The influence of inhibition on spontaneous network burst dynamics. A : network burst length and interval probability distribution for control and 5 ␮ M picrotoxin (PTX). Network bursts became longer but also occurred at longer intervals (10 networks, DIV 22–30). B : relative change of various activity parameters. Each bar represents the mean Ϯ SE of the medians from all networks in A . Values were normalized to control condition. Network burst interval, length, and number of spikes increased significantly (Wilcoxon signed rank test, * P Ͻ 0.05; ** P Ͻ 0.01). Average long-term global firing rate and thus the total number of spikes recorded did not change significantly. The small decrease of the number of sites with bursts was due to a subset of recording sites that had only 1 or 2 spikes/burst under PTX and thus did not fulfill the burst criterion. Absolute values: interval, 17.1 Ϯ 1.8 s and 30.3 Ϯ 3.7 s; length, 0.41 Ϯ 0.04 s and 0.83 Ϯ 0.14 s; number of spikes, 109 Ϯ 16 and 260 Ϯ 49; firing rate, 9.8 Ϯ 1.6 Hz and 12.3 Ϯ 1.4 Hz; number of sites with bursts, 25.3 Ϯ 2.4 and 22.6 Ϯ 2.7. 

Contexts in source publication

Context 1

... Ϫ ␣ t ). Response delay modulation followed a single exponential decay function y ( t ) ϭ Be Ϫ ␤ t ϩ C . The modulation of stimulus-response relations persisted under the blockage of inhibition, suggesting modulatory mechanisms, such as synaptic depletion, during the burst and subsequent replenishment in the period of inactivity (Cohen and Segal 2011). Our findings suggest that trial-by-trial variability in neuronal networks arises, to a significant extent, from state-dependent, input-output relationships. Alternating periods of bursting and inactivity modulate neuronal excitability, such that it is low directly after bursts and recovers gradually during inactivity. Single electrical stimuli induced early responses locally and a polysynaptic transfer of activity to more distant areas, showing as late responses (Fig. 3 C ). The length of responses with both early and late components increased with increasing delays of the stimulus to the preceding burst; concomitantly, polysynaptic delays decreased. Comparing response delays with prestimulus activity revealed a remarkable relation: variations of prestimulus inactivity in the range of seconds correlated with changes of the delay of late responses of tens of milliseconds (Fig. 4, C and D ). How can stimulus timing modulate response length and delay? Inhibition shortened the responses at most sites and increased response delays. Response modulation persisted, however, when the networks were disinhibited (Fig. 7, B and C ), suggesting that inhibition interacts with additional mechanisms modulating stimulus-response relations. We therefore propose that short-term synaptic depression (STD) by spontaneous bursts, due to depletion of readily releasable neurotransmitter vesicles, limits response length and delay in conjunction with GABAergic inhibition. STD modulates synaptic transmission depending on the temporal characteristics of presynaptic input (Tsodyks and Markram 1997; Tsodyks et al. 1998). Sustained synaptic vesicle exocytosis during a burst depletes the readily releasable pool until firing ceases. Subsequent replenishment increases resource availability with increasing time after a burst. Placing a stimulus in the late recovery phase yields longer responses for nearby sites because more synapses have recovered. Correspondingly, delays for distant sites decrease because synaptic input to these neurons increases as more synapses recover, and thus integration times shorten. Although we could not directly validate STD and the depletion of presynaptic resources, the rate of replenishment and release probability that controlled population burst duration and timing in CA3 pyramidal cells support it (Staley et al. 1998). STD has been reported for synapses in culture (Opitz et al. 2002; Vogt et al. 2005), and the rate of replenishment is in good agreement with spontaneous burst intervals (3–16 s) (Stevens and Wesseling 1998). Synaptic vesicle depletion in hippocampal microcultures terminated spike-triggered network bursts (Cohen and Segal 2011). Furthermore, compared with cellular excitability modulation, a model of activity-dependent synaptic depression better replicated the dynamics of oscillatory discharges and increasing response lengths with longer duration of preceding inactivity in the chick spinal cord (Tabak et al. 2000, 2001). A close link between single-neuron threshold dynamics and magnitude of synchronized network activity has been demonstrated recently in cortical neuronal networks in vitro too (Wallach and Marom 2012). In addition, spike- frequency adaptation in single neurons during high bursting activity could further affect stimulus-response dynamics. Giugliano et al. (2004) have previously described comparable collective dynamics for cultured cortical neurons and for leaky integrate-and-fire neurons with spike-frequency adaptation. A build-up of the adaptation during the transition from silence to bursting could mediate the termination of bursts. Although it is largely unknown which biological mechanisms generate and modulate synchronous network-wide bursting, a variety of functional roles has been suggested (Lisman 1997; Meister et al. 1991; Mongillo et al. 2008). What can be understood, though, is the causal relation between bursting and inactivity through the correlation between preceding or following interval and burst duration (Tabak et al. 2001). Our findings suggest that