Results from rodent somatosensory (barrel) cortex, however, have generally contradicted those in the visual system. VSD imaging of cortical responses to whisker deflection have revealed lower-amplitude and more spatially confined responses during Up states compared with Down states (Petersen et al., 2003; Civillico and Contreras, 2012). A quenching effect of Up states on whisker-evoked responses in barrel cortex is also evident from the reduced spiking output of single cortical neurons compared to the Down state (Sachdev et al., 2004; Hasenstaub et al., 2007; **Figure 6**). Discrepancies between visual and somatosensory cortex regarding the influence of Up states in sensory responsiveness could have a number of explanations. As suggested above, the relation between the reversal potential of the sensory-evoked synaptic response and the average membrane potential during the Up state is one factor that could determine the direction in which the Up state affects responsiveness. If the sensory-evoked synaptic reversal potential is comparable to the membrane potential during the Up state, there will hardly be any driving force for the sensory response during the Up state. The relative combinations of excitatory and inhibitory conductances recruited by sensory stimulation determine the sensory-evoked synaptic reversal potential. It could be that the precise combination of these conductances leads to a more hyperpolarized reversal potential in barrel cortex compared to visual cortex. In support of the notion that low driving force during the Up state accounts for the reduced effectiveness of sensory stimulation compared to the Down state, sensory-evoked PSPs in barrel cortex neurons were significantly larger during Down states compared to Up states (Sachdev et al., 2004); in visual cortex, no significant difference was found between PSPs evoked in the Up vs. the Down state (Haider et al., 2007). In contrast, injection of depolarizing current during the Down state in barrel-cortical neurons to maintain the membrane potential at the level encountered during Up states enhanced spiking output to whisker stimulation (Hasenstaub et al., 2007; **Figure 6**), which is inconsistent with the notion that a reduction of driving force alone accounts for reduced sensory-evoked responses during the Up state. Additionally, consistent with in vitro work (Shu et al., 2003a; see ''Up states affect intrinsic responsiveness'' Section), injection of artificial PSPs into barrel-cortical neurons more readily elicited spiking during Up states than during Down states (Hasenstaub et al., 2007).

Thus, the diminished response in barrel cortex to whisker deflection during Up states does not seem attributable to properties intrinsic to neurons, such as their depolarization, spike threshold, or membrane conductance, but rather to network effects. Network-level mechanisms for decreased responsiveness to whisker stimulation during Up states in barrel cortex likely involve an overall decreased stimulus-evoked synaptic conductance compared to the Down state, most likely due to depression of thalamo- and corticocortical synapses during network activity, and a relative increase of the contribution of inhibition over excitation to the stimulus-evoked synaptic conductance during the Up state compared to the Down state. Both of these possibilities were suggested via estimates of stimulus-evoked synaptic conductance and the contributions of excitation and inhibition to this conductance in Up vs. Down states in barrel cortex (Hasenstaub et al., 2007). One would therefore predict that in visual cortex, where Up states enhance responses to sensory stimuli, stimulus-evoked synaptic conductances are not significantly smaller in the Up state compared to the Down state, or that evoked inhibition is not comparatively larger in the Up state compared to the Down state. Whether there is a difference between barrel cortex and visual cortex in these regards is not known. Interestingly, whereas the response to brief whisker deflections is diminished by the

Down state compared to the Up state. Decreased driving force due to depolarization during the Up state is unlikely to explain this effect since it is not seen with depolarizing current injection during the Down state. Network effects (e.g., thalamocortical synaptic depression or increased intracortical synaptic inhibition) are more likely to account for reduced responsiveness in barrel cortex neurons during the Up state compared to the Down state. (Right) Conversely, in cat visual cortex, drifting-grating stimuli evoke larger spiking output during Up states compared to Down states. Left adapted by permission from the Society for Neuroscience: Journal of Neuroscience (Hasenstaub et al., 2007), © 2007. Right adapted by permission from the American Physiological Society: Journal of Neurophysiology (Haider et al., 2007), © 2007.

occurrence of Up states, responses to temporally prolonged whisker stimulation are enhanced (Hasenstaub et al., 2007). Thus, the effect of Up states on sensory-evoked responses in cortex can also depend on the dynamics of the stimulus.

Intensity of the sensory stimulus is another possible factor that determines the direction in which Up states modulate sensory responses in cortex. This issue was recently addressed in rat auditory cortex, in which a range of sound stimulus intensities was used, and whose effects on cortical responses were compared between Up and Down states (Reig et al., 2015). In this study, the direction in which Up states modulated neuronal responsiveness during sensory stimulation depended on stimulus strength: responses to weak stimuli were potentiated and responses to strong stimuli were diminished by Up states. The authors attributed the stimulus-intensity-dependent effect of Up states on cortical responses to the competition between thalamocortical network excitability and neuronal membrane conductance, both of which increase during Up states. In essence, high network excitability, associated with Up states, favors low-intensity stimuli, whereas low membrane conductance, associated with Down states, favors high-intensity stimuli. Another possible mechanism for the stimulus-intensitydependent effect of Up states on neuronal responsiveness (i.e., potentiation at low intensities and suppression at high intensities) was suggested by Shu et al. (2003a), who described an identical effect using artificial EPSPs as stimuli during both natural Up states and simulated Up states via the injection of conductance noise. In this case, noise facilitates spiking probability to small synaptic inputs (those that would cause spiking <50% of the time during the Down state) due to a floor effect (only the depolarizing components of the noise can affect spiking probability), yet diminishes spiking probability to large synaptic inputs (those that would cause spiking >50% of the time during the Down state) due to a ceiling effect (only the hyperpolarizing components of the noise can affect spiking probability). Thus, stimulus-intensity-dependent effects of Up states on neuronal responsiveness could be due solely to the effects of membrane potential variance on individual cortical neurons.

### UP STATES AS A MODEL OF CORTICAL GAIN CONTROL

Since the onset and termination of Up states is quite rapid (a few tens of milliseconds), such periods of enhanced cortical network activity could provide a substrate for the moment-tomoment changes in the routing of information by the cortex, such as is required for processing the context of sensory stimuli, maintaining objects in working memory, or attention. While veritable ''Up states,'' as distinguished from intervening hyperpolarized periods, have only been unequivocally observed during slow-wave sleep, under certain types of anesthesia, and to some degree to during quiet wakefulness, the rapid increases in synaptic barrages in the cortical network that characterize Up states might also characterize the rapid changes in excitability that would be required for the flexible processing of information (McCormick et al., 2004; McCormick and Yuste, 2006; Haider and McCormick, 2009). In essence, the same neuronal machinery that is spontaneously engaged during sleep may also be adapted by the waking cortex to adaptively route signals on a fast time-scale according to behavioral demands. Consequently, investigation of the cellular and network characteristics of Up states not only provides an understanding of the nature of cortical activity during sleep, but may also provide insight into the mechanisms associated with rapid changes in functional connectivity during waking behavior.

A fundamental operation in neuronal networks is gain modulation, defined as multiplicative or divisive transformations of the neuronal input-output function. Changes in gain amplify or reduce neuronal responsiveness with minimal effects on stimulus selectivity or receptive field structure (Sclar and Freeman, 1982; Carandini and Heeger, 1994). Such a transformation facilitates the interaction among multiple variables in the spiking output of a single neuron. One of the earliest demonstrations of the computational role of gain modulation was the multiplicative increase in visual responses in posterior parietal cortex by eye position (Andersen and Mountcastle, 1983). In addition to implementing sensorimotor transformations, gain modulation has also been shown to play a role in the enhancement of sensoryevoked responses by spatial or feature-based attention (Connor et al., 1996, 1997; McAdams and Maunsell, 1999; Treue and Martinez-Trujillo, 1999; Williford and Maunsell, 2006).

Changes in membrane potential depolarization, membrane potential variance, and membrane conductance, all features of cortical Up states, are ideal candidate mechanisms for rapid gain modulation. Yet, since many basic changes of the neuronal membrane, such as depolarization and shunting, in either model neurons or neurons in vitro only effect additive or subtractive shifts in the neuronal input-output function (Holt and Koch, 1997), pure or nearly pure changes in neuronal gain based on fast synaptic signaling (i.e., via ionotropic glutamate and GABAA receptors) have historically been rejected. Many models of gain modulation have relied on more complex mechanisms (Srinivasan and Bernard, 1976; Salinas and Abbott, 1996; Hahnloser et al., 2000). When neurons are embedded in a recurrently active network, however, the presence of synaptic noise fundamentally alters the ability of membrane potential, membrane potential variance, and membrane conductance to modulate gain (Hô and Destexhe, 2000; Chance et al., 2002; Fellous et al., 2003; Mitchell and Silver, 2003; Murphy and Miller, 2003; Shu et al., 2003a; Kuhn et al., 2004). In the presence of synaptic noise, the relation between membrane potential and firing rate is not a linear function with a threshold, as is the case in quiescent networks, but a power law, in which firing rate relates to membrane potential by raising the latter by an exponent (Miller and Troyer, 2002). When the relation between membrane potential and firing rate obeys a power-law function, simple manipulations of the neuronal membrane, such as depolarization and hyperpolarization, can change neuronal gain (Murphy and Miller, 2003). Indeed, such multiplicative modulations due to depolarization alone have been described during Up states in visual cortex in vivo (Haider et al., 2007). Thus, enhanced barrages of synaptic inputs, which occur on a rapid time-scale in local cortical networks, could produce immediate changes in neuronal gain in the subset of neurons responsible for momentary behavioral demands. In another model of gain modulation by synaptic inputs, neuronal gain is increased by the removal of these inputs (Chance et al., 2002). In this model, EPSPs and IPSPs must be removed in precise proportion to keep membrane potential constant while decreasing membrane conductance. Which model of synaptic-input-dependent gain control is employed by the cortex during active behavior is unclear, but each provides testable predictions: in one model, behaviorally relevant gain control is associated with depolarization, while in the other model, gain control is associated with a decrease in membrane conductance and a constant membrane potential.

### CONCLUSIONS

The slow oscillation is a fundamental feature of the corticothalamic system; during behavioral periods associated with effective disconnection from the sensory environment, it is essentially the default activity pattern of the entire cortical mantle. Through the use of various recording and imaging techniques in in vivo and in vitro preparations, considerable progress has been made in elucidating the cellular and network mechanisms involved in the synchronous cycling of Up and Down states in both local and disparate cortical networks.

There are many further avenues for investigation of the mechanisms and functions of the slow oscillation. Among the most crucial are the causal roles of thalamic activity in the initiation, persistence, and termination of Up states, the causal roles of inhibitory interneurons vs. intrinsic hyperpolarizing conductances in Up state termination, the functions of slow rhythmic activity in quiescent behavioral states, and the precise relation between network activity during the Up state and network activity associated with active sensory and cognitive processing. While these are all quite ambitious questions, the necessary technologies for addressing them at the

### REFERENCES

single-neuron, microcircuit, and large-scale network levels are emerging.

## AUTHOR CONTRIBUTION

GTN wrote the manuscript.

### ACKNOWLEDGMENTS

I thank Barry W. Connors for his insightful commentary on drafts of this manuscript. This work was supported by NIH grant NS-050434 and the Robin Chemers Neustein Graduate Fellowship in Brain Science, sponsored by the Brown Institute for Brain Science.

slow oscillation. J. Physiol. 590, 3987–4010. doi: 10.1113/jphysiol.2012. 227462

of thalamic neurons. Proc. Natl. Acad. Sci. U S A 98, 4172–4177. doi: 10. 1073/pnas.061013698

forebrain neurons recorded in association with electroencephalogram in anesthetized rats. J. Neurosci. 20, 1505–1518.

**Conflict of Interest Statement**: The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Neske. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# The Thalamus as a Low Pass Filter: Filtering at the Cellular Level does Not Equate with Filtering at the Network Level

William M. Connelly 1, 2 \*, Michael Laing3 , Adam C. Errington3 and Vincenzo Crunelli 1, 4

*1 Division of Neuroscience, School of Biosciences, Cardiff University, Cardiff, UK, 2 The John Curtin School of Medical Research, Eccles Institute of Neuroscience, The Australian National University, Canberra, ACT, Australia, 3 School of Medicine, Neuroscience and Mental Health Research Institute, Cardiff University, Cardiff, UK, 4 Department of Physiology and Biochemistry, University of Malta, Msida, Malta*

In the mammalian central nervous system, most sensory information passes through primary sensory thalamic nuclei, however the consequence of this remains unclear. Various propositions exist, likening the thalamus to a gate, or a high pass filter. Here, using a simple leaky integrate and fire model based on physiological parameters, we show that the thalamus behaves akin to a low pass filter. Specifically, as individual cells in the thalamus rely on consistent drive to spike, stimuli that is rapidly and continuously changing over time such that it activates sensory cells with different receptive fields are unable to drive thalamic spiking. This means that thalamic encoding is robust to sensory noise, however it induces a lag in sensory representation. Thus, the thalamus stabilizes encoding of sensory information, at the cost of response rate.

#### Edited by:

*Paul R. Adams, State University of New York at Stony Brook, USA*

#### Reviewed by:

*Scott Hooper, Ohio University, USA Ya-tang Li, California Institute of Technology, USA*

> \*Correspondence: *William M. Connelly<EMAIL_ADDRESS>
Received: *29 September 2015* Accepted: *22 December 2015* Published: *14 January 2016*

#### Citation:

*Connelly WM, Laing M, Errington AC and Crunelli V (2016) The Thalamus as a Low Pass Filter: Filtering at the Cellular Level does Not Equate with Filtering at the Network Level. Front. Neural Circuits 9:89. doi: 10.3389/fncir.2015.00089* Keywords: thalamus, sensory neuroscience, integrate-and-fire neuron, computational neuroscience, neural noise

### INTRODUCTION

The thalamus lies at a cross roads between the external world and the cerebral cortex (Steriade, 2003). All senses excluding olfaction pass through the thalamus, where they are subjected to some kind of processing, before being routed to the cortex. The action of the thalamus in this context has been likening to a gate, that is to say, only letting through information as dictated by higher areas (Wang et al., 2006; McAlonan et al., 2008; Saalmann and Kastner, 2011). It has also been proposed that the thalamus acts as a frequency-sensitive filter, generating spikes more easily when some time-dependent component of the sensory stimuli is correct (Heggelund et al., 2003).

