The integrative properties of cortical neurons in vivo
One of our main research effort is presently to understand the electrophysiological properties and dendritic integration in neocortical pyramidal neurons in vivo. We have designed computational models based on three-dimensional reconstructions of cat neocortical pyramidal neurons. The output of the models was compared with the intracellular data obtained in these cells (in collaboration with Denis Paré, Rutgers University, USA). This approach was used to constrain the distribution and conductance of synaptic inputs in soma and dendrites of pyramidal neurons [2,3,5] (see  for experimental data).
This approach was used to investigate various aspects of the electrophysiology in vivo, such as estimating the distribution of synaptic conductance in cortical neurons during synchronized thalamic inputs , estimating the somatic vs. dendritic contributions of sodium currents in the genesis of action potentials in vivo , the role of inhibition in controlling back-propagating action potentials , estimating the release conditions at excitatory and inhibitory synapses during activated states of the cerebral cortex [5,12,13].
One of our most important result was to provide for the first time an estimation of the conductance due to synaptic bombardment in vivo by combining computational models with intracellular recordings of pyramidal neurons before and after microperfusion of TTX . The experiments were obtained by Denis Paré and the data was analyzed by our group. This study revealed that action-potential dependent synaptic bombardment is responsible for a massive decrease of input resistance [4,5], which can potentially have drastic consequences on the electrophysiological behavior of neocortical pyramidal cells in vivo, a conclusion also reached for thalamic neurons . In particular, we focused on analyzing periods of intense synaptic activity with electrophysiological properties similar to the wake state (Fig. 1A). Comparing intracellularly-recorded cells before and after TTX revealed that synaptic activity is responsible for a 5-fold decrease in input resistance .
Using models of reconstructed pyramidal neurons, we explored the consequences of synaptic bombardment on dendritic integration and cellular responsiveness [5,6]. The model was constrained by data collected with both K-acetate and K-Cl filled pipettes, and the measured membrane potential (Vm) provided estimates of the respective contributions of excitatory and inhibitory synapses. To reproduce all experimental results, the simulated synaptic activity had to be of relatively high frequency (1-5 Hz) at excitatory and inhibitory synapses. In addition, synaptic inputs had to be significantly correlated (correlation coefficient around 0.1) in order to reproduce the amplitude of Vm fluctuations recorded experimentally (see  for details).
The impact of this massive increase in synaptic conductance on dendritic integration and cellular responsiveness was investigated for passive neurons and neurons with voltage-dependent Na+/K+ currents in soma and dendrites [5,6]. In passive neurons, correlated synaptic bombardment greatly enhanced electrotonic attenuation. Similarly, in the presence of dendritic voltage-dependent currents, the convergence of hundreds of synaptic inputs was required to evoke action potentials reliably. In this case however, dendritic voltage-dependent currents minimized the variability due to input location, with distal apical synapses being as effective as synapses on basal dendrites. Synaptic background activity provided other useful properties: it enhanced the responsiveness of the pyramidal neuron (Fig. 1B), a property which has clear advantages at the network level . The neuron can also perform efficient detection of correlations within thousands of random input sources , and display several types of resonance phenomena, including stochastic resonance .
In collaboration with Michelle Rudolph (UNIC), the integrative properties of neocortical pyramidal neurons were studied under in vivo conditions simulated by computational models [9,12]. The presence of high-conductance fluctuations induces a stochastic state in which active dendrites are fast-conducting and have a different dynamics of initiation and forward-propagation of Na+-dependent dendritic spikes. Synaptic efficacy, quantified as the probability that a synaptic input specifically evokes a somatic spike, was roughly independent of the dendritic location of the synapse (Fig. 1C). Synaptic inputs evoked precisely timed responses (milliseconds), which also showed a reduced location dependence. These remarkable properties were found to apply for a broad range of kinetics and density distributions of voltage-dependent conductances, as well as for different dendritic morphologies. Synaptic efficacies were, however, modulable by the balance of excitation and inhibition in background activity, for all synapses at once. Thus, models predict that the intense synaptic activity in vivo can confer advantageous computational properties to neocortical neurons: they can be set to an integrative mode which is stochastic, fast-conducting, and optimized to process synaptic inputs at high temporal resolution independently of their position in the dendrites [9, 10, 12].
