Modeling the effect of locus coeruleus firing on cortical state dynamics and single-trial sensory processing Houman Safaaia, Ricardo Nevesb, Oxana Eschenkob, Nikos K. Logothetisb,c,1, and Stefano Panzeria,1 a Neural Computation Laboratory, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy; bDepartment of Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, 72076 Tü bingen, Germany; and cDivision of Imaging Science and Biomedical Engineering, University of Manchester, Manchester M13 9PT, United Kingdom

Contributed by Nikos K. Logothetis, August 20, 2015 (sent for review June 22, 2015)

Neuronal responses to sensory stimuli are not only driven by feedforward sensory pathways but also depend upon intrinsic factors (collectively known as the network state) that include ongoing spontaneous activity and neuromodulation. To understand how these factors together regulate cortical dynamics, we recorded simultaneously spontaneous and somatosensory-evoked multiunit activity from primary somatosensory cortex and from the locus coeruleus (LC) (the neuromodulatory nucleus releasing norepinephrine) in urethane-anesthetized rats. We found that bursts of ipsilateral-LC firing preceded by few tens of milliseconds increases of cortical excitability, and that the 1- to 10-Hz rhythmicity of LC discharge appeared to increase the power of deltaband (1–4 Hz) cortical synchronization. To investigate quantitatively how LC firing might causally influence spontaneous and stimulus-driven cortical dynamics, we then constructed and fitted to these data a model describing the dynamical interaction of stimulus drive, ongoing synchronized cortical activity, and noradrenergic neuromodulation. The model proposes a coupling between LC and cortex that can amplify delta-range cortical fluctuations, and shows how suitably timed phasic LC bursts can lead to enhanced cortical responses to weaker stimuli and increased temporal precision of cortical stimulus-evoked responses. Thus, the temporal structure of noradrenergic modulation may selectively and dynamically enhance or attenuate cortical responses to stimuli. Finally, using the model prediction of single-trial cortical stimulus-evoked responses to discount single-trial state-dependent variability increased by ∼70% the sensory information extracted from cortical responses. This suggests that downstream circuits may extract information more effectively after estimating the state of the circuit transmitting the sensory message.

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oscillations state dependence somatosensation

via a highly distributed noradrenaline release in the forebrain (5). In particular, the LC contributes to regulation of arousal and sleep; it is involved in cognitive functions such as vigilance, attention, and selective sensory processing (5–7); and it modulates cortical sensory responses and cortical excitability (8). Here, we investigated how LC firing influences spontaneous and stimulus evoked cortical activity by performing simultaneous extracellular recordings of spontaneous and somatosensorystimulation–evoked neural activity in the primary somatosensory cortex (S1) and in both ipsilateral LC (i-LC) and contralateral LC (c-LC) in urethane-anesthetized rats. We first use these data to investigate the statistical relationships between the temporal structure of LC firing and the changes in cortical excitability, and we then construct a dynamical systems model of the temporal variations of cortical multiunit activity (MUA) that describes quantitatively the dynamic relationships between LC firing, spontaneous cortical activity dynamics, and cortical sensory-evoked responses. We use this model to study how a specific neuromodulatory input may influence the information content and the readout of cortical information representations of sensory stimuli. Results Neurophysiological Recordings from Somatosensory Cortex and LC in Urethane-Anesthetized Rats. To investigate the relationship be-

tween the dynamics of noradrenergic cell firing and of ongoing and stimulus-evoked cortical activity, we recorded simultaneously the multiunit spiking activity in S1 and in LC of urethane-anesthetized rats (n = 4). MUA in S1 was recorded using a Significance

| dynamical systems | information coding |

Understanding what makes a cortical neuron fire is fundamental to understand how neural circuits operate. We used simultaneous recordings from the locus coeruleus (the neuromodulatory nucleus releasing norepinephrine) and from the somatosensory cortex to formulate a mathematical model explaining how cortical responses originate from the interplay of the sensory drive that cortical neurons receive, the spontaneous dynamics of cortex, and the effect of neuromodulation. Our work provides a hypotheses about how the temporal structure of locus coeruleus burst firing regulates the amplitude and timing of changes in cortical excitability and may selectively amplify responses to salient sensory stimuli. It also suggests that downstream circuits may better decode the activity of a cortical sensory network after estimating its neuromodulatory state.

