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High-frequency “burst” clusters of spikes are a generic output pattern of many neurons. While bursting is a ubiquitous computational feature of different nervous systems across animal species, the encoding of synaptic inputs by bursts is not well-understood. We find that bursting neurons in the rodent thalamus employ “multiplexing” to differentially encode low- and high-frequency stimulus features associated with either T-type calcium “low-threshold” or fast sodium spiking events, respectively, and these events adapt differently. Thus, thalamic bursts encode disparate information in three channels: 1) burst size, 2) burst onset time, and 3) precise spike timing within bursts. Strikingly, this latter “intraburst” encoding channel shows millisecond-level feature selectivity, and adapts across statistical contexts to maintain stable information encoded per spike. Consequently, calcium events both encode low-frequency stimuli and, in parallel, gate a transient window for high-frequency, adaptive stimulus encoding by sodium spike timing, allowing bursts to efficiently convey fine-scale temporal information.
Complex spiking patterns are a defining property of thalamic neurons and arise from the interplay between fast and slow intrinsic membrane properties. Fast sodium-dependent action potentials (APs) in thalamic neurons can be driven by slow depolarizations resulting from the activation of the T-type calcium current (IT) (Jahnsen and Llinas, 1984a). IT availability is tuned by membrane potential, and at physiological extremes, this voltage-dependency supports discrete “modes” of spiking: a stimulus may trigger either a single “burst” of high frequency (>100 Hz) APs overlaid on a low-threshold calcium spike (LTS) or a train of regular “tonic” APs when IT is unavailable.
This complex intrinsic property is common to all thalamic systems (Llinas and Steriade, 2006), and the characteristics of IT appear to be evolutionarily conserved and subject to significant functional constraints (Senatore et al., 2012). However, despite the ubiquity of this markedly nonlinear behavior, the functional role of thalamic bursting is not understood. Early studies of thalamic information processing largely focused on the difference between the two spiking modes, suggesting that thalamic bursting may not encode any information and instead indicates a state of “sensory uncoupling” (Coenen and Vendrik, 1972, Livingstone and Hubel, 1981) or serves as a strong but unspecific “wake-up call” to the cortex, while tonic spiking serves to encode fine stimulus details (Sherman, 2001).
More recently, this strict burst/tonic functional dichotomy has been rejected with the widespread observation of burst spiking in awake animals (Ramcharan et al., 2000, Fanselow et al., 2001, Martinez-Conde et al., 2002, Weyand et al., 2001, Swadlow and Gusev, 2001). Furthermore, in vivo studies in the cat primary visual thalamus have demonstrated that thalamic bursts can convey significant information about sensory inputs (Guido and Weyand, 1995, Weyand et al., 2001, Reinagel et al., 1999, Martinez-Conde et al., 2002), particularly in response to stimuli with naturalistic spatiotemporal structure and correlation (Wang et al., 2007, Lesica and Stanley, 2004, Denning and Reinagel, 2005, Lesica et al., 2006, Alitto et al., 2005). Thalamic neurons also adapt in response to ongoing stimulation (Simons and Carvell, 1989, Maravall et al., 2013, Lesica et al., 2007), and control of adaptation has been associated with modulation of bursting (Mease et al., 2014, Whitmire et al., 2016, Wolfart et al., 2005).
Much of the progress in understanding how thalamic spiking patterns encode information has been made by characterizing in vivo responses to complex, naturalistic stimuli in intact circuits using reverse correlation (de Boer and Kuyper, 1968), Linear-Nonlinear modeling (Korenberg and Hunter, 1986), and/or information theoretic methods (Butts et al., 2010, Alitto et al., 2005, Lesica et al., 2006, Lesica and Stanley, 2004, Reinagel et al., 1999, Maravall et al., 2013, Petersen et al., 2008, Lesica et al., 2007, Gaudry and Reinagel, 2008, Denning and Reinagel, 2005). These studies have shown that compared to tonic spikes, burst onset timing carries distinct sensory information (Reinagel et al., 1999, Alitto et al., 2005, Lesica et al., 2006, Lesica and Stanley, 2004, Denning and Reinagel, 2005), and that the number of spikes in a burst (Gaudry and Reinagel, 2008) or spiking “episode” (Butts et al., 2010) can carry additional information. In combination with the known intrinsic properties of thalamic neurons, these studies predict that thalamic stimulus encoding is largely shaped by IT. However, the systems-level advantage of in vivo preparations—the ability to map spiking patterns to peripheral sensory inputs—also makes it difficult to disambiguate circuit and single neuron properties, experimentally control the precise statistics of currents driving the neuron of interest, or manipulate biophysical properties. Therefore, questions regarding intrinsic information processing in single neurons are currently most tractable using in vitro methods.