network bursts may depress synaptic transmission to a fixed low threshold (Fig. 2 B ) and that this, in conjunction with inhibition (Fig. 6), terminates a burst. Synaptic efficacy would then recover in the following period of inactivity until spontaneous fluctuations, e.g., of the activity of small populations of neurons (Gritsun et al. 2010), trigger the next burst. Removing inhibition allowed bursts to become longer and thus deepen the synaptic depression. Consistently, the minimal periods of recovery to a level that enables the next spontaneous burst became longer too (Fig. 6). Recovery exceeding this minimum in the period until the next burst is initiated builds up resources that extend the duration of the upcoming burst. Disinhibition facilitates spatial-temporal propagation. Evoked responses propagate from the site of stimulation. Recording sites with exclusively late responses were more distant to the stimulation site than those with early and late responses (Fig. 3 C ), suggesting that early responses reflect direct stimulation or monosynaptic connections. In addition, we found response delays generally increasing with increasing distance-to-stimulation site (Fig. 8 A ). The connectivity in these cultured networks is not spatially homogeneous but because of density and developmental effects, tends to be clustered and includes long-range connections (Kriegstein and Dichter 1983; Soriano et al. 2008). This likely contributes to a rich set of connection motives, resulting in a broad range of response delays and directions of propagation. In addition, propagation speeds would vary locally. We found that propagation speeds largely depended on the individual network and to a smaller degree, on the timing of stimulation (Fig. 8 C ). The median propagation speed across all networks and postburst intervals was 0.20 mm/ms. Our findings are in good agreement with the properties of the propagation activity upon electrical or sensory stimulation of cortical tissue in vitro and in vivo. In vivo, direct anti- or orthodromic activation of the most excitable elements, namely the axons (Nowak and Bullier 1998; Tehovnik et al. 2006), in the vicinity of the stimulation site is conveyed polysynaptically into distant areas (Biella et al. 2002; Butovas and Schwarz 2003). Propagation speeds for tone-evoked responses were Ϸ 0.1 mm/ms in deep layers of auditory cortex (Sakata and Harris 2009) and Ϸ 0.1– 0.25 mm/ms for visual- evoked responses in visual cortex (Grinvald et al. 1994). In our study, disinhibition by blockage of GABA A receptors increased the correlation between response delay and distance- to-stimulation site and thus facilitated the propagation of excitation (Fig. 8 B ). The median propagation speed increased, and the SD across all networks decreased. The latter was mainly due to a smaller variability of propagation speeds across different networks and therefore suggests a strong het- erogeneity in the strength and spatial distribution of inhibition across different networks. For individual networks, however, we saw an increased modulation of propagation speed by the timing of stimulation. This could be explained by stronger synaptic depression after longer bursts with more spikes under PTX, followed by full recovery during periods of inactivity. The observation that the contribution of inhibition to the modulation of the responses changed with distance to the stimulation site suggests that whereas local inhibition strongly shapes the properties of local responses, it appears to show with a greater effect on response reliability during polysynaptic transmission toward distant network locations. This would be in agreement with the assumption of mainly local output of inhibitory neurons and long-range excitatory connectivity (Eytan et al. 2003). Network responses at some distance would thus decreasingly depend directly on the specific design of the stimulus but indirectly through its shaping influence on local responses and recruitment. Defined interaction with ongoing activity. Stimulation at fixed lags relative to bursts at a selected feedback site decreased response-length variability below the level of variability for spontaneous burst length (Fig. 5 C ). Responses under fixed IstimI and thus varying lags to preceding bursts varied approximately as much as spontaneous bursts. These findings confirm that the state of the network at the moment of stimulation critically determines neuronal responsiveness (Arieli et al. 1996; Curto et al. 2009; Hasenstaub et al. 2007; Kisley and Gerstein 1999). Our goal was to obtain analytical models for state-dependent stimulus-response relations, and we found nonlinear interactions between the duration of prestimulus inactivity and response properties. Previous models assuming a linear superposition of a reproducible response with a response component determined by the network’s activity state at stimulus onset (Arieli et al. 1996) were refined by Kisley and Gerstein (1999), who showed that the variability itself can be state dependent. Current models for sensory-evoked responses in functional cortices incorporated the dynamics of ongoing activity and a longer history of prestimulus activity (Curto et al. 2009; Hasenstaub et al. 2007). For example, late responses upon click stimuli showed stronger modulation with the network state than early components (Curto et al. 2009), and increasing response spikes correlated with increasing time after termination of an UP state and transition to a DOWN state (Hasenstaub et al. 2007). The functional ...

