Dominique Debanne
email: dominique.debanne@inserm.fr

Michaël Russier

The contribution of ion channels in input-output plasticity

Keywords:

Persistent changes that occur in brain circuits are classically thought to be mediated by long-term modifications in synaptic efficacy. Yet, many studies have shown that voltage-gated ion channels located at the input and output side of the neurons are also the subject to persistent modifications. These channels are thus responsible for intrinsic plasticity that is expressed in many different neuronal types including glutamatergic principal neurons and GABAergic interneurons. As for synaptic plasticity, activation of synaptic glutamate receptors initiate persistent modification in neuronal excitability. We review here how synaptic input can be efficiently altered by activity-dependent modulation of ion channels that control EPSP amplification, spike threshold or resting membrane potential. We discuss the nature of the learning rules shared by intrinsic and synaptic plasticity, the mechanisms of ion channel regulation and the impact of intrinsic plasticity on induction of synaptic modifications.

2.

Introduction

Information storage in the brain is classically thought to result from long-lasting modifications of chemical synaptic transmission. Support to this has been provided by many studies showing up-or down-regulation of synaptic transmission following specific regimes of synaptic activity. For instance, long-term synaptic potentiation (LTP) occurs following high frequency stimulation of afferent glutamatergic inputs at many synaptic pathways including the Schaffer collateral-CA1 cell synapse [START_REF] Bliss | A synaptic model of memory: Long-term potentiation in the hippocampus[END_REF][START_REF] Malenka | Postsynaptic factors control the duration of synaptic enhancement in area CA1 of the hippocampus[END_REF], mossy-fibre-CA3 cell synapse [START_REF] Zalutsky | Comparison of two forms of long-term potentiation in single hippocampal neurons[END_REF], visual neocortical inputs [START_REF] Artola | Long-term potentiation and NMDA receptors in rat visual cortex[END_REF], and glutamatergic afferents to inhibitory interneurons [START_REF] Lamsa | Anti-Hebbian long-term potentiation in the hippocampal feedback inhibitory circuit[END_REF]. Long-term synaptic depression (LTD) is induced homosynaptically following low frequency stimulation of glutamatergic inputs. Evidence for homosynaptic LTD has been provided at the Schaffer collateral-CA1 cell synapse [START_REF] Dudek | Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade[END_REF][START_REF] Mulkey | Mechanisms underlying induction of homosynaptic long-term depression in area CA1 of the hippocampus[END_REF], inputs to visual cortical neurons [START_REF] Kirkwood | Common forms of synaptic plasticity in the hippocampus and neocortex in vitro[END_REF]. LTP and LTD have been shown to be induced associatively when a synaptic input is paired with postsynaptic spiking activity. LTP is induced at Schaffer collateral inputs when glutamatergic input is synchronously paired with burst of action potentials [START_REF] Gustafsson | Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials[END_REF][START_REF] Kelso | Hebbian synapses in hippocampus[END_REF][START_REF] Sastry | Associative induction of posttetanic and long-term potentiation in CA1 neurons of rat hippocampus[END_REF] whereas LTD results of asynchronous activation of these two stimuli [START_REF] Debanne | Asynchronous pre-and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro[END_REF][START_REF] Debanne | Cooperative interactions in the induction of long-term potentiation and depression of synaptic excitation between hippocampal CA3-CA1 cell pairs in vitro[END_REF]. These forms of associative synaptic plasticity led to the emergence of the spike-timing-dependent plasticity (STDP) rule [START_REF] Abbott | Synaptic plasticity: Taming the beast[END_REF][START_REF] Feldman | The spike-timing dependence of plasticity[END_REF] in which positive correlation between excitatory post-synaptic potentials (EPSPs) and single spikes led to LTP whereas their negative correlation led to LTD [START_REF] Bi | Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type[END_REF][START_REF] Debanne | Long-term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures[END_REF][START_REF] Feldman | Timing-based LTP and LTD at vertical inputs to layer II/III pyramidal cells in rat barrel cortex[END_REF][START_REF] Markram | Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs[END_REF].

All these synaptic modifications are specific to the synapse stimulated during the cellular conditioning [START_REF] Bliss | A synaptic model of memory: Long-term potentiation in the hippocampus[END_REF][START_REF] Debanne | Asynchronous pre-and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro[END_REF][START_REF] Malenka | Postsynaptic factors control the duration of synaptic enhancement in area CA1 of the hippocampus[END_REF] and may thus allow high capacity of information storage. However, synaptic plasticity appears to not constitute the sole manner to modify input-output function and voltage-gated channels located at the input and output sides of neurons are also subject to activity-dependent modification [START_REF] Debanne | Plasticity of intrinsic neuronal excitability[END_REF][START_REF] Titley | Toward a neurocentric view of learning[END_REF][START_REF] Zhang | The other side of the engram: Experience-driven changes in neuronal intrinsic excitability[END_REF]. Here, we review recent in vitro works devoted to the role of ion channels in the modulation of input-output function in mammalian neurons. First, we will consider the different ways of modulating input-output function at the neuronal scale. Then, we will review the learning rules of input-output plasticity on the basis of those defined for synaptic modifications. Finally, we will discuss intrinsic plasticity in GABAergic interneurons, the impact of ion channel regulation on induction of synaptic plasticity and intrinsic plasticity in vivo.

that is achieved by synaptic and intrinsic mechanisms. Whereas expression mechanisms of synaptic plasticity are well identified today and involve either presynaptic change in neurotransmitter release or postsynaptic change in glutamate receptor density or function (Fig. 1A), modulation of input-output function can be achieved through at least 3 different types of functional modulation: change in EPSP amplification (Fig. 1B), spike threshold modulation (Fig. 1C) and membrane potential adjustment (Fig. 1D) [START_REF] Debanne | Plasticity of intrinsic neuronal excitability[END_REF]. In addition, modulation of the balance between synaptic inhibition and excitation is responsible for apparent input-output plasticity that occurs following induction of LTP [START_REF] Lu | Calcineurin-mediated LTD of GABAergic inhibition underlies the increased excitability of CA1 neurons associated with LTP[END_REF][START_REF] Orr | Beta-Amyloid inhibits E-S potentiation through suppression of cannabinoid receptor 1-dependent synaptic disinhibition[END_REF] or LTD [START_REF] Kim | Association of mGluR-dependent LTD of excitatory synapses with endocannabinoid-dependent LTD of inhibitory synapses leads to EPSP to spike potentiation in CA1 pyramidal neurons[END_REF].

Control of EPSP amplification

Changes in EPSP amplification represent a powerful mean to alter input-output function in central neurons. Ion channels located in dendrites and in the cell body are activated by EPSPs [START_REF] Magee | Dendritic integration of excitatory synaptic input[END_REF][START_REF] Shah | Cortical HCN channels: Function, trafficking and plasticity[END_REF][START_REF] Spruston | Pyramidal neurons: Dendritic structure and synaptic integration[END_REF]. As a consequence, they shape EPSP waveform by either boosting or attenuating the synaptic response (Fig. 1B). A good example for this is provided by hyperpolarization-activated cyclic nucleotide-gated (HCN) cationic channels responsible for the h-current [START_REF] Magee | Dendritic lh normalizes temporal summation in hippocampal CA1 neurons[END_REF]. These channels are activated at resting membrane potential and attenuate EPSP amplitude through their deactivation. Thus, any modulation of h-channels may increase or decrease EPSP-spike coupling [START_REF] Gastrein | The role of hyperpolarization-activated cationic current in spiketime precision and intrinsic resonance in cortical neurons in vitro[END_REF]. The down-regulation of these channels have been shown to enhance EPSP summation [START_REF] Wang | Bidirectional changes in spatial dendritic integration accompanying long-term synaptic modifications[END_REF] and input-output function [START_REF] Campanac | Downregulation of dendritic I(h) in CA1 pyramidal neurons after LTP[END_REF] following LTP induction. Kv4.2 is another voltagegated ion channel located in the dendrites that attenuates both EPSP amplitude and back-propagating action potentials in distal dendrites [START_REF] Hoffman | K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons[END_REF]. The down-regulation of Kv4.2 channel activity results in enhancement of both EPSP amplitude and local back-propagation [START_REF] Frick | LTP is accompanied by an enhanced local excitability of pyramidal neuron dendrites[END_REF][START_REF] Kim | Regulation of dendritic excitability by activity-dependent trafficking of the A-type K+ channel subunit Kv4.2 in hippocampal neurons[END_REF]. As synaptic plasticity, the modulation of EPSP amplification is generally local as other inputs remain unchanged (Campanac & Debanne, 2008;[START_REF] Wang | Bidirectional changes in spatial dendritic integration accompanying long-term synaptic modifications[END_REF]. EPSPs are also shaped by small conductance calcium-activated K + (SK) channels. Calcium influx through NMDAR has been shown to activate SK channels located in the dendritic spines thus attenuating EPSP amplitude and duration [START_REF] Adelman | Small-conductance Ca 2+ -activated K+ channels: Form and function[END_REF][START_REF] Faber | SK channels regulate excitatory synaptic transmission and plasticity in the lateral amygdala[END_REF][START_REF] Ngo-Anh | SK channels and NMDA receptors form a Ca 2+ -mediated feedback loop in dendritic spines[END_REF]. Interestingly, SK channels are downregulated following stimulation of synaptic metabotropic glutamate receptor subtype 5 (mGluR5) resulting in enhancement of EPSPspike coupling [START_REF] Sourdet | Long-term enhancement of neuronal excitability and temporal fidelity mediated by metabotropic glutamate receptor subtype 5[END_REF]. Nevertheless, EPSP-spike coupling in cortical neurons is poorly determined by EPSP amplitude and highly dependent on the rate and the waveform of dendritic EPSPs [START_REF] Larkum | Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons[END_REF]. In cerebellar Purkinje cells, EPSP amplitude has also limited control over cell firing but pharmacological modulation of SK channel and SK-dependent plasticity strongly regulate spike firing [START_REF] Ohtsuki | Synaptic potential and plasticity of an SK2 channel gate regulate spike burst activity in cerebellar purkinje cells[END_REF].