Recent in vitro studies have provided richer understanding of the biophysical properties supporting bursting, demonstrating that IT is active at depolarized resting potentials seen in the awake state (Bessaih et al., 2008, Lambert et al., 2013, Dreyfus et al., 2010) and also contributes to presumed “tonic” spiking patterns (Deleuze et al., 2012). However, despite agreement between in vitro and in vivo lines of evidence that thalamic information processing is more nuanced than binary switches between tonic and burst output modes, it is unknown how features of synaptic inputs are encoded by thalamic bursts.
In the present study we use direct current injection into single neurons along with manipulation of channel dynamics to evaluate how the intrinsic properties of thalamic neurons shape their coding properties. We apply in vitro reverse correlation and Linear Nonlinear modeling in rodent thalamic neurons of the posterior medial thalamic nucleus (POm) using whole-cell patch clamp recordings and Gaussian noisy current stimulation. POm is a “higher-order” thalamic nucleus in the whisker system which receives diverse and well-characterized synaptic inputs, including powerful excitatory inputs from layer 5B (L5B) of barrel cortex (Groh et al., 2013, Groh et al., 2008, Reichova and Sherman, 2004, Mease et al., 2016c, Sherman and Guillery, 2006). For a subset of experiments, we used the presence of these L5B inputs to precisely target neurons in POm (Groh et al., 2008). These approaches allowed us to quantify thalamic single neuron computation in isolation from network-level effects while limiting assumptions about input statistics. We could then quantify how characteristics of the input current are encoded by different properties of thalamic bursts and relate this code to underlying biophysical mechanisms.
We begin by framing the issue of burst encoding using in vivo POm data illustrating that thalamic bursts are not uniform (see also (Reinagel et al., 1999, Wang et al., 2007, Martinez-Conde et al., 2002, Gaudry and Reinagel, 2008)) and vary with respect to size, frequency, and spike timing within burst events. We next establish our in vitro analysis approach by comparing the classic burst and tonic modes in the Linear-Nonlinear model framework and with information theoretic methods. Our preparation allows us to study the encoding properties of thalamic bursts at a higher level of detail than in previous work, and to determine how intrinsic thalamic adaptive properties change the encoding as the statistical context of the current stimulus varies.
Our first main result is that bursts convey an unexpected level of stimulus detail via multiple channels: the times and sizes of burst events, and most strikingly, the precise timing of APs within bursts as well. These data show that thalamic neurons employ multiplexed stimulus encoding in that bursts can simultaneously encode both high- and low-frequency information. The second main result is that burst onset initiates a brief period of efficient encoding in which adaptation normalizes AP initiation according to background fluctuations. These findings suggest that the post-synaptic cortical targets of thalamic neurons may have access to a far richer, more dynamic description of synaptic inputs than has been assumed to date, and show how many characteristics of thalamic computation measured at the circuit level arise from the intrinsic properties of single thalamic neurons.
In vivo, spontaneous cortical oscillations drive POm thalamic neurons to spike without application of additional stimuli (Groh et al., 2013, Mease et al., 2016c) (Fig. 1). Fig. 1A shows an example recording of POm bursts and Fig. 1B a group of such recordings reported previously (Mease et al., 2016c). Spiking events are non-uniform, in that bursts can contain a variable number of spikes and for each neuron, the timing of successive spikes varies between events. The distribution of successive interspike intervals (ISIs) (Fig. 1C) shows that ISIs vary over a window of more than 3 ms, even when spike order is taken into consideration. Our goal here is to determine how these features of bursts encode underlying synaptic inputs.