The proposition that the thalamus acts as a high-pass filter has been most thoroughly explored in the vibrotactile thalamocortical system: the thalamic ventroposterior medial (VPm) nucleus and the barrel cortex. Here there is clear evidence that when the whisker is driven by a sinusoidal deflection, cortical, and thalamic spiking rates are higher with increasing stimulus frequency (Arabzadeh et al., 2003; Khatri et al., 2004). However, this effect cannot be completely ascribed to thalamic filtering, due to the velocity sensitive nature of the sensory organ (Hartings et al., 2003; Gerdjikov et al., 2010). Conversely, both the neurons of the lateral geniculate nucleus (LGN) and the primary visual cortex have most often been shown to produce low pass or band pass behavior (Hawken et al., 1996; Van Hooser et al., 2013). Again, however, this result is confounded by the fact that the retinal processing itself acts as either a low pass or band pass filter (Shapley and Victor, 1978).

The fact that individual neurons in the thalamus act as highpass filters in terms of input rate vs. output rate is a necessary consequence of the neural membrane being a leaky capacitor. Specifically, a certain amount of charge must be delivered into a neuron in a given time to bring it to the threshold for firing and this can only be achieved when the neuron's inputs fire above certain rate. However, filtering in the context of firing rate must be considered separately from filtering in terms of what data the neural circuit is extracting from its input. That is to say, one can imagine a hypothetical neural system that codes for a particular property of a sensory stimuli, where increasing the rate of change of that property causes a significant increase in the firing rate of neurons in the system, but the system itself loses the ability to encode that property. For instance, consider a stimuli that can be in two states, and two populations of neurons coding for these two states: when one population is active the neural system is encoding one state, when the other population is active the system is encoding the other state. Finally, if both populations are active at the same time, the system encoding is ambiguous. When the stimuli is slowly changing between its two states, the neurons in each population might fire slowly, but so long as the two populations are not active at the same time, then the neural system should be able to encode the two stimuli. However, when the stimuli is rapidly switching between these two states, the neurons in our hypothetical system begin firing more rapidly. If the stimuli is switching rapidly enough the two cell populations will become active at the same time and the neural system lose encoding ability. Thus, when considered on a single cell basis, the network appears to behave as a high-pass filter (that is, the neurons fire faster as the stimulus property changes faster), but when considered from a population standpoint, the network is in fact behaving as a low-pass filter (the network loses the ability to encode the stimulus as the stimulus property changes faster).

Here we report, using a computational approach, based on a highly simplified, yet biologically reasonable model that the thalamus necessarily works to stabilize sensory representations in the presence of noise in a manner akin to a low pass filter.

### METHODS

### In vitro Electrophysiology

Wistar rats, of either sex, at postnatal days 20–30 were anesthetized with isoflurane and decapitated in accordance with the United Kingdom Animals (Scientific Procedures) Act of 1986 and local ethical committee approval. As described previously by Turner and Salt (1998) brains were rapidly removed and 300µm-thick slices containing the dorsal lateral geniculate nuclei and an intact retinogeniculate pathway were cut in continuously oxygenated sucrose aCSF (Errington et al., 2010). Slices were incubated for at least 1 h before being transferred to the recording chamber where they were continuously perfused (∼2 ml/min) with warmed (32–34◦C) oxygenated recording aCSF containing the following (in mM) 125 NaCl, 5 KCl, 25 NaHCO3, 1.25 NaH2PO4, 1 MgCl2, 2 CaCl2, 25 glucose. Whole-cell patch-clamp recordings were made using pipettes (resistance, 2–4 M) containing the following (in mM): 135 K-methylsulfonate, 10 HEPES, 10 Na-phosphocreatine, 4 MgCl2, 4 Na-ATP, 0.4 mM Na-GTP, pH 7.3, 300 mOsm. Current clamp was performed with a Multiclamp 700B preamplifier (Molecular Devices). Experimental data were filtered at 6 kHz, digitized at 20 kHz (Digidata 1322A; Molecular Devices), and acquired using pClamp 10 software (Molecular Devices). Electrical stimulation was evoked with a constant current stimulus isolator (DS3, Digitimer) through a bipolar tungsten electrode (Frederick Haer) in the presence of the GABAA receptor antagonist gabazine (10µm), and the GABAB receptor antagonist 55845 (1µm; Tocris).

### Computational Modeling

The network model was realized in Python 2.7. All cells were simple leaky integrate-and-fire neurons with no explicitly enforced refractory period. When Vm reached threshold, a 1 ms long spike was generated, after which Vm was reset to the resting membrane potential. The model consisted of two separate layers, a sensory layer that responded to a stimuli referred to as the retinal ganglion cell (RGC) layer, and a integrative layer, referred to as the thalamocortical cell (TCC) layer, that received input from the RGC layer (**Figure 1**).

For RGCs, membrane current was calculated as a sum of two currents, a noisy current and a sensory current. The noisy current was an Ornstein–Uhlenbeck process with a time constant (1/kOU) of 5 ms and an amplitude (σou) that was varied between 0 and 120 pA (**Figures 1A,B,C**; Destexhe et al., 2001). The sensory current was a designed to model vision, and was a current whose amplitude varied in a Gaussian fashion with distance from the visual stimuli [D(n,t)]. The maximum this current reached was 200 pA, which meant the maximum visually evoked firing rate for a RGC was ∼80 Hz (**Figures 1A,E**; Croner and Kaplan, 1995). This Gaussian current had a standard deviation (σD) of 2.5% of visual space. Visual space was defined as the maximum field within which RGCs could code, with 0 representing one end, and 1 representing the other. With 200 RGCs, the center of each RGC's receptive field [p(n)] was centered at 0.5 % of visual space from its neighbors. RGCs had a membrane resistance of 260 M and a membrane capacitance of 96 pF, giving them a membrane time constant of 25 ms (O'Brien et al., 2002). RGCs had a threshold of 20 mV depolarized to rest. It should be noted that these properties intentionally give the RGCs a relatively flat frequency-response profile, allowing us to resolve the filtering properties of the TCC layer without being confounded by filtering at the retinal level.

TCCs had a membrane resistance of 70 M and a membrane capacitance of 160 pF, giving them a membrane time constant of 11 ms (Crunelli et al., 1987; White and Sur, 1992). Excitatory input to TCCs was modeled as a current that synaptic input caused to instantaneously increase by 750 pA and which decayed with first-order kinetics and a time constant of 1.6 ms (Chen and Regehr, 2000). This produced a unitary excitatory postsynaptic potential (EPSP) 3.5 mV in amplitude. Spiking threshold was set at 9 mV (see Section Results).

In order to decode the information in a given layer at a given time [P(t)], we sought to use a maximum likelihood estimator (MLE) approach, that is to calculate the value of D(t) that

noise.

maximizes the probability of getting a particular pattern of neural activity. However, under the assumption that the probability of any neuron in a given layer firing was an arbitrary Gaussian function of its distance to the stimuli, we were left with an expression that was mathematically uncooperative, and in our hands at least, could only be solved by numerical methods. Given this, we attempted a much simpler approach, where the position information encoded in any layer at time t, was simply the average p(n) of all spiking neurons at time t, given by the equation.

$$P(t) = \frac{1}{\sum\_{n=1}^{N} \mu(n, t)} \sum\_{n=1}^{N} \mu\left(n, t\right) p(t)$$

where u(n,t) is either 1 or 0 depending on whether neuron n is firing at time t, or not. Fortunately, the MLE of P(t) calculated numerically for all possible patterns of a small population of neurons (n = 24), produces values almost identical to that calculated via the mean approach (Linear regression: Slope = 0.95, R 2 = 0.96, n = 8388608). Thus, the mean approach was used. In order to give some measure of the stability of the encoding over time we calculated the standard deviation of P(t) over time (σT). We also sought to capture some measure of spatial accuracy of the encoding. Thus, we used the mean over time of the average distance between p(n) of all spiking neuron and the target (σP), that is

$$\delta\_P = E[\frac{1}{\sum\_{n=1}^N \mu(n,t)} \sum\_{n=1}^N \mu(n,t)\Delta D(n,t)]$$

Simulations were performed with a fixed time-step of 0.5 ms. Phase (ϕ) information was extracted by performing a Fast Fourier Transform on P(t), and the results are presented as the phase in the cell layer minus the phase of the target. Phase responses were fit with the following function:

$$\varphi = \tan^{-1}(-2\pi f \mathbf{v})$$

where 1/2πτ gives the corner frequency of the filter, or π/4 point. Statistical tests were performed using linear regression via Matlab R2014b (Mathworks).

### RESULTS

In order to make a reasonable model of thalamic behavior, the native properties of retinogeniculate transmission was studied in vitro. TCCs (n = 26) in the dLGN were patch clamped and input from the optic tract was evoked using a ramping stimulation intensity to recruit minimal events and to investigate the threshold for action potential generation (**Figures 2A,B,C**). The evoked EPSPs had the hallmarks of retinogeniculate EPSPs in that they had all-or-none responses as opposed to the graded recruitment typical for corticothalamic EPSPs (Turner and Salt, 1998). Across all cells and stimulation intensities, the distribution of EPSPs amplitudes (n = 461 events) clearly formed two peaks, one at 3.2 mV and one at 5.9 mV (95% confidence interval 3.1–3.2 mV and 5.7–6.0 mV, respectively) and the largest subthreshold EPSP recorded was 7.9 mV (**Figure 2D**). We believe these peaks represent the recruitment of one and two retinogeniculate axons, respectively. As no subthreshold EPSP was ever seen with an amplitude that matched three times the single axon event, we believe this demonstrates that dLGN TCCs at rest require, on average, the coincident input of three retinal EPSPs to be driven to spike. These results fit with others who reported that one or two subthreshold unitary events could be recruited in dLGN neurons, and the development evidence that dLGN TCCs receive input from 3 to 5 RGCs (Turner and Salt, 1998; Chen and Regehr, 2000; Tavazoie and Reid, 2000; Hong and Chen, 2011).

Based on these data we developed a simple model (see Section Methods), involving 120 integrate-and-fire neurons representing a simplified RGC layer, connected to either 60, 120, or 240 TCCs, consistent with the ratio of RGC to LGN neurons (Spear et al., 1996). Cells in the RGC layer were connected in a visuotopic manner to neurons in the TCC layer, such that each TCC received input from the four (unless stated otherwise) "nearest" RGCs, while needing three coincident EPSPs to spike (**Figure 1A**). RGCs were driving by a sum of two currents. The first component was membrane noise modeled as an Ornstein–Uhlenbeck process, whose parameter σOU dictated the magnitude of the noise and subsequent noise induced firing rate (**Figures 1B,C**; Equation 1). The second current had a Gaussian receptive field with a full-width at half-maximum

FIGURE 2 | Basic Properties of LGN thalamocortical neurons and their retinogeniculate EPSPs. (A) Overlaid traces showing the response of an LGN cell to current injection. (B) Overlaid traces showing the recruited retinogeniculate EPSPs in response to optic nerve stimulation. Events marked with red oval are truncated spikes. (C) Calculated EPSP size vs. stimulation intensity for the cell shown in (B), clearly showing the lack of graded recruitment of EPSP amplitude. (D) The histogram of EPSP amplitudes across all cells and events, clearing showing two peaks, where the amplitude of the larger peak is essentially twice the amplitude of the smaller peak. The cell in (C) had events only from the smaller amplitude peak.

of ∼6% of the visual field such that during complete visual activation RGCs would fire at a maximum of ∼80 Hz (**Figure 1E**; Equation 1; Croner and Kaplan, 1995). As expected for a simple leaky integrate-and-fire neuron, when one considered the rate of EPSP input against the ratio of the output spiking rate to the input EPSP rate, each individual cell functioned as a high pass filter (**Figure 1D**). It is important to note, that while this model is explicitly of the visual system, it should not be assumed that we have tried to make this model replicate all the features of the visual system. Indeed, we have purposefully kept the model simple to allow it to generalize to other sensory system. Thus, while we have called the sensory layer the RGC layer, it should more be thought of as a set of sensory cells who have some arbitrary receptive field, and hence could just as well be called the "trigeminal nucleus layer" with each cell having a preferred direction of whisker deflection (Minnery et al., 2003).

The position information at any time for each cell layer [P(t)] was calculated when the simulation was exposed to a single stationary visual stimuli taking up 20% of the visual space (**Figure 1**; Equation 3). The standard deviation of P(t), σT, acted as a measure of the stability of the representation over time (**Figure 1**; Equation 4). Higher values of σT are seen as an indicator of poorer network performance due to the reasonable assumption that information encoded in a network should not change if the input does not change. As the membrane noise of the RGC layer was increased, σT increased in both RGC and TCC layers (P < 1 × 10−28) (**Figures 3A–C**). Given that in this model TCCs receive their sole input from RGCs, it might seem reasonable to assume that the thalamic layer could only report the stimulus position as accurately as the TCC layer (receptive field half widths were almost identical between individual RGC and TCC, at 2.5 and 2%, respectively). However, apart from when RGCs had a subthreshold level of noise and the thalamic layer was made up of less cells than the RGC layer, the thalamic layer had significantly lower values of σT, (P < 1 × 10−12). Furthermore, when considering σT in just TCCs, increasing the ratio of cells in the TCC layer to RGC layer (while maintaining the number of inputs that each TCC receives, meaning that each RGC projects to more TCCs) caused the values of σT to drop (P = 0.003), presumably due to the simple fact that there were more TCCs available to be directly driven by visually stimulate RGCs. More importantly however, the result that σT was lower in the TCC layer than the RGC layer was independent of the ratio of TCCs to RGCs over this range (**Figure 3C**). This clearly shows that integration by the TCC layer enhances the stability of the visual representation over time, however, how does it affect the spatial accuracy? Therefore, to measure how integration by the TCC layer affects spatial accuracy, we calculated σP, a measure which was in essence the average distance between each active cell and the center of the visual target (**Figure 1**; Equation 5).