Modulation of spike threshold

Input-output function may also be altered via modulation of ion channels that control the spike threshold (Fig. 1C). Voltage-gated Na + (Nav) and K + (Kv) channels determine the spike threshold [START_REF] Bean | The action potential in mammalian central neurons[END_REF]. Shift of Nav activation towards hyperpolarized values lowers the spike threshold and increases excitability following induction of longterm synaptic potentiation in CA1 pyramidal neurons [START_REF] Xu | Activity-dependent longterm potentiation of intrinsic excitability in hippocampal CA1 pyramidal neurons[END_REF]. Down-regulation of Kv1 channels following chronic activity-deprivation with pharmacological treatment in hippocampal neurons [START_REF] Cudmore | Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current[END_REF] or following cochlea removal in auditory neurons [START_REF] Kuba | Redistribution of Kv1 and Kv7 enhances neuronal excitability during structural axon initial segment plasticity[END_REF], lowers the spike threshold and increases intrinsic excitability. It should be noted that in contrast to change in EPSP amplification, spike-threshold modulation is global since it may affect all incoming inputs.

Modification of resting membrane potential

Change in resting membrane potential (RMP) represents the third manner to modulate input-output function by non-synaptic mechanisms (Fig. 1D). In hippocampal granule cells, high frequency firing induces long-term depolarization (LT-Depol) of their RMP by approximately 8-10 mV [START_REF] Mellor | Mediation of hippocampal mossy fiber long-term potentiation by presynaptic Ih channels[END_REF] that is mediated by a protein kinase A-dependent up-regulation of HCN channels. Whereas the upregulation of HCN channels leads to attenuated EPSP amplitude and therefore to a reduction in intrinsic excitability (see above), the net effect here is however an increased excitability. In fact, the large depolarization of RMP (8-10 mV) largely dominates the excitability reduction caused by the attenuation of excitatory synaptic inputs. Here again, this modulation is global as all inputs will be equally affected. 3. Learning rules for input-output plasticity

Hebbian changes in input-output function

Hebbian synaptic plasticity represents the better described forms of synaptic modifications. According to the Bienenstock Cooper & Munro rule [START_REF] Bienenstock | Theory for the development of neuron selectivity: Orientation specificity and binocular interaction in visual cortex[END_REF], it can be induced homosynaptically by modulation of synaptic frequency [START_REF] Bear | A synaptic basis for memory storage in the cerebral cortex[END_REF][START_REF] Cooper | The BCM theory of synapse modification at 30: Interaction of theory with experiment[END_REF]. Hebbian synaptic modification in the hippocampus and neocortex can also be induced by the degree of correlation between preand postsynaptic activity and is referred to as spike-timing dependent plasticity or STDP [START_REF] Feldman | The spike-timing dependence of plasticity[END_REF]. Both forms of Hebbian plasticity are associated with intrinsic plasticity that are synergistic to the induced synaptic changes [START_REF] Debanne | Plasticity of intrinsic neuronal excitability[END_REF].

In CA1 pyramidal neurons, long-term synaptic potentiation (LTP) is associated with an increased firing probability in response to the tetanized or paired input (Fig. 2A) whereas long-term synaptic depression (LTD) is associated with a decreased firing probability (Fig. 2B) in response to the stimulated input (Campanac & Debanne, 2008;[START_REF] Daoudal | Bidirectional plasticity of excitatory postsynaptic potential (EPSP)-spike coupling in CA1 hippocampal pyramidal neurons[END_REF]. Interestingly, the STDP rule defined for synaptic transmission also applies to EPSP-spike coupling (Fig. 2C). These modification in EPSP-spike coupling are supposed to result from changes in EPSP amplification. In fact, EPSP summation is altered in a synergistic manner with synaptic modifications induced by STDP protocols [START_REF] Wang | Bidirectional changes in spatial dendritic integration accompanying long-term synaptic modifications[END_REF]. Most Hebbian modifications in input-output function require NMDA-receptor activation for their induction and are input-specific, i.e. no modification occurs on control inputs. More recently, brief episodes of firing at 10 Hz in CA3 pyramidal neurons have been shown to enhance input resistance and integration of distal EPSP [START_REF] Hyun | Kv1.2 mediates heterosynaptic modulation of direct cortical synaptic inputs in CA3 pyramidal cells[END_REF]. Hebbian intrinsic plasticity is not specific to hippocampal neurons and long-lasting increase in intrinsic excitability (IE) has been reported in neocortical neurons following synaptic [START_REF] Desai | Early postnatal plasticity in neocortex of Fmr1 knockout mice[END_REF][START_REF] Sourdet | Long-term enhancement of neuronal excitability and temporal fidelity mediated by metabotropic glutamate receptor subtype 5[END_REF] or intrinsic [START_REF] Cudmore | Long-term potentiation of intrinsic excitability in LV visual cortical neurons[END_REF][START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF][START_REF] Paz | Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo[END_REF] activation paradigms. Hebbian intrinsic plasticity is also observed in cerebellar neurons. In deep cerebellar nuclei, granule and Purkinje neurons, IE was found to be enhanced in parallel of LTP induced by high frequency stimulation [START_REF] Aizenman | Rapid, synaptically driven increases in the intrinsic excitability of cerebellar deep nuclear neurons[END_REF][START_REF] Armano | Long-term potentiation of intrinsic excitability at the mossy fiber-granule cell synapse of rat cerebellum[END_REF][START_REF] Belmeguenai | Intrinsic plasticity complements long-term potentiation in parallel fiber input gain control in cerebellar Purkinje cells[END_REF]. In all these cases, induction of intrinsic plasticity requires NMDA-receptor activation. Expression mechanisms in cerebellar neurons involve regulation of SK channels [START_REF] Belmeguenai | Intrinsic plasticity complements long-term potentiation in parallel fiber input gain control in cerebellar Purkinje cells[END_REF][START_REF] Ohtsuki | SK2 channel modulation contributes to compartment-specific dendritic plasticity in cerebellar Purkinje cells[END_REF] and HCN channels [START_REF] Shim | Longterm depression of intrinsic excitability accompanied by synaptic depression in cerebellar Purkinje cells[END_REF].