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esponsiveness of cortical sensory neurons is state dependent. In other words, the neural responses to a sensory stimulus do not only depend on the features of extrinsic sensory inputs but also on intrinsic network variables that can be collectively defined as the “network state” (1). Cortical sensory neurons receive information about the external world from peripheral receptors via feedforward sensory pathways. However, the abundance of recurrent and feedback connectivity (2) may generate ongoing activity that shapes the background on which the afferent information is processed (3). In addition, neuromodulatory inputs from neurochemically specialized brain nuclei that are not part of the direct spino-thalamo-cortical pathway can modulate the dynamics of cortical networks (4), as well as control the animal’s behavioral state. The concurrent integration of information about the external world and about internal states is likely to be central for computational operations of cortical circuits and for the production of complex behavior, yet its mechanisms and implications for neural information processing are still poorly understood. The locus coeruleus (LC) is a brainstem neuromodulatory nucleus that likely plays a prominent role in shaping cortical states 12834–12839 | PNAS | October 13, 2015 | vol. 112 | no. 41

Author contributions: H.S., O.E., N.K.L., and S.P. designed research; H.S., R.N., O.E., and S.P. performed research; H.S. and S.P. contributed new reagents/analytic tools; H.S. and S.P. analyzed data; and H.S., R.N., O.E., N.K.L., and S.P. wrote the paper. The authors declare no conflict of interest. Freely available online through the PNAS open access option. 1

To whom correspondence may be addressed. Email: [email protected] or nikos. [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1516539112/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1516539112

How the Dynamics of LC Firing Influences Cortical State Changes. To understand the role of noradrenergic cell firing in shaping cortical dynamics, we first investigated whether there were systematic temporal relationships between them during spontaneous activity. (Unless otherwise stated we hereafter report mean ± SEM as statistics computed over the dataset.) We computed the cross-correlogram between the time course of i-LC firing [which was the LC that—in agreement with anatomical connectivity (9) and other results reported in Supporting Information—influenced ipsilateral cortical MUA the most] and that of cortical MUA, finding that it peaked when i-LC activity was shifted back by ∼20–25 ms (Fig. S2A). In addition, we computed—using transfer entropy (TE) (see ref. 10 and Supporting Information)—the amount of causation exerted by i-LC MUA on cortical MUA, and we compared it with the amount of causation exerted by cortex on i-LC. We found that the TE from i-LC to cortex was significant (P < 0.001, t test) and was 2.9 ± 1.1 times larger (P < 0.001; paired t test) than in the reverse direction (Fig. 1D; see also Fig. S2). Together, these results support the hypothesis that LC firing exerts a causal influence on cortex within few tens of milliseconds. To further investigate how the temporal structure of LC firing may influence that of cortical activity, we then computed the correlation between the frequency spectrum of i-LC MUA and that of S1 MUA (both computed from the same 1.5-s spontaneous activity window). To focus on genuine time variations of LC firing, we normalized the power of i-LC MUA to its time average in the trial. We found (Fig. 1F) a significant (P < 0.01, paired t test) positive correlation between the low-frequency (1– 10 Hz) power of i-LC MUA and the power of delta-band (1– 4 Hz) cortical MUA. This positive correlation suggests that one Safaai et al.

Fig. 1. Relationship between firing of LC and cortex. (A) Example trial showing the time course of data and model during the state detection and the prediction period of spontaneous activity. (Top) Raster of spikes recorded in each cortical channel. (Middle) Mass cortical MUA (sum of spikes from all cortical channel, plotted as black dashed line and expressed in units of spikes per second per channel) is compared with the output of true-LC (red line) and no-LC (green) model. (Lower) Time course of i-LC (black line) and c-LC (gray line) MUA, plotted in SD units (SDUs). (B) Example trial showing data and model during the state detection period and the prediction period of stimulus-evoked activity. Conventions are as in A, with the addition of a series of gray vertical pulses plotting the model’s stimulus-drive function obtained in this trial. (C) Power spectra (normalized by the total power in the 1- to 50-Hz range) of cortical MUA (Left) and i-LC MUA (Right). (D) TE computed from either c- or i-LC to S1 or in the opposite direction. Power spectra (normalized by the total power in the 1- to 50-Hz range) of cortical MUA (Left) and i-LC MUA (Right). Results plotted as mean ± SEM over the dataset. (E) The fraction of elevation (with respect to the phase in which MUA is minimal) of the real MUA of i-LC and cortex plotted against the phase of cortical activity in delta (1–4 Hz)-band. Results are plotted as mean ± SEM across dataset (n = 830 spontaneous trials) in C and as mean across dataset and bootstrap-estimated SD in D and E. (F) Average over the dataset of the Pearson correlation between i-LC power (normalized by the i-LC firing rate in the trial) and cortical power at each frequency.

effect of the low-frequency rhythmicity of LC is to increase the power of low-frequency synchronized fluctuations of cortical excitability. In other words, the low-frequency rhythmicity of LC MUA amplifies low-frequency cortical state variations. We note that the delta cortical power did not correlate (P > 0.2, t test) with LC averaged firing rate (Fig. S3A), and thus the amplification of cortical slow oscillations was specifically related to low-frequency rhythmicity of LC activity. However, there was a significant (P < 0.01, paired t test) negative correlation between LC firing rate and S1 MUA power in the 5- to 20-Hz range, suggesting that the level of tonic LC firing varies across cortical states (11). Finally, we investigated the relationship between the timing of i-LC firing and of the cortical delta-band state fluctuations. We expressed the timing of low-frequency fluctuations between periods of low and high cortical excitability using the phase of PNAS | October 13, 2015 | vol. 112 | no. 41 | 12835

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linear electrode array (28 contacts with 50-μm spacing) covering most of the cortical depth and placed in the S1 hindpaw representation in the hemisphere contralateral to the stimulated paw. Hereafter, we analyzed the mass cortical MUA obtained pooling spiking activity from all cortical electrodes (abbreviated as “cortical MUA”). The LC MUA was recorded using two single electrodes each placed in the LC core, i-LC and c-LC to the S1 recording site. We recorded data both during stretches of spontaneous neural activity and during intermittent somatosensory stimulation. Specifically, trains of five electrical pulses were delivered to the hindpaw; the pulses were presented at three different frequencies (15, 25, and 35 Hz) and three different amplitudes (1, 3, and 5 mA), and each of the nine stimulus types were delivered in random order with a 10-s interval and were repeated 20–30 times per session. In absence of sensory stimulation (spontaneous periods), cortical spiking activity was highly synchronized across neurons and underwent slow variations in excitability, with typically one to four peaks of spontaneous firing per second alternating with periods of reduced firing (Fig. 1 A and B and Fig. S1 A and B). Consequently, the power spectrum of spontaneous cortical MUA (Fig. 1C) had the highest power at low frequencies. Spontaneous MUA of i-LC and c-LC was characterized by phasic elevations of firing (called “bursts” hereafter) alternating with periods of reduced activity (Fig. 1 A and B). The bursts of LC MUA happened typically four to seven times per second, and thus were more frequent than the peaks of spontaneous cortical firing. Power spectra of LC MUA (Fig. 1C) showed a local peak in the 4- to 7-Hz range, capturing the rhythmic nature of the timing of LC bursts. S1 neurons responded to the pulses of somatosensory stimulation (Fig. 1B and Fig. S1 C and D) with a short-latency discharge (likely reflecting primarily spinothalamic input) and a longer-latency sustained component (likely reflecting also nonspecific input and engagement of recurrent or top-down networks). After somatosensory stimulation, both LCs fired before the S1 longer-latency response (Fig. 1B and Fig. S1 C and D).

delta-band cortical MUA, with phase π and 0 representing the peak and trough of cortical firing, respectively (Fig. 1E). We found that—consistent with results obtained during NREM sleep (8)—i-LC was significantly phase-locked (Rayleigh test, P < 0.05) to the cortical delta rhythm, and that it fired preferentially one-eighth of cycle (π/4 radians) ahead of peak cortical excitability. This suggests that a burst of LC firing (such as, e.g., those plotted in Fig. 1 and Fig. S1) facilitates the transition to a state of higher cortical excitability after a few tens of milliseconds. A Dynamical Systems Model of the Relationship Between LC Firing and Cortical State Changes. Our goal was to characterize quanti-

tatively if and how the dynamics of the spontaneous low-frequency changes in cortical excitability interacts with the firing of LC neurons and with the afferent sensory drive to generate statedependent cortical representations of stimuli. Extending the work of ref. 12, we described quantitatively the time course of cortical MUA with a simple discrete-time dynamical system inspired by the FitzHugh–Nagumo model (13). In brief, the model (schematized in Fig. 2A and Fig. S4, and denoted hereafter as the “true-LC model”) describes cortical activity in an effective (rather than biophysically detailed) way. It contains activity variables that can be interpreted as summarizing the total rate of excitatory and inhibitory neurons in a cortical network and it contains terms of self-excitation and inhibition that lead to ongoing intrinsic fluctuations of the activity, as well as an input term describing the stimulus drive to the cortical network following the application of a somatosensory stimulus. Importantly, it also models the potential causal effect of LC on

Fig. 2. Schematics and performance of the model. (A, Top) Time course of cortical MUA is modeled as a self-exciting and inhibiting dynamical system coupled to a neuromodulatory input (MUA recorded in the LCs) and a stimulus drive. (Bottom) The model was fitted to real cortical MUA during a state detection period of spontaneous activity (from t = −1.5 to 0 s), and then it was solved in the prediction period (from t = 0 s onward). (B) Time average during the state detection period of the normalized absolute fit error of the no-LC and true-LC model. (C) Time average over the 100- to 200-ms range of the prediction period of the noise correlation between the variation around the trial average of cortical MUA at a given time and the following five predictions: MUA predicted by either no-LC or true-LC model, by synchronization index (S.I.) during the state detection period, by deltaband phase of cortical MUA (indicated as ϕ0) or by the MUA amplitude (ν0) at stimulus onset. In B and C, graphs plot mean ± SEM over the dataset (n = 830 spontaneous trials, n = 826 evoked trials). In all figures, the single asterisk (*), double asterisk (**), and triple asterisk (***) indicate significance values of P < 0.05, 0.01, and 0.001, respectively.

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cortex by including as input the MUA time series from both i- and c-LC (shifted in the past by a lag of 20 ms, whose value optimized model performance; Supporting Information). The best-fit parameters define our estimate of the cortical state and are used to predict the cortical activity afterward. This model contains both “activity state” model variables (such as S1 and LC firing) that describe cortical dynamics persisting on shorter timescales of few tens to few hundred milliseconds, and “dynamic-state” variables (such as the couplings in the dynamical systems model that specify how cortical MUA evolve in time) that describe properties of network dynamics on a timescale of seconds (12). To determine quantitatively cortical states, we first fitted the model to periods of spontaneous activity by minimizing (over a 1.5-s “state detection” or “fit” period) the error between the S1 MUA and its model prediction. To test how well the model kept tracking cortical dynamics, we then generated a prediction of cortical MUA in a postfit period (by solving the dynamics of the model with the best-fit parameters and the initial conditions given by the activity at the end of the fit period) for a further “prediction period” (until 500 ms after the end-of-fit period when predicting continuation of spontaneous activity, and until 300 ms after the end of paw stimulation when predicting responses to stimulation). To evaluate the specific effect of the time course of LC firing on the dynamics of synchronized cortical states, we compared the performance of the true-LC model (in which the time evolution of cortical MUA depended both on past cortical activity and past LC activity) to that of a second model, named “no-LC” model and similar to the one introduced in ref. 12, in which evolution of cortical MUA depended only on its own past but not on LC firing (Supporting Information). Examples of fits to individual periods of cortical spontaneous and stimulus-evoked activity are reported in Fig. 1 A and B and Fig. S1 A–D. Although both models followed reasonably well cortical firing dynamics, the true-LC model fitted and predicted it better. In particular, the true-LC model generated low-frequency fluctuations of cortical MUA with higher power than the no-LC model, and this led to a better match with the real cortical MUA (Fig. 1 A and B and Fig. S1 A–D). The true-LC model predicted better also the single-trial cortical response to the somatosensory stimulus (Fig. 1B and Fig. S1 C and D), suggesting that its more accurate representation of cortical states leads to a better prediction of the interaction between stimulus drive and ongoing activity that may generate the single-trial response to the stimulus. We quantified systematically the ability of the different models to represent the dynamics of ongoing spontaneous cortical activity. We found (Fig. 2B) a significant (P < 0.001, paired t test) advantage (35% reduction of fit error) of the true-LC model over the no-LC model in describing cortical dynamics during the fit period. This advantage was genuine and not simply due to the larger number of parameters in the LC model (Supporting Information). Moreover, the true-LC model predicted better the MUA in postfit periods of spontaneous activity, with an increase (P < 0.01; paired t test) of ∼90% of the Pearson correlation between real and model-predicted cortical MUA (Fig. S5A). The true-LC model also predicted better than the no-LC model the trial-averaged amplitude of the cortical MUA evoked by each stimulus (signal correlation between model and data; Fig. S5B; P < 0.001, paired t test) and the trial-to-trial variability of singletrial responses around their mean (noise correlations between model and data; Fig. 2C; P < 0.01, paired t test). In sum, the trueLC model predicted better both spontaneous and stimulus-evoked S1 dynamics. We performed further analyses of our models (reported in full in Supporting Information) that established that the prediction of the variations across trials of cortical stimulusevoked MUA obtained from both the no-LC and the true-LC model was much better than the prediction obtained from simpler proxies of cortical states such as the synchronization index Safaai et al.

