### The Dynamic-clamp: real-time interaction between models and living neurons

The dynamic-clamp consists of injecting computer-generated conductances in living neurons using an intracellular electrode. Because the quantity physically injected in the neuron is a current, which depends on the Vm, I = g * (V-Erev), and because the Vm is continuously changing due to the injected current, one needs to continously re-calculate the current to be injected as a function of the current value of the Vm. This requires to establish a real-time loop between the neuron and the computer which calculates the conductance. The conductance g can be calculated according to model equations, which can be complex, as long as the real-time condition is respected (i.e., the computer has to be fast enough).

We have used this technique in many experimental situations: first, it was used to recreate in vivo-like activity by injecting the conductances produced by a stochastic point-conductance model of synaptic activity. This artificial synaptic activity was injected in rat prefrontal cortex cells in vitro (by Jean-Marc Fellous in Terrence Sejnowski lab), to successfully recreate 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 [1]. Thus, this study showed that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically. The same technique was subsequently used by many other laboratories (see also Section 2.1).

In collaboration with Thierry Bal (UNIC), we have used this technique to investigate the responsiveness of thalamic relay neurons under in vivo-like conditions using dynamic-clamp experiments [2] (see also Section 2.2). These experiments (realized by Thierry Bal's team) demonstrated that synaptic noise has a tremendous influence on the "relay" function of thalamic neurons. Thalamic neurons are traditionally viewed as functioning in two distinct modes of firing, the "burst" mode (conferred by the presence of the T-type Ca2+current), and a "tonic" mode where only single spikes are produced, more compatible with the relay function of thalamic neurons. With synaptic noise, however, this duality disappears as bursts and single spikes are produced at all membrane potentials. Interestingly, the probability of generating spikes (combining bursts and single spikes) becomes almost independent of the Vm level in the presence of synaptic noise. The presence of the T-type Ca2+ current boosts the response at hyperpolarized levels. This remarkable property is also compatible with a relay function, but only of all spikes are combined. These results suggest that intrinsic neuronal properties influence responsiveness differently in the presence of synaptic noise, and that both intrinsic properties and noise must be taken into account to fully understand the responsiveness of central neurons in physiological conditions [2].

The dynamic-clamp technique can also be used to test methods to extract conductance or related variables. The "VmD" method to extract synaptic conductances [3], the "STA" method to extract spike-triggered averages of synaptic conductances [4], the "PSD" method to extract kinetic properties of synaptic conductances [5] were all tested in real neurons using the dynamic-clamp technique (in collaboration with Thierry Bal at the UNIC). The VmD method was recently extended to single Vm traces, an approach which was also tested using dynamic-clamp [6]. These approaches were reviewed in a recent article [7] and chapter [12] (see also Section 4.2).

Recently, in collaboration with Romain Brette (formerly postdoc in my group, now at Ecole Normale Sup\'erieure, Paris) and Thierry Bal (UNIC), we have developed a new method for performing high-resolution dynamic-clamp and voltage-clamp recordings [8]. This method takes advantage of the real-time feedback between a computer and the recorded neuron (the same setup as for dynamic-clamp experiments). This real-time feedback can be used to design a new type of recording paradigm, which we call Active Electrode Compensation'' (AEC), and which consists of a real-time computer-controlled compensation of the electrode artefacts, leading to high precision recordings. The method is particularly interesting for injecting conductance noise in dynamic-clamp, which can be performed with unprecedented accuracy using the AEC technique [8,11].

These dynamic-clamp experiments collectively illustrate the great power and the variety of paradigms in which the dynamic-clamp technique is used. The dynamic-clamp and related paradigms were the subject of a recent book edited by A. Destexhe and T. Bal [9]. These paradigms range from injecting artificial conductances in cardiac cells, neurons or dendrites, artificially connect different neurons, create "hybrid" networks of real and artificial cells, re-create in vivo conditions by providing a synthetic synaptic background activity, as well as use the dynamic-clamp to correct the recording according to a computational model of the electrode. These paradigms show that computational models directly interact with living neurons, which is perhaps one of the most spectacular progress that has happened in the interaction between theory and experiments in biology [9] (see [10-13] for reviews of the contributions of our lab).

Recent progress in the combination of models and dynamic-clamp experiments were obtained to model the response of neurons to conductance-based stimuli [14], as well as extracting full conductance traces from Vm recordings [15]. In the first study, the dynamic-clamp was used to simulate a spectrum of cortical inputs in cortical neurons; these data were then used to fit different models and determine which model best accounts for the response of cortical neurons [14]. In the second study, the dynamic-clamp was used to test a new oversampling method to estimate full conductance time courses from Vm recordings [15].

A recent paper [16] reviews results from different studies pointing to the fact that in cortex, spontaneous activity cannot be considered as "background noise'', but is of comparable -- or even higher -- amplitude than evoked sensory responses. In particular, the impact of network state on spiking activity is major in awake animals, suggesting that the ongoing activity is dominant. Dynamic-clamp experiments have been decisive to obtain such results [16, 17].

In a recent dynamic-clamp study in collaboration with Thierry Bal and Gilles Ouanounou [18], we measured the transfer function of Layer V cortical neurons in mice visual cortex by using perforated patch recordings. This study revealed that it is possible to obtain a compact description of the transfer function of individual pyramidal neurons, which is very useful for building mean-field models. The study also evidenced a strong cell to cell diversity of firing responses. Using a theoretical model, it was found that heterogeneous levels of biophysical properties such as sodium inactivation, sharpness of sodium activation and spike frequency adaptation account for the observed diversity of firing rate responses. Because the firing rate response will determine population rate dynamics during asynchronous neocortical activity, these results show that cortical populations are functionally strongly inhomogeneous.