Understanding how variation in neural responses encodes properties of the sensory scene or synaptic input currents is a natural application for information theoretic approaches (Rieke et al., 1997, Shannon and Weaver, 1963), and these methods have been applied to thalamic spike trains recorded in vivo (e.g. (Gaudry and Reinagel, 2008, Reinagel et al., 1999, Butts et al., 2010, Denning and Reinagel, 2005)). Information theory allows one to quantify how knowledge of a given neural response (e.g. the number of spikes in a burst, or the timing of a spike) reduces the uncertainty—mathematically, the entropy of the distribution—about the stimulus (e.g. motion of a whisker, or the net synaptic current). This reduction in uncertainty is the information carried by the response about the stimulus and is commonly measured in bits; each bit of information indicates a two-fold decrease in uncertainty.
Averaging across the group of in vivo recordings in Fig. 1, the entropy of burst size is 0.77 ± 0.47 bits, and the spike-timing entropy of spikes within bursts is 1.9 ± 1.0 bits (time bin=0.4 ms). These variable quantities are channels by which thalamic spiking events can possibly encode information. Motivated by these in vivo observations of burst variability, we next investigate how information about complex inputs can be encoded by the properties of POm bursts in a controlled in vitro setting.
As is characteristic of all thalamic relay neurons, POm neurons in brain slices respond to depolarizing current steps (Fig. 2A) with either high frequency (>100 Hz) “bursts” of APs when hyperpolarized, or regular “tonic” APs when depolarized (Jahnsen and Llinas, 1984a, Landisman and Connors, 2007). In burst mode, sodium APs are overlaid on a “low-threshold spike” (LTS), the slow (~50 ms) depolarization arising from activation of the transient low-threshold calcium current IT.
To understand how complex, time-varying stimuli are encoded during these two spiking modes, we measured the intrinsic stimulus encoding of POm neurons during stimulation with broadband Gaussian “noise” current (Fig. 2B). Neurons responded with complex AP patterns in each mode, but the overall spiking modes were maintained. In burst mode, responses consisted of clusters of APs overlaid on slow LTS depolarizations (Fig. 2B, left), with burst events consisting of two or more APs accounting for more than half of all events (38±21%,29±9%,18±9%, and 15±21%, for event sizes of 1, 2, 3 or 4 or more APs, respectively; n=15). In contrast, in tonic mode, neurons produced APs at irregular intervals in response to the same current waveform (Fig. 2B, right). The cumulative interspike interval (ISI) distributions reflect these distinct patterns (Fig. S1A,B). In the following, we refer to either single APs or bursts of APs as “spiking events.”
We characterized the intrinsic computation of each thalamic neuron as a Linear-Nonlinear cascade (Fig. 2C–E) consisting of 1) a spike-triggering current feature and, 2) a measure of sensitivity to that feature, mapping input stimuli to output spiking events. These two model components quantify the temporal pattern of input current that trigger APs and the relative selectivity the neuron has for this pattern. From the responses to noise, we calculated the relevant feature as the “event-triggered average” (ETA) current by triggering on either the first AP in a burst spiking event or single APs in tonic mode. The ETA shows the combination of current inputs which on average are most successful in driving spiking events.
ETATonic (Fig. 2C, gray) was a relatively brief depolarizing current, indicating that tonic APs were generated by a sharp monophasic depolarization within a 10 ms window. This ETATonic is similar in form to ETAs measured in cortical neurons, e.g. (Mease et al., 2013). In contrast, the burst mode ETABurst (Fig. 2C, black) had a more complex biphasic shape and long integration window, combining 1) a slow (~200 ms) oscillation consisting of a hyperpolarizing current followed by a broad depolarizing current, and 2) a very fast (<5 ms) oscillation consisting of a brief hyperpolarizing current followed by a sharp depolarization immediately preceding the AP. This “compound” shape resembles the sum of two separate ETAs with long and short integration windows.
Thus, the AP-triggering feature space changes dramatically in timescale and amplitude between burst and tonic modes, particularly with regard to the range of stimulus frequencies encoded. We project the raw current stimulus I(t) into the dimensions defined by ETABurst and ETATonic (Fig. 2D) by finding the vector dot product between each feature and the stimulus preceding each spiking event. This procedure gives filtered stimuli sBurst and sTonic which measure the similarity between the raw stimuli and the ETAs. The two spiking modes enhance distinct frequency components of the stimulus (Fig. S1C): in tonic mode, intermediate frequencies are retained in sTonic, while in burst mode, very low and very high frequencies are emphasized in sBurst due to the compound “slow-fast” shape of ETABurst. In contrast to previous analysis of the filtering properties of visually-evoked tonic spikes and bursts (Lesica and Stanley, 2004), the preservation of high frequencies in sBurst suggests that the timing of burst events can simultaneously encode fast and slow stimulus patterns.
