|Alain Destexhe (2007), Scholarpedia, 2(11):1341.||doi:10.4249/scholarpedia.1341||revision #88146 [link to/cite this article]|
The term high-conductance state describes a particular state of neurons within an active network, as typically seen in vivo, such as for example in awake and attentive animals. In single neurons, the high-conductance state is defined by the fact that the total synaptic conductance received by the neuron (averaged over a period of time) is larger than its resting (leak) conductance. This article describes the experimental evidence for high-conductance states, the modeling of such states, and their computational consequences. Dynamic-clamp experiments to "re-create" high-conductance states in vitro are also presented in the last section.
Experimental evidence for high-conductance states
High-conductance states have been described most profusely in the thalamocortical system, and in particular, in cerebral cortex. Most of the data have been obtained in intracellular recordings under anesthesia, and in some cases, in awake or naturally sleeping animals (reviewed in Destexhe et al., 2003). In awake animals, the cerebral cortex (and more generally the entire brain) displays an "activated" state, with distinct characteristics compared to other states like slow-wave sleep or anesthesia. These characteristics include a sustained depolarized membrane potential (Vm) and irregular firing activity (Fig. 1A, Awake). The electroencephalogram (EEG) displays low-amplitude irregular activity (often called "desynchronized EEG"; see Fig. 1A, Awake).
In contrast, during slow-wave sleep, both intracellular and EEG activities are phasic and follow low-frequency rhythms (Fig. 1A, Slow-Wave Sleep). The most prominent rhythm consists of slow-wave complexes in the EEG, which are paralleled with up/down state dynamics intracellularly. During the "up" state (Red bars in Fig. 1A), the Vm is depolarized and the activity is similar to wakefulness; during the "down" state, all cortical neurons are hyperpolarized and do not fire. During anesthesia, several anesthetics (such as urethane or ketamine-xylazine) induce EEG and cellular dynamics very similar to slow-wave sleep. For instance, ketamine-xylazine anesthesia induces up states very similar to sleep up states (see red bars in Fig. 1B). For extensive reviews on EEG and neuronal dynamics during activated and sleep states, see Steriade (2001, 2003), Steriade and McCarley (1990), McCormick and Bal (1997).
There is ample evidence that the "up" states of slow-wave sleep represent dynamics very close to the activated states of the brain (for a recent review, see Destexhe et al., 2007). At the level of EEG and intracellular activities, the dynamics seen during up states are extremely similar to that during wakefulness. An illustrative example of this similarity is that electrical stimulation of the brain stem (pedunculopontine tegmentum, or PPT) can transform the up/down state dynamics into the typical desynchronized EEG of activated states (Fig. 1B). Following the PPT stimulation, the activated state appears as a "prolonged" up state (see Steriade et al., 1993; Rudolph et al., 2005). Thus, it seems that the "up" states constitute a relatively good approximation of the network state during activated states (although these states are different, as shown for example by conductance measurements).
Other types of anesthetics, such as barbiturates, do not induce dynamics comparable to either activated or slow-wave sleep states but rather depress cortical activity and induce an EEG dominated by slower frequencies such as spindles or slower rhythms (Fig. 1C). The Vm is hyperpolarized, and rarely makes excursions to depolarized values. The most depressed state is obtained in vitro, in the absence of any particular manipulation to excite cortical activity (Fig. 1D). In this case, the Vm is at rest with rare synaptic events of very small amplitude (Fig. 1D, insets).
The fact that activated states are also high-conductance states can be seen by injection of current to reveal the conductance state of the membrane, as shown in Fig. 2. During ketamine-xylazine anesthesia, the Vm distribution is bimodal, reflecting the up and down states (see Fig. 2A). Injection of constant hyperpolarizing or depolarizing current has a strong effect on the down state (diamonds in Fig. 2A), but has a much smaller effect on the up states (* in Fig. 2A). In other words, the up states are of very high membrane conductance (note that the same results are obtained with purely subthreshold activity, so it is not due to the conductances of action potentials). During deep barbiturate anesthesia, the behavior is similar to the down state (Fig. 2B), and therefore of low conductance, further indicating that this type of anesthesia is not adequate to study activated states of the brain.