This view was refined more recently by considering more realistic models with dendrites [19]. We could do this because the dynamic-clamp experiments [18] were conceived independent of a specific model: we characterized the cell response as a function of three parameters, the mean Vm, the level of Vm fluctuations and the effective membrane time constant (which depends on the conductance state of the cell). This allowed us to re-use the same data but in a paradigm where the inputs are in dendrites. We discovered a more complex relation between excitatory and inhibitory inputs, which effect may depend on their location in dendrites. This study opens the way to design mean-field models of neurons with dendrites (work in progress).

[1] Destexhe, A., Rudolph, M., Fellous, J-M. and Sejnowski, T.J. Fluctuating synaptic conductances recreate in-vivo-like activity in neocortical neurons. Neuroscience 107: 13-24, 2001 (see abstract)

[2] Wolfart, J., Debay, D., Le Masson, G., Destexhe, A. and Bal, T. Synaptic background activity controls spike transfer from thalamus to cortex. Nature Neuroscience 8: 1760-1767, 2005 (see abstract)

[3] Rudolph, M., Piwkowska, Z., Badoual, M., Bal., T. and Destexhe, A. A method to estimate synaptic conductances from membrane potential fluctuations. Journal of Neurophysiology 91: 2884-2896, 2004 (see abstract)

[4] Pospischil, M., Piwkowska, Z., Rudolph, M., Bal, T. and Destexhe, A. Calculating event-triggered average synaptic conductances from the membrane potential. Journal of Neurophysiology 97: 2544-2552, 2007 (see abstract)

[5] Destexhe, A. and Rudolph, M. Extracting information from the power spectrum of synaptic noise. Journal of Computational Neuroscience 17: 327-345, 2004 (see abstract)

[6] Pospischil, M., Piwkowska, Z., Bal, T. and Destexhe, A. Extracting synaptic conductances from single membrane potential traces. Neuroscience 158: 545-552, 2009 (see abstract)

[7] Piwkowska, Z., Pospischil, M., Brette, R., Sliwa, J., Rudolph-Lilith, M., Bal, T. and Destexhe, A. Characterizing synaptic conductance fluctuations in cortical neurons and their influence on spike generation. J. Neurosci. Methods 169: 302-322, 2008 (see abstract)

[8] Brette, R., Piwkowska, Z., Monier, C., Rudolph-Lilith, M., Fournier, J., Levy, M., Frégnac, Y., Bal, T. and Destexhe, A. High-resolution intracellular recordings using a real-time computational model of the electrode. Neuron 59: 379-391, 2008 (see abstract)

[9] Destexhe, A. and Bal, T. (Editors) Dynamic-Clamp: From Principles to Applications, Springer, New York, 2009.

[10] Piwkowska Z, Bal T and Destexhe A. An introduction to the dynamic-clamp electrophysiological technique and its applications. In: Dynamic-Clamp: From Principles to Applications, Edited by Destexhe A and Bal T, Springer, New York, pp.~1-30 , 2009.

[11] Brette R, Piwkowska Z, Monier C, Gomez Gonzalez JF, Fr\'egnac Y, Bal T and Destexhe A. Dynamic clamp with high resistance electrodes using active electrode compensation in vitro and in vivo. In: Dynamic-Clamp: From Principles to Applications, Springer, New York, pp. 347-382, 2009.

[12] Piwkowska Z, Pospischil M, Rudolph-Lilith M, Bal T and Destexhe A. Testing methods for synaptic conductance analysis using controlled conductance injection with dynamic clamp. In: Dynamic-Clamp: From Principles to Applications, Edited by Destexhe A and Bal T, Springer, New York, pp.~115-140, 2009.

[13] Sadoc G, Le Masson G, Foutry B, Le Franc Y, Piwkowska Z, Destexhe A and Bal T. Recreating {\it in vivo}--like activity and investigating the signal transfer capabilities of neurons: Dynamic-clamp applications using real-time NEURON. In: Dynamic-Clamp: From Principles to Applications, Edited by Destexhe A and Bal T, Springer, New York, pp.~287-320, 2009.

[14] Pospischil M, Piwkowska Z, Bal T and Destexhe A. Comparison of different neuron models to conductance-based post-stimulus time histograms obtained in cortical pyramidal cells using dynamic-clamp in vitro. Biological Cybernetics 105: 167-180, 2011 (see abstract)

[15] Bedard, C., Behuret, S., Deleuze, C., Bal, T. and Destexhe, A. Oversampling method to extract excitatory and inhibitory conductances from single-trial membrane potential recordings. J. Neurosci. Meth. 210: 3-14, 2012 (see abstract)

[16] Destexhe, A. Intracellular and computational evidence for a dominant role of internal network activity in cortical computations. Curr Opinion Neurobiol. 21: 717-725, 2011 (see abstract)

[17] Destexhe, A. 20 years of "noise" - Contributions of computational neuroscience to the exploration the effect of background activity on central neurons. In: 20 years of Computational Neuroscience, Edited by Bower J, Springer, New York, pp. 167-186, 2013 (see abstract)

[18] Zerlaut, Y., Telenczuk, B., Deleuze, C., Bal, T., Ouanounou, G. and Destexhe, A. Heterogeneous firing rate response of mice layer V pyramidal neurons in the fluctuation-driven regime. J. Physiol. 594: 3791-3808, 2016 (see abstract)

[19] Zerlaut, Y. and Destexhe, A. Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice Layer V pyramidal neurons. PLOS Comp. Biol. 13: e1005452, 2017 (see abstract)

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