Homeostatic plasticity of input-output function

Hebbian mechanisms are destabilizing as they tend to reinforce active circuits and depress inactive ones. Neural circuits can be stabilized when homeostatic regulation is introduced to adjust both synaptic strength and intrinsic excitability [START_REF] Turrigiano | Homeostatic plasticity in the developing nervous system[END_REF]. Homeostatic plasticity of IE has been originally reported in visual cortical neurons (Desai, Rutherford, & Turrigiano, 1999b) and is today observed in virtually all neuronal types. Chronic activity deprivation induced pharmacologically [START_REF] Cudmore | Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current[END_REF][START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF][START_REF] Karmarkar | Different forms of homeostatic plasticity are engaged with distinct temporal profiles[END_REF][START_REF] Shim | mGlu1 receptor mediates homeostatic control of intrinsic excitability through Ih in cerebellar Purkinje cells[END_REF] or by sensory deprivation [START_REF] Kuba | Redistribution of Kv1 and Kv7 enhances neuronal excitability during structural axon initial segment plasticity[END_REF][START_REF] Maffei | Multiple modes of network homeostasis in visual cortical layer 2/3[END_REF][START_REF] Milshtein-Parush | Sensory deprivation triggers synaptic and intrinsic plasticity in the hippocampus[END_REF] enhances IE. Reduced IE is observed following elevated network activity [START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF][START_REF] Karmarkar | Different forms of homeostatic plasticity are engaged with distinct temporal profiles[END_REF][START_REF] Kirchheim | Regulation of action potential delays via voltage-gated potassium Kv1.1 channels in dentate granule cells during hippocampal epilepsy[END_REF]. Thus, homeostatic plasticity rule is per se anti-Hebbian.

Two ion channels that dampen excitability have been particularly studied in homeostatic regulation of IE: (1) Kv1 channels located in axons of pyramidal neurons which determine spike threshold and intrinsic excitability [START_REF] Rama | The role of axonal Kv1 channels in CA3 pyramidal cell excitability[END_REF], and (2) HCN channels located in the dendrites that dampens all depolarizing events such as EPSPs [START_REF] Magee | Dendritic lh normalizes temporal summation in hippocampal CA1 neurons[END_REF]. Down-regulation of Kv1 channel activity has been identified as a major mechanism for the increased excitability observed in CA3 pyramidal neurons after chronic blockade of glutamate receptors [START_REF] Cudmore | Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current[END_REF] and in auditory neurons following cochlear removal [START_REF] Kuba | Redistribution of Kv1 and Kv7 enhances neuronal excitability during structural axon initial segment plasticity[END_REF]. Conversely, Kv1 channel activity is up-regulated in dentate granule cells following epileptiform activity [START_REF] Kirchheim | Regulation of action potential delays via voltage-gated potassium Kv1.1 channels in dentate granule cells during hippocampal epilepsy[END_REF], indicating that Kv1 channel activity can be bidirectionally adjusted to maintain constant circuit activity. In CA1 pyramidal neurons, h-current is homeostatically regulated following induction of extremely large synaptic modifications [START_REF] Brager | Plasticity of intrinsic excitability during long-term depression is mediated through mGluR-dependent changes in I(h) in hippocampal CA1 pyramidal neurons[END_REF][START_REF] Fan | Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I(h)[END_REF] or following bidirectional chronic manipulation of network activity [START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF].

Homeostatic plasticity is typically induced by persistent modulation of activity lasting few tens of hours [START_REF] Cudmore | Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current[END_REF]Desai et al., 1999b;[START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF][START_REF] Karmarkar | Different forms of homeostatic plasticity are engaged with distinct temporal profiles[END_REF]. However, homeostatic increase in excitability can also be induced by brief stimulation. For instance, in vestibular neurons [START_REF] Nelson | Long-lasting increases in intrinsic excitability triggered by inhibition[END_REF] and cerebellar Golgi cells [START_REF] Hull | Hyperpolarization induces a long-term increase in the spontaneous firing rate of cerebellar Golgi cells[END_REF], a transient hyperpolarization (20-300 sec) results in enhanced IE. In both cases, potentiation of IE requires the down-regulation of BK channel activity. One may notice that in contrast to cortical pyramidal cells that are mostly silent at rest, vestibular or cerebellar neurons correspond to pacemaker cells that fire continuously at frequency ranging between 5 and 10 Hz. Recently, it has been shown that unilateral loss of inner hear triggers rapid potentiation of excitability in vestibular neurons thus enabling adaptive compensatory increases in optokinetic reflex gain [START_REF] Nelson | BK channels are required for multisensory plasticity in the oculomotor system[END_REF].

How can Hebbian and homeostatic intrinsic plasticity be linked together?

Theoretical work suggests that Hebbian and homeostatic plasticity, despite their antagonistic rules, may work hand-in-hand [START_REF] Zenke | Hebbian plasticity requires compensatory processes on multiple timescales[END_REF]. The modulation of HCN channels following induction of synaptic modification provides a good example for such complex interaction. While large LTP (> +200%) is associated with decreased IE due to the up-regulation of HCN channel activity [START_REF] Fan | Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I(h)[END_REF] (Fig. 3A), small LTP (< +100%) is combined with increased IE resulting from down-regulation of HCN channel (Campanac & Debanne, 2008) (Fig. 3B andC). The opposite holds true for LTD. Large LTD (< -50%) results in a HCN-dependent increase in IE [START_REF] Brager | Plasticity of intrinsic excitability during long-term depression is mediated through mGluR-dependent changes in I(h) in hippocampal CA1 pyramidal neurons[END_REF] whereas small LTD (> -30%) results in a HCN-dependent decrease in IE [START_REF] Gasselin | Plasticity of intrinsic excitability during LTD is mediated by bidirectional changes in h-channel activity[END_REF] (Fig. 3D-F). Taken together, these results indicate that IE follows a single plasticity rule linking Hebbian and homeostatic plasticity (Fig. 3G). This multiple regulation of HCN channel implies distinct induction and expression pathways [START_REF] Brager | Plasticity of intrinsic excitability during long-term depression is mediated through mGluR-dependent changes in I(h) in hippocampal CA1 pyramidal neurons[END_REF][START_REF] Fan | Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I(h)[END_REF][START_REF] Gasselin | Plasticity of intrinsic excitability during LTD is mediated by bidirectional changes in h-channel activity[END_REF][START_REF] Santoro | TRIP8b splice variants form a family of auxiliary subunits that regulate gating and trafficking of HCN channels in the brain[END_REF].

Activity-dependent regulation of excitability in GABAergic interneurons

Principal neurons are not the only cell type to express intrinsic plasticity. GABAergic interneurons also display several forms of longterm regulation of IE. High-frequency stimulation of the glutamatergic inputs to dentate basket cells induces LT-Depol of their resting membrane potential that results from calcium-permeable AMPA receptordependent modulation of the Na + /K + ATPase pump [START_REF] Ross | Long-term plasticity in interneurons of the dentate gyrus[END_REF]. Inhibition levels in cortical circuits have been shown to be finely tuned through Kv1-dependent modulation of the spike threshold in basket cells. Neuregulin 1 receptor ErbB4 strongly regulates Kv1 channel activity and intrinsic excitability in parvalbumin positive basket cells (PV-BC) [START_REF] Li | Neuregulin 1 regulates excitability of fast-spiking neurons through Kv1.1 and acts in epilepsy[END_REF]. Synaptic stimulation of mGluR5 induces long-lasting potentiation of IE in PV-BCs that is mediated by the down-regulation of Kv1 channel activity [START_REF] Campanac | Enhanced intrinsic excitability in basket cells maintains excitatory-inhibitory balance in hippocampal circuits[END_REF]. Enhanced excitability in PV-BCs is due to hyperpolarized spike threshold and is thought to compensate enhanced synaptic and intrinsic excitation in pyramidal neurons. Interestingly, the reciprocal modulation of IE has been reported in somatosensory PV interneurons following activity-deprivation [START_REF] Gainey | Rapid disinhibition by adjustment of PV intrinsic excitability during whisker map plasticity in mouse S1[END_REF][START_REF] Sun | Experience-dependent intrinsic plasticity in interneurons of barrel cortex layer IV[END_REF]. Thus, this suggests that Kv1-dependent regulation of neuronal excitability is bidirectional in PV-BC. Most cortical PV interneurons express Er81, a transcription factor highly regulated by activity and involved in the activation pathway of Ca 2+ /calmodulin-dependent kinase I and in the control of levels of Kv1.1 channels in PV interneurons [START_REF] Dehorter | Tuning of fast-spiking interneuron properties by an activity-dependent transcriptional switch[END_REF]. Thus, Er81 level is high in weakly active circuits (corresponding to high levels of Kv1.1 channels) whereas it is low in highly active circuits (corresponding to low levels of Kv1.1 channels). Reduced input resistance has also been reported in fast-spiking interneurons from the dentate gyrus following synaptic stimulations of the mossy-fibers [START_REF] Dasgupta | Calcium permeable AMPA receptor-dependent long lasting plasticity of intrinsic excitability in fast spiking interneurons of the dentate gyrus decreases inhibition in the granule cell layer[END_REF]. This modulation is mediated by HCN channels and depends on activation of calcium-permeable AMPA receptor. Computer simulations indicate that intrinsic plasticity in interneurons robustly modulates both the coherence and frequency of network activity [START_REF] Dasgupta | Heterogeneous network dynamics in an excitatoryinhibitory network model by distinct intrinsic mechanisms in the fast spiking interneurons[END_REF].