The ETAs quantify which patterns of stimuli are encoded in thalamic spiking events at different membrane potentials, but do not indicate how selective the neuron is for these patterns, i.e. how closely the input must match the ETA for a spiking event to occur. To further examine the changes in information encoding between tonic and burst mode, we quantified how different values of filtered stimuli sBurst and sTonic map to the occurrence of spiking events (Fig. 2E) by sampling IO relations P(event|sBurst) and P(event|sTonic ) (see Methods). Neurons in tonic mode encoded current stimuli more precisely across a narrower dynamic range, as the slope of P(event|sTonic ) was greater than that of P(event|sBurst) by an approximate factor of two (median slopes were 1.2 [IQR=1.1–1.5] and 2.4 [IQR=2.2–2.7] for burst and tonic IO relations, respectively; p<0.05 two-tailed Wilcoxon rank sum test; data pooled from 7 neurons recorded in both firing modes). This finding is in agreement with (Wolfart et al., 2005), who found that hyperpolarization and concomitant increase in IT availability broadened thalamic IO relations. However, given that the two spiking modes show very different responses to identical stimuli (Fig. 2B), this change in IO relation was not as dramatic as might be expected--most of the difference in computation was captured by the change in the shape of the ETA (Fig. 2C).
Repeated presentation of a noisy stimulus allowed us to calculate how much information about the stimulus was encoded by the timing of burst and tonic spiking events (Methods, Supplemental Results, Fig. S2 and (Fairhall et al., 2006, Brenner et al., 2000); see (Gaudry and Reinagel, 2008, Denning and Reinagel, 2005, Reinagel et al., 1999) for related analysis in the visual thalamus). Burst events were typically at least 2 bits more informative about the stimulus than were tonic events (Fig. S2A,B), in agreement with (Reinagel et al., 1999) and previous reports that burst events are more precise than tonic spikes (Zeldenrust et al., 2013, Whitmire et al., 2016, Kepecs and Lisman, 2003). We next calculated Ifract, the fraction of information captured by the ETA (Fairhall et al., 2006). Ifract for ETATonic reached a maximum of ~70% at smaller (1–1.5 ms) dt, whereas Ifract for ETABurst reached a maximum of ~55% at larger (10–12 ms) dt (Fig. S2C). Ifract in burst mode was also nonzero for dt < 10 ms, indicating that burst spiking events also carried high-frequency information, consistent with the filtering properties of ETABurst (Fig. 2C,D). Notably, maximum Ifract was always less for burst mode than for tonic mode, suggesting that the LN model characterization using burst spiking events as stereotyped “unitary” events failed to capture some aspect of stimulus encoding in burst mode. We next examine this discrepancy in more detail by considering the role of AP count within bursts.
The disparity in timescales between the ETAs (Fig. 2C) matched the difference in kinetics between the voltage-gated sodium and calcium currents controlling excitability in thalamic neurons. Burst mode is controlled by the voltage-dependent availability of both IT and INa, while during tonic mode, IT is mostly inactivated due to depolarization (Jahnsen and Llinas, 1984a, Jahnsen and Llinas, 1984b). As depolarization simplifies the structure of ETABurst from a biphasic current to a single more generic depolarizing current, the slow timescales most likely arise from the kinetics of IT (Jahnsen and Llinas, 1984a). Indeed, the application of the IT channel blocker mibefradil (Fig. S3) had a similar effect on the ETA as depolarization. Together, these experiments demonstrate that the slow oscillatory ETABurst shape reflects initial deinactivation (hyperpolarizing lobe) and subsequent activation (depolarizing lobe) of IT.