Increasing the amplitude of the RGC membrane noise significantly increased σP in both layers (P < 1 × 10−30), but unlike σT, altering the ratio of RGCs to TCCs have no effect on σP (P = 0.9). Again, however, the TCC layer proved to be more accurate, having a significantly lower σP (P < 5 × 10−18; **Figure 3D**). Simply put, these data show that integration by the TCC layer allows the TCC layer to provide a more temporally stable and spatially accurate representation than the RGC layer, by filtering out "occasional" noise-driven spikes from the RGC layer. One could consider occasional spikes as high frequency input, not in the sense of high frequency EPSPs, but as a high frequency change in which position information that is being supplied to the TCC layer. That is, if the stimuli rapidly moved to a new position and then back to its original position, it could create spike patterns in the RGC layer very similar to noise: one or two spikes in an otherwise silent spike history. If the TCC layer does not respond to these high frequency changes in the stimuli, then we could see the TCC layer as acting like a low pass filter.

If the TCC layer is in fact acting as a low pass filter for sensory information, then like all low pass filters, it must come at a cost in terms of response rate. This effect could be clearly seen when the visual stimuli was instantly stepped from one part of the visual space to another, as the RGC layer took only approximately 4 ms to encode the new position, while the TCC layer took 8 ms (**Figure 4A**). This effect was investigated in a more quantitative fashion by moving the visual stimuli across the visual space in a sinusoid at increasing frequencies up to 50 Hz (**Figure 4B**). The RGC layer was able to accurately follow the visual stimuli, and at no point did it encode beyond π/4 radians behind the stimuli (**Figure 4C**). The TCC layer, on the other hand, fell behind to this extent at less than 20 Hz (**Figure 4D**). Increasing the noise the RGC layer allowed the TCC to follow at higher frequencies (σOU = 30 pA: π/4 point: 12 ± 0.5 Hz; σOU = 100 pA: π/4 point: 36 ± 0.3 Hz, P < 1 × 10−10). The fact that increasing noise in the RGC layer allows the TCC layer to respond more rapidly to RGC input is presumably due to the increased synaptic drive the TCC layer receives due to noise driven retinal spikes. This brings TCCs closer to threshold, meaning they need to integrate less stimulus driven input to fire. Thus, the TCC layer fails to produce an accurate representation of sensory input that changes above ∼10 Hz.

We have already demonstrated that the filtering effect of the thalamic layer is robust to changes in the numerical ratio of RGC to TCCs, however, we have not investigated how changes in the convergence onto TCCs effects their ability to filter input noise. In order to investigate this we altered the convergence of RGCs onto TCCs in tandem with changing the amplitude of retinal EPSCs. We did this in such a way that an individual TCC might receive, for instance, input from two times as many RGCs but with each one having one half the synaptic weight, thus keeping the total synaptic drive approximately equal. By increasing the convergence of RGCs onto TCCs, the TCC layer became increasingly robust to noise in the RGC cells, both in terms of σT (P = 0.0004) and σP (P < 1 × 10−7 ; **Figures 5A,B**). However, this came at the cost of increasingly slow frequency response (TC:RGC = 1:1, σOU = 30 pA, EPSC × 0.5: π/4 point: 6.0 ± 0.5 Hz; EPSC × 4: π/4 point: 60 ± 0.3 Hz; P < 1 × 10−16; **Figures 5C,D**). Therefore, across a variety circuit configurations, including ones where single RGC spikes are capable of driving TCC

histograms showing the distribution of the decoded position of the stimuli [P(t)] in the RGC layer, in the presence of no retinal noise (σOU = 0) and a large degree of retinal noise (σOU = 120 pA). The central heat map shows the distribution of P(t) across a range of retinal noise. Note the broadening of the distribution of P(t) as the amplitude of the retinal noise increases. (B) The same data as presented in (A), but for the TCC layer. Again, as the noise in the RGC layer increases, the distribution of P(t) broadens, but to lesser degree. (C) The effect of network architecture (the ratio of TCCs to RGCs) and retinal noise on the distribution of P(t) (σT ). As retinal noise increases, in both the RGC and TCC layers, σT increases, but over most of the parameter space, the TCC layer has a significantly lower value of σT , that is, the encoding of position is more stable over time. (D) The effect of network architecture and retinal noise on the accuracy of encoding (σP). Again, retinal noise causes worse performance in both layers but the thalamic layer performs better at all but the lowest levels of retinal noise. However, the ratio of TCCs to RGCs has no effect on performance.

spikes (EPSC × 4), the thalamic layer still acts as a low-pass filter.

### DISCUSSION

Visual acuity is as high, or higher, than the density of RGCs predict (Wässle et al., 1981; Gauthier et al., 2009; Rossi and Roorda, 2010), a fact that may be surprising, given the inherent noise of RGC discharges and the fact that RGCs converge onto TCCs (Croner and Kaplan, 1995). Here we show that TCCs act as a low-pass filter, reducing the consequence of noise driven spikes in the RGCs. However, this behavior comes at a cost: slowing the rate of response.

While this model was explicitly a model of visual system, there is little to suggest the same effect will not be seen in other sensory pathways, as the other sensory pathways share numerous similarities. For instance, input from the trigeminal nuclei to the VPM is also mediated by very large unitary events and that each TCC in the VPM is probably contacted by a small number of trigeminal neurons (Spacek and Lieberman,

Frontiers in Neural Circuits | www.frontiersin.org January 2016 | Volume 9 | Article 89 |

a step change in the position of the stimuli, note the response of the TCC layer is significantly delayed relative to the response of the RGC layer. (B) Two sections of the response of the RGC and TCC layers to a sinusoidal input of increasing spatial frequency (σ*ou* = 0.03). (C) The phase of the RGC layer response with respect to the stimuli, showing the minimal phase shift and general independence from the magnitude of retinal noise. (D) The phase of the TCC response with respect to the stimuli, showing the large phase shift than that seen in the RGC layer, and the effect that increasing retinal noise decreases the phase shift seen in the TCC layer.

1974; Castro-Alamancos, 2002). Furthermore, we have shown that the filtering effect is robust to changes in the underlying connectivity.

Despite the fact that this result was consistent even when model parameters were pushed outside of what has been demonstrated in the native system, one needs to ask whether these results fit with published data. The response of LGN and VPM cells are known to be phase lagged relative to input from RGCs and trigeminal nucleus cells, respectively. However, the reported latency between the RGC and LGN activation (measured as the slope of the phase lag in cycles against frequency) is larger in vivo (∼15 ms) than reported here (∼5 ms), though similar to that reported for trigeminal to VPM (∼3–6 ms; Lee et al., 1981; Hartings et al., 2003). Furthermore, there is evidence that thalamic cells do filter sensory noise. Hartings et al. (2003) demonstrated that the noisy (non-modulated) component of the spiking rate of trigeminal nucleus increases almost by a factor of 10 as the rate of whisker stimulation increases, however, the noisy component of the firing rate in VPM neurons is almost unchanged.

We have shown that the TCC layer of our model accurately encodes the information in the RGC layer up to approximately 10 Hz. While this may seem far from optimal, it is worth considering the nature of the information the RGC can provide. Studies in the cat have shown that the retina cannot encode changing information up to arbitrarily high frequencies, and in fact RGC discharges are significant phase shifted relative to visual stimuli above 10 Hz, and have a π/4 point of ∼3 Hz (Shapley and Victor, 1978). Thus, the phase shift cause by the TCC may well be minimal in the scope of the visual pathway.

One needs to consider the terminology use in this paper. If we define a channel as the collection of inputs to a network that code for nearly identical stimulus features, then we are describing the thalamic layer as behaving as a low-pass filter in the domain of the rate channel change and not in the domain of rate of input in a given channel. Concretely, a channel could be a collection of trigeminal nucleus neurons that response to a whisker being deflected in a given direction, while another channel would be a collection of neurons who respond when the whisker is deflected in a direction perpendicular to the first

direction. Then we are describing the thalamus as limiting the rate at which information on how rapidly the whisker is shifting between moving in those two directions can be transferred, while providing noise immunity and stability of encoding. Indeed, if we consider the domain of the rate of channel change (e.g., the rate of the whisker shifting between moving in two perpendicularly oriented directions), and the domain of the rate of input in a given channel (e.g., mechanosensory current), then these two domains can be thought of almost as inverses, as a stimuli that causes only one channel to be active (low frequency channel change) should cause a consistent drive to a particular set of cells (high frequency input within a given channel). Conversely, a stimuli that is changing rapidly which channels is being driven will drive infrequent input in any given channel. This means that the low-pass behavior of the thalamic layer in the domain of the rate of channel change is a direct consequence of the high-pass behavior of the individual cells in the layer.

networks with larger convergence and smaller EPSPs.

The decoding algorithm used here, which was the mean of the centers of the receptive fields of all active cells, and is essentially equivalent to a MLE, was very simple and did not take into account the temporal structure of the neural discharge, or correlation between cells (Usrey et al., 1998; Reinagel and Reid, 2000). This method was chosen because of its simplicity, and the ease of interpreting the results it generates. Moreover, we doubt using a different method would change the fundamental nature of the result: that the thalamic layer will not spike in response to rare input, thereby filtering out noise. This result has been demonstrated in another model (Martinez et al., 2014). However, due to being much closer to the in vivo case, this model was far more complex and is applicable to only the visual system.

In conclusion, we have shown that over a wide range of circuit parameters, in terms of changes in the nature of a stimuli, thalamic neurons act as a low pass filter for sensory information. This behavior comes as a consequence of the fact that the cells in the thalamus act as high pass filters in terms of the rate at which they are driven. By only spiking during sustained high frequency input, thalamic cells filter out noise from their inputs allowing higher accuracy and higher stability decode of the stimuli. This however, comes at a cost, in that it produces a delay in transmission of information. We do not propose that this is the only function of the thalamus, but simply that it is a necessary consequence of the fact that TCCs must integrate charge before spiking.

### REFERENCES

### AUTHOR CONTRIBUTIONS

WC performed simulations and data analysis. ML and AE performed and designed in vitro experiments. WC, ML, AE, and VC wrote the manuscript.

### FUNDING

This work was supported by a Wellcome Trust programme grant (91882, V. Crunelli).

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Connelly, Laing, Errington and Crunelli. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Stimulus Contrast and Retinogeniculate Signal Processing

Daniel L. Rathbun1,2 , Henry J. Alitto1,3 , David K. Warland1,3 and W. Martin Usrey 1,3 \*

1 Center for Neuroscience, University of California, Davis, Davis, CA, USA, 2 Institute for Ophthalmology and Center for Integrative Neuroscience, University of Tübingen, Tübingen, Germany, 3 Department of Neurobiology, Physiology, and Behavior, University of California, Davis, Davis, CA, USA

Neuronal signals conveying luminance contrast play a key role in nearly all aspects of perception, including depth perception, texture discrimination, and motion perception. Although much is known about the retinal mechanisms responsible for encoding contrast information, relatively little is known about the relationship between stimulus contrast and the processing of neuronal signals between visual structures. Here, we describe simultaneous recordings from monosynaptically connected retinal ganglion cells and lateral geniculate nucleus (LGN) neurons in the cat to determine how stimulus contrast affects the communication of visual signals between the two structures. Our results indicate that: (1) LGN neurons typically reach their half-maximal response at lower contrasts than their individual retinal inputs and (2) LGN neurons exhibit greater contrastdependent phase advance (CDPA) than their retinal inputs. Further analyses suggests that increased sensitivity relies on spatial convergence of multiple retinal inputs, while increased CDPA is achieved, in part, on temporal summation of arriving signals.

Keywords: retina, LGN, coding, vision, thalamus

### Edited by:

Patrick O. Kanold, University of Maryland, USA

### Reviewed by:

Judith Hirsch, University of Southern California, USA Michael M. Halassa, New York University, USA

#### \*Correspondence:

W. Martin Usrey<EMAIL_ADDRESS>
Received: 04 November 2015 Accepted: 03 February 2016 Published: 19 February 2016

#### Citation:

Rathbun DL, Alitto HJ, Warland DK and Usrey WM (2016) Stimulus Contrast and Retinogeniculate Signal Processing. Front. Neural Circuits 10:8. doi: 10.3389/fncir.2016.00008

## INTRODUCTION

All visual information leaving the eye is conveyed in the spiking activity of retinal ganglion cells. Given the limited dynamic range of these cells and the dramatically varying statistics of visual stimuli in the natural world, efficient encoding of visual information requires processing that responds to the statistics of the visual input. Contrast gain control is a prominent mechanism used by the visual system to meet the challenge of encoding visual information in diverse visual environments. Contrast gain control refers to the nonlinear receptive field property whereby a neuron's gain and temporal dynamics are dependent upon stimulus contrast. Specifically, the response gain of neurons in the early visual system, including the retina, LGN, and V1 decreases as stimulus contrast increases, causing contrast response functions to saturate at contrasts below 100%. Additionally, as stimulus contrast increases, these same visual neurons become more responsive to stimuli with high temporal frequencies, and they exhibit a contrast-dependent phase advance (CDPA) in their responses to periodic stimuli. Although contrast gain control is first established within the retina, an open and unresolved question is how contrast gain control is enhanced between the retina and the LGN.