Consequences of input-output intrinsic plasticity on induction of synaptic plasticity

Regulation of dendritic conductance may alter induction of synaptic plasticity. For instance, the homeostatic regulation of h-channels not only modulates EPSP summation [START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF][START_REF] Shah | Seizure-induced plasticity of h channels in entorhinal cortical layer III pyramidal neurons[END_REF] but also stabilizes synaptic plasticity rules [START_REF] Gasselin | Homeostatic regulation of h-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons[END_REF][START_REF] Mishra | High-conductance states and A-type K+ channels are potential regulators of the conductance-current balance triggered by HCN channels[END_REF]. Furthermore, the down-regulation of SK channel activity as shown to occur following synaptic activation of mGluR5 [START_REF] Sourdet | Long-term enhancement of neuronal excitability and temporal fidelity mediated by metabotropic glutamate receptor subtype 5[END_REF] facilitates LTP induction at cortical [START_REF] Faber | SK channels regulate excitatory synaptic transmission and plasticity in the lateral amygdala[END_REF][START_REF] Jones | Dendritic small conductance calcium-activated potassium channels activated by action potentials suppress EPSPs and gate spike-timing dependent synaptic plasticity[END_REF] and hippocampal [START_REF] Tigaret | Convergent metabotropic signaling pathways inhibit SK channels to promote synaptic plasticity in the hippocampus[END_REF] synapses. Finally, the down-regulation of Kv4 channel activity observed following induction of LTP facilitates locally the back-propagation of the action potential [START_REF] Frick | LTP is accompanied by an enhanced local excitability of pyramidal neuron dendrites[END_REF] and may help to induce LTP associatively at neighboring synapses [START_REF] Chen | Deletion of Kv4.2 gene eliminates dendritic A-type K+ current and enhances induction of long-term potentiation in hippocampal CA1 pyramidal neurons[END_REF].

Molecular mechanisms of input-output plasticity

Expression mechanisms of synaptic plasticity have been extensively studied over the last 30 years and revealed several key features. First, glutamate receptors present at the synapse are phosphorylated by many protein kinases such as CaMKII [START_REF] Herring | Long-term potentiation: from CaMKII to AMPA receptor trafficking[END_REF][START_REF] Lisman | Mechanisms of CaMKII action in longterm potentiation[END_REF] or PKC [START_REF] Sacktor | The genetics of PKMzeta and memory maintenance[END_REF]. Other kinases such as PKA and mTOR are involved respectively in presynaptic LTP [START_REF] Huang | A genetic test of the effects of mutations in PKA on mossy fiber LTP and its relation to spatial and contextual learning[END_REF] and in induction of BDNF-dependent LTP [START_REF] Tang | A rapamycin-sensitive signaling pathway contributes to long-term synaptic plasticity in the hippocampus[END_REF]. Glutamate receptors show a gain in their function when they are phosphorylated (i.e. they generate a larger current upon activation by glutamate). Two protein phosphatases, PP1 or PP2 (calcineurin), occupy a critical position in the induction of synaptic LTD [START_REF] Lisman | A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory[END_REF][START_REF] Winder | Roles of serine/threonine phosphatases in hippocampal synaptic plasticity[END_REF]. Second, synaptic receptors are mobile within the dendritic spine [START_REF] Herring | Long-term potentiation: from CaMKII to AMPA receptor trafficking[END_REF] and insertion of AMPA receptors have been shown to represent a major way to enhance synaptic efficacy [START_REF] Penn | Hippocampal LTP and contextual learning require surface diffusion of AMPA receptors[END_REF].

Many of the key molecular actors identified in synaptic plasticity are also found in intrinsic plasticity. For instance, the phosphorylation of Kv4.2 by PKA and PKC not only reduces the current by shifting activation curve of the A-current [START_REF] Hoffman | Downregulation of transient K+ channels in dendrites of hippocampal CA1 pyramidal neurons by activation of PKA and PKC[END_REF] but it also facilitates internalization of Kv4.2 [START_REF] Kim | Regulation of dendritic excitability by activity-dependent trafficking of the A-type K+ channel subunit Kv4.2 in hippocampal neurons[END_REF], both leading to a loss of function of these channels. CaMKII phosphorylation is required for the homeostatic modulation of HCN channels following LTP induction [START_REF] Fan | Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I(h)[END_REF]. BDNF determines homeostatic plasticity of intrinsic excitability (Desai, Rutherford, & Turrigiano, 1999a). Regulation of Kv1 channels has been shown to depend on mTOR [START_REF] Campanac | Enhanced intrinsic excitability in basket cells maintains excitatory-inhibitory balance in hippocampal circuits[END_REF][START_REF] Raab-Graham | Activity-and mTORdependent suppression of Kv1.1 channel mRNA translation in dendrites[END_REF]. Calcineurin is involved in both the homeostatic dispersion of Kv2.1 [START_REF] Misonou | Regulation of ion channel localization and phosphorylation by neuronal activity[END_REF] following chronic excitation and the relocation of the axon initial segment [START_REF] Evans | Calcineurin signaling mediates activity-dependent relocation of the axon initial segment[END_REF].

Input-output intrinsic plasticity in vivo

Most of the recent advances in understanding induction and expression mechanisms of intrinsic plasticity come from in vitro studies. A large bundle of papers has been devoted to the search for changes in cellular excitability correlated with learning and memory in the mammalian brain. Learning-driven changes in neuronal excitability have been reported following classical conditioning, fear conditioning or spatial exploration in hippocampal, cerebellar and cortical neurons. Active neurons during conditioning display in vitro excitability in conditioned animals that is significantly higher than in naïve or pseudoconditioned animals [START_REF] Disterhoft | Conditioning-specific membrane changes of rabbit hippocampal neurons measured in vitro[END_REF][START_REF] Oh | Watermaze learning enhances excitability of CA1 pyramidal neurons[END_REF][START_REF] Santini | Fear conditioning and extinction differentially modify the intrinsic excitability of infralimbic neurons[END_REF][START_REF] Schreurs | Dendritic excitability microzones and occluded long-term depression after classical conditioning of the rabbit's nictitating membrane response[END_REF]. Because of population analysis used in most of these studies, changes in excitability of physiologically characterized neurons in vivo remain uncertain.

The gap has been filled more recently with studies of intrinsic excitability in single cortical neurons before and after cellular conditioning [START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF][START_REF] Paz | Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo[END_REF]. Increased or decreased excitability has been observed in rat motor cortical neurons following repeated bursting at 30 Hz [START_REF] Paz | Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo[END_REF] or at 10 Hz [START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF]. These regulation in excitability involved either shift in input-output curves, or modulation of spike-threshold by ~2 mV [START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF]. Interestingly, the polarity of the intrinsic change was related to the neuron firing rate in control conditions [START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF], suggesting that intrinsic changes rather act as a homeostatic mechanism.

Conclusion and perspective

Synaptic plasticity has been extensively studied over the last 30 years but it appears to represent only a portion of functional plasticity. Striking progress has been made these recent years in understanding learning rules and in identifying expression mechanisms of intrinsic plasticity. Intrinsic plasticity is bidirectional, induced in parallel to synaptic plasticity and has been shown to be expressed at nearly all cellular types. Many different ion channels involved in intrinsic plasticity have been identified. But many questions are still pending. For example, most if not all studies reported in this review comes from in vitro works. Only a handful of in vivo studies devoted to intrinsic plasticity has been reported with physiologically realistic induction protocols [START_REF] Mahon | Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo[END_REF][START_REF] Paz | Multiple forms of activity-dependent intrinsic plasticity in layer V cortical neurones in vivo[END_REF]. Further studies must be performed to monitor IE in cortical or cerebellar neurons during the acquisition of a simple behavioral task. To reach this aim, new methods and experimental tools will have to be developed. Synaptic and intrinsic changes occur often in parallel. Dissection of the respective contribution of synaptic and intrinsic plasticity in the modulation of synaptic circuits is another challenge for the next years that will require development of new strategies. What are the mechanisms behind the tight link between synaptic and intrinsic changes? New imaging methods will have to be developed to simultaneously follow the trafficking of synaptic receptors and ion channels following induction of plasticity. The future will probably help to answer all these questions.