Thus, the slow component of ETABurst can be thought of as triggering an IT-dependent LTS, while the fast component determines the precise timing of the leading sodium AP in a burst. To examine these two channels separately, we decomposed ETABurst as a linear combination of two separate dimensions (Fig. 3A, Fig. S4A): 1) slow ETACa, and 2) fast ETANa (see Methods). Measured as Ifract of the total information carried by spiking event times (Fig. 3B), ETACa or ETANa individually captured less information than the compound feature ETABurst, but taken jointly, captured more total information, especially at short timescales. However, it should be noted the information calculated jointly may be artificially high, as ETACa and ETANa are not orthogonal, although nearly so (see Methods).
The utility of this decomposition is seen when considering bursts of different sizes (Fig. 3C). Here, we ignore the precise timing of APs within a burst and treat bursts as single events with different AP counts, which typically varied between 1–5 APs per spiking event. To illustrate the motivation behind this analysis, we calculated the compound ETABurst separately for bursts with different AP counts (Fig. S4B): larger bursts are preceded by a larger slow oscillation and a smaller fast oscillation. To quantify how ETANa and ETACa stimulus features are encoded in thalamic AP trains, we project the raw stimulus I(t) into a two dimensional space of sNa versus sCa (Fig. 3C). We then parse the burst-size-dependent change in feature selectivity into the simplified dimensions of ETACa and ETANa by examining how the joint event-triggering stimulus distribution P(sNa, sCa|event) changes as a function of spiking event size.
Most importantly, sCa was highly predictive of output AP count (event size). Fig. 3C shows P(sNa, sCa|event) for a representative recording. Each marker represents one spiking event (e.g. a single AP or a burst of 2 or more APs), colored according to the number of associated sodium APs. Within this two-dimensional space, the event-triggering stimulus distribution shifts according to event size: as event size increases, sCa increases and sNa decreases. P(sNa|event) and P(sCa|event) were negatively correlated for all neurons (mean r = −0.25±0.11, n=15). Fig. S4C summarizes this tradeoff versus event size: for spiking events with only one sodium AP, fast and slow frequencies were equally important, but as AP count increased, the importance of the slow feature dominated.
We interpret these data as showing that LTSs that trigger more sodium APs encode more information about the slow feature and are triggered by larger slow oscillations (i.e. larger sCa), and that the precise time of the first sodium AP in such large events is less dependent on high-frequency fluctuations (i.e. smaller sNa). We quantified information IETA captured by ETANa and ETACa as a function of burst size (Fig. S4D) by examining how the distributions of sCa and sNa changed as a function of AP count (Supplemental Methods). This approach showed a comparable trend: bursts of increasing AP count encoded more information about the slow feature ETACa (IETA = 2.4 ± 0.2, 3.3 ± 0.2, and 3.7 ± 0.2 bits for AP counts of 1, 2, and 3 or more, respectively; bin size = 0.2 σ; mean ± SEM for n=7 neurons), whereas information about the fast feature ETANa was greatest for spiking events with only one AP (IETA = 2.4 ± 0.4, 1.1 ± 0.3, and 1.1 ± 0.4 bits for AP counts of 1, 2, and 3 or more, respectively; bin size = 0.2 σ; mean ± SEM for n=7 neurons).
While the LTS slow depolarization is often referred to as a “spike”, the shape of the LTS is not always stereotyped. Instead, the amplitude and duration of the LTS are strongly dependent on membrane potential history, as seen in the original report by Jahnsen and Llinas (Jahnsen and Llinas, 1984a). In our case, stimulation with a complex noise current evoked LTSs with variable amplitude. LTS amplitude was positively correlated with sCa, the projection onto the slow ETACa. We quantified the LTS by calculating the average event-triggered membrane potential (Fig. 3D), which showed a clear progression in the shape of the LTS as a function of the number of APs: greater numbers of sodium APs are associated with larger LTSs that 1) were preceded by more hyperpolarization, and had 2) longer duration, 3) greater amplitude, and 4) a faster rate of rise. These last two points predict that-- as we observed-- fast fluctuations are less important to initial spiking, for the following reasons: more boosting depolarization from the LTS ensures precise AP timing regardless of additional high-frequency inputs, and a faster rate of rise ensures a lower sodium activation threshold due to decreased fast sodium channel inactivation during the approach to threshold. In fact, there was a very clear correspondence between the value of sCa and the size of the resultant LTS (Fig. 3D, inset), which is consistent with larger sCa being associated with greater numbers of APs.