More direct evidence for high-conductance states must be obtained by direct comparison between active states and the true resting state of the neuron. Such an estimate was obtained by using microdialysis of the drug tetrodotoxin (TTX) in cat parietal cortex (Pare et al., 1998). TTX blocks all Na+ channels and therefore completely suppresses all action-potential dependent activity. Using TTX microdialysis enables one to keep the same neuron recorded during active states and after complete suppression of network activity, thereby revealing its resting state. Input resistance (Rin) measurements revealed that taking the "up" states of ketamine-xylazine anesthesia as reference, these active states have about 5 times more synaptic conductance compared to the resting state of the cell (Fig. 2C; Pare et al., 1998; Destexhe and Pare, 1999). These results are not affected by the Vm level and by spiking activity (identical results are obtained at hyperpolarized, subthreshold levels) and Rin measurements correspond to the linear portion of the I-V curve, suggesting little or no contamination by intrinsic voltage-dependent currents (Destexhe and Pare, 1999; see also discussion in Monier et al., 2008).
Various measurements have also been obtained during active states in vivo, usually by comparing "up" and "down" states under various anesthetics such as ketamine-xylazine or urethane. Such estimates are very variable, ranging from up to several-fold smaller Rin in "up" states (Contreras et al., 1996; Pare et al., 1998; Petersen et al., 2003; Leger et al., 2005), to nearly identical Rin between "up" and "down" states or even larger Rin in "up" states (Metherate and Ashe, 1993; Zou et al., 2005; Waters and Helmchen, 2006). The latter paradoxical result may be explained by voltage-dependent rectification (Waters and Helmchen, 2006) or the presence of K+ currents in down-states (Zou et al., 2005). Consistent with the latter, cesium-filled electrodes have negligible effects on the "up" state, but greatly abolish the hyperpolarization during the "down" states (Timofeev et al., 2001). Moreover, the Rin of the "down" state differs from that of the resting state (after TTX) by about two-fold (Pare et al., 1998). It is thus clear at least that the "down" state is very different from the true resting state of the neuron. Finally, conductance measurements in awake and naturally sleeping animals have revealed a wide diversity between cell to cell in cat cortex (Rudolph et al., 2007), ranging from large (much larger than leak conductance) to mild (smaller or equal to the leak) synaptic conductances. On average, the synaptic conductance was estimated as about three times the resting conductance, with breaks into about one third excitatory and two third inhibitory conductance. Strong inhibitory conductances were also found in artificially evoked active states using PPT stimulation (Rudolph et al., 2005).
Models of high-conductance states
Interestingly, the notion of high-conductance states, and the fact that neurons could integrate differently in such states, was first proposed by modeling studies. By integrating the sustained synaptic conductance arising from network activity into models, Barrett (1975) for motoneurons, and later Holmes and Woody (1989) for pyramidal cells, predicted that synaptic activity could have a profound impact on dendritic integration. This theme was then investigated using biophysically and morphologically more precise models in cortex (Bernander et al., 1991; Destexhe and Pare, 1999) and cerebellum (Rapp et al., 1992; De Schutter and Bower, 1994). Such models have predicted a number of computational consequences of background activity and high-conductance states in neurons (see next section).
In parallel to these investigations, the "noisy" aspect of background activity in neurons was also the subject of considerable attention in computational neuroscience. Synaptic activity is usually modeled by a source of current noise in the neuron (Levitan et al., 1968; Tuckwell, 1988), and thus the membrane potential is described by a stochastic process. More recently, the background activity was modeled by fluctuating conductances instead of fluctuating currents (Destexhe et al., 2001). In this case, the synaptic conductances are stochastic processes, which in turn influence Vm dynamics. The advantage of the latter representation is that the high-conductance state of the membrane can be specifically reproduced and modulated. It can also be injected in a real neuron in order to recreate the high-conductance state artificially (see Section "[[Dynamic clamp|Dynamic-clamp]] experiments").
It is important to note that simplified models are not only good for dynamic-clamp experiments, but they also allow mathematical treatment. The fluctuating conductance model has been subject to several mathematical analyses at the subthreshold level (Rudolph and Destexhe, 2003c, 2005; Richardson, 2004; Lindner and Longtin, 2006), which yielded methods to extract conductances from intracellular recordings (Rudolph et al., 2004; Pospischil et al., 2007). Various mathematical studies of the firing dynamics of neurons with conductance-based inputs were also proposed (see for example Burkitt et al., 2003; Moreno-Bote and Parga, 2005; Muller et al., 2007) and have consequences on network dynamics with conductance-based inputs (Meffin et al., 2004; see also Shelley et al., 2002). Such studies are only possible with simplified models, such as the integrate and fire model.