Fig. 1 .

 1 Fig. 1. Multiple mechanisms of input-output plasticity. (A) Synaptic contribution to input-output modulation. Potentiation of synaptic transmission through an increase in transmitter release and/or postsynaptic receptor density is characterized by an enhanced excitatory post-synaptic current (EPSC). At the axon initial segment (AIS), the excitatory post-synaptic potential (EPSP) becomes large enough to cross the action potential (AP) threshold. As synaptic strength is regulated, EPSP slope is enhanced. (B) Change in EPSP amplification. When dendritic HCN or Kv4 channels (green) are regulated, the resulting EPSP is amplified and crosses the spike threshold. Note that here the synaptic current (EPSC) is kept constant to clearly distinguish intrinsic from synaptic changes and the initial EPSP slope remains unchanged. These first two modifications (A & B) are local because they do not affect all synaptic inputs. (C) Change in spike threshold. Spike firing increases as a result of hyperpolarization of AP threshold by the regulation of voltage-gated ion channels (Nav or Kv1) located at the AIS. Here again, the excitatory synaptic current (EPSC) remains unchanged. (D) Depolarization of resting membrane potential. Following modulation of voltage-gated channels (HCN) or ion pumps (Na/K ATPase), the resting membrane potential of the neuron is depolarized. Thus, an action potential is now trigged by the EPSP. The synaptic current (EPSC) remains unchanged. These last two modifications (C & D) are global because they may affect all synaptic inputs. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .Fig. 3 .

 23 Fig.2. Input-output plasticity after STDP induction. A. Induction of LTP by positive pairing (PP, see inset). Left, time-course of the EPSP slope measured on individual responses in a single experiment (delay: +12 ms). Right, facilitation of input-output function in the same cell (EPSP-spike (or E-S) potentiation). Plot of the firing probability as a function of EPSP slope before (black) and after LTP induction (red). B. Induction of LTD by negative pairing (NP) with a delay of -6 ms. Left, timecourse of LTD. Right, depression of the input-output function (EPSP-spike (or E-S) depression). Plot of the firing probability as a function of EPSP slope before (black) and after LTD induction (green). C. STDP rules for synaptic transmission (left) and for EPSP-spike plasticity (right). Adapted fromCampanac and Debanne (2008). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Acknowledgments

Supported by INSERM, CNRS, AMU and FRM (DVS20131228768 & DEQ2018083983). We are indebted to Emilie Campanac, Celia Gasselin & Yanis Inglebert for their contribution in the original work on which is based this review paper.


Wenjuan Wei
email: wenjuan.wei@cstb.fr

Olivier Ramalho

Mickaël Derbez

Jacques Ribéron

Séverine Kirchner

Corinne Mandin

Applicability and relevance of six indoor air quality indexes

Keywords: IAQ index, volatile organic compounds, particulate matter, housing, building certification

The evaluation of indoor air quality (IAQ) in buildings is complex because IAQ involves a broad spectrum of substances and agents that vary over time and space. To address this complexity, IAQ indexes are used to describe, classify and improve IAQ by providing easy-to-understand and comprehensive rankings of IAQ levels in buildings. Although many IAQ indexes have been proposed all over the world, their relevancy regarding the evaluation of IAQ levels has not been fully studied in a large number of dwellings. In this study, six measurement-based IAQ indexes proposed for use in the USA, France, Taiwan, and Hong Kong were evaluated. The calculation of IAQ levels was based on nine indoor parameters measured in 567 French dwellings, i.e., indoor air temperature, relative humidity, and concentrations of formaldehyde, total volatile organic compounds, radon, carbon monoxide, carbon dioxide, PM2.5, and PM10. A factorial analysis using the multiple correspondence analysis and the hierarchical cluster analysis methods was performed to determine whether the calculated IAQ levels of different indexes in the studied dwellings were repeatable across all indexes. The results showed that three of the indexes tended to provide only positive IAQ ratings, while the other three indexes were more discriminating.

Three classes of IAQ levels in dwellings, along with indoor parameters associated with each class, were identified. All of the indoor parameters were associated with the classification of IAQ 2 levels, while the formaldehyde concentration and relative humidity were the key parameters to identify the dwellings with the best IAQ.

Introduction

Indoor air quality (IAQ) in buildings is associated with occupants' health and comfort [START_REF] Hulin | Indoor air pollution and childhood asthma: variations between urban and rural areas[END_REF][START_REF] Wolkoff | Indoor air pollutants in office environments: assessment of comfort, health, and performance, International[END_REF][START_REF] Haverinen-Shaughnessy | An assessment of indoor environmental quality in schools and its association with health and performance[END_REF]. IAQ can be affected by many parameters, such as the emission of indoor pollutants, the intrusion of outdoor pollutants, chemical reactivity, sorption and desorption phenomena, air change rate, indoor temperature and relative humidity. To facilitate the understanding of IAQ issues by nonprofessionals and to promote the improvement of IAQ, indexes have been created worldwide over the past decades. These indexes have often been incorporated into indoor environment quality (IEQ) evaluations. Within IEQ indexes, IAQ, thermal comfort, acoustic comfort and visual comfort are the primary areas considered in the proposed frameworks [START_REF] Wong | A multivariate-logistic model for acceptance of indoor environmental quality (IEQ) in offices[END_REF][START_REF] Bluyssen | Towards new methods and ways to create healthy and comfortable buildings[END_REF][START_REF] Catalina | IEQ assessment on schools in the design stage[END_REF][START_REF] Jin | Towards productivity indicators for performancebased façade design in commercial buildings[END_REF][START_REF] Kim | Nonlinear relationships between individual IEQ factors and overall workspace satisfaction[END_REF][START_REF] Heinzerling | Indoor environmental quality assessment models: a literature review and a proposed weighting and classification scheme[END_REF][START_REF] Fassio | Linear, non-linear and alternative algorithms in the correlation of IEQ factors with global comfort: a case study[END_REF]. In Green Building certifications, IAQ is also evaluated as a part of the life-cycle assessment of the building's sustainability [START_REF] Wei | Indoor air quality requirements in green building certifications[END_REF].

Many indexes are available for the evaluation of IAQ in buildings. Two different approaches are commonly employed to construct IAQ indexes: questionnaires and indoor measurements.

Existing IAQ indexes are frequently based on a single approach. IAQ indexes based on questionnaires include questions related to perceived IAQ and/or the indoor comfort of occupants, e.g., the ABCD Tool proposed in the Netherlands [START_REF] Van Dijken | The ABCD Tool for Schools, Proceedings of Healthy Buildings 2009[END_REF] or checklists describing building facilities, including ventilation performances, e.g., Indoor airPLUS proposed by the USA Environmental Protection Agency (EPA) [13]. Approaches and questions vary because the objective differs among indexes.

More frequently, IAQ indexes are measurement-based, such as the BILGA index proposed in France and reviewed by Kirchner et al. [START_REF] Kirchner | Elaboration d'indices de la qualite de l'air interieur: phase 1: inventaire des indices disponibles[END_REF] and the IAQ Certification proposed in Hong Kong [START_REF]A guide on indoor air quality certification scheme for offices and public places[END_REF]. Common indoor parameters include indoor temperature, relative humidity, airborne pollutants in the gas phase, and particles, measured on a given time-scale. The score of an IAQ index can be calculated using complex equations, such as the Indoor Environmental Index (IEI) proposed in the USA [START_REF] Moschandreas | The indoor air pollution index[END_REF][START_REF] Sofuoglu | The link between symptoms of office building occupants and in-office air pollution: the indoor air pollution index[END_REF][START_REF] Moschandreas | The indoor environmental index and its relationship with symptoms of office building occupants[END_REF]. Alternatively, the score of an IAQ index can be obtained by comparing the measured values in a given time interval to the thresholds associated with the same exposure duration proposed, e.g., by the World Health Organization, or in national regulations, such as for the Indoor Environment Index (IEITW) proposed in Taiwan [START_REF] Chiang | A study on the comprehensive indicator of indoor environment assessment for occupants' health in Taiwan[END_REF].

Existing IAQ indexes have not been applied to a large number of buildings. The objective of this study was thus to apply the existing IAQ index frameworks to a dataset of measurements obtained from a representative sample of 567 dwellings across France, to address the extent to which the indexes are respectively able to classify the buildings, i.e., to discriminate the IAQ levels, and to analyze the repeatability of the calculated IAQ levels across all indexes in those dwellings.