The presence of the high frequency component ETANa shows that the timing of the initial AP in a burst is sensitive to particular stimulus patterns, and not simply triggered by the LTS depolarization. This finding suggests that subsequent “intraburst” APs in a burst might also encode particular stimulus features. This possibility is important because thalamic bursts have been regarded as inflexible, stereotyped events that signal the occurrence of environmental change (Sherman and Guillery, 2006), rather than conveying detailed information about the stimulus in the specific temporal patterns of spikes. In contrast to our previous treatment of bursts of APs as single events in Fig. 3, we next found LN models as a function of AP time within bursts (Fig. 4) by calculating the values of high-frequency stimuli sNa which drove intraburst APs.
In the case that the timing of intraburst APs depends only on the underlying LTS depolarization, the distribution of event-triggering high-frequency stimuli P(sNa|event) for these APs should be identical to P(sNa), creating a flat IO relation. Contrary to this expectation, sNa|event for intraburst APs was on average positive, indicating intraburst selectivity for high-frequency inputs. Furthermore, the selectivity for high frequencies varies as a function of time relative to the initial AP in a burst. This result comes from examining how the distribution of sNa for intraburst APs changes for successive APs, i.e finding P(sNa, t|event), where t is time relative to the first AP in a burst.
Fig. 4 shows the time-resolved selectivity for sNa throughout a burst, with IO relations P(event|sNa, t) in (Fig. 4A), and the corresponding values of sNa plotted versus time t relative to initial AP in a burst event (Fig. 4B). Values of sNa are shaded according to AP order in the burst, and the black overlay shows mean sNa value plotted by mean t within 5 ms intervals. In a case where ETANa is entirely irrelevant to the generation of APs and APs are driven only by the underlying LTS depolarization, the IO relations P(event|sNa, t) (Fig. 4A) would be flat (dotted lines), and the corresponding projections (Fig. 4B) would be centered at zero with a standard deviation of one. Contrary to these expectations, mean sNa values were always positive, and showed a distinctive progression throughout the course of the burst, indicating that throughout a burst, intra-burst AP timing becomes increasingly dependent on ETANa, increasing the slope of P(event|sNa, t). (Fig. 4A). For subsequent APs occurring ~2–7 ms after the first AP, the importance of high frequencies is at a minimum, but steadily increases for APs occurring later in the burst, with mean sNa reaching a maximum for the latest APs.
What causes this progression in selectivity for high frequencies? We found that the time course of selectivity (Fig. 4B) for ETANa was tightly linked to the depolarization from the LTS (Fig. 4C). Replotting the mean sNa value by membrane potential during segments of the LTS (Fig. 4D) revealed a strong linear relationship between high-frequency selectivity (mean sNa) and depolarization (correlation coefficient r = −0.84 ± 0.22, n=15 neurons). Taken together, these observations suggest that while initial APs may be mostly dependent on the underlying LTS calcium event, later APs are increasingly sensitive to high-frequency inputs that occur while the LTS decays. Thus, the ETACa stimulus feature which drives the LTS shifts the neuron into a transient regime of selectivity for fast stimulus features similar to ETANa.
To illustrate this point in an alternative but complementary way, we plot ETAt triggered on APs from different periods t within a burst (Fig. 4E). The waveform correlated to initial APs in a burst is ETANa and is a simple depolarizing transient; in contrast, intermediate APs at the peak of the LTS are driven by smaller depolarizing transients preceded by brief hyperpolarization. Finally, for later APs, the ETAs simplify and become increasingly similar to ETATonic for the same neuron. We quantify similarity between tonic and intraburst ETAs and see the same progression (Fig. 4F) across all neurons. This finding directly demonstrates the changing importance of high-frequency stimulus components during the course of the LTS, and suggests that intraburst encoding is comparable to the purely tonic firing regime, particularly for initial and later APs which do not receive maximal depolarizing drive from the LTS. These high frequencies have not been explicitly represented in previous in vivo work where visual stimuli typically varied more slowly than the noise current used here.
These data demonstrate that the information coding capacity of thalamic bursts is contained not simply in the burst onset time or total AP count, but also in the precise timing of APs within a burst. This simultaneous encoding of distinct stimulus characteristics is an example of “multiplexing”-- a strategy which greatly enhances the coding efficiency of single neurons (Fairhall et al., 2001, Panzeri et al., 2010).