(S.I.; Fig. S6C) or the cortical delta-phase or MUA amplitude at the time of stimulus application (Fig. 2C), demonstrating the value of dynamical systems in describing cortical states. To characterize the aspects of cortical dynamics that were better described by the true-LC model, we calculated the difference between the power of real cortical activity and that of the model at each frequency during spontaneous cortical dynamics (normalized dividing it by the total power in the 1- to 10-Hz range). This difference was positive for both models but was much larger for the no-LC model, especially in the delta frequency band (Fig. 3A), suggesting that the no-LC model generates too little delta-band power in comparison with real cortical MUA, and that introducing LC firing into the model increases the power of the low-frequency cortical fluctuations that it can generate, thereby improving the accuracy of the description of cortical dynamics. We then computed—as we did in real data— the correlation between spectra of i-LC MUA and of model S1 MUA. We found (Fig. S7C) a positive (P < 0.01, t test) correlation between the power of the i-LC MUA at low frequencies (1–10 Hz) and the power of model delta-band cortical MUA, as in real data. This suggests that the model captures the key role of lowfrequency LC rhythmicity in increasing the power of low-frequency synchronized cortical state variations (see Supporting Information for further analyses). The reason was that the best-fit parameters (Fig. S8) of the nonlinear coupling term between i-LC and cortical MUA had a sign that allowed LC bursts to either increase or decrease cortical excitability depending on whether cortical MUA is in the ascending or descending phase of its up-down state dynamics, thus adding oscillatory power to cortex (Fig. S9). Finally, we found that the phase coherence between real and model cortical MUA was higher (P < 0.001, paired t test) for the true-LC than for the no-LC model (Fig. 3B), because the trueLC model uses the timing of LC bursts to better predict the timing of peaks and troughs of cortical excitability. Extracting Sensory Information from State-Dependent Cortical Codes: Discounting State-Dependent Trial-to-Trial Variability. The large

trial-to-trial variability of cortical responses is a major obstacle in the readout of neural codes (14). Our results above—and several previous studies—show that variations in cortical state (12, 15– 17) and neuromodulation (4) contribute to trial-to-trial cortical response variability. Here, we explore the consequences of successfully modeling the neuromodulatory cortical state for the decoding of cortical responses to sensory stimuli. Given that our models can partly account for and predict the trial-to-trial variations of stimulus-evoked MUA responses, these model predictions can be used to increase the information about stimuli extracted from cortical activity. More sensory information can be obtained by simply subtracting out the estimated Safaai et al.

Fig. 4. Gaining sensory information by discounting model predictions of trial-to-trial variability. (A) This mechanism is exemplified with a single trial taken from real data. Stimulus 1 was presented in this trial, and the cortical MUA response in this trial (dark-blue full line) is plotted against the trialaveraged response to stimulus 1 (dashed blue) and to stimulus 2 (dashed red) for a 0- to 300-ms period after stimulus offsets. The true-LC model predicts that the response variation around the trial average in this trial was positive (thus, the model prediction of what should be subtracted—shown with black arrows—was negative). The subtraction of the predicted variability from the single-trial response produces a “discounted” response (light-blue full line) that is much closer to the trial-averaged response to the stimulus 1 that was presented in that trial, and it is thus much easier to decode, than the original response. (B) Time course of mutual information about the somatosensory stimuli computed from either the original cortical MUA at a given time, or after discounting from it the trial-to-trial variability using the predictions of each model. Results are plotted as mean ± SEM over n = 43 stimulus pairs.

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Fig. 3. Model performance in the frequency domain. (A) Difference between power spectrum of real MUA and MUA of true-LC and no-LC models, normalized by the mean power of real MUA power in the 1- to 10-Hz band. The black horizontal line shows the frequency range with significant difference between the two models. (B) The phase coherence between the delta-bands of the real cortical MUA and of the MUA predicted by each of the two models. A and B plot mean ± SEM over the dataset (n = 830 spontaneous trials).

state-induced trial-to-trial variations of these responses. This idea is illustrated with real data in Fig. 4A, which shows the time course of the trial-averaged stimulus-evoked S1 MUA to two stimuli of different intensity in a single example trial. This trial elicited a firing rate whose strength was in-between the mean rates of these two stimuli. This intermediate- strength response could conceivably have arisen either in response to the weakest stimulus when the network was in excitable state or in response from the strongest stimulus when the network was less excitable. This ambiguity can be resolved by computing the trial-to-trial variability predicted by the network state. In this example, the predicted variability was positive (indicating that the network was in a more excitable state). The subtraction of the predicted variability from the singletrial response (black downward arrows in Fig. 4A) produces a “variability-discounted” response much closer to the trial-averaged response of stimulus presented in that trial (and thus much easier to decode) than the original response. To quantify the effect of the reduction of variability on stimulus discrimination, we computed (see ref. 14 and Supporting Information) the information about which somatosensory stimulus was presented that is available in the original cortical MUA, and the information that can be extracted when subtracting out the state-dependent variability. Note that the prediction of statedependent variability was obtained by the model without any knowledge about which stimulus was presented, and that subtracting variability may not always be the optimal way to discount it. Thus, the difference between these two information values is a robust lower bound to the information that can be gained by discounting the state-dependent variability captured by the models. To avoid confounds resulting from differences in the pulse application times, we computed only information between pairs of stimuli with equal pulse frequency, but different intensity of the delivered electrical current. The time course of the information instantaneously available in these neural activities after the end of stimulus, averaged over all pairs of stimuli and sessions, is reported in Fig. 4B. We found that discounting the variability of MUA with the output of both true-LC and no-LC models leads to obtain significantly (P < 0.001, paired t test) more information than with the nondiscounted original MUA. The gain in information due to state variability discount was particularly large in the late (125–200 ms) sensory response component, which has

been shown to be particularly relevant for behavior (18). Across the 125- to 200-ms late-response period, the gain of information of the denoised responses over the information present in the original MUA was in the range of 32–71% for the true-LC model and 18–39% for the no-LC model. The advantage of the true-LC model over the no-LC model was statistically significant (P < 0.05, paired t test). Importantly, the information gained by discounting the variability estimated by the dynamical state models was much larger than the information that would be obtained by simply subtracting out the MUA at the time of stimulus application of by predicting state with S.I. or the cortical delta-phase or MUA amplitude at the time of stimulus presentation (Fig. S10A). This shows the worth of dynamical systems for extracting information from neural data. Modeling the Effect of LC Phasic Activation on Cortical Responses to Stimuli. We finally used our model to study how phasic activation

of LC may shape the cortical information representation of sensory stimuli. Phasic activation of LC refers to brief transient bursts of firing of LC neurons, which may happen spontaneously or be brought about by electrical stimulation of LC or by a salient external event (5). We created a series of simulated single-trial cortical responses to somatosensory stimuli using the true-LC model with the bestfit parameters and stimulus-drive functions taken from all trials in real data. For all such simulated trials, we ran two sets of calculations. In the first set, describing normal spontaneously occurring states, we ran the model using the true-LC time course in that trial as neuromodulatory input. In the second set, we simulated the effect of phasic activation of LC by adding to the true-LC dynamics a brief burst of firing (Fig. 5A) whose amplitude and timing was chosen to maximize the amplitude of the resulting stimulus-evoked response. We then inferred the specific effect of phasic LC activation by comparing the stimulusevoked cortical MUA across these two simulations. We found (Fig. 5B) that phasic LC activation increased the time-averaged amplitude of the MUA in the 125- to 200-ms post–end-of-stimulus late component that gives maximal stimulus information. We also observed a reduction of trial-to trial variability in response peak time and in rise time during the late response window when using phasic LC activation before stimulus presentation (Fig. 5C). Significant (P < 0.001, paired t test) reduction of variability was obtained even in the presence of trial-to-trial jitter between time of phasic LC activation and of stimulus application, as long as the jitter range was below 110 ms for peak time and below 40 ms for rise time (Fig. S11). The increased response to weaker stimuli and the increased precision of cortical spike times following phasic electrical stimulation of LC has been empirically reported (6, 19). Our model provides a possible mechanistic explanation of such previous findings. Our model predicts that, in a nonvigilant state (as is the rat state in our study), cortex will be more consistently excitable if the stimulus is presented shortly after the additional phasic LC activation, thereby making cortex more responsive particularly to weaker stimuli and quenching part of the fluctuations of excitability that cause variability of stimulus-evoked responses. Discussion Recently, much research has focused on how brain states affect the dynamics of cortical sensory responses (1, 15, 16, 20). In particular, statistical models have been developed to describe the relationships between indicators of network states and the spike counts observed in response to a stimulus (15–17). Our study adds critical insights about the dynamic interplay of spontaneous and stimulus-evoked activity. By formalizing state dependence using a dynamical system (12), we were able to capture important temporal relationships—for example, the relationship between periodic burst of LC firing and the amplitude and timing of 12838 | www.pnas.org/cgi/doi/10.1073/pnas.1516539112

Fig. 5. Simulating the effect of phasic LC input on the model stimulus responses. (A) Schematic of the simulated experiment: A phasic LC activation (shown in purple) is added to the recorded spontaneous LC firing (shown in gray). The stimulus-evoked MUA of the model after phasic stimulation is then compared with the stimulus-evoked MUA of the same model without the addition of the phasic LC pulse. (B) The cortical MUA model response to each of the stimuli averaged in the 125- to 200-ms post–end-of-stimulus response period. Full lines report stimulus-evoked responses with (purple) and without (gray) LC phasic activation, whereas the dashed black line reports spontaneous activity averaged in a randomly selected 75-ms period before the stimulus. For this plot, the nine stimuli indicated on the x axis were sorted according to their mean response across all recordings. (C) The SD across trials at fixed stimulus of the model’s peak response time and of the rise time, with and without addition of the phasic LC activation to the model. Throughout this figure, results are plotted as mean ± SEM over the dataset (n = 826 evoked trials).

changes in cortical excitability—which are not captured by spike count models that average the neural response over time. Moreover, by outperforming a widely used frequency analysis-based predictor of behavioral responses and of cortical responsiveness from neural recordings—the phase of low-frequency oscillations (21–23)—the dynamical systems approach shows the ability to capture complex nonperiodic temporal features that are relevant for sensory processing and that cannot be fully described by a frequency-band analysis. This underscores the promise of the dynamical systems approach to elucidate how neural circuits shape sensory processing. An important addition of our work to previous models of state dependence was the inclusion of the contribution of an important neuromodulator—the noradrenergic system. Our results support the hypothesis that the temporal structure of LC firing causally influences cortical dynamics and that, in particular, LC bursts may play a key role in regulating both the amplitude and timing of low-frequency cortical oscillations. Our model provides two predictions that can be tested by future interventional experiments designed to specifically manipulate the temporal structure of LC bursts: that their low-frequency rhythmicity increases the amplitude of cortical delta fluctuations and that their timing regulates when cortex is maximally responsive to stimuli and influences the spike timing reliability of cortical neurons. Although slow oscillations have a neocortical origin (24), our results raise the possibility that LC may be a key component of a larger network including thalamocortical loops (25) that may regulate slow oscillation and mediate their large-scale synchronization. LC phasic activity may modulate slow oscillations via direct coerulear-cortical projections or indirectly via temporal synchronization of activity within multiple members of the ascending system or cortico-thalamic loops. The role of LC in this potentially wide network could be investigated by generalizing this work to model the interaction between LC and multiple simultaneously recorded cortical and thalamic regions, and the resulting model predictions could be directly tested by future interventional experiments. Our data were obtained in anesthetized animals. However, this still allows speculating about the influence of phasic LC Safaai et al.