Context 2

... preceded short responses, whereas no or weak spontaneous bursting activity preceded long responses (Fig. 4 A ). The capability to evoke long responses drastically decreased directly after spontaneous bursts but increased with increasing delay of the stimulus to the last burst. Further analyses revealed that the response length for individual recording sites correlated best with the duration of inactivity before the stimulus, if compared with a weighted spike history or the number of spikes in the preceding burst (Fig. 4 E ). We thus used this interval as a quantitative indicator of the local network state prior to stimulation. With increasing duration of network inactivity, response lengths increased exponentially and eventually saturated (Fig. 4 B ), described by a saturating exponential of the form A ( 1 Ϫ e Ϫ ␣ t ), where A and ␣ are fit parameters, and t is the duration of the inactivity interval preceding the stimulus. The dependency of response length on prestimulus inactivity decreased at recording sites with exclusively late responses (Fig. 4 F ). Instead, the delays of the responses at these sites were clearly correlated with prestimulus activity (Fig. 4 C ). Recent bursting activity resulted in large delays of the polysynaptic response to stimulation, and longer phases of inactivity preceding stimuli led to short delays, indicating progressive recovery of excitability within the network. Response delays exponentially decreased with longer prestimulus inactivity and saturated at a low level ( Ϸ 25 ms poststimulus; Fig. 4 D ). This relation followed the function Be Ϫ ␤ t ϩ C . Overall, the time constant ␤ for response delay was shorter than the time constant ␣ for response length (mean: ␣ ϭ 0.19 1/s, ␤ ϭ 0.41 1/s; median: ␣ ϭ 0.15 1/s, ␤ ϭ 0.25 1/s; 26 and 91 sites, 9 and 16 experiments, 8 and 13 networks; DIV 22–30 and DIV 22–38 for response length and delay, respectively). Response length and delay were thus modulated by ongoing activity, and stimulus efficacy depended on the state of the network at the moment of stimulation. To test whether a defined timing of stimulation relative to spontaneous bursting can enhance re- sponse reproducibility, we developed a closed-loop electrical stimulation paradigm. variability. An activity-triggered stimulation paradigm placed stimuli at predefined times relative to spontaneous activity and thus allowed us to successively evaluate the network’s state- dependent input/output relationships. The networks were stimulated with a set of fixed lags after the end of spontaneous bursts during baseline activity (Fig. 5 A ). Stimulation at fixed lags resulted in smaller coefficients of variation for response lengths compared with when the timing of stimulation was randomized across trials (Fig. 5 B ). To generalize this finding, we compared the reproducibility of responses with closed- loop, fixed-lag stimulation against the standard open-loop stimulation with fixed IstimI (Fig. 5 C ). Responses to fixed-lag stimulation with 0.5-, 1-, and 2-s postburst intervals plus minimal IstimI were compared with those from stimulation with fixed IstimI of 10 and 20 s. We analyzed recording sites with combined early and late responses and defined response variability as the ratio between SD of response length and spontaneous burst length. This enabled us to assess response- length variability across different networks, since it normalized the variability of evoked responses by the intrinsic variability of spontaneous bursts. Response variability for stimulation with fixed IstimI was mainly distributed around one, i.e., responses varied as much as the length of spontaneous bursts (Fig. 5 C ). Stimulation with fixed lags reduced response variability to a level below spontaneous burst variability with a peak at 0.7. We thus used this protocol in the remainder of this study to examine the influence of inhibition on spontaneous and evoked activity dynamics. The role of inhibition. Our results, so far, showed how bursts depress network excitability. Subsequent recovery prepares the network for the next spontaneous burst or evoked response. Which biological mechanisms govern the modulation of stimulus-response relations is currently unclear. Synaptic depletion during bursts followed by replenishment and prevailing wide- spread inhibition after the end of bursts are two possibly concurrent processes. To expose the role of the inhibitory system more clearly, we performed a set of experiments blocking inhibition with the GABA A receptor antagonist PTX. We first asked what the influence is of inhibition on the dynamics of network bursting. Furthermore, we tested whether fading inhibition after network bursts could account for the progressive decrease of the response delay with increasing time since the last spontaneous burst. Confirming inhibitory activity in the network, we found an average increase of network burst intervals (88%), network burst length (163%), and number of spikes (183%; Fig. 6 B ) after application of PTX (10 networks; DIV 22–30). Interestingly, the gross firing rate (average across 0.5 h) remained unchanged. This indicates an intrinsically regulated balance between the overall level of activation and inactivation. The seeming decrease in the number of recording sites with bursts under PTX was due to a subset of recording sites that contributed with only one to two spikes/network burst and thus did not fulfill the burst criterion anymore. Thus disinhibition leads to a reorganization of activity toward longer and enhanced spiking during network bursts that needed a longer time to initiate spontaneously. The following analyses evaluate how disinhibition modulates the structure of the stimulus-response relation. Whereas some response properties changed significantly from control to PTX, the dependency on the duration of prestimulus inactivity persisted (Fig. 7, A–C ). Absolute delays between stimulus and response for individual recording sites typically decreased, resulting in an average decrease by 37.5% [30.7 Ϯ 2.4 ms (mean Ϯ SE) and 19.2 Ϯ 1.4 ms, control and PTX, respectively; Fig. 7 A ]. Response length increased by 185.0% (0.17 Ϯ 0.01 to 0.49 Ϯ 0.02 s), and the number of spikes/response increased by 84.4% (7.8 Ϯ 0.5 to 14.4 Ϯ 1.0 spikes). The modulation of response delays by the duration of prestimulus inactivity, however, persisted under disinhibition (Fig. 7, B and C ). We thus asked for the temporal dependency on response delay in the time after spontaneous bursting und disinhibition. The change, ⌬ delay ϭ delay control Ϫ delay PTX, estimates this influence for increasing periods of inactivity before stimulation. The most recording sites had a fixed contribution of inhibition ( ⌬ delay Ϸ constant, 128 / 238 sites, 54%). At all other locations, the influence of disinhibition decreased with time after a burst, suggesting a decreasing influence of inhibition. Among those, one subset ( group 1 , 12%; Fig. 7 B ) started at positive differences and decayed with negative slopes. The remainder (group 2, 34%; Fig. 7 C ) started at negative differences and decayed with positive slopes. Interestingly, the recording sites in group 1 tended to be closer to the stimulation site than those in group 2 (Fig. 7 D ). These analyses suggest that the effect of inhibition on response delay for each recording site depends both on the timing of stimulation relative to the last burst and its distance to the stimulation site, which raises the question of how the spatiotemporal dynamics of evoked activity is affected by disinhibition. To this end, we quantitatively assessed changes of response delay under control and PTX with respect to the distance-to- stimulation site and the timing of stimulation. Linear regression of the form y(x) ϭ kx ϩ m was fit to the data under control and PTX for experiments with different postburst intervals. The R 2 estimated the correlation between response delay and distance-to- stimulation site, and the inverse of the regression slope estimated the speed of propagation. Response delays were positively correlated with the distance-to-stimulation site in the majority of experiments under control conditions (Fig. 8, A and B ; P Ͻ 0.05 for 55 / 108 postburst intervals). This effect was enhanced under disinhibition, as the distribution of R 2 clearly shifted to larger values with PTX (Fig. 8 B ; P Ͻ 0.05 for 96 / 104 postburst intervals). These data indicate a propagation of evoked activity from the site of stimulation that is facilitated further by blocking GABAergic inhibition. A possible mechanism could be a more reliable activation of postsynaptic neurons due to reduced inhibitory inputs in polysynaptic responses, e.g., because of, on average, more long- range projections of excitatory neurons. In support of this is that the average response reliability for the upper quintile of recording sites with largest delays to the first spike in the response increased more strongly from control to PTX (58% vs. 73%) than that for all other sites with smaller delays (70% vs. 73%). The slope of the regression was extracted when the linear regression model provided a significant good fit (F-test for goodness of fit, ␣ ϭ 5%; for three experiments, ␣ was set to 9%). The goodness-of-fit criterion was reached for 65 / 108 postburst intervals under control and 85 / 104 with PTX. Propagation speed increased with longer postburst intervals and was typically higher within the same network under disinhibition (Fig. 8 C ). Disinhibition thus increased the correlation between response delay and distance-to-stimulation site and pronounced the dependence of activity propagation on the timing of stimulation. The variability of network responses to identical stimuli is a key issue in many neurobiological and neurotechnological paradigms and has been attributed to interactions between ongoing and evoked neuronal activity. We reduced this interaction to simple electrical stimuli applied ...