The axons of retinal ganglion cells target several central structures, including the lateral geniculate nucleus (LGN) of the thalamus which in turn provides monosynaptic excitation to primary visual cortex (V1). Although the response properties of retinal ganglion cells and LGN neurons are generally quite similar (Hubel and Wiesel, 1961; Cleland et al., 1971; Levick et al., 1972; So and Shapley, 1981; Lee et al., 1983; Cleland and Lee, 1985; Kaplan et al., 1987; Mastronarde, 1987, 1992; Usrey et al., 1999; Rathbun et al., 2010), there are significant differences, and one of the most prominent of these involves the relationship between stimulus contrast and neuronal activity. In particular, LGN neurons display greater contrast gain control than their retinal inputs (Kaplan et al., 1987; Scholl et al., 2012; but see Sclar, 1987).

Factors that influence the feedforward communication of retinal signals to LGN neurons include the convergence of retinal inputs onto individual LGN neurons and the temporal summation of arriving signals. Studies in the cat indicate that LGN neurons typically receive convergent input from 2 to 5 retinal ganglion cells (Cleland et al., 1971; Cleland, 1986; Hamos et al., 1987; Mastronarde, 1992; Usrey et al., 1999; Reid and Usrey, 2004; Martinez et al., 2014). Likewise, the excitatory postsynaptic potentials (EPSPs) evoked from the spikes of individual retinal axons interact over interspike intervals (ISIs) of up to ∼30 ms to increase the likelihood of bringing an LGN neuron to spike threshold (Mastronarde, 1987; Usrey et al., 1998; Levine and Cleland, 2001; Rowe and Fischer, 2001; Carandini et al., 2007; Sincich et al., 2007; Weyand, 2007; Rathbun et al., 2010). The goal of this study was to determine whether and how convergence and temporal summation contribute to the transmission and processing of contrast information between the retina and LGN.

To determine the influence of stimulus contrast on retinogeniculate communication and visual processing in the retina and LGN, we made simultaneous recordings from monosynaptically connected retinal ganglion cells and LGN neurons in the anesthetized cat and measured neuronal responses to drifting sinusoidal gratings that varied in stimulus contrast. Consistent with predictions from past studies (Kaplan et al., 1987; Scholl et al., 2012), our results demonstrate that the contrast needed to evoke a half-maximal response (C50) is lower for LGN neurons than for their individual retinal afferents. Further analysis suggests that this effect relies on the integration of multiple retinal inputs by individual LGN neurons. Our results also reveal that CDPA—a hallmark of contrast gain control—is significantly greater for LGN neurons than for their individual retinal afferents. To probe the underlying mechanism responsible for the CDPA changes, we applied a model of ISI-based filtering to recorded retinal spike trains. Results from this effort reveal that an ISI-based filtering mechanism of retinal spikes can produce CDPA in target neurons. Taken together, these results indicate that the LGN is more than a simple relay station, as it adjusts both the sensitivity and timing of visual signals en route from retina to cortex.

### MATERIALS AND METHODS

### Animal Preparation

Six adult cats of both sexes were used in this study. All surgical and experimental procedures conformed to NIH guidelines and were carried out with the approval of the Animal Care and Use Committee at the University of California, Davis. Anesthesia was induced with ketamine (10 mg/kg, IM) and thiopental sodium (10 mg/kg, IV; supplemented as needed). Animals received a tracheotomy and were placed in a stereotaxic apparatus where the temperature, electrocardiogram (ECG), electroencephalogram (EEG), and expired CO2 were monitored continuously for the duration of the experiment. All wound margins were infused with lidocaine and anesthesia was maintained with a continuous infusion of thiopental sodium (2–3 mg/kg/h, IV). If physiological monitoring indicated a low level of anesthesia, additional thiopental was given and the rate of continuous infusion was increased. A midline scalp incision was made and the cortical surface above the LGN was exposed through a craniotomy which was filled with agarose. The lateral margin of each eye was dissected and each sclera was glued to a rigid post mounted on the stereotaxic frame. These posts secured the eyes and facilitated the introduction of a trans-scleral guide tube for retinal recordings. The nictitating membranes were retracted with 10% phenylephrine and flurbiprofen sodium drops were administered (1.5 mg/h) to prevent miosis. The eyes were refracted, fitted with appropriate contact lenses, and focused on a tangent screen located 172 cm in front of the animal. The positions of area centralis and the optic disk were plotted by back-projecting the retinal vasculature of each eye onto the tangent screen. Once all surgical procedures were complete, animals were paralyzed with vecuronium bromide (0.2 mg/kg/h, IV) and mechanically respired.

### Electrophysiological Recording and Visual Stimuli

A multielectrode array (Thomas Recording, Marburg, Germany) was used to record from individual LGN neurons from seven independently positioned microelectrodes. The locations of receptive fields measured using the array were used to guide the placement of the retinal electrode. To record from retinal ganglion cells, a tungsten-in-glass microelectrode was introduced into the posterior chamber of the eye through a guide tube and positioned using a custom-made manipulator. Neural responses were amplified, filtered and recorded to a personal computer with a Power 1401 data acquisition interface and the Spike 2 software package (Cambridge Electronic Design, Cambridge, UK). The spikes from individual neurons were isolated using template matching and parametric clustering.

Visual stimuli were created with a VSG 2/5 visual stimulus generator (Cambridge Research Systems, Rochester, UK) and presented on a gamma-calibrated Sony monitor with a mean luminance of 38 cd/m2 . Receptive fields were mapped in space and time using a binary white-noise stimulus and reverse-correlation analysis (Reid et al., 1997; Rathbun et al., 2007). To examine the influence of stimulus contrast on the timing and strength of neuronal responses and the efficacy of retinogeniculate communication, recordings were made while neurons were excited with drifting sinusoidal gratings (4 Hz, optimal spatial frequency). Gratings were shown for 4 s, followed by 4 s of mean gray, at 10 different contrast levels (random order), spaced logarithmically from 1 to 100%. The complete stimulus set was presented 100–300 times, as permitted by recording stability.

X and Y cells were distinguished on the basis of receptive field size, response latency, and time course of response (Usrey et al., 1999). Although recordings were made from both X and Y cells in the LGN, there was a heavy sampling bias for Y-type cells in the retina (see also Rathbun et al., 2010). Consequently, only Y-cell pairs were examined in this study. It is worth noting that Y-type cells are well suited for studying contrast-dependent processing, as they generally exhibit stronger contrast gain control and CDPA than X cells (Shapley and Victor, 1978).

### Data Analysis

### Cross Correlation Analysis

Cross-correlation analysis was used to identify monosynaptically connected retinogeniculate cell pairs (**Figure 1**). A crosscorrelogram was generated by creating a histogram of LGN spikes relative to each retinal spike. The presence of a sharp, short-latency peak in the cross-correlogram was taken as evidence of a monosynaptically-connected pair of cells (Cleland et al., 1971). For quantitative analysis, cross-correlation bins contributing to the peak were identified using a bin size of 0.1 ms. The peak bin was first identified and all neighboring bins greater than three standard deviations above the baseline mean were considered part of the peak; where the baseline consisted of bins ranging from 30 to 50 ms on either side of the peak bin. Because each count in the cross-correlogram peak represents a single retinal spike that was relayed by the LGN neuron to cortex, these retinal spikes were termed ''relayed'' spikes whereas the remaining retinal spikes were termed ''non-relayed'' spikes. Likewise, LGN spikes that contributed to the cross-correlogram peak were termed ''triggered'' spikes, indicating that they were evoked by the simultaneously recorded retinal ganglion cell; and the remaining LGN spikes were termed ''non-triggered'' spikes (i.e., spontaneous spikes or spikes evoked from a source other than the simultaneously recorded retinal ganglion cell). Two values used to quantify the strength of communication between a simultaneously recorded retinal ganglion cell and LGN neuron are efficacy and contribution (Levick et al., 1972), where efficacy is the percentage of retinal spikes that evoked an LGN spike (i.e., relayed spikes) and contribution is the percentage of LGN spikes evoked from a particular retinal input (i.e., triggered spikes).

### Response Curve Fitting

To determine the amplitude and phase of responses to drifting gratings, spike times were expressed relative to the phase of the sinusoid cycle, producing a cyclic histogram for each contrast. A constrained nonlinear optimization procedure (MATLAB function: nlinfit; The Mathworks, Natick, MA, USA) was used to fit each cyclic histogram with the positive-only rectification of the following sinusoidal equation:

$$R(t) = A \* \sin\left(\omega \* t + \theta\right) + b \tag{1}$$

where R(t) is the magnitude of the cyclic histogram at time t, A is the response amplitude at the modulation frequency, ω is angular frequency of the drifting stimulus in radians per second, t is time in seconds, θ is the response phase determined by the vector sum of phases for all spikes in the cyclic histogram, and the baseline (b) indicates the value below which the sinusoid is rectified. The baseline was constrained to range between –A and 2 ∗ A. For each spike train, cyclic histograms were fitted sequentially from low to high contrast with the additional constraint that b was monotonically decreasing. This procedure was found to produce more useful estimates of the modulated response amplitude and response phase, independent of contrast-induced changes in rectification, than a standard Fourier decomposition algorithm available in MATLAB (fft), and is analogous to estimation of the F1.

responses and blue indicates OFF responses. Scale bar denotes 1◦ of visual angle. The cross-correlogram was calculated from a 6000 s recording that contained 154,152 retinal spikes and 21,697 LGN spikes. Red line indicates shuffle-corrected baseline.

For each spike train, the contrast response function was fitted with a hyperbolic ratio (Albrecht and Hamilton, 1982; MATLAB function: fminunc; The Mathworks, Natick, MA, USA):

$$R(\text{C}) = \frac{R\_{\text{max}} \ast \text{C}^n}{\text{C}^n + \text{C}\_{50}^n} + b \tag{2}$$

where R(C) is the response for a given contrast C, Rmax is the maximal response amplitude across contrasts, the exponential n reflects the sensitivity of the response function, C50 is the contrast corresponding to 50% of the maximal response, and b denotes baseline and was set as the response to the lowest contrast (1%).

As contrast increased, response phase was often observed to advance progressively earlier in the stimulus cycle. This phenomenon will be referred to as CDPA to distinguish it from absolute phase advance relative to the stimulus. In order to quantify CDPA, a first-order polynomial was fit to the curve of phase vs. log (contrast) over the middle six contrasts presented (range: 2.78–35.94% contrast; see **Figure 4**). The resultant slope quantifies CDPA magnitude in units of degree/octave. In earlier reports, CDPA has sometimes been expressed as the amount of phase advance over the eightfold range from 1.25 to 10% contrast (Shapley and Victor, 1978; Sclar, 1987). Because, we found that phase estimates were often unreliable at very low levels of contrast, we chose to exclude response values from contrasts less than 2.78%. The upper contrast limit was chosen to exclude saturation effects and falls near or below the C50 for all curves.

### Modeling Contrast-Dependent Phase Advance

Results from previous studies show that retinal spikes following short ISIs are more effective in evoking LGN responses than retinal spikes following longer ISIs (Mastronarde, 1987; Usrey et al., 1998; Levine and Cleland, 2001; Rowe and Fischer, 2001; Carandini et al., 2007; Sincich et al., 2007; Weyand, 2007; Rathbun et al., 2010). Given that the mean firing rate of retinal ganglion cells typically increases as contrast increases, there will necessarily be a shift in the distribution of ISIs as a function of contrast. To determine the extent to which the augmentation of CDPA measured in the LGN relative to the retina could be accounted for by the contrast-dependent shift in ISI distribution, we generated simulated LGN spike trains based on weighting actual retinal spikes in experimentally recorded data according to the ISI vs. spike efficacy relationship curve calculated from responses to white-noise stimulation (Rathbun et al., 2010). For example, if 30% of retinal spikes following an ISI of 10–15 ms were found to evoke an LGN spike compared to only 15% of retinal spikes following an ISI of 15–20 ms, then these two groups of retinal spikes were assigned weights of 0.3 and 0.15, respectively (Alitto and Usrey, 2015) as their contributions to the simulated LGN spike train. This process was repeated for every retinal spike and simulated spike trains were analyzed in exactly the same manner as those from real LGN neurons, as described above.

#### Statistical Analysis

Unless otherwise indicated, population data is summarized by the mean and standard error of the mean. Wilcoxon's signed-rank test (MATLAB function: signrank; The Mathworks, Natick, MA, USA) was used to determine p values for all pairwise statistical tests.

### RESULTS

### Comparing Contrast Response Functions in Retina and LGN

Simultaneous recordings were made from 10 pairs of monosynaptically-connected retinal ganglion cells and LGN neurons in order to study the influence of stimulus contrast on neuronal responses across the retinogeniculate synapse (see ''Materials and Methods'' Section; **Figure 1**). Responses to contrast-variant drifting grating stimuli (4 Hz, optimal spatial frequency) were used to determine the C50, defined as the contrast to evoke 50% of maximum response, for each neuron in our sample (n = 19; all Y cells). The C50 is therefore a good metric for contrast gain control as it tends to be lowest for neurons that exhibit greater contrast saturation. Across our sample of connected cells, LGN neurons typically had significantly lower C50 values than their simultaneously recorded retinal input (**Figures 2A,B**; p = 0.02), indicating that LGN neurons display greater contrast gain control than their retinal counterparts.

To determine whether the decrease in C50 that occurred between pre-and postsynaptic neurons was the result of a selective filtering of retinal spikes, we compared C50 values for relayed and non-relayed retinal spikes (see ''Materials and Methods'' Section). As shown in **Figures 2C,D**, there was not a significant difference in C50 between the two classes of retinal spikes (p = 0.23). Thus, it seems unlikely that the difference in C50 values between retina and LGN can be attributed to the selective filtering of spikes generated by the simultaneously recorded retinal ganglion cells.