Materials and methods

Existing IAQ indexes

Existing IAQ indexes were retrieved from peer-reviewed papers using the Web of Science and Google Scholar sites as well as a review of worldwide IAQ indexes performed in 2006 by Kirchner et al. [START_REF] Kirchner | Elaboration d'indices de la qualite de l'air interieur: phase 1: inventaire des indices disponibles[END_REF]. Due to the difficulty of matching questions between the index schemes and the available dataset, IAQ indexes based on questionnaires were not used in this study. Thus, only measurement-based IAQ indexes were tested and compared. Six IAQ indexes were studied: the Indoor Environmental Index (IEI) [START_REF] Moschandreas | The indoor air pollution index[END_REF][START_REF] Sofuoglu | The link between symptoms of office building occupants and in-office air pollution: the indoor air pollution index[END_REF][START_REF] Moschandreas | The indoor environmental index and its relationship with symptoms of office building occupants[END_REF] proposed in the USA, the indexes proposed in France by the Laboratory of Hygiene of Paris (LHVP), CLIM 2000, and BILGA reviewed by Kirchner et al. [START_REF] Kirchner | Elaboration d'indices de la qualite de l'air interieur: phase 1: inventaire des indices disponibles[END_REF], the Indoor Environment Index (IEITW) proposed by two universities in Taiwan [START_REF] Chiang | A study on the comprehensive indicator of indoor environment assessment for occupants' health in Taiwan[END_REF], and the Indoor Air Quality Certification (IAQC) proposed by the Indoor Air Quality Management Group in the government of Hong Kong [START_REF]A guide on indoor air quality certification scheme for offices and public places[END_REF]. It was unknown whether the IAQ indexes originally developed for offices and public places, i.e., IEI and IAQC indexes, could be applied in dwellings. Nevertheless, their methods were interesting to be tested in the frame of this study and the target parameters are consistent with the ones that are relevant when studying IAQ in dwellings. Therefore, these indexes were also included in the present study.

Table 1 presents the parameters included in the six IAQ indexes. The number of indoor parameters ranges from 3 to 12. Measurements of indoor carbon monoxide (CO) and carbon dioxide (CO2) concentrations are included in all the indexes. Measurements of indoor formaldehyde (HCHO) concentrations are integrated into four indexes followed by measurements of total VOC (TVOC), bacteria, nitrogen dioxide (NO2), and PM10 concentrations, which are included in three indexes. None of the indexes includes specific VOCs or semi-volatile organic compounds. The sampling period in the CLIM 2000 index is 1 h for CO and nitrogen dioxide (NO2) and varies between 1 h and 24 h for formaldehyde. The sampling period in the BILGA index varies between 8 h and 24 h for CO2, 15 min and 24 h for CO, 1 h and approximately 2 weeks for NO2 and SO2. The sampling period in the IAQC index consists of an 8-h continuous sampling or 4 time-discontinuous samplings with a 30 min sampling period each time. The sampling strategy for the other indexes is not specified in the respective references. Scores for IAQ indexes were obtained following two approaches, i.e., the IEI, LHVP, CLIM 2000, and BILGA indexes calculated scores using complex equations, while the IEITW and IAQC indexes obtained scores by comparing the values of parameters with proposed thresholds (Table 2). The calculation method for each IAQ index is reported in Table 3. For the IEI index, all the parameters in each category have the same weight while all the categories have the same weight calculating the final score. For the other indexes, all the parameters have the same weight.

After the calculation was performed, each indoor environment was classified into an IAQ level based on the score of the IAQ index, as described in Table 4.

IAQ index Method and baseline equations

where 𝐸 𝑚𝑜𝑦 𝑃 is the average concentration of pollutant P; 𝑉𝑅𝐼 𝑇 𝑃 and 𝑉𝑅𝐿 𝑇 𝑃 are the limit and important risk values of pollutant P defined by the index, respectively [START_REF] Kirchner | Elaboration d'indices de la qualite de l'air interieur: phase 1: inventaire des indices disponibles[END_REF].

IEITW

Scores are associated with thresholds of indoor parameters [START_REF] Chiang | A study on the comprehensive indicator of indoor environment assessment for occupants' health in Taiwan[END_REF].

IAQC IAQ levels are associated with thresholds of indoor parameters [START_REF]A guide on indoor air quality certification scheme for offices and public places[END_REF]. (mechanical or passive stack) while 30% of the dwellings were naturally ventilated [START_REF] Langer | Indoor environmental quality in French dwellings and building characteristics[END_REF]. The night-time air exchange rate varied between 0.05 h -1 and 9.4 h -1 among dwellings [START_REF] Langer | Indoor environmental quality in French dwellings and building characteristics[END_REF]. The measurements were performed for one week (7 days) in each dwelling, except for radon measurements, which were obtained over 2 months. Indoor temperature, relative humidity, and CO2 were measured continuously in the main bedroom of each dwelling. The concentrations of aldehydes and volatile organic compounds (VOCs) were measured through passive samplers in the main bedroom. PM2.5 and PM10 were sampled in the living room in the evening and over the weekend. Radon concentrations were measured with passive dosimeters over two months in the living room and in the main bedroom. Finally, the CO concentration was measured continuously in each room where a combustion device was present. For temperature, relative humidity, CO, and CO2, the weekly arithmetic means of the continuous measurements were calculated. Detailed information regarding the measurement methods and results can be found elsewhere [START_REF] Langer | Indoor environmental quality in French dwellings and building characteristics[END_REF][START_REF] Ramalho | French permanent survey on indoor air quality -Part 1.: measurement protocols and quality control[END_REF][START_REF] Derbez | French permanent survey on indoor air quality -Part 2.: questionnaires and validation procedure of collected data[END_REF][START_REF] Kirchner | Etat de la qualité de l'air dans les logements français[END_REF][START_REF] Brown | Relationships between socioeconomic and lifestyle factors and indoor air quality in French dwellings[END_REF].

This dataset was used for the determination of IAQ levels in dwellings by different IAQ indexes;

for each of the 567 dwellings, the score of each IAQ index was calculated using the equations reported in Table 3. Because the information of the sampling period in some indexes was not clearly recorded, the dataset was applied for the calculation of the IAQ index regardless of the sampling period.

Parameters such as ozone, nitrogen dioxide, fungi, and bacteria considered in some indexes were not measured in the 567 dwellings. IEITW index was fully assessed since all the target parameters were measured. The unmeasured parameters represented 13%, 33%, 25%, 50%, and 33% of the total weight for IEI, LHVP, CLIM 2000, BILGA, and IAQC indexes, respectively.

To run and compare as many IAQ indexes as possible, these indexes were used in the calculation and marked as "modified", while calculations associated with the unmeasured parameters were not performed. It indicated that all the unmeasured parameters were assumed as being below the limit of detection. Moreover, TVOC concentrations were not measured in the French survey.

Consequently, in the present study, the TVOC concentration was assumed to be the sum of the concentrations of the measured VOCs (n=16). The concentrations below the respective limit of detection (LOD) were replaced by LOD/2, and the concentrations below the respective limit of quantification (LOQ) were replaced by LOQ/2. When a measurement failed in one dwelling, the indexes' scores were calculated without the missing data. The missing data varied at random among the dwellings. Therefore, since different parameters are considered within each index, the dwellings with missing values differed among the index calculations. To make a comparison based on the same set of dwellings, the ones having missing data were kept. This was considered to have a minor impact on the results. For example, the calculation of LHVP index had 7% missing data.

Comparison of IAQ indexes applied to French dwellings

The IAQ levels provided by each index are categorical data. To compare these data, a factorial analysis was performed using the multiple correspondence analysis (MCA) method. The MCA was performed using SPAD 7.4 data mining software (Decisia, Levallois-Perret, France) on an indicator matrix created from the initial table (567 rows representing the dwellings and 6 columns representing the calculated scores for the respective indexes). Moreover, the measured values of indoor environmental parameters in the dwellings were also added to the MCA as continuous illustrative data. Second, the dwellings were classified based on their IAQ levels using the hierarchical cluster analysis (HCA) method to analyze the common feature of dwellings in each class.