Adaptation to sustained stimulation is a key computation in the rodent somatosensory system (Maravall et al., 2013, Maravall et al., 2007, Whitmire et al., 2016), and given the complex intrinsic feature selectivity of thalamic neurons we report here, we hypothesized that these computational properties might support adaptation at the level of single cells (Mease et al., 2013). To determine if how and if POm stimulus encoding adapts to shifts in statistical context, we switched the standard deviation (σ) of the stimulus (Fig. 5A,B and S5A–C) and compared LN models across σ conditions (Fig. S5D–G and Fig. 5C,D). The fast ETANa and slow ETACa channels showed very different adaptive responses, in that changing σ altered the essential shape of the event-triggering currents encoded by slow LTS events, but not fast sodium APs (Fig. S5D–G).
Most importantly, for the fast feature ETANa, the IO relation had the same fundamental shape, regardless of σ. An increase in σ decreased the slope and increased the dynamic range of both P(event|sCa) (Fig. 5C) and P(event|sNa) (Fig. 5D). However, when re-expressed in normalized units, this difference disappeared for P(event|sNa/σ) (Fig. 5D). This property is a hallmark of adaptive “gain scaling” behavior (Fairhall et al., 2001, Maravall et al., 2007, Mease et al., 2013), in which a neuron’s excitability adjusts precisely to maintain the same information encoded per AP, regardless of the overall statistical context. In marked contrast, the normalized IO relations P(event|sCa/σ) retained the σ-dependent decrease in selectivity. Thus, both the slow ETA feature and the neurons’ sensitivity to that feature depend on the statistical context of the stimulus. We conclude that stimulus encoding by sodium APs and calcium LTSs adapts differently with respect to changes in stimulus context.
We find that the contribution of IT to thalamic excitability and bursting initiates a transient but efficient period of stimulus encoding: an initial selectivity for slow inputs by IT-mediated LTSs and subsequent variance-independent selectivity for fast inputs by sodium APs. This finding suggests a role for bursts in transmitting fine stimulus details–a function that was largely assigned to the tonic thalamic relay mode.
At voltages with available IT, thalamic spiking events encode three types of information: 1) the timing of a spiking event indicates the occurrence of a slow oscillation (Fig. 2), 2) the number of APs generated during a spiking event indicates the amplitude of this slow oscillation (Fig. 3), and most strikingly, 3) the precise timing of APs within a spiking event encode the timing of very fast oscillations (Fig. 4). This encoding scheme is an example of a multiplexed code in which both overall spike count and spike timing carry information (Fairhall et al., 2001, Panzeri et al., 2010), and reveals that the raw information coding capacity of thalamic neurons is far greater than previously reported.
To establish our analysis framework, we show that burst and tonic spiking events encode very different patterns of current (Fig. 2C). This finding is agreement with studies in the visual thalamus showing that bursts evoked by noisy or natural scene stimuli are triggered by periods of inhibitory visual stimuli followed by excitatory visual stimuli integrated over hundreds of milliseconds whereas single tonic spikes are evoked by visual stimuli favoring excitation within 100 ms of the spike (Alitto et al., 2005, Butts et al., 2010, Wang et al., 2007, Gaudry and Reinagel, 2008, Lesica and Stanley, 2004, Lesica et al., 2006, Reinagel et al., 1999). We find that this circuit-level feature encoding can occur on the level of membrane potential dynamics of single thalamic neurons, as the slow component (ETACa) of ETABurst had a temporally broad (>200 ms), biphasic shape (Fig. 2C), integrating temporally offset inhibitory and excitatory currents, whereas ETATonic was only excitatory and had a comparatively brief integration window. We predict that the overall balance between slow modulatory excitatory and inhibitory inputs to POm (Sherman and Guillery, 2006) would serve to fix the shape of the event-triggering stimulus feature between the extremes of ETABurst and ETATonic (Fig. 2C) via slow changes in membrane potential and the consequent availability of IT.
In contrast to these previous studies, the fast component (ETANa) of ETABurst demonstrates that burst onset timing can also encode high-frequency stimuli in addition to slower inhibitