that excitatory and inhibitory conductances are modulating in counterphase during visual stimulation by moving gratings.

Let’s consider leaky neuron equation model with the AMPA-, GABA- and NMDA-receptor mediated synaptic currents: \[\label{e1} C {dV \over dt}=-g_L(V -V_L)+g_{AMPA} (V_E-V )+g_{GABA} (V_I-V )+g_{NMDA} ~f_{NMDA}(V ,Mg) ~(V_E-V ) + I\] where \(C\) is the membrane capacity; \(g_L\) is the membrane time constant; \(V_L\), \(V_E\), \(V_I\) are the reversal potentials of the leak, excitatory and inhibitory currents, correspondingly; \(I\) is the current through electrode; \(f_{NMDA}=1/(1+Mg/3.57 ~\exp(-0.062~V))\) is the voltage dependence function of NMDA-conductance with the magnesium concentration \(Mg\).

The experimental method of conductance estimations was proposed for both voltage- (Borg-Graham et al., 1996) and current-clamp modes (Anderson et al., 2000). These versions give almost equivalent estimates if the input signals are slow enough in comparison with the membrane time constant (Monier et al., 2008). The synaptic currents are supposed to be linearly dependent on voltage, distinguishing excitatory (\(g_E\)) and inhibitory (\(g_I\)) conductances. Thus the equation of current conservation in the voltage-clamp mode is the following: \[\label{e2} -g_E (V-V_E)-g_I (V-V_I)-G_L (V-V_L)+I = 0\] Estimations of \(g_E(t)\) and \(g_I(t)\) require two recorded currents \(I_1(t)\) and \(I_2(t)\) at two voltage levels \(V_1\) and \(V_2\). The result is \[\nonumber g_I(t)=(-G_L(V_1-V_L)(V_2-V_E)+G_L(V_2-V_L)(V_1-V_E)-I_2(t)(V_1-V_E)+I_1(t)(V_2-V_E))\] \[/((V_1-V_I)(V_2-V_E) -(V_2-V_I)(V_1-V_E)),\] \[\nonumber g_E(t)=(-G_L(V_1-V_L)(V_2-V_I)+G_L(V_2-V_L)(V_1-V_I)-I_2(t)(V_1-V_I)+I_1(t)(V_2-V_I))\] \[/((V_1-V_E)(V_2-V_I) -(V_2-V_E)(V_1-V_I))\]

An example of a comparison of the true AMPA, GABA and NMDA conductances with the estimations is presented in Fig. 1. In simulations we considered sinusoidal \(g_{AMPA}\) and \(g_{NMDA}\), mimicking visual stimulation by moving gratings, and constant \(g_{GABA}\). The “measured” currents \(I_1(t)\) and \(I_2(t)\) were calculated from eq.(\ref{e1}) by setting \(V(t)=V_1\) and then \(V(t)=V_2\), correspondingly. As seen, the obtained \(g_E(t)\) is close to \(g_{AMPA}(t)\), whereas \(g_I(t)\) is very far from \(g_{GABA}(t)\). \(g_I(t)\) oscillates in counterphase with \(g_E(t)\), as in estimates made in vivo with sinusoidal gratings stimuli (Anderson et al., 2000; Priebe and Ferster, 2005; Monier et al., 2008), whereas the true inhibitory conductance was set to be constant. Monier et al. wrote that they clamped neurons only at membrane potential more hyperpolarized than -40 mV, in order to suppress the NMDA current, but the theoretical estimations show that the effect of NMDA is still strong in that case. Also, the total synaptic conductance \(g_E(t)+g_I(t)\) is underestimated. This contradiction points to the necessity to take NMDA-component into consideration.

Estimations of \(g_{AMPA}\), \(g_{GABA}\) and \(g_{NMDA}\) require measurements of currents at three voltage levels and solving linear algebraic equation composed of the steady-state eq.(1) applied at those three voltages. In our case of absent noise and parameters from Fig. 1, such estimations almost precisely reconstruct the conductances (data not shown). Similarly, in our recent study of interictal discharges (Amakhin et al., 2016) the estimations of \(g_{AMPA}\), \(g_{GABA}\) and \(g_{NMDA}\) were performed from multi-level recordings in VC-mode. Estimations of \(g_E\) and \(g_I\) with conventional method have shown not qualitatively but quantatively different results. Alternative to these multi-level estimations are the conventional two-level estimations of \(g_E(t)\) and \(g_I(t)\) with the hold voltages equal to \(V_I\) and \(V_E\), which give \(g_I(t)\) equal to \(g_{GABA}(t)\) and \(g_E(t)\) close to \(g_{AMPA}\), thus ignoring \(g_{NMDA}\) (simulations not shown).

The voltage-dependence of NMDA-conductance makes an effect of amplification which exposes as a negative conductance (Monier et al., 2008; Smirnova et al., 2015). The effect might also be necessary to take into account in the techniques of single-trial conductance estimation (Bedard et al., 2012; Chizhov et al., 2014).

Thus, we conclude that not accounting of NMDA-component in synaptic conductance estimation compromises evidences of excitation and inhibition counterphase modulation during grating visual stimulation in the striate cortex.

**Acknowledgments:** The reported study was supported by the RFBR research project 15-04-06234.

**Reference**

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