Context 3

... vitro that were spiking spontaneously with bursts of variable lengths and IBIs. The effect and efficacy of these stimuli depended on the time delay between previous network burst and the stimulus, the distance to the stimulation site, and the efficacy of GABAergic inhibition. We derived analytical stimulus-response relations and found that response-length modulation is best described by a saturating exponential function y ( t ) ϭ A ( 1 Ϫ e Ϫ ␣ t ). Response delay modulation followed a single exponential decay function y ( t ) ϭ Be Ϫ ␤ t ϩ C . The modulation of stimulus-response relations persisted under the blockage of inhibition, suggesting modulatory mechanisms, such as synaptic depletion, during the burst and subsequent replenishment in the period of inactivity (Cohen and Segal 2011). Our findings suggest that trial-by-trial variability in neuronal networks arises, to a significant extent, from state-dependent, input-output relationships. Alternating periods of bursting and inactivity modulate neuronal excitability, such that it is low directly after bursts and recovers gradually during inactivity. Single electrical stimuli induced early responses locally and a polysynaptic transfer of activity to more distant areas, showing as late responses (Fig. 3 C ). The length of responses with both early and late components increased with increasing delays of the stimulus to the preceding burst; concomitantly, polysynaptic delays decreased. Comparing response delays with prestimulus activity revealed a remarkable relation: variations of prestimulus inactivity in the range of seconds correlated with changes of the delay of late responses of tens of milliseconds (Fig. 4, C and D ). How can stimulus timing modulate response length and delay? Inhibition shortened the responses at most sites and increased response delays. Response modulation persisted, however, when the networks were disinhibited (Fig. 7, B and C ), suggesting that inhibition interacts with additional mechanisms modulating stimulus-response relations. We therefore propose that short-term synaptic depression (STD) by spontaneous bursts, due to depletion of readily releasable neurotransmitter vesicles, limits response length and delay in conjunction with GABAergic inhibition. STD modulates synaptic transmission depending on the temporal characteristics of presynaptic input (Tsodyks and Markram 1997; Tsodyks et al. 1998). Sustained synaptic vesicle exocytosis during a burst depletes the readily releasable pool until firing ceases. Subsequent replenishment increases resource availability with increasing time after a burst. Placing a stimulus in the late recovery phase yields longer responses for nearby sites because more synapses have recovered. Correspondingly, delays for distant sites decrease because synaptic input to these neurons increases as more synapses recover, and thus integration times shorten. Although we could not directly validate STD and the depletion of presynaptic resources, the rate of replenishment and release probability that controlled population burst duration and timing in CA3 pyramidal cells support it (Staley et al. 1998). STD has been reported for synapses in culture (Opitz et al. 2002; Vogt et al. 2005), and the rate of replenishment is in good agreement with spontaneous burst intervals (3–16 s) (Stevens and Wesseling 1998). Synaptic vesicle depletion in hippocampal microcultures terminated spike-triggered network bursts (Cohen and Segal 2011). Furthermore, compared with cellular excitability modulation, a model of activity-dependent synaptic depression better replicated the dynamics of oscillatory discharges and increasing response lengths with longer duration of preceding inactivity in the chick spinal cord (Tabak et al. 2000, 2001). A close link between single-neuron threshold dynamics and magnitude of synchronized network activity has been demonstrated recently in cortical neuronal networks in vitro too (Wallach and Marom 2012). In addition, spike- frequency adaptation in single neurons during high bursting activity could further affect stimulus-response dynamics. Giugliano et al. (2004) have previously described comparable collective dynamics for cultured cortical neurons and for leaky integrate-and-fire neurons with spike-frequency adaptation. A build-up of the adaptation during the transition from silence to bursting could mediate the termination of bursts. Although it is largely unknown which biological mechanisms generate and modulate synchronous network-wide bursting, a variety of functional roles has been suggested (Lisman 1997; Meister et al. 1991; Mongillo et al. 2008). What can be understood, though, is the causal relation between bursting and inactivity through the correlation between preceding or following interval and burst duration (Tabak et al. 2001). Our findings suggest that network bursts may depress synaptic transmission to a fixed low threshold (Fig. 2 B ) and that this, in conjunction with inhibition (Fig. 6), terminates a burst. Synaptic efficacy would then recover in the following period of inactivity until spontaneous fluctuations, e.g., of the activity of small populations of neurons (Gritsun et al. 2010), trigger the next burst. Removing inhibition allowed bursts to become longer and thus deepen the synaptic depression. Consistently, the minimal periods of recovery to a level that enables the next spontaneous burst became longer too (Fig. 6). Recovery exceeding this minimum in the period until the next burst is initiated builds up resources that extend the duration of the upcoming burst. Disinhibition facilitates spatial-temporal propagation. Evoked responses propagate from the site of stimulation. Recording sites with exclusively late responses were more distant to the stimulation site than those with early and late responses (Fig. 3 C ), suggesting that early responses reflect direct stimulation or monosynaptic connections. In addition, we found response delays generally increasing with increasing distance-to-stimulation site (Fig. 8 A ). The connectivity in these cultured networks is not spatially homogeneous but because of density and developmental effects, tends to be clustered and includes long-range connections (Kriegstein and Dichter 1983; Soriano et al. 2008). This likely contributes to a rich set of connection motives, resulting in a broad range of response delays and directions of propagation. In addition, propagation speeds would vary locally. We found that propagation speeds largely depended on the individual network and to a smaller degree, on the timing of stimulation (Fig. 8 C ). The median propagation speed across all networks and postburst intervals was 0.20 mm/ms. Our findings are in good agreement with the properties of the propagation activity upon electrical or sensory stimulation of cortical tissue in vitro and in vivo. In vivo, direct anti- or orthodromic activation of the most excitable elements, namely the axons (Nowak and Bullier 1998; Tehovnik et al. 2006), in the vicinity of the stimulation site is conveyed polysynaptically into distant areas (Biella et al. 2002; Butovas and Schwarz 2003). Propagation speeds for tone-evoked responses were Ϸ 0.1 mm/ms in deep layers of auditory cortex (Sakata and Harris 2009) and Ϸ 0.1– 0.25 mm/ms for visual- evoked responses in visual cortex (Grinvald et al. 1994). In our study, disinhibition by blockage of GABA A receptors increased the correlation between response delay and distance- to-stimulation site and thus facilitated the propagation of excitation (Fig. 8 B ). The median propagation speed increased, and the SD across all networks decreased. The latter was mainly due to a smaller variability of propagation speeds across different networks and therefore suggests a strong het- erogeneity in the strength and spatial distribution of inhibition across different networks. For individual networks, however, we saw an increased modulation of propagation speed by the timing of stimulation. This could be explained by stronger synaptic depression after longer bursts with more spikes under PTX, followed by full recovery during periods of inactivity. The observation that the contribution of inhibition to the modulation of the responses changed with distance to the stimulation site suggests that whereas local inhibition strongly shapes the properties of local responses, it appears to show with a greater effect on response reliability during polysynaptic transmission toward distant network locations. This would be in agreement with the assumption of mainly local output of inhibitory neurons and long-range excitatory connectivity (Eytan et al. 2003). Network responses at some distance would thus decreasingly depend directly on the specific design of the stimulus but indirectly through its shaping influence on local responses and recruitment. Defined interaction with ongoing activity. Stimulation at fixed lags relative to bursts at a selected feedback site decreased response-length variability below the level of variability for spontaneous burst length (Fig. 5 C ). Responses under fixed IstimI and thus varying lags to preceding bursts varied approximately as much as spontaneous bursts. These findings confirm that the state of the network at the moment of stimulation critically determines neuronal responsiveness (Arieli et al. 1996; Curto et al. 2009; Hasenstaub et al. 2007; Kisley and Gerstein 1999). Our goal was to obtain analytical models for state-dependent stimulus-response relations, and we found nonlinear interactions between the duration of prestimulus inactivity and response properties. Previous models assuming a linear superposition of a reproducible response with a response component determined by the network’s activity state at stimulus onset (Arieli et al. 1996) were refined by Kisley and Gerstein (1999), who showed that the variability itself can be state dependent. Current models for sensory-evoked responses in functional ...