Estimates indicate that individual LGN neurons in the cat typically receive monosynaptic input from approximately 2–5 retinal ganglion cells (Cleland et al., 1971; Cleland, 1986; Hamos et al., 1987; Mastronarde, 1992; Usrey et al., 1999; Reid and Usrey, 2004; Martinez et al., 2014). To address the possibility that this convergence contributes to the shift in C50 between retinal ganglion cells and LGN neurons, we divided the spikes generated by each LGN neuron in our sample into two categories: those evoked (or ''triggered'') by the simultaneously recorded retinal ganglion cell, and those evoked from other sources (''non-triggered''), including other retinal ganglion cells. Across our sample of cells, C50 values were significantly lower for non-triggered LGN spikes compared to triggered spikes (**Figures 2E,F**; p < 0.05). This finding is consistent with the idea that an LGN cell's contrast response function is shifted in the direction of its most sensitive input which, because of convergence, is likely to be an input other than the simultaneously recorded retinal ganglion cell.

We next examined whether the exponent ''n'' from the equation used to fit the contrast response functions differed between connected retinal and LGN neurons (see ''Materials and Methods'' Section). In general, this exponent can be taken

#### FIGURE 2 | Continued

Comparison between spike classes for hyperbolic ratio fit parameters. (A,C,E) Contrast response functions for a single example pair (Pair 16, filled symbol in B,D,F,G) where raw data is plotted with circles, solid lines denote the hyperbolic ratio fit, and dashed lines indicate the C50. (B,D,F) Scatterplots of C50 for retinal and LGN spikes (B), relayed and non-relayed retinal spikes (D), and triggered and non-triggered LGN spikes (F). (G) Scatterplot comparing the exponent n between retinal and LGN spike trains. In all scatterplots, solid diagonal line denotes unity.

to quantify the linearity of the contrast response function, with small exponents indicating a relatively linear curve, and larger exponents indicating nonlinear expansion below the inflection point and compression above it. Consistent with Duong and Freeman (2008), we found that the expansive nonlinearity at low contrasts (n > 1) was present for all of the Y-type retinal ganglion cells and LGN neurons in our sample. However, we did not find a significant difference in the exponent term n between pre- and postsynaptic neurons, suggesting that this feature of the contrast response function is passed on, unaltered, from retina to LGN (**Figure 2G**; p = 0.375). It is worth noting that the single outlier in **Figure 2G** corresponds to an LGN neuron which exhibited a significantly stronger F2/F1 ratio than any other cell in this study. This pair of cells also represents the only pair in the sample in which the classification of the retinal ganglion cell was not clear (the LGN neuron was Y type). With that said, this cell pair did not differ from the rest of the sample in all of the other analyses performed.

### Comparing Contrast-Dependent Phase Advance in Retina and LGN

CDPA is another hallmark of nonlinear processing in the early visual system. As contrast increases, neurons in the retina, LGN and visual cortex are reported to respond progressively earlier relative to the phase of the stimulus (Shapley and Victor, 1978; Dean and Tolhurst, 1986; Sclar, 1987; Alitto and Usrey, 2004). While this effect is partly due to a decrease in latency with increasing contrast, it is also believed to result from an increase in transience that is induced by contrast gain control mechanisms (**Figure 3**, Shapley and Victor, 1978). Importantly, models of geniculocortical processing often incorporate an increase in the CDPA from LGN to cortex (Kayser et al., 2001). While a similar increase from retina to LGN has been hypothesized, this increase has yet to be demonstrated directly. One study that examined this question through a meta-analysis of the existing literature found no difference between the two structures (Kayser et al., 2001). Paired-cell recording, however, provide a particularly sensitive tool to examine directly subtle differences in the responses of LGN neurons and their retinal inputs.

Consistent with previous reports, our sample of Y-type retinal ganglion cells exhibited an average phase advance of ∼55◦ over the 2.78–35.94% contrast ranges (Shapley and Victor, 1978 reported ∼50◦ ). More importantly, a comparison of CDPA between simultaneously recorded retinal ganglion cells and LGN neurons revealed that CDPA is significantly greater for LGN neurons than their recorded retinal inputs

(p = 0.027; **Figures 4A,B**). This finding confirms the hypothesis that the influence of contrast gain control progressively increases throughout the early visual system. In examining differences between spike classes, we found that relayed retinal spikes exhibited significantly greater CDPA values than nonrelayed retinal spikes (**Figures 4C,D**; p = 0.004), suggesting that the increase in CDPA from retina to LGN relies, in part, on a selective filtering of retinal spikes. Across our sample of cell pairs, there was not a significant difference between CDPA values calculated from triggered and non-triggered LGN spikes (**Figures 4E,F**; p = 0.777), suggesting that signals from simultaneously recorded and non-recorded retinal ganglion cells experienced comparable levels of CDPA.

### Modeling Changes in Contrast-Dependent Phase Advance

Previous research has shown that the retinal interspike interval (ISI) has a strong influence on the generation of postsynaptic

responses in the LGN, as retinal spikes following short ISIs (<30 ms) are significantly more likely to evoke a postsynaptic spike than retinal spikes following longer ISIs (Carandini et al., 2007). Given this, we asked whether an ISI-based filter for retinogeniculate communication could underlie the increase in CDPA, described above. As a first step, we determined the influence of stimulus contrast on the distribution of ISIs in retinal spike trains. Across our sample of retinal ganglion cells, the distribution of ISIs was shifted toward lower ISIs as contrast increased (**Figures 5A,B**), consistent with the expected inverse relationship between firing rate and ISI.

We next quantified the relationship between ISI and the efficacy of retinal spikes in evoking postsynaptic responses for each retinogeniculate pair of simultaneously recorded neurons in our sample. Similar to previous results (Rathbun et al., 2010), retinal spikes with the shortest preceding ISIs were most effective in evoking postsynaptic responses (**Figure 5C**). Finally, we combined the ISI distributions that were determined for each contrast with the ISI filter to determine the extent to which the filter could reproduce the CDPA effect (see ''Materials and Methods'' Section). This model tests the hypothesis that simple, temporal filtering of retinal spikes, as estimated by the

contrast on mean and median ISI for all Y-class retinal ganglion cells. (C) ISI-based efficacy filter for the sample pair. Shaded regions in (A,C) denote error bars.

ISI-spike efficacy curve, can directly contribute to the increased CDPA of LGN neurons. For the modeled data, as with the original data, we found that relayed spikes had significantly greater CDPA when compared to non-relayed spikes (**Figure 6**; p = 0.014). While the magnitude of this effect was less than what was found in the original data (2.0 ± 0.1 vs. 5.0 ± 1.6 degree/octave, respectively; see ''Discussion'' Section), this result suggests that temporal filtering indeed plays a significant role

in the increased CDPA that occurs across the retinogeniculate synapse.

### DISCUSSION

Stimulus contrast is one of the most salient features encoded in the activity of neurons in the retina and LGN. Indeed, the center/surround organization of retinal and LGN receptive fields is ideal for detecting local changes in contrast. Although the spatial organization of retinal and LGN receptive fields are quite similar, past studies indicate that LGN neurons display greater contrast gain control, on average, than retinal ganglion cells. Given the significance of stimulus contrast for nearly all aspects of visual processing, it is surprising that relatively little attention has been paid to how contrast responses are transformed as they pass from retina to LGN (Kaplan et al., 1987; Cheng et al., 1995).

Here, we compared the responses of monosynaptically connected Y-type retinal ganglion cells and LGN neurons in the cat as a function of stimulus contrast. Consistent with the view that nearly all spikes in the LGN are triggered by retinal action potentials (Kaplan and Shapley, 1984; Sincich et al., 2007), we found the overall shape of contrast response functions to be similar for simultaneously recorded retinal ganglion cells and LGN neurons. However, our results also demonstrate that the semisaturation contrast (C50) is significantly lower for LGN neurons compared to their simultaneously recorded retinal input, indicating that contrast gain control is enhanced by the LGN and that LGN responses begin to saturate at lower contrasts than their retinal inputs. Further analysis suggests that this decrease in C50 relies, at least in part, on convergence of multiple retinal inputs onto individual LGN neurons. With convergence, LGN neurons receive input from an ensemble of retinal ganglion cells that have a range of sensitivity profiles, and the most sensitive of these inputs will be those that influence LGN activity under low contrast conditions, thereby shifting C50 values toward lower contrasts. Because individual LGN neurons are estimated to receive convergent input from approximately 2–5 retinal ganglion cells, our recording configuration was unlikely to include the most sensitive retinal input, a view consistent with the finding that non-triggered retinal spikes (spikes evoked from other sources) have lower C50 values than spikes triggered by the simultaneously recorded retinal ganglion cell.

Past efforts have shown that CDPA is most robust for Y cells (Shapley and Victor, 1978). Our investigation of CDPA in monosynaptically connected Y-type retinal ganglion cells and LGN neurons reveals that LGN neurons exhibit greater CDPA than their retinal inputs. Our results also show that relayed retinal spikes exhibit greater CDPA than non-relayed spikes, suggesting that contrast gain control exerts an influence on spike transmission at the retinogeniculate synapse. To gain insight into the possible mechanisms that underlie the increase in CDPA between the retina and LGN, we developed a model to examine whether temporal filtering of incoming retinal spikes could produce CDPA. In this model, retinal spikes following a short ISI (<30 ms) are more effective in driving a postsynaptic spike than retinal spikes following longer ISIs. Results from this effort revealed that relayed spikes had greater CDPA than non-relayed spikes, although the magnitude of this effect was less than that measured between retinal ganglion cells and LGN neurons in vivo. While additional mechanisms, including polysynaptic interactions and local inhibition, likely contribute to increased transience and the increased CDPA of LGN neurons, ISI filtering provides a simple feed-forward

### REFERENCES

mechanism by which gain control can be augmented in the visual pathway.

In summary, simultaneous recordings of monosynaptically connected retinal ganglion cells and LGN neurons showed enhancement of contrast gain control mechanisms by the LGN. Two measures of contrast gain control: (1) increased sensitivity to low-contrast stimuli and (2) CDPA, were both greater for individual LGN neurons compared to their simultaneously recorded retinal inputs. Further analyses suggests that increased sensitivity is achieved via spatial convergence of multiple retinal inputs, while increased CDPA is achieved, in part, on temporal summation of arriving signals. Taken together, these results reveal a breadth of processing strategies, both spatial and temporal, employed by the thalamus to transform visual signals en route from retina to cortex.

### AUTHOR CONTRIBUTIONS

DLR contributed to experimental design, data collection, data analysis, and manuscript preparation. HJA contributed to data analysis and manuscript preparation. DKW contributed to data analysis and manuscript preparation. WMU contributed to experimental design, data collection and manuscript preparation.

### FUNDING

This work was supported by National Eye Institute Grants EY 13588, EY12576, and T32 EY15387, and the German ministry for education and research (BMBF) 031 A 308 and 01GQ1002.

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Rathbun, Alitto, Warland and Usrey. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Presynaptic Adenosine Receptor-Mediated Regulation of Diverse Thalamocortical Short-Term Plasticity in the Mouse Whisker Pathway

Giovanni Ferrati 1 , Francisco J. Martini 1 and Miguel Maravall 1,2 \*

1 Instituto de Neurociencias de Alicante UMH-CSIC, Sant Joan d'Alacant, Spain, 2 School of Life Sciences, Sussex Neuroscience, University of Sussex, Brighton, UK

Short-term synaptic plasticity (STP) sets the sensitivity of a synapse to incoming activity and determines the temporal patterns that it best transmits. In "driver" thalamocortical (TC) synaptic populations, STP is dominated by depression during stimulation from rest. However, during ongoing stimulation, lemniscal TC connections onto layer 4 neurons in mouse barrel cortex express variable STP. Each synapse responds to input trains with a distinct pattern of depression or facilitation around its mean steady-state response. As a result, in common with other synaptic populations, lemniscal TC synapses express diverse rather than uniform dynamics, allowing for a rich representation of temporally varying stimuli. Here, we show that this STP diversity is regulated presynaptically. Presynaptic adenosine receptors of the A1R type, but not kainate receptors (KARs), modulate STP behavior. Blocking the receptors does not eliminate diversity, indicating that diversity is related to heterogeneous expression of multiple mechanisms in the pathway from presynaptic calcium influx to neurotransmitter release.

#### Edited by:

Vincenzo Crunelli, Cardiff University, UK

#### Reviewed by:

Heiko J. Luhmann, Institut für Physiologie und Pathophysiologie, Germany James T. Porter, Ponce School of Medicine and Health Sciences, Puerto Rico

\*Correspondence:

Miguel Maravall<EMAIL_ADDRESS>
Received: 05 November 2015 Accepted: 05 February 2016 Published: 23 February 2016

#### Citation:

Ferrati G, Martini FJ and Maravall M (2016) Presynaptic Adenosine Receptor-Mediated Regulation of Diverse Thalamocortical Short-Term Plasticity in the Mouse Whisker Pathway. Front. Neural Circuits 10:9. doi: 10.3389/fncir.2016.00009 Keywords: vibrissae, somatosensory, tactile, whole-cell, short-term plasticity, patch clamp, in vitro

### INTRODUCTION

Visual, auditory and somatosensory information reaches the neocortex by way of thalamocortical (TC) synapses. Moment-to-moment changes in the size and reliability of these synaptic connections, termed short-term synaptic plasticity (STP), shape the information that reaches the cortex and determine how the response of a thalamic neuron to a sensory event is transmitted. STP acts as a filter of presynaptic patterns, preferentially transmitting particular frequencies or events (e.g., bursts as compared to single spikes; Fortune and Rose, 2001; Abbott and Regehr, 2004; Buonomano and Maass, 2009). When stimulated from rest, ''driver'' synapses

**Abbreviations:** STP, short-term plasticity; TC, thalamocortical; ISI, inter-stimulus interval; PSP, post-synaptic potential; VPM, ventral posterior medial thalamic nucleus; TCS, slope of instantaneous tuning curve; ACSF, artificial cerebrospinal fluid; DNDS, dinitrostilbene-2,20 -disulfonic acid; DPCPX, 8-Cyclopentyl-1,3-dipropylxanthine; CPT or 8-CPT, 8-Cyclopentyl-1,3-dimethylxanthine; UBP 310, (S)-1-(2-Amino-2-carboxyethyl)-3-(2-carboxy-thiophene-3 yl-methyl)-5-methylpyrimidine-2,4-dione; NS-102, 6,7,8,9-Tetrahydro-5-nitro-1H-benz[g]indole-2,3-dione 3-oxime.

from TC neurons onto excitatory neurons in layer 4 show STP dominated by strong depression (Stratford et al., 1996; Gil et al., 1997, 1999; Chung et al., 2002; Bruno and Sakmann, 2006; Sherman and Guillery, 2006; Lee and Sherman, 2008; Viaene et al., 2011). However, stimulation from rest does not reproduce the physiologically relevant in vivo situation in which sensory information does not arrive against a background of perfect silence. Rather, thalamic spiking as delivered to the cortex consists of ongoing sensory and contextual activity (Slézia et al., 2011; Poulet et al., 2012; Ollerenshaw et al., 2014; Bale et al., 2015; Crunelli et al., 2015; McCormick et al., 2015; Urbain et al., 2015). Prior activity sets the amount of TC synaptic depression: active synapses are effectively ''pre-depressed'' (Castro-Alamancos and Oldford, 2002; Castro-Alamancos, 2004; Boudreau and Ferster, 2005; Reig et al., 2006). The ongoing STP state of synapses determines the regime of operation of the TC network and conditions how information is transmitted (Buonomano and Maass, 2009).