Thus, two types of models were considered in the literature, one type consists of models with dendrites where an explicit representation of the stochastic release at many synapses was used. The other type of model consists of an "effective", single-compartment representation of the neuron subject to synaptic noise. As we will see below, both approaches have been very useful to investigate and predict computational consequences of high-conductance states.
Computational consequences of high-conductance states
Computational models have predicted several interesting computational consequences of high-conductance states (reviewed in Destexhe et al., 2003). The first consequence is a bit obvious but is important to be mentioned: Neuronal responses in high-conductance states are fundamentally probabilistic because of the high variability of responses due to the presence of fluctuating background activity (Fig. 3A). It is necessary to use repeated trials for any given response, and calculate the probability of spiking. This variability and the use of probabilities are well-known from in vivo electrophysiologists, who routinely calculate "post-stimulus time histograms" (PSTH) from their data. Integrating the probability of response after the stimulus gives the total probability that a spike is emitted (the total "output" of the neuron), as shown in Fig. 3B.
The second property of high-conductance states is that not only do they switch neurons to probabilistic devices, but they also profoundly change their response properties. The response curve, which is obtained by representing the total response probability (integrated over time after stimulus) against stimulus amplitude, is all-or-none for a deterministic neuron, reflecting the spike threshold (Fig. 3B, red). In this case, the spike can only tell whether the stimulus is larger than the threshold. In the presence of background activity, the response curve is different, it is smooth and spans a whole range of input amplitudes (Fig. 3B, green). In this case, the probability of spiking is indicative of the input amplitude. In particular, for small-amplitude inputs (those in the physiological range), which are normally subthreshold, the neuron's response probability is enhanced (* in Fig. 3B). This enhanced responsiveness is a very robust feature of neurons in the presence of synaptic background activity (Ho and Destexhe, 2000; Shu et al, 2003), and a similar phenomenon has also been called "gain modulation" (Chance et al., 2002), reflecting the fact that the slope of the response curve is modulated by background inputs. Investigating the effect of the different components of background activity revealed that the conductance shifts the response curve (rightward arrow in Fig. 3B), while the "noise" component modulates the slope (gain) of the response curve (Ho and Destexhe, 2000; Chance et al., 2002; Shu et al., 2003; Mitchell and Silver, 2003; Prescott and De Koninck, 2005). It is important to note that the type modulation by background activity will depend strongly on the intrinsic properties of the neurons. An inverse gain modulation can be observed (Fellous et al., 2003) and may be explained by potassium conductances (Higgs et al., 2006). Similarly, the dual response (burst vs. single-spike) of thalamic relay neurons is also strongly affected by the presence of background activity and the two modes may no longer be distinguishable (Wolfart et al., 2005; see Section "Dynamic-clamp experiments" below).
It must be noted that the phenomenon of enhanced responsiveness is similar to stochastic resonance phenomena, which have been thoroughly studied by physicists (reviewed in Gammaitoni et al., 1998; Wiesenfeld and Moss, 1995). Stochastic resonance is a noise-induced enhancement of the signal-to-noise ratio in nonlinear systems; it usually appears as a peak of the signal-to-noise ratio as a function of noise amplitude (thus the system appears to "resonate" for an optimal amount of noise). While neurons can also show such a behavior if subject to noise (Levin and Miller, 1996; Stacey and Durand, 2000), the situation is more complex than for classic stochastic resonance phenomena, because in neurons the noise source is also a conductance source, and conductances have an additional shunting effect (see Rudolph and Destexhe, 2001).
A third consequence of high-conductance states is that they may fundamentally change dendritic integration properties, as illustrated in Fig. 4. An inherent property of dendrites and other cable structures is voltage attenuation. This is true in particular for pyramidal neurons: synaptic inputs can experience strong attenuation in the neuron's resting state (Fig. 4A, red). If the high-conductance state of the membrane is integrated as a static conductance component (i.e., increasing the leak conductance of the membrane), the attenuation is much more severe (Fig. 4A, blue): inputs arising at 400 microns and more from the soma are almost totally attenuated. This phenomenon is perfectly predictable by cable theory. Remarkably, if the full high-conductance state is simulated, the spiking probability shows a surprisingly low dependence on the location of inputs in dendrites (Fig. 4A, green). This location independence can be explained by dendritic excitability. In quiescent conditions, synaptic inputs arising in distal dendrites can elicit a local dendritic spike, but such a spike is hard to evoke and typically does not propagate well across the dendritic structure (Fig. 4B, top). In high-conductance states, as shown above, the behavior is highly variable, and there is a little probability that evoked spikes propagate all the way to the soma (Fig. 4B, bottom). The probability that a local dendritic spike propagates to the soma and evokes a somatic spike is inversely proportional to distance (Fig. 4C, yellow curve). Conversely, the probability that synaptic inputs evoke a local dendritic spike increases with distance (because the local input resistance is higher for distal dendrites; see Fig. 4C, blue curve). The multiplication of these two probabilities gives the spike probability of synaptic inputs and is necessarily less dependent on location (Fig. 4C, red curve). Thus, according to this "stochastic integrative mode" (Rudolph and Destexhe, 2003), the neuron could perhaps solve one long-standing problem, how to equally integrate inputs situated at different locations in extended dendritic trees. This equalization mechanism depends on both intrinsic properties (dendritic excitability) and the presence of synaptic noise.
Another important consequence of high-conductance states is on temporal processing. The large conductance is necessarily associated with a reduced membrane time constant, which is visible in the faster response to injected current (Fig. 2C, averaged traces). As proposed more than 30 years ago (Barrett, 1975), this reduced time constant should favor finer temporal discrimination (Holmes and Woody, 1989; Bernander et al., 1991; Destexhe and Pare, 1999). In excitable dendrites, small membrane time constants also promote fast-propagating action potentials, resulting in a reduced location-dependence of EPSP timing (Destexhe and Rudolph, 2003), which is likely to facilitate the association of distant inputs. The neuron also has a superior ability to distinguish and process high-frequency inputs, compared to low-conductance states. This is illustrated in Fig. 5, which displays the temporal resolution of a neuron represented against the input frequency. In quiescent or low-conductance states, neurons can follow inputs up to a maximal frequency which is usually around 40-50 Hz (Fig. 5, red curve). In high-conductance states, the neuron can lock its response to larger frequencies (up to more than 100 Hz in the example of Fig. 5, green curve).
Other advantages of high-conductance states on temporal processing have been noted by modeling studies. If both excitatory and inhibitory conductances are large during high-conductance states, slight variations of either excitation or inhibition can be very effective in modifying spiking probability. As a consequence, neurons can reliably detect faint changes in temporal correlation of the random activity of their inputs (Halliday, 1999; Salinas and Sejnowski, 2000; Rudolph and Destexhe, 2001). This type of response is interesting, because changes in correlation do not change the average conductance nor the average Vm, but they uniquely appear as changes of the level of fluctuations (variances) of the conductances and of the Vm. In this case, neurons respond to a signal which is not carried by the mean activity of conductances, which thus constitute an example of a paradigm which cannot be modeled by rate-based models.
High-conductance states also impact on the operating mode of cortical neurons. Neurons can operate either as coincidence detectors or as temporal integrators, which determines whether the cortex encodes information by the precise timing of spikes, or by average firing rates. Modeling studies monitored the spike output of neurons submitted to a full spectrum of multisynaptic input patterns, from highly coincident to temporally dispersed (Marsalek et al., 1997; Kisley and Gerstein, 1999). It was found that generally the spike output jitter is less than the input jitter, indicating that neurons synchronize the responses and reduce their temporal dispersion. In high-conductance states, however, the temporal dispersion was found to be nearly identical between input and output (Rudolph and Destexhe, 2003b), indicating that both operating modes can be used in parallel in cortical networks in such states.
Finally, models predict that the high-conductance state implies strong (passive) voltage attenuation, as shown in Fig. 3A (middle panel). This strong attenuation should favor the electrical isolation of dendritic segments with respect to each other, for subthreshold events. This would result in a dendritic tree in which subregions could independently integrate synaptic inputs and perform relatively independent computations. This concept is consistent with the "dendritic subunits" postulated in previous theoretical studies (Mel, 1994).
A particularly elegant way to evaluate the impact of high-conductance states is to recreate these states in real neurons in vitro using computer-generated in vivo-like activity. Because such activity requires adding artificial conductances to the neuron, one needs to use an appropriate technique, called the dynamic-clamp. This technique was introduced in 1993 independently by two laboratories (Robinson and Kawai, 1993; Sharp et al., 1993) and is now well-established (Prinz et al., 2004). The dynamic-clamp consists of injecting computer-generated conductances into a real neuron through the recording electrode. Because the conductance depends on voltage, one needs to continuously update the current to be injected as a function of the voltage which is changing dynamically. Thus, the computer must run the conductance models in real time to be able to communicate in a perfectly timed fashion with the recording setup, and in particular the amplifier of the intracellular signal.
The first study to inject synaptic noise in cortical neurons using dynamic-clamp and artificially recreate high-conductance states was proposed about 6 years ago (Destexhe et al., 2001), and was followed by a number of studies which investigated different aspects of high-conductance states using this technique (Chance et al., 2002; Prescott and Dekoninck, 2003; Fellous et al., 2003; Shu et al., 2003; Wolfart et al., 2005). To this end, one needs first to generate an appropriate model of stochastic synaptic activity because thousands of synapses releasing randomly cannot be simulated in real time. A stochastic "point-conductance" model was proposed (Destexhe et al., 2001), which consists in two fluctuating synaptic conductances described by one-variable stochastic processes (Fig. 6A; red and blue traces). These processes are adjusted to match the total conductance seen at the soma during background activity. These conductances are then injected in dynamic-clamp (Fig. 6A) in order to reproduce the conductance measurements in the TTX experiments (Fig. 6B; compare with Fig. 2C). Other properties can also be used to better constrain the model, such as the mean and standard deviation of the Vm, the spontaneous firing rate, the variability of spiking, or the power spectrum of the Vm fluctuations.
One of the properties of high-conductance states, the enhanced responsiveness, was thoroughly tested in dynamic-clamp experiments. Injection of stochastic conductances in cortical neurons in vitro profoundly altered their responsiveness, or equivalently, neuronal gain (Chance et al., 2002; Fellous et al., 2003; Prescott et al., 2003; Shu et al., 2003). The "noise" component of background activity was found to reduce the gain in most cases, as illustrated in Fig. 6C. However, in some cases, noise may increase the gain (Fellous et al., 2003), a property which could be explained by the presence of strong after-hyperpolarization conductances (Higgs et al., 2006).
High-conductance states were also re-created in neuronal types which express strong and prominent intrinsic properties, such as the bursting neurons of the thalamus. Thalamic relay cells classically display two modes of firing (Llinas and Jahnsen, 1982): at depolarized potentials, they respond to excitatory stimuli rather classically, by producing regular trains of spikes ("tonic mode"); at hyperpolarized potentials, the same stimuli evoke full-blown bursts of action potentials ("burst mode"). However, this classification has been challenged recently in a dynamic-clamp study where high-conductance states were reproduced in thalamic neurons (Wolfart et al., 2005). Instead of responding in two distinct modes, thalamic relay neurons mixed single-spike and burst responses at all membrane potentials. This suggests that both single-spikes and bursts equally participate to transmitting information. Consistent with this, if one calculates spiking probabilities by mixing bursts and single-spikes, the responsiveness is independent on both Vm level and on the frequency of the input (Fig. 6D). In this case, this situation is possible only because of the presence of the calcium current generator of bursts. It was suggested that this constitutes an efficient "relay" for thalamic neurons (Wolfart et al., 2005), and this relay is possible only from the interaction between intrinsic neuronal properties and synaptic noise. In other words, it is only possible in high-conductance states.
Thus, dynamic-clamp experiments support the idea that stochastic conductances stemming from intense network activity are responsible for an enhancement of responsiveness in cortical neurons, and more generally a fundamental change of responsiveness in all neuronal types. Moreover, the amount of conductance and Vm fluctuations identified in vivo are largely in the range needed to drastically alter the responsiveness of neurons, which suggests that these phenomena occur well within the physiological situation. It is also one of the basis by which different "states" of activity of the network can yield different responsiveness (reviewed in Destexhe and Contreras, 2006). This is in agreement with previous observations that state changes induced by stimulating the ascending activating systems lead to enhanced responsiveness (Steriade, 1970; Singer et al., 1976).
Computational models and experiments have shown that there is a large amount of synaptic background activity in cortical neurons in vivo, and that this activity can confer numerous computational advantages to neurons. We summarize below these "computational principles", possible ways to test them experimentally, and interesting directions for future work.
Probabilistic and irregular behavior
A straightforward property of high-conductance states is that due to the seemingly random synaptic activity, neurons are inherently stochastic and responses show considerable variability (Fig. 3A), as typically found in vivo (Dean, 1981; Holt et al., 1996). The appropriate measure for such responses is to compute probabilities, as routinely done in vivo through the use of post-stimulus time histograms. This variability should disappear at the population level if responses from many neurons are pooled together (Shadlen and Newsome, 1998). Thus, neuronal populations should produce sensitive, precise and discriminative responses during high-conductance states, if the responses of a large number of neurons are pooled together.
Enhanced responsiveness and gain modulation
Less straightforward is the observation that the "noisy" aspect of high-conductance states can lead to an enhancement of responsiveness to some inputs. This observation was first reported from modeling studies (Ho and Destexhe, 2000), and then investigated experimentally using dynamic-clamp injection of in vivo-like synaptic noise (Destexhe et al., 2001; Chance et al., 2002; Fellous et al., 2003; Prescott and Dekoninck, 2003; Shu et al., 2003; Wolfart et al., 2005; Higgs et al., 2006), confirming some of the predictions formulated by models. Enhanced responsiveness was also tested using real network activity, but contradictory results were obtained when comparing responses in "up" and "down" states (see section "Experimental evidence for high-conductance states"). A possible reason for the discrepancies is that some of these studies used a unique input amplitude which is insufficient (inputs can be either more or less responsive depending on their amplitude; see Fig. 3B). More experiments should be realized by using a range of different input amplitudes.
An attractive possibility is that the enhanced responsiveness by synaptic noise can be used as an attentional mechanism (Ho and Destexhe, 2000; Shu et al., 2003). By modulating the amount of background activity (ie, the "conductance state"), it should be possible to switch entire networks from unresponsive to responsive states. This possibility should be investigated by designing appropriate experiments and models.
Modulation of intrinsic neuronal properties
Synaptic noise affects neuronal responsiveness, but what happens when neurons express dominant intrinsic properties, such as bursting ? This question was addressed so far only for thalamic neurons (Wolfart et al., 2005). This study revealed that the classic "tonic" and "burst" modes of firing in thalamic relay cells were profoundly altered. With synaptic noise, these modes are no longer distinguishable because bursts and single-spikes participate to all responses. It was also shown that strong K+ conductances can change the sign of gain modulation in cortical neurons (Higgs et al., 2006). How extrinsic noise interacts with intrinsic neuronal properties is at present only very partially understood, and should be investigated by future studies.
Modulation of dendritic integration
Enhanced responsiveness may also influence local dendritic processing. The interplay between excitable properties (dendritic spikes) and synaptic noise can result in an equalization of the efficacy of individual synapses (Fig. 4). These predictions have so far not been tested experimentally - it would require to recreate the correct conductance state all along the cable structure, which is at present difficult to achieve. More generally, how synaptic noise influences dendritic integration is a complex problem very partially understood, and which will also require further modeling and experimental studies.
Increased temporal resolution
Temporal processing was the first consequence that was put forward by modeling studies (Barrett, 1975; Holmes and Woody, 1989; Bernander et al., 1991; Destexhe and Rudolph, 2003). Neurons in high-conductance states necessarily have a faster membrane which allows sharp temporal processing (see example in Fig. 5). Surprisingly few experimental studies have investigated this aspect, which also constitutes a very interesting direction to be explored in the future.
In conclusion, cortical neurons and networks can display a variety of high-conductance states. Such states clearly have a profound impact on neuronal integrative properties and responsiveness. Contrary to the intuitive notion that noise is detrimental, the noisy high-conductance states can set neuronal populations to produce sensitive, precise and discriminative responses. These themes were pioneered by modeling studies, and were more recently subject to thorough experimental investigation. The understanding of how network state in general modulates integrative properties and information flow (and vice-versa) is only at its early stage, and will require a continuous association of experiments and computational models.
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