Results and discussion

IAQ levels in French dwellings

The scores of the modified LHVP index in 518 dwellings (91%) were below 3, i.e., classified as "Good ventilation". The scores of the modified CLIM 2000 index in all the dwellings were below 1, i.e., classified as "Good IAQ". The scores of the modified BILGA index were below 0 in 556 dwellings (98%), i.e., considered as "Excellent IAQ". Thus, the modified LHVP, modified CLIM 2000, and modified BILGA indexes tended to classify the dwellings in good IAQ levels. The lack of discrimination for these indexes may be because not all parameters were considered in the present study, as some parameters were not measured in the French survey.

However, the WHO IAQ guidelines [START_REF]WHO Guidelines for Indoor Air Quality: Selected Pollutants[END_REF] were exceeded in some dwellings for CO, benzene and radon. Thus, the IAQ cannot be qualified as "good" for the entire set of dwellings, as suggested by these three indexes. When an IAQ index is based on an average score of all parameters, an individual parameter may exceed the threshold.

Conversely, the IAQ levels of the 567 dwellings classified by the modified IEI, IEITW, and modified IAQC indexes were more distributed, as shown in Figures 1, 2 and 3, respectively. The IAQ levels of more than half of the 567 dwellings were in the middle of the scale. For example, the scores of the modified IEI index in 329 dwellings (58%) ranged from 4 to 6 (where 0 is "good" and 10 is "bad"). The score of the IEITW index in 339 dwellings (60%) was 40 (where 80 is "good" and 20 is "bad"). The IAQ level in 295 dwellings (52%) was "good" based on the modified IAQC index.

IEI, LHVP, CLIM 2000, BILGA, IEITW, and IAQC indexes had 10, 2, 3, 4, 4, and 3 IAQ levels, respectively. Six IAQ levels, provided by the calculations of the six indexes respectively, were calculated for each dwelling. The combination of the six IAQ levels may differ from one dwelling to another. In total, 62 combinations of IAQ levels were identified for the set of 567 dwellings. The most frequent combination of IAQ levels showed that 28% of the dwellings (n=157) had a "medium" IAQ. The second most frequent combination of IAQ levels showed that 9.5% of the dwellings (n=54) had the worst IAQ level. Fourteen combinations of indexes included more than 10 dwellings each, while seventeen combinations of indexes included only 1 dwelling each. The expression of the IAQ level differs among indexes. However, the levels can be compared using the MCA method. Because 100% of the dwellings had the same IAQ level of the modified CLIM 2000 index, this index was not considered in the MCA method. The database of calculated IAQ levels was described in a 10-dimensional space according to the MCA. Axes 1 and 2 in Fig. 4, accounting for 21% and 14% of the inertia, respectively, were the most important dimensions.

The "Excellent" level of the modified IAQC (IAQC: E) index was associated with scores between 1 and 3 of the modified IEI index (where 0 is "good" and 10 is "bad"). The "Good" level of the modified IAQC index (IAQC: G) was associated with scores between 4 and 5 of the modified IEI index and scores of 40 of the IEITW index (where 80 is "good" and 20 is "bad").

The "Not Good" level of the modified IAQC index (IAQC: NG) was associated with scores between 6 and 10 of the modified IEI index, scores of 20 of the IEITW index, and scores higher than 3 of the modified LHVP index ("Bad ventilation"). Scores between 3 and 4 of the modified IEI index were associated with scores of 60 and 80 of the IEITW index, and scores between 8 and 9 of the modified IEI index were associated with scores ≥0 of the modified BILGA index (from limited to unacceptable risk). Overall, the IAQ levels of the studied indexes were relevant and comparable.

The correlation coefficients between the illustrative variables (indoor environmental parameters)

and the two factorial axes were calculated, which provided the coordinates of the illustrative variables in the defined plane. The position of an illustrative variable in the defined plane presents the direction in which the strong correlation between the variable and the axis lies, especially when the variable is near the correlation circle whose radius is 1. Indoor environmental parameters (illustrative variables) were related to axis 1, indicating that the indoor parameters were relevant for distinguishing the worst IAQ levels from the best ones. Axis 2 separated the best IAQ levels from the other good ones, mostly because of the formaldehyde concentration and relative humidity. temperature; IEI index "Good": 0, "Bad": 10; LHVP index "Good ventilation": <3, "Bad ventilation": >3; BILGA index "Excellent": <0, "Risk insignificant": 0, "Risk limited": (0, 1), "Risk inacceptable": ≥1; IEITW index "Good" to "Bad": 80 to 20; IAQC index "Excellent": E, "Good": G, "Not Good": NG. The size of the symbol represents the quality of representation in the defined plane, e.g., small symbols can be seen as above or below the plane. The shape and the color of the symbol distinguish the indexes. The arrows represent the projected illustrative variables.)

Classification of dwellings based on HCA

The HCA suggested a partition of the dwellings in three classes according to their IAQ levels (Fig. 5). In this figure, each dot represents the vector of IAQ levels for a specific dwelling (or group of dwellings with the same combination). The size of the dot is proportional to the cos 2 of the projection of the data for a given dwelling on the surface of axes 1 and 2. Each dwelling was classified in one group (class). The first group of dwellings (class 1) consisted of 32 dwellings (6%). Of the dwellings in class 1, 97% had scores less than 0 ("Excellent") of the modified BILGA index and less than 3 of the modified LHVP index ("Good ventilation"). In class 1, 97%

of the dwellings had a modified IEI index score of less than 3 (where 0 is "good" and 10 is "bad"), and 25% of the dwellings had an "Excellent" level of the modified IAQC index (Table 5).

Class 1 could be considered as the group of dwellings with the best IAQ levels for the majority of indexes. Class 2 included 341 dwellings (60%), and all of these dwellings had scores of less than 0 of the modified BILGA index, while 95% of the dwellings had scores of less than 3 of the modified LHVP index. This class also included 93% of dwellings with a "Good" level of the modified IAQC index, 60% of dwellings with scores of 80 on the IEITW index (where 80 is "good" and 20 is "bad"), and 83% of dwellings with scores between 3 and 5 of the modified IEI index. Class 2 could be considered as the group of dwellings with overall good IAQ levels. Class 3 consisted of 194 dwellings (34%); of the dwellings in class 3, 97% were on the "Not Good" level of the modified IAQC index. This class also included 78% of dwellings with scores higher than 8 of the modified IEI index and 96% of dwellings with scores of 20 on the IEITW index.

Class 3 could be considered as the group of dwellings with the worst or less than average IAQ levels.

The ellipse presents the average value of the IAQ level in each class. The ellipses between classes 2 and 3, as well as those between classes 1 and 3, were well defined, suggesting that the partition between the dwellings having the worst IAQ and the other dwellings was clear, and that most of the indexes were consistent in defining the worst IAQ cases. However, 55 dwellings (9.7% of the 567 dwellings) with a "Not Good" level of the modified IAQC index had scores of 40 or 60 on the IEITW index. Similarly, 55 dwellings with an "Excellent" level of the modified IAQC index had scores of 40 or 60 on the IEITW index. The ellipses of class 1 and class 2 overlapped because the projections of the positions of the IAQ levels in the defined plane overlapped for some dwellings. It indicated that the IAQ indexes were not completely consistent in defining the best IAQ cases.

Indoor environmental parameters were associated with different IAQ levels, thus varying among classes, as reported in Table 6. Indoor parameters in the three classes were compared with the parameter thresholds proposed in the IAQ indexes. The strictest thresholds of formaldehyde and TVOC concentrations were proposed in the IEITW index. The formaldehyde arithmetic mean concentration of the 3 classes was higher than the threshold for a score of 60 on the IEITW index, while it was lower than the thresholds of the IAQ levels of the other indexes. The mean TVOC concentrations of the 3 classes were higher than the threshold for a score of 80 on the IEITW index, while they were lower than the threshold of the "Good" level of the modified IAQC index.

CO concentrations in French dwellings were generally lower than the thresholds of the IAQ indexes. Only the mean concentration of CO in class 3 was higher than the threshold for a score of 80 on the IEITW index and for an "Excellent" level of the modified IAQC index. The mean concentration of CO2 in classes 1 and 2 was generally lower than the thresholds of the best levels of the IAQ indexes. The PM10 concentration in class 3 was higher than the threshold for a score of 60 on the IEITW index and for an "Excellent" level of the modified IAQC index. Due to the various thresholds across the indexes, the IAQ levels estimated by different indexes were necessarily inconsistent in some cases. IEI index "Good": 0, "Bad": 10; LHVP index "Good ventilation": <3, "Bad ventilation": >3; BILGA index "Excellent": <0, "Risk insignificant": 0, "Risk limited": (0, 1), "Risk inacceptable": ≥1; IEITW index "Good" to "Bad": 80 to 20; IAQC index "Excellent": E, "Good": G, "Not Good": NG.

Limitations of the study

The assumptions for the assessment of the IAQ indexes in the French dataset may lead to bias in the analysis. First, although the selected indexes rank IAQ levels in buildings, the objectives may differ among the indexes, e.g., the LHVP index aims to indicate indoor ventilation performance.

Therefore, the conclusion about repeatability across all IAQ indexes in ranking some buildings may be biased. Due to their different objectives, the indexes, although not consistent, may be suitable in different circumstances. Second, the dataset of the 567 dwellings did not include the measurement of some indoor environmental parameters, e.g., bacteria and NO2 concentrations, which were included in some IAQ indexes. These indexes were considered while the calculation associated with the unmeasured parameters was not performed. Because we did not consider all of the parameters, the IEI, LHVP, CLIM 2000, BILGA, and IAQC indexes were only partially evaluated. Third, the information of the sampling period in some of the indexes was not clearly recorded. The sampling period in the French dwelling survey may differ from that in IAQ indexes. Therefore, this study may not fully replicate the actual indexes as developed. Finally, the TVOC concentration was assumed to be the sum of the concentrations of the measured compounds. This assumption may lead to a bias in the calculation, which cannot be quantified.

Conclusions

Six IAQ indexes proposed in the USA, France, Taiwan, and Hong Kong were applied to a dataset of IAQ measurements in French dwellings to test their applicability for determining IAQ levels using a simple and integrative method and to evaluate their repeatability across all indexes.

Three of the indexes, LHVP, CLIM 2000, and BILGA, were not discriminant and classified most of the dwellings into good IAQ levels. The lack of discrimination for these indexes may be because not all parameters were considered in the present study, as some parameters were not measured in the French survey. The rankings of the other three indexes, IEI, IEITW, and IAQC, were more distributed among the 567 dwellings. The classification of dwellings according to their combination of IAQ index scores suggested that 34% of the dwellings had an unfavorable IAQ. However, the indexes were not fully consistent in determining dwellings with a good IAQ.

The indoor environmental parameters used to calculate the scores from the measured concentrations and the comparison thresholds differed among the indexes, which might explain the inconsistencies found in this study.

Some challenges of IAQ indexes remain: the parameters should be based on the objective and the restraint of an IAQ index which need to be clearly defined. The thresholds of parameters should take into account the health effects while they are determined to discriminate IAQ levels.

This exploratory study serves as a step toward developing an integrative indicator to determine IAQ to increase the building manager and public's awareness.

Table 1 .

 1 Indoor parameters considered in the measurement-based IAQ indexes unmeasured parameters in the dataset of 567 French dwellings considered in this study

Fig. 1 .Fig. 3 .

 13 Fig. 1. IAQ levels in the 567 French dwellings based on the modified IEI index

Fig. 4 .

 4 Fig. 4. Multiple correspondence analysis of IAQ levels in French dwellings (HCHO: formaldehyde; CO: carbon monoxide; CO2: carbon dioxide; RH: relative humidity; T:

Fig. 5 .

 5 Fig. 5. Classification of the French dwellings based on hierarchical cluster analysis of IAQ levels (The size of the symbol represents the quality of representation in the defined plane, e.g., small symbols can be seen as above or below the plane.)

Table 2

 2

				. Parameter thresholds in IAQ indexes
		HCHO	TVOC	CO	CO2	PM2.5	PM10	T	RH	Radon
		(µg/m 3 )	(µg/m 3 )	(ppm)	(ppm)	(µg/m 3 )	(µg/m 3 )	(˚C)	(%)	(Bq/m 3 )
	IEI			(mg/m 3 )
		60	200	10	1000	40	150	19-25	35-55
	LHVP			5	1000
	CLIM			(mg/m 3 ) (mg/m 3 )
	2000
		60		30	4500
	BILGA			(mg/m 3 ) (mg/m 3 )
				14	9000
	IEITW	(ppb)
	20	1000	3000	15	2500		350
	40	100	300	9	1000		150
	60	16	100	4.5	800		50
	80	8	50	2	600		25
	IAQC
	Excellent 30	200	1.7	800		20	20-25.5 40-70 150
	Good	100	600	8.7	1000		180	25.5	70	200
	T: Temperature; RH: Relative humidity.

Table 3 .

 3 Methods and associated equations used to calculate measurement-based IAQ indexeswhere the IEI index consists of the Indoor Discomfort Index (IDI) and the Indoor Air Pollution Index (IAPI); L, I, J, K are the number of parameters in each category; 𝐶𝐴 𝑖,𝑜𝑝𝑡 , 𝐶𝐴 𝑖,𝑜𝑏𝑠 , 𝐶𝐴 𝑖,𝑢𝑐𝑙 , and 𝐶𝐴 𝑖,𝑙𝑐𝑙 are the optimum,

	IAQ index	Method and baseline equations
	IEI	𝐼𝐷𝐼 =	1 𝐿	𝐿 ∑ 10 𝑖=1	|𝐶𝐴 𝑖,𝑜𝑝𝑡 -𝐶𝐴 𝑖,𝑜𝑏𝑠 | 𝐶𝐴 𝑖,𝑢𝑐𝑙 -𝐶𝐴 𝑖,𝑙𝑐𝑙

observed, upper limit, and lower limit values of temperature or relative humidity, respectively; 𝐶 𝑖,𝑗,𝑘 max , 𝐶 𝑖,𝑗,𝑘 obs , 𝐶 𝑖,𝑗,𝑘 min , and 𝐶 𝑖,𝑗,𝑘 dmc are the maximum, observed, minimum, and limit concentrations of pollutants, respectively. This index was originally proposed for office buildings. In the present study, 𝐶𝐴 𝑖,𝑜𝑝𝑡 , 𝐶𝐴 𝑖,𝑢𝑐𝑙 , and 𝐶𝐴 𝑖,𝑙𝑐𝑙 were retrieved from the original American study of the IEI index [16-18], while 𝐶 𝑖,𝑗,𝑘 max , 𝐶 𝑖,𝑗,𝑘 obs , 𝐶 𝑖,𝑗,𝑘 min , and 𝐶 𝑖,𝑗,𝑘 dmc were calculated from the dataset of French dwellings. where [𝐷𝑇𝐵] is the concentration of the total bacteria. 𝑃 𝐼 BILGA = max[𝐼𝐴𝑄(𝑃, 𝑇)]

Table 4 .

 4 IAQ levels assigned after the calculation of the index scores

	IAQ index	IAQ levels associated with scores as qualified by the authors
	IEI	Good to bad: 0 to 10
	LHVP	Good ventilation: <3, Bad ventilation: >3
	CLIM 2000	Good: (0, 1); Polluted: (1, 2); Dangerous: >2
	BILGA	Excellent: <0; Risk insignificant: 0; Risk limited: (0, 1);
		Risk inacceptable: ≥1
	IEITW	Good to bad: 80 to 20
	IAQC	Excellent (E), Good (G), Not Good (NG)

Table 5 .

 5 IAQ levels within each of the three classes of dwellings

	IAQ index	IAQ level	No. of dwellings	% of dwellings
				Class 1	Class 2	Class 3
	Modified IEI (1, 2)	3	67	33	0
		(2, 3)	29	100	0	0
		(3, 4)	103	0	88	12
		(4, 5)	168	0	80	20

Table 6 .

 6 Mean indoor parameters within each of the three classes of dwellings

	Parameter	Arithmetic mean
		All dwellings	Class 1	Class 2	Class 3
		(n=567)	(n=32; 6%)	(n=341; 60%)	(n=194; 34%)
	T (˚C)	21	22	21	20
	RH (%)	49	46	47	51
	Formaldehyde (µg/m 3 )	23	18	21	26
	TVOC (µg/m 3 )	213	96	141	356
	PM2.5 (µg/m 3 )	37	22	30	54
	PM10 (µg/m 3 )	54	30	43	80
	Radon (Bq/m 3 )	66	49	61	78
	CO (ppm)	1.7	0.9	1.1	2.9
	CO2 (ppm)	848	612	682	1164

n: number of dwellings; T: temperature; RH: relative humidity.

Acknowledgments

The preparation of this manuscript was performed during a scientific visit to CSTB (WW) and was supported by a grant from the "Carnot Program" (Grant 2011).