We recently determined the population-level variability of STP in TC connections during ongoing stimulation (Díaz-Quesada et al., 2014). Recording responses of layer 4 excitatory neurons in acute TC slices, we found that although different TC connections share prominent depression during stimulation from rest, STP during ongoing stimulation is highly heterogeneous across connections. Some TC connections are strongly depressing and respond more weakly to shorter interstimulus intervals, while others facilitate and show an enhanced response to shorter intervals. A given temporal stimulus pattern can facilitate some synapses while depressing others, implying that different TC synapses are strong at distinct times during ongoing activity. This range of behaviors does not define separate categories of STP; instead, connections form a continuum. STP variability applies across identified spiny stellate neurons, and occurs even for different recordings carried out in the same slice (Díaz-Quesada et al., 2014).

The mechanisms governing the diversity of STP across excitatory lemniscal TC synapses are unknown and could potentially include pre- and postsynaptic loci. Here, we used whole-cell patch clamp recordings in acute slices to uncover mechanisms whose expression covaries with the amount and tendency of STP and localize them pre- or postsynaptically.

### MATERIALS AND METHODS

### Slice Preparation

All procedures were performed in accordance with national and European Union policies for the care and use of animals in research. The study was approved by the Instituto de Neurociencias and CSIC Ethical Review Committees. TC slices (Agmon and Connors, 1991) were obtained from male and female ICR mice between 14–25 postnatal days of age. This age is later than the established critical period for TC synaptic plasticity (Crair and Malenka, 1995) and the period when sensory responses have been described as facilitating (Borgdorff et al., 2007); over this range of ages, the distribution of STP values does not depend on age (Díaz-Quesada et al., 2014). Slices (350 µm thickness) were prepared with conventional methods (Díaz-Quesada and Maravall, 2008): after killing the animal, the brain was placed in ice-cold cutting solution bubbled with carbogen (95% O2, 5% CO2) and containing (in mM): 110 Cl-choline, 25 NaHCO3, 25 D-glucose, 11.6 Na-aspartate, 7 MgSO4, 3.1 Na-pyruvate, 2.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2. The brain was split at the midline and each hemisphere placed on a custom-made wedge at a slope of 50◦ . Hemispheres were placed lying on their medial face at a tilt of 10◦ on the sloped surface of the wedge, with the left hemisphere glued onto the right side of the wedge with its rostral edge facing down and the right hemisphere arranged symmetrically. Around three TC slices were collected per hemisphere. Slices were cut on a vibratome (Campden Instruments Integraslice 7550M; Leica VT1000S) and transferred to a chamber containing artificial cerebrospinal fluid (ACSF) continuously perfused with carbogen and incubated at 34◦C for ∼30 min. They were then kept at room temperature until used. ACSF composition was usually (in mM): 127 NaCl, 25 NaHCO3, 25 D-glucose, 2.5 KCl, 1.25 NaH2PO4, 2 MgCl2, 1 CaCl2 unless otherwise noted. However, to examine the effects of [Ca2+] on STP diversity, the ACSF composition was modified by increasing CaCl2 concentration to 2 or 4 mM while reducing [MgCl2] to 1 or 0.5 mM respectively. All chemicals were from Sigma-Aldrich unless otherwise noted.

### Recordings

Patch electrodes were pulled from borosilicate glass (1.5 mm outer diameter, 0.86 mm inner; 3–6 MΩ) and filled with internal solution containing (in mM) 130 K-methylsulfonate, 10 Na-phosphocreatine, 10 HEPES, 4 MgCl2, 4 Na2-ATP, 3 Na-ascorbate, and 0.4 Na2-GTP; pH 7.33, 287–303 mOsm. To ensure that measured STP was purely monosynaptic, the internal solution incorporated the intracellular GABAA antagonist dinitrostilbene-2,20 -disulfonic acid (DNDS), a chloride channel blocker (Dudek and Friedlander, 1996; Covic and Sherman, 2011). DNDS (1 mM; Tocris) worked effectively in TC connections (Díaz-Quesada et al., 2014). Kynurenic acid, a blocker of ionotropic glutamate receptors, was tested at various concentrations and found to provide reliable partial blockade at 150 µM. To manipulate adenosine receptor activation, we used the receptor (A1R) agonist adenosine (9-β-D-Ribofuranosyladenine, Adenine riboside, Adenine-9-β-D-ribofuranoside) and two different antagonists, DPCPX and 8-CPT (all from Tocris). For kainate receptor manipulation we used antagonists UBP 310 (Tocris) and NS-102. Recordings were performed at room temperature (24◦C). Earlier work found no evidence that temperature (24◦C vs. 33◦C) influences STP during ongoing stimulation (Díaz-Quesada et al., 2014).

Neurons were selected based on morphological criteria using infrared differential interference contrast optics and patched in the whole-cell mode. Cells with small spherical cell bodies (∼10–15 µm in diameter) and dendrites confined to L4, typical of spiny stellate neurons, were chosen. Recordings were not corrected for liquid junction potential. Neuronal responses were measured while stimulating with depolarizing square pulses of 500 ms duration and increasing intensity; only neurons displaying a regular spiking phenotype (McCormick et al., 1985), clearly distinct from fast spiking or low threshold spiking cells, were included in the analyzed data set. Input resistance was 150–500 MΩ and access resistance was under 10% of input resistance; recordings were discarded if access resistance was unstable or the resting membrane potential drifted by more than 10 mV. Data were acquired with an Axon Multiclamp 700-B amplifier (Molecular Devices), filtered at 4–10 kHz, and sampled at 20 kHz (PCI 6040-E; National Instruments) under the control of software custom-written in Matlab (The Mathworks; Pologruto et al., 2003).

### Electrical Stimulation

TC fibers were stimulated with a Pt-Ir concentric bipolar electrode (FHC; outer pole diameter 200 µm, inner pole diameter 25 µm) located in the white matter; a stimulus isolator generated monophasic pulses (Iso Flex; A.M.P.I.). All stimuli were generated in Matlab. To restrict stimulation to a reduced number of fibers (putatively down to a single fiber), we first searched for a stimulus amplitude at which a clear PSP was seen in a fraction of trials. We then further increased amplitude to a level such that PSP size remained stable but each temporally isolated single stimulus evoked a successful response in almost all trials (Díaz-Quesada et al., 2014). This approach ensured that failures of stimulation were negligible, but kept low the number of stimulated fibers. At this stimulation intensity, successful PSPs maintained their stereotypical shape throughout a train of repetitive stimulation, suggesting that the fibers contributing to the response remained stable. Experiments with unstable success probability or response characteristics (latency, shape) were discarded. Stimulus amplitudes were 1–15 µA, towards the lower end of previously reported thresholds for TC activation and an order of magnitude lower than thresholds for antidromic activation of corticothalamic neurons (Rose and Metherate, 2001).

Stimulation protocols were adapted from Díaz-Quesada et al. (2014). In brief, they consisted of sequences of regular and irregular pulse trains. A regular train was followed by an irregular train, both with the same average frequency (4.59 Hz) and duration (21 pulses, 4.36 s). The regular train had a constant ISI and the irregular train consisted of pulses at different interspersed intervals in the range 13–806 ms. A single specific irregular train was used. Each sequence (9 s long) was repeated 10–15 times per recording; each trial lasted 10 s, including periods of silence during which baseline properties were monitored. Additionally, there was a stimulation pause between trials >5 s (trial start corresponded to condition ''from rest''). All protocols were applied with the same stimulation intensity.

### Analysis

To compute PSP amplitude, we searched for the first membrane potential peak in the window extending from 0.5 to 12 ms after the stimulation pulse, averaged the membrane potential over five data samples (from −0.1 to 0.1 ms relative to the raw peak), and subtracted a baseline averaged over 2 ms immediately preceding the stimulation pulse. This short baseline effectively compensated for depolarization caused by earlier PSPs. Mean PSP amplitude was computed separately for each stimulus in a train after removing stimulus artifacts with median filtering. The steady-state response level was assessed by discarding the first five PSPs from stimulation onset (i.e., approximately the first second of stimulation), and computing the mean amplitude over all remaining PSPs.

We quantified STP magnitude using two measures, as follows. First, for each connection we constructed a tuning curve, plotting PSP magnitude as a function of the preceding ISI during ongoing irregular stimulation. Tuning curves were constructed only from steady-state PSPs, discarding the first few responses from rest. We computed the slope of the tuning curve by linear regression over the range of intervals up to 218 ms. This tuning curve slope (TCS) provided a simple measure of whether a connection tended to respond more to shorter or to longer ISIs. Connections with smaller responses to short intervals (i.e., to high instantaneous frequencies) had positive TCS, while connections with larger responses to short intervals had negative TCS. This simple quantification of response tuning disregards effects on timescales longer than a single ISI. We also computed each connection's relative response upon transitioning from stimulation at a constant frequency to irregular stimulation at a higher frequency, hereafter referred to as ''facilitation index''. To obtain the facilitation index, we took the ratio of the average PSP amplitude evoked after the first two intervals after the switch from regular to irregular stimulation, to the steady-state PSP amplitude just before the switch. The resulting index was <1 when the mean response amplitude was reduced upon transitioning to higher-frequency irregular stimulation, and >1 when amplitude was increased. The facilitation index was potentially sensitive to timescales longer than a single ISI; its goal was to quantify the degree of context-dependent facilitation or depression during ongoing stimulation.

All analyses were conducted in Matlab (The Mathworks).

## RESULTS

### STP During Ongoing Stimulation Depends on Presynaptic Mechanisms

To search for mechanisms regulating differences in STP across TC synapses, we performed whole-cell patch clamp recordings of postsynaptic potentials (PSPs) from visually identified regular spiking neurons located in layer 4 of mouse TC slices (**Figure 1A**).

The observed diversity of STP across different synapses could result from the differential contribution of disynaptic inhibition to the overall synaptic response. Responses of layer 4 neurons to TC stimulation have a strong disynaptic inhibitory component (Agmon and Connors, 1991; Porter et al., 2001; Gabernet et al., 2005; Wilent and Contreras, 2005; Sun et al., 2006; Cruikshank et al., 2007; Daw et al., 2007). An observed short-term facilitation

presynaptic mechanisms. (A) Example of recording of post-synaptic potential (PSP) responses to ongoing thalamocortical (TC) stimulation (mean of eight traces). Scale bars: 300 ms, 0.5 mV. Dots at bottom, times of stimulation. Stimulation at constant frequency shown in yellow; stimulation just after transition to irregular train, in magenta; later irregular stimulation, in gray. The facilitation index was obtained by dividing the average response just after switching to irregular stimulation (magenta dots) by the average steady-state response at constant frequency (yellow dots). (B) Facilitation index dependance on extracellular [Ca2+]. In (B–E), each connected pair of points is one recording. Bars represent population median. Asterisks denote statistically significant difference between distributions (tests are indicated in main text). Facilitation index values decrease and become more narrowly distributed as [Ca2+] increases. (C) Tuning curve slope (TCS) dependance on extracellular [Ca2+]. Distribution becomes narrower as [Ca2+] increases. (D) Kynurenic acid partial block of postsynaptic glutamate receptors decreases EPSP size. (E) Kynurenic acid application has no systematic effect on facilitation index. (F) Kynurenic acid has no systematic effect on TCS.

of the PSP response could potentially arise from faster short-term depression of the inhibitory component relative to the excitatory component (Beierlein et al., 2003; Gabernet et al., 2005; Higley and Contreras, 2006; Heiss et al., 2008). However, in previous work we showed that disynaptic inhibition is not necessary for STP diversity by conducting experiments under intracellular blockade of GABAA receptors: a similar range of behaviors, encompassing depression to facilitation, is found in recordings with intact inhibition and recordings where GABAergic inputs are blocked (Díaz-Quesada et al., 2014). Thus monosynaptic TC connections to cortical layer 4 display STP diversity, which must originate in differences in the properties of those connections.

STP diversity could be pre- or postsynaptically regulated. We conducted a series of experiments to establish the locus of regulation, as follows. Earlier results had shown that extracellular [Ca2+] influences STP, because there was significantly less depression at [Ca2+] = 1 mM than at 2 mM (Díaz-Quesada et al., 2014). This suggested a presynaptic locus for STP regulation (Zucker and Regehr, 2002; Fioravante and Regehr, 2011). We reasoned that, if the main locus is presynaptic, saturating presynaptic terminals with a much higher extracellular [Ca2+] (4 mM) should further bias results towards depression, possibly decreasing STP variability across the recorded population. To test this, we recorded TC synaptic responses in a set of neurons while switching extracellular [Ca2+] from 1 to 4 mM (see ''Materials and Methods'' Section). As expected, increasing [Ca2+] to 4 mM induced an increase in onset PSP response (because of an enhanced initial probability of neurotransmitter release) followed by faster depression. This was reflected in a significant change towards lower values of the facilitation index (p = 0.016, Wilcoxon signed-rank test, n = 7 recordings; **Figure 1B**). Moreover there was a significant reduction in the heterogeneity of STP across neurons, such that synapses became depressing (p = 0.0026, 2-dimensional Kolmogorov-Smirnov two-sample test, n = 7; **Figures 1B,C**). These results show that STP diversity is influenced by [Ca2+] in a manner consistent with presynaptic regulation of neurotransmitter release.