More recently, we generated simplified stochastic models of synaptic background activity . These models can be injected in living cells in vitro in order to recreate in vivo-like activity, as we demonstrated by using the dynamic-clamp technique. Injection of a stochastic point-conductance model in rat prefrontal cortex cells in vitro (by Jean-Marc Fellous in Terrence Sejnowski lab) 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. Thus, many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically.
It seems clear from these studies that the principal neurons from cerebral cortex, pyramidal neurons, are strongly affected by the synaptic background activity present in vivo. Not only their basic electrophysiological properties, but also their integrative mode seem to depend on background activity. A number of computational advantages can be delineated (reviewed in ref. ), such as enhanced responsiveness and sensitivity, larger coding range and sharper temporal resolution. Understanding the modes of operations of these neurons in states comparable to wakefulness is a task that will require a tight combination of experiments and computational models, both at the single-cell and network level
This subject was reviewed in two review articles [10,14] and a monograph with Michelle Rudolph . It was also recently reviewed by book chapters [16,17], including a chapter specifically focused on the impact of synaptic noise on dendrites .
A more recent application was to evaluate how such cellular properties may help to understand the response properties seen at the network level. We have shown previously that the presence of synaptic noise changes the response function of neurons [6, 10, 11], which can be seen as a modulation of the gain of the neurons. This type of modulation was used in a recent study to explain contradictory observations in the auditory system . We could show that the gain modulation conferred by synaptic noise can explain these sensory responses quantitatively. This constitutes evidence that these properties of modulation by noise can have impact at the network level.
This theme was further explored by modeling how network activity can control the burst responses of neurons in the somatosensory cortex in monkey . We found that the burst responses following stimulation of the median nerve are remarkably precise; these burst patterns and their precision can be reproduced by a simple model of spiking neuron if refractoriness can be taken into account. The exact pattern is also modulated by network activity. Thus, the study shows that touch information is coded as very precise spike patterns, and because refractoriness is present in all neurons, the same principles may be general and apply to other brain areas.
Finally, we started a study of the transfer function of cortical neurons, based on in vitro measurements  (see Dynamic Clamp section). We showed that there is a considerable heterogeneity in the responses of cortical neurons, and that part of this heterogeneity can be explained by different excitability properties. In a further modeling study , we investigated this paradigm using neuron models with dendritic inputs. We found that, like point neurons, the spiking response is determined by the level of excitatory and inhibitory inputs, the conductance, and their level of fluctuations. However, with dendrites there is a more complex interplay between proximal and distal inputs, and in some cases increasing the input level can suppress firing. This shows that cells differentially couple to network activity and that the speed of the fluctuations is an important determinant of neuron responses. This is a first step towards obtaining the transfer function of neurons with dendrites, and design realistic mean-field models.
 Destexhe, A., Contreras, D., Steriade, M., Sejnowski, T.J., and Huguenard, J.R. In vivo, in vitro and computational analysis of dendritic calcium currents in thalamic reticular neurons. J. Neuroscience 16: 169-185, 1996. (see abstract)
 Contreras, D., Destexhe, A. and Steriade, M. Intracellular and computational characterization of the intracortical inhibitory control of synchronized thalamic inputs in vivo. J. Neurophysiol. 78: 335-350, 1997. (see abstract)
 Paré, D., Lang, E.J. and Destexhe, A. Inhibitory control of somatic and dendritic sodium spikes in neocortical pyramidal neurons in vivo: an intracellular and computational study. Neuroscience 84: 377-402, 1998. (see abstract)
 Paré, D., Shink, E., Gaudreau, H., Destexhe, A. and Lang, E.J. Impact of spontaneous synaptic activity on the resting properties of cat neocortical neurons in vivo. J. Neurophysiol. 79: 1450-1460, 1998. (see abstract)
 Destexhe, A. and Paré, D. Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J. Neurophysiol., 81: 1531-1547, 1999. (see abstract)
 Hô, N. and Destexhe, A. Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons. J. Neurophysiol., 84: 1488-1496, 2000. (see abstract)
 Rudolph, M. and Destexhe, A. Correlation detection and resonance in neural systems with distributed noise sources. Physical Review Letters 86: 3662-3665, 2001 (see abstract)
 Rudolph, M. and Destexhe, A. Do neocortical pyramidal neurons display stochastic resonance? J. Computational Neuroscience 11: 19-42, 2001 (see abstract)
 Rudolph, M. and Destexhe, A. A fast conducting, stochastic integrative mode for neocortical neurons in vivo. Journal of Neuroscience 23: 2466-2476, 2003 (see abstract)
 Destexhe, A., Rudolph, M., and Paré, D. The high-conductance state of neocortical neurons in vivo. Nature Reviews Neuroscience 4: 739-751, 2003 (see abstract)
 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)
 Rudolph, M., Pelletier, J-G., Paré, D. and Destexhe, A. Characterization of synaptic conductances and integrative properties during electrically-induced EEG-activated states in neocortical neurons in vivo. Journal of Neurophysiology 94: 2805-2821, 2005 (see abstract)
 Rudolph, M., Pospischil, M., Timofeev, I. and Destexhe, A. Inhibition determines membrane potential dynamics and controls action potential generation in awake and sleeping cat cortex. Journal of Neuroscience 27: 5280-5290, 2007 (see abstract)
 Destexhe, A. High-Conductance State. Scholarpedia 2: 1341 (2007).
 Destexhe, A. and Rudolph, M. Neuronal Noise. Springer, New York, 2012.
 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)
 Destexhe, A. and Rudolph-Lilith, M. Noisy dendrites: models of dendritic integration in vivo. In: The Computing Dendrite, Edited by Cuntz H., Remme M, & Torben-Nielsen B, Springer, New York, pp. 173-190, 2014 (see abstract)
 Reig, R., Zerlaut, Y., Vergara, R., Destexhe, A. and Sanchez-Vives, M. Gain modulation of synaptic inputs by network state in auditory cortex in vivo. Journal of Neuroscience 35: 2689-2702, 2015 (see abstract)
 Telenczuk, B., Kempter, R., Curio, G. and Destexhe, A. Refractriness accounts for variable spike burst responses in somatosensory cortex. eNeuro 4: e0173-17, 2017 (see abstract)
 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)
 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)
Figure 1: Modulation of integrative properties of neocortical neurons by synaptic noise. A. Intracellular recording of a neuron from cat parietal cortex during EEG-activated states in vivo (recording from Denis Paré, Rutgers University, USA). The membrane potential (Vm) is characterized by the presence of large amounts of fluctuations (synaptic noise). B. Enhancement of responsiveness by synaptic noise. A computational model of cortical pyramidal cell in the presence of synaptic noise simulated by the random release at thousands of glutamatergic and GABAergic synapses distributed in soma and dendrites. Left: the response to excitatory synaptic inputs is probabilistic (red line; 40 trials shown). Right: response curve of the neuron in quiescent conditions (red), with synaptic noise (greed) and with an equivalent static conductance (blue). Synaptic noise modifies the gain of the neuron and enhances the responsiveness to low-amplitude inputs (*). C. Equalization of synaptic inputs. Excitatory synaptic inputs were simulated in dendrites at different path distances from the soma (scheme in left). The spiking response probability is indicated as a function of amplitude and path distance. Synaptic efficacy is weakly dependent on the position of the synapse in the dendritic tree (figure modified from Ho & Destexhe, J. Neurophysiol., 2000; Rudolph & Destexhe, J. Neurosci., 2003; Destexhe et al., Nat. Reviews Neurosci., 2003).
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