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most cortico-cortical synapses connect proximal neurons (27), the state variables will often be shared by the neuron sending a message and the neuron receiving it; thus, state-dependent decoding may work well for many cortical computations. Materials and Methods These data were recorded from four male Sprague–Dawley rats (250–350 g). All experiments were approved by local authorities (Regierungspräsidium Tübingen, Germany, Referat 35, Veterinärwesen), in accordance with the regional animal welfare committee pursuant to §15 of the German Animal Welfare Act (Kommission nach §15 des Tierschutzgesetzes), and fully complied with Directive 2010/63/EU of the European Union and of the council on the protection of animals used for scientific purposes. MUA was simultaneously collected from 28 electrodes (array spacing, 50 μm; impedance, 200 kΩ) placed in the paw representation area of the right-hemisphere S1 cortex (S1) while the rats were anesthetized with urethane. At the same time, MUA was also recorded from both left and right LC using single microelectrodes. We recorded responses to nine different trains of electrical left hindpaw stimulations (three different frequencies and three different amplitudes) and during spontaneous activity before the stimulus application. A finite-difference dynamical systems model of cortical S1 MUA (Eqs. S1– S5) was fit to the data by choosing model parameters minimizing the fit error (Eq. S9) between real S1 MUA and its model prediction during a 1.5-s fit period of spontaneous activity. The model was also used to predict the time course of cortical MUA for further periods of spontaneous or stimulusevoked activity. We described the data using two models: the true-LC model that contains a coupling term between LC activity and cortical dynamics (Eq. S5), and a no-LC model that does not have this coupling term. Information and TE were computed from Eqs. S11–S13 using a brute-force estimation of the neural response probability discretized into a small number of bins and using bias corrections (28). Full details on neurophysiological procedures and analysis are described in SI Materials and Methods. ACKNOWLEDGMENTS. We thank J. Assad, T. Fellin, P. Series, and members of S.P.’s laboratory for useful feedback. This work was supported by the European Commission (FP7-ICT-2011.9.11/284553, “SICODE,” and FP7-20072013/PITN-GA-2011-290011, “ABC”), by the Max Planck Society, and by the Autonomous Province of Trento (“Grandi Progetti 2012,” “ATTEND”). 17. Ecker AS, et al. (2014) State dependence of noise correlations in macaque primary visual cortex. Neuron 82(1):235–248. 18. Sachidhanandam S, Sreenivasan V, Kyriakatos A, Kremer Y, Petersen CCH (2013) Membrane potential correlates of sensory perception in mouse barrel cortex. Nat Neurosci 16(11):1671–1677. 19. Lecas JC (2004) Locus coeruleus activation shortens synaptic drive while decreasing spike latency and jitter in sensorimotor cortex. Implications for neuronal integration. Eur J Neurosci 19(9):2519–2530. 20. Kayser C, Wilson C, Safaai H, Sakata S, Panzeri S (2015) Rhythmic auditory cortex activity at multiple timescales shapes stimulus-response gain and background firing. J Neurosci 35(20):7750–7762. 21. Vanrullen R, Busch NA, Drewes J, Dubois J (2011) Ongoing EEG phase as a trial-by-trial predictor of perceptual and attentional variability. Front Psychol 2:60. 22. Thut G, Miniussi C, Gross J (2012) The functional importance of rhythmic activity in the brain. Curr Biol 22(16):R658–R663. 23. Schroeder CE, Lakatos P (2009) Low-frequency neuronal oscillations as instruments of sensory selection. Trends Neurosci 32(1):9–18. 24. Destexhe A (2011) Intracellular and computational evidence for a dominant role of internal network activity in cortical computations. Curr Opin Neurobiol 21(5): 717–725. 25. Lemieux M, Chen JY, Lonjers P, Bazhenov M, Timofeev I (2014) The impact of cortical deafferentation on the neocortical slow oscillation. J Neurosci 34(16):5689–5703. 26. Usher M, Cohen JD, Servan-Schreiber D, Rajkowski J, Aston-Jones G (1999) The role of locus coeruleus in the regulation of cognitive performance. Science 283(5401): 549–554. 27. Braintenberg V, Schuetz A (1998) Cortex: Statistics and Geometry of Neuronal Connectivity (Springer, Berlin). 28. Magri C, Whittingstall K, Singh V, Logothetis NK, Panzeri S (2009) A toolbox for the fast information analysis of multiple-site LFP, EEG and spike train recordings. BMC Neurosci 10:81. 29. Marzo A, Totah NK, Neves RM, Logothetis NK, Eschenko O (2014) Unilateral electrical stimulation of rat locus coeruleus elicits bilateral response of norepinephrine neurons and sustained activation of medial prefrontal cortex. J Neurophysiol 111(12):2570–2588. 30. Mormann F, Lehnertz K, David P, Elger CE (2000) Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D 144(3-4):358–369.

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NEUROSCIENCE

firing when salient stimuli are presented during a nonvigilant state. Phasic LC activity may selectively facilitate responses to task-relevant processes and filter away responses to irrelevant events (7) or orient attention to salient events (5). Fluctuations in cortical excitability may be a key mechanism for the selection of salient variables (23) as they permit selective amplification or attenuation of stimulus responses depending on whether stimuli are presented at more or less excitable states. Thus, the ability of the low-frequency rhythmicity of LC bursts to enhance the power of fluctuations in cortical excitability may enhance salient variables. Our work highlights the importance of timing of LC burst: suitably timed LC burst (for example, triggered by an alerting stimulus) can very rapidly trigger transitions into excitable cortical states, which in turn decrease the threshold for cortical responses and thus dynamically facilitate the processing of salient or attended events. That LC bursts may modulate dynamically the threshold for cortical processing and regulate stimulus selection was proposed in connectionist models (26). Our work identifies potential neural mechanisms and reveals the precise timescales of this phenomenon. The state dependence of neural responses profoundly constrains how neural circuits exchange information. State dependence may either force neurons to transmit information only using codes that are robust to state fluctuations (e.g., relative firing rates), or may force downstream neurons to gain information about the state of the networks sending the sensory messages and then to use the knowledge of state to properly interpret neural responses. Our results suggest that the latter information transmission scheme is feasible, because detecting state by either monitoring the dynamics of cortical ongoing activity alone or by also monitoring the dynamics of noradrenergic modulation substantially increased the amount of information about sensory stimuli in the late response components relevant for behavior. Given that ongoing dynamics appears correlated over relatively large spatial scales and that norepinephrine is released diffusely, it seems conceivable that state variables are shared by other neurons in the same or a nearby region. Because

Modeling the effect of locus coeruleus firing on cortical state dynamics and single-trial sensory processing.

Neuronal responses to sensory stimuli are not only driven by feedforward sensory pathways but also depend upon intrinsic factors (collectively known a...
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