As well as presynaptic mechanisms, did postsynaptic mechanisms play a significant role in setting each connection's effective STP? One such contribution could come from differences across synapses in postsynaptic summation: for example, broader PSPs might lead to greater effective facilitation. However, differences in PSP width do not influence a connection's facilitation index and thus do not contribute to STP diversity (Díaz-Quesada et al., 2014). We decided to test specifically for an effect of differences in glutamate receptor activation on STP. We reasoned that any effects of NMDA receptor (NMDAR)-mediated summation, or of modulation in postsynaptic receptor activation (e.g., in saturation or desensitization), would be reduced as a result of partial receptor blockade. We thus partially blocked ionotropic glutamate receptors by adding kynurenic acid to the extracellular ACSF (Elmslie and Yoshikami, 1985). At a concentration of 150 µM, kynurenic acid significantly decreased steady-state PSP magnitude (p = 0.016, Wilcoxon signed-rank test, n = 7; **Figure 1D**), consistent with a reduced postsynaptic response to neurotransmitter release. However, kynurenic acid had no effect either on facilitation index (p = 0.94, Wilcoxon signed-rank test, n = 7; **Figure 1E**) or on TCS (p = 0.38, Wilcoxon signed-rank test, n = 7; **Figure 1F**). Thus, STP diversity remained unaffected by manipulation of postsynaptic ionotropic glutamate receptors.

### STP is Regulated by Presynaptic Adenosine Receptor Activation

Which presynaptic mechanisms could modulate STP differentially across synapses? Several mechanisms in the pathway leading from Ca2+ entry to neurotransmitter release could potentially contribute. One prominent mechanism modulating synaptic release involves the action of local neurotransmitters through presynaptically expressed receptors (Zucker and Regehr, 2002). We hypothesized that one or several such types of release modulation could contribute to the regulation of STP.

Adenosine reduces synaptic excitation through the action of presynaptic receptors that inhibit glutamate release (Lupica et al., 1992; Scanziani et al., 1992; Shen and Johnson, 2003; Nicoll and Schmitz, 2005). In TC synapses, application of adenosine decreases EPSCs and increases paired-pulse facilitation (Fontanez and Porter, 2006). To test whether release probability and STP in TC connections can be differentially modulated by adenosine receptors, we recorded responses to TC stimulation before and after adding 100 µM of adenosine to the bath. Consistent with a presynaptic site of action, application of adenosine significantly increased pairedpulse ratios (p = 0.024, Wilcoxon signed-rank test, n = 11; **Figure 2A**) but caused no significant change in membrane potential (p = 0.24, Wilcoxon signed-rank test, n = 11; median depolarization 0.97 mV). Adenosine increased the facilitation index during ongoing stimulation (p = 0.0049, Wilcoxon signedrank test, n = 11; **Figure 2B**), shifting the distribution of STP behaviors expressed in the data set. Median TCS was unchanged (p = 0.97, Wilcoxon signed-rank test, n = 11; **Figure 2C**), but variability in this parameter decreased (p = 0.0009, F-test). This decrease in variability was accounted for by the subset of synapses which, in the absence of added adenosine, had the highest release probability and depressed most strongly: only this minority of synapses had their release probability significantly dampened by adenosine. The dissociation of effects on facilitation index and TCS indicates that adenosine tonically downregulated release probability across the range of intervals (Moore et al., 2003), because the slope relating probability to interval duration was unchanged for the majority of synapses.

Which receptor mediated the modulatory action of adenosine? A1 receptors appear to underpin the inhibitory effects of adenosine on glutamate release (Wu and Saggau, 1994; Dunwiddie and Masino, 2001), including in TC synapses (Fontanez and Porter, 2006). We evaluated the impact of A1 receptors on STP by using the antagonists DPCPX and CPT. We recorded responses to TC stimulation in control ACSF and after addition of 1 µM DPCPX or, in a separate set of experiments, 2 µM CPT. Inhibiting A1 receptors caused a significant change in TCS towards more positive values: i.e., synapses became relatively more responsive to longer rather than shorter intervals (DPCPX: p = 0.0011, Wilcoxon signedrank test, n = 16; CPT: p = 0.0078, Wilcoxon signed-rank test, n = 6; **Figure 2E**). We interpret this as indicating that A1 receptor inhibition prevented adenosine from limiting glutamate release, leading to a greater tendency towards depression, and more substantial recovery after longer intervals. Conversely, neither DPCPX nor CPT caused a significant difference in facilitation index (DPCPX: p = 0.61, Wilcoxon signed-rank test, n = 16; CPT: p = 0.078, Wilcoxon signed-rank test, n = 6;

**Figure 2D**). These effects again shifted the distribution of STP behaviors as compared to control conditions, but did so in the opposite direction to the experiments described above involving application of adenosine. In conclusion, activation of A1 adenosine receptors modulates STP of TC synapses.

increases TCS.

### Absence of Evidence for a Role of Kainate Receptors in Regulation of STP

Our experiments demonstrated that activation and manipulation of A1 receptors shifts STP behavior but does not eliminate its diversity. Thus, multiple mechanisms act together to determine STP in each synapse. A possible additional mechanism for regulating STP through neurotransmitter action is modulation by presynaptic KARs. KARs can be powerful presynaptic regulators of synaptic efficacy and STP (Lerma and Marques, 2013). In developing TC synapses, KARs containing GluK1–3 subunits are expressed presynaptically and regulate neurotransmission (Kidd et al., 2002; Urbano and Lerma, 2006; Jouhanneau et al., 2011). We therefore hypothesized that KARs could help modulate release probability and set the level of STP. To test this idea, we compared STP of responses to TC stimulation in layer 4 neurons before and after application of either the selective GluK1 antagonist UBP 310 (10 µM) or the GluK2 antagonist NS-102 (20 µM). We found no consistent effect of UBP 310 across recordings, suggesting that the operation of GluK1 receptors does not systematically modulate STP in TC synapses (p = 0.57 for facilitation index, p = 0.73 for TCS, Wilcoxon signed-rank test, n = 9; **Figure 3A**). Similarly, we found no consistent effect of NS-102 application (p = 0.57 for facilitation index, p = 0.054 for TCS, Wilcoxon signed-rank test, n = 9; **Figure 3B**). In conclusion, these experiments found no consistent evidence for a role of these receptor subunits in regulating STP under ongoing stimulation.

### DISCUSSION

Recent work from our laboratory has shown that TC connections do not constitute a population with uniform dynamics. Rather, lemniscal TC connections onto layer 4 spiny stellate neurons

receptor activation. Each connected pair of points is one recording. Bars represent population median. (A) No significant effect on facilitation index (left) or on TCS (right) of application of UBP 310, a specific blocker of GluK1-containing receptors. (B) No significant effect on facilitation index (left) or on TCS (right) of application of NS-102, a specific blocker of GluK2-containing receptors.

respond with diverse STP when stimuli arrive against a background of ongoing activity (Díaz-Quesada et al., 2014). A continuum of STP behaviors is represented across the population. This heterogeneity implies that each synapse is preferentially tuned to certain stimulation intervals, and potentially allows TC pathways to convey rich information about temporal patterns at the population level (Abbott and Regehr, 2004; Buonomano and Maass, 2009; Lee and Buonomano, 2012; David and Shamma, 2013; Chabrol et al., 2015). For example, TC synapses with specific dynamics could act as channels preferentially conveying certain information (e.g., facilitating synapses could act as burst detectors and depressing synapses as ''wake-up'' signals). Here, we addressed the mechanisms that underpin the diversity of STP. We found evidence for presynaptic regulation of diversity. Modulation of A1 adenosine receptor activation shifts the STP set point.

Many presynaptic mechanisms mediate the complex process from Ca2+ entry to exocytosis (Zucker and Regehr, 2002; Fioravante and Regehr, 2011). Diversity of STP within a single population of synapses indicates variability in the expression of this machinery. We found that activation and manipulation of A1 receptors shifts STP behavior but does not eliminate its diversity across the synaptic population (Kerr et al., 2013). This implies that several mechanisms act together to set the overall type and level of STP for each synapse. In our earlier results, the progression of STP during stimulation from rest comprised an initial phase dominated by depression, superimposed with steady-state behavior that could incorporate a varying degree of facilitation (Díaz-Quesada et al., 2014): accounting for this behavior requires phenomena beyond uniform resource depletion (Beck et al., 2005; Kandaswamy et al., 2010; Müller et al., 2010; Hennig, 2013).

We have explored one additional potential mechanism for regulating STP—modulation by KARs. Presynaptically expressed KARs regulate synaptic efficacy (Lerma and Marques, 2013) and are expressed in TC synapses (Kidd et al., 2002; Urbano and Lerma, 2006; Jouhanneau et al., 2011). However, our recordings in the presence of subunit-specific pharmacological blockers of GluK1 and GluK2 failed to find evidence for a role of these receptor subunits in STP under ongoing stimulation. We also performed experiments in slices from knock-out mice for the GluK1 subunit and double knockouts for the GluK1 and GluK2 subunits (Mulle et al., 1998, 2000; courtesy of Juan Lerma laboratory): these also failed to find a shift in STP behavior across TC synapses (data not shown).

Key questions for future work concern the impact of different mechanisms linking Ca2+ entry to triggering of release. STP diversity could result from dynamical regulation of STP at each synapse (Sippy et al., 2003; Cheetham et al., 2007; Branco et al., 2008; Pfister et al., 2010; Carvalho and Buonomano, 2011; Yang and Xu-Friedman, 2012). Multiple steps in the pathway from action potential to exocytosis can be subject to modulation (terminal size; Ca2+ influx, distribution and sensing; determination of vesicle availability and fusion; e.g., Sippy et al., 2003; Mochida et al., 2008; Welzel et al., 2011; Zhao et al., 2011; Ermolyuk et al., 2012; Leal et al., 2012; Sylwestrak and Ghosh, 2012; Baden et al., 2014; Fioravante et al., 2014; Calloway et al., 2015; Körber et al., 2015; reviewed in Branco and Staras, 2009; Fioravante and Regehr, 2011; de Jong and Fioravante, 2014). Moreover, additional mechanisms sited postsynaptically as well as presynaptically, and not ruled out by the present study (e.g., metabotropic glutamate receptors, GABAB receptors) could also help tune each connection's particular STP behavior. Is diversity essentially random (Ribrault et al., 2011), or regulated via modulation of a specific subset of mechanisms? Are these parameters regulated locally at the synapse level or are they set at a cell-wide level (Armbruster and Ryan, 2011; Ermolyuk et al., 2012; Ariel et al., 2013)? Supporting the latter possibility, there is evidence from other pathways that STP properties cluster postsynaptically, i.e., different synapses onto the same neuron can share STP of a similar nature (Branco et al., 2008; Yang and Xu-Friedman, 2012), consistent with postsynaptic regulation by the target cell (Blackman et al., 2013). However, in our present TC data set, preliminary analysis shows no evidence of postsynaptic clustering (data not shown).

### REFERENCES

### AUTHOR CONTRIBUTIONS

GF and FJM performed experiments. FJM and MM wrote code for data analysis. GF, FJM and MM analyzed and interpreted the data. MM drafted the article; all authors read and approved the final manuscript.

### ACKNOWLEDGMENTS

Financial support was provided by grants from: the Spanish Ministry of Science and Innovation (BFU2008-03017/BFI and BFU2011-23049, co-funded by the European Regional Development Fund; Consolider Program CSD2007-00023); and the Valencia Regional Government (ACOMP2010/199 and PROMETEO/2011/086). GF was supported by the ''Symbad'' Marie Curie ITN program (European Commission, Seventh Framework Programme, grant agreement 238608). We thank Ana Valero-Paternain and John Wesseling for experimental advice and Juan Lerma for advice and for kindly sharing resources.

**Conflict of Interest Statement**: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2016 Ferrati, Martini and Maravall. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Dynamic Analysis of the Conditional Oscillator Underlying Slow Waves in Thalamocortical Neurons

François David1, 2, 3, 4, 5, 6, 7 \*, Vincenzo Crunelli 1, 8, Nathalie Leresche5, 6, 7 and Régis C. Lambert 5, 6, 7 \*

1 Neuroscience Division, School of Biosciences, Cardiff University, Cardiff, UK, 2 Lyon Neuroscience Research Center, Centre National de la Recherche Scientifique UMR 5292, Lyon, France, 3 Lyon Neuroscience Research Center, Institut National de la Santé et de la Recherche Médicale U1028, Lyon, France, 4 Faculté de Médecine, Université Claude Bernard, Lyon, France, 5 Sorbonne Universités, UPMC Université Paris 06, UM 119, Neuroscience Paris Seine, Paris, France, 6 Centre National de la Recherche Scientifique, UMR 8246, Neuroscience Paris Seine, Paris, France, 7 Institut National de la Santé et de la Recherche Médicale, U1130, Neuroscience Paris Seine, Paris, France, 8 Department of Physiology and Biochemistry, University of Malta, Msida, Malta

During non-REM sleep the EEG shows characteristics waves that are generated by the dynamic interactions between cortical and thalamic oscillators. In thalamic neurons, low-threshold T-type Ca2+ channels play a pivotal role in almost every type of neuronal oscillations, including slow (<1 Hz) waves, sleep spindles and delta waves. The transient opening of T channels gives rise to the low threshold spikes (LTSs), and associated high frequency bursts of action potentials, that are characteristically present during sleep spindles and delta waves, whereas the persistent opening of a small fraction of T channels, (i.e., ITwindow) is responsible for the membrane potential bistability underlying sleep slow oscillations. Surprisingly thalamocortical (TC) neurons express a very high density of T channels that largely exceed the amount required to generate LTSs and therefore, to support certain, if not all, sleep oscillations. Here, to clarify the relationship between T current density and sleep oscillations, we systematically investigated the impact of the T conductance level on the intrinsic rhythmic activities generated in TC neurons, combining in vitro experiments and TC neuron simulation. Using bifurcation analysis, we provide insights into the dynamical processes taking place at the transition between slow and delta oscillations. Our results show that although stable delta oscillations can be evoked with minimal T conductance, the full range of slow oscillation patterns, including groups of delta oscillations separated by Up states ("grouped-delta slow waves") requires a high density of T channels. Moreover, high levels of T conductance ensure the robustness of different types of slow oscillations.

 The various cellular activities that are expressed by thalamocortical (TC) neurons during sleep

#### Edited by:

Miles A. Whittington, University of York, UK

#### Reviewed by:

Roger D. Traub, IBM T.J. Watson Research Center, USA Heiko J. Luhmann, Institut für Physiologie und Pathophysiologie, Germany

#### \*Correspondence:

François David<EMAIL_ADDRESS>Régis C. Lambert<EMAIL_ADDRESS>
Received: 23 October 2015 Accepted: 08 February 2016 Published: 25 February 2016

#### Citation:

David F, Crunelli V, Leresche N and Lambert RC (2016) Dynamic Analysis of the Conditional Oscillator Underlying Slow Waves in Thalamocortical Neurons. Front. Neural Circuits 10:10. doi: 10.3389/fncir.2016.00010 oscillations tightly depend on the expression of low-threshold T-type Ca2+ channels (T channels; Leresche et al., 1991; Williams et al., 1997a; Crunelli et al., 2014). In fact, while these channels are almost fully inactivated in the range of membrane potentials associated to the wake state (but see Lambert et al., 2014), during non-REM sleep the progressive reduction in the depolarizing tone exerted by modulatory afferents onto both cortical and thalamic neurons (McCormick, 1992) allows T channel de-inactivation. As a consequence, the recruitment of deinactivated T channels generates large inward currents resulting in transient depolarizations, called low-threshold spike (LTS). Thus, rhythmic LTSs, often crowned by bursts of high-frequency (>200 Hz) action potentials, are present in TC neurons during sleep spindles (7–14 Hz; Steriade et al., 1993b; Contreras and Steriade, 1996; David et al., 2013) and delta waves (0.5–4 Hz; Steriade et al., 1993a), and an LTS is almost invariably present at the start of each Up state of sleep slow oscillations in TC neurons (**Figure 2A**; Steriade et al., 1993a). Up states interspersed with periods of hyperpolarization (i.e., Down states) are the thalamic cellular hallmarks of sleep slow (<1 Hz) waves (**Figure 2A**). Moreover, slow waves group together periods of sleep spindle and delta waves (Steriade, 2006), and these periods of delta oscillations that are visible during the Down state of the cellular counterpart of sleep slow waves in TC neurons have been named "grouped-delta slow waves" (**Figure 2A**; Steriade et al., 1993a; Hughes et al., 2002; Crunelli et al., 2015). Importantly, the interaction of the leak current with a small number of de-inactivated T channels opening with a low (but non-zero) probability in a narrow range of membrane potentials around −60 mV (i.e., ITwindow; Perez-Reyes, 2003; Dreyfus et al., 2010) is necessary for the generation of the membrane potential bistability that in TC neuron underlies the expression of the Up and Down state dynamics of sleep slow waves (Williams et al., 1997a; Toth et al., 1998; Hughes et al., 2002; Dreyfus et al., 2010).

Despite these key roles for T channels in sleep waves, it is still not known how the density of the T-type Ca2+ current (IT) affects each sleep oscillation. We previously demonstrated that robust LTSs can be evoked even when up to 70% of the T channel population is pharmacologically blocked (Dreyfus et al., 2010), suggesting that the high T channel expression that is present in TC neurons is not required for LTS generation during delta and slow oscillations. A high T channel expression in TC neurons, however, may be crucial to provide a level of ITwindow sufficient for the generation of the UP and Down state dynamics underlying slow oscillations in this type of thalamic neurons.

Here, using both in vitro experiments and TC neuron simulation, we systematically investigated the impact of the T conductance level on the various sleep oscillations intrinsically generated in TC neurons. Since IT can be controlled by various modulatory mechanisms (Lambert et al., 2006; Huc et al., 2009), we also investigated the effects of the ATP- and voltagedependent regulation that potentiates the amplitude of IT in sensory TC neurons (Leresche et al., 2004). Our results show that although stable delta oscillations can be evoked with minimal T conductance, the full range of slow oscillation patterns, including simple Up and Down state transitions and the more complex "grouped-delta slow waves," requires a high density of T channels or a potentiation of the current. Moreover, high levels of IT ensure the robustness of different slow wave oscillations over a larger range of leak conductance values.

### MATERIALS AND METHODS

### Slice Preparation and Recordings

All procedures involving experimental animals were carried out in accordance with the UK Animals (Scientific Procedure) Act, 1986 and Cardiff Ethical Review Committee guidelines. Thalamic slices from a 3-year old cat were prepared as described previously (Hughes et al., 2002). Briefly, the cat was deeply anesthetized with a mixture of O2 and NO2(2:1) and 5% isoflurane, a wide craniotomy was performed to remove the brain and coronal slices of the thalamus (300–400 µm) that contain the dorsal lateral geniculate nucleus (LGN), were prepared and incubated at 35◦C for 1 h before being maintained at room temperature. For recording, slices were perfused with a warmed (35 ± 1 ◦C) continuously oxygenated (95% O2, 5% CO2) artificial CSF (ACSF) containing the following (in mM): 134 NaCl, 2 KCl, 1.25 KH2PO4, 1 MgSO4, 2 CaCl2, 16 NaHCO3, and 10 glucose.

Intracellular recordings, using the current clamp technique, were performed with standard-wall glass microelectrodes filled with 1 M potassium acetate (resistance, 80–120 MOhm) and connected to an Axoclamp-2A amplifier (Molecular Devices, Sunnyvale, CA) operating in bridge mode. Membrane potentials were digitized at 25 kHz using pClamp 9 (Molecular Devices). All recordings in the LGN were obtained from lamina A. Impaled cells were identified as TC neurons using established criteria (Pirchio et al., 1997; Turner et al., 1997). Sleep oscillations (including slow oscillations <1 Hz) were induced by bath application of 50 µM (±)-1-aminocyclopentane-trans-1,3 dicarboxylic acid (trans-ACPD) followed by changes in steadystate current injections to allow neurons to express different slow oscillations, as previously shown (Hughes et al., 2004). SR95531 (gabazine, 10 µM), CGP54626 (20 µM), D-APV (50 µM), and CNQX (10 µM) were included in the bath solution to block both GABA-A and GABA-B as well as NMDA and AMPA glutamatergic synaptic inputs onto TC neurons, respectively. The T channel antagonist, TTA-P2 (kindly provided by Merck Inc, USA), was made up as a 10 mM stock solution in dimethylsulfoxide and kept at −20◦C until use at a final concentration of 500 nM.

### Simulations

All simulations were performed using the Matlab based programs (Mathworks, Natick, MA) or xppaut continuation application developed by Ermentrout (2002), and were run with a fixed time step of 0.02 ms using the Euler integration method. For simulations, the system was initiated at a point close to the Up state and the simulation results were analyzed only after stabilization of the simulation result (i.e., 50 s after the start of the simulation).

The single-compartment TC neuron model based on (Williams et al., 1997a; Hughes et al., 2002), expressed the essential physiological properties of these neurons (**Figure 2**). Ionic currents were simulated following Hodgkin-Huxley formalism.

The membrane potential (V) was described by the following equation:

$$\text{C}\_{m}dV/dt = -I\_{Leak} \text{--} \, I\_{T} \text{-} I\_{TP} \text{--} \, I\_{\text{h}} \text{--} I\_{\text{CAN}} \text{--} I\_{Kir} \text{-} I\_{Kir} \text{-} I\_{Kir}$$

where Cm (50 pF) is the membrane capacitance, ILeak is a potassium leak current (reversal potential = −95 mV), IT is the T current, ITP is the potentiated component of the T current, Ih is the hyperpolarization-activated nonspecific cationic current, ICAN is the Ca2+ activated non-selective cation current, INa is the voltage-dependent Na+ current and IKir is K+ current which includes the inward and delayed rectifier components. All current units are pA. Each current was simulated as follows:

IT:

$$I\_T = \mathcal{g}\_T \cdot m^3(V) \cdot h(V) \cdot (V(t) - E\_T),$$

where gT is the maximal conductance and ET = 180 mV is the reversal potential for Ca2+ flux. m and h are activation and inactivation variables, respectively, which are defined as follows:

$$\begin{aligned} m\_{\infty,T} &= \frac{1}{1 + \exp\left(-\frac{\nu + 63}{7.8}\right)}, \\ \tau\_{m,T} &= 0.612 + \frac{1}{\exp\left(\frac{V + 16.8}{18.2}\right) + \exp\left(-\frac{V + 131.6}{16.7}\right)}, \\ h\_{\infty,T} &= \frac{1}{1 + \exp\left(\frac{\nu + 83.5}{6.3}\right)}, \\ \text{if } V &< -80 \text{ } \tau\_{h,T} = \exp\left(\frac{V + 467}{66.6}\right) \\ \text{otherwise } \tau\_{h,T} &= \left[28 + \exp\left(\frac{V + 21.88}{10.2}\right)\right] \end{aligned}$$

ITP:

The potentiated component of the T current was modeled by multiplying the T current by a voltage-dependent coefficient P representing the fraction of phosphorylated ("potentiated") channels (see Leresche et al., 2004 for details)

$$\text{Irp} = \text{grp} \cdot m^3(V) \cdot h(V) \cdot P(V) \cdot (V(t) - Er)$$

The voltage dependence of P is related to the steady-state inactivation of IT as followed (**Figure 1A**):

$$P\_{\infty,T} = 1 - h\_{\infty,T} \quad \text{\tiny{\tiny{\tau}\_{P,T}}} = \Im 000 - \frac{2700}{\{1 + \exp(-(V + 65))\}}$$

Ih:

$$I\_h = \mathcal{g}\_h \cdot m^3(V) \cdot (V(t) - E\_h)$$

gh = 8 nS

$$m\_{\infty, \hbar} = \frac{1}{1 + \exp(\frac{v + 75}{5.5})}, \text{ if } V < -77.57,$$

$$\pi\_{\hbar} = \frac{120819.5}{\exp(-0.0614 \cdot V)} \text{ otherwise } \tau\_{\hbar} = \frac{29.54}{\exp(0.0458 \cdot V)}$$

FIGURE 1 | Parameters of the potentiated component of the T current and the Ca2+ activated non-selective cation current. (A) The potentiated component of the T current is controlled by a voltage-dependent coefficient P whose kinetics and steady values are presented according to membrane potentials. (B) The Ca2+ activated non-selective cation channel (CAN) is controlled by two variables pCANand cca depending upon Ca2+ concentration as plotted.

ICAN (**Figure 1B**):

$$I\_{CAN} = \mathcal{g}\_{CAN} \cdot cca \cdot (V(t) - E\_{CAN})$$

gCAN = 12 nS

$$ca\_{\infty, \text{CAN}} = \frac{a\_{\text{ca}}}{a\_{\text{ca}} + b\_{\text{cca}}} \quad \tau\_{\text{cca,CAN}} = \frac{1}{a\_{\text{ca}} + b\_{\text{cca}}}$$

$$a\_{\text{cca}} = 0.075 \cdot p\_{\text{CAN}} \quad b\_{\text{cca}} = 0.00075$$

$$p\_{\infty, \text{CAN}} = \frac{1.25 \cdot 10^7 \cdot [Ca^{2+}]^4}{1.25 \cdot 10^7 \cdot [Ca^{2+}]^4 + 0.2} \quad \tau\_{\text{p,CAN}} = \frac{1}{1.25 \cdot 10^7 \cdot [Ca^{2+}]^4 + 0.2}$$

The calcium concentration ([Ca2+], in mM) is governed by the Ca2+ influx through T channels and a Ca2+ pump that controls intracellular Ca2+ levels.

$$\left[Ca^{2+}\right] = -\left(I\_T + I\_{TP}\right)\frac{0.0052}{Area \cdot Depth} - 5 \cdot \left[Ca^{2+}\right]^2$$

where Area is 5000 µm2 and Depth is 0.1 µm. INa:

$$\begin{aligned} I\_{\rm Na} &= g\_{\rm Na} m (V)^3 \cdot h (V) \cdot (V - E\_{\rm Na+}) \\ g\_{\rm Na} &= 1320 n S \\ a\_{m, \rm Na} &= 0.32 \frac{-V - 49.3}{\{e^{(-V - 49.3)/4} - 1\}} \\ b\_{m, \rm Na} &= 0.28 \frac{-V - 22.3}{1 - e^{(-V - 22.3)/5}} \\ m\_{\infty, \rm Na} &= \frac{a\_{m, \rm Na}}{a\_{m, \rm Na} + b\_{m, \rm Na}} \quad \tau\_{m, \rm Na} = \frac{1}{a\_{m, \rm Na} + b\_{m, \rm Na}} \end{aligned}$$

$$a\_{h,Na} = 0.128 \ e^{\frac{-V - 45A}{18}} \ b\_{h,Na} = \frac{4}{e^{\frac{-V - 22A}{5} + 1}}$$

$$b\_{\infty,Na} = \frac{a\_{h,Na}}{a\_{h,Na} + b\_{h,Na}} \quad \tau\_{h,Na} = \frac{1}{a\_{h,Na} + b\_{h,Na}}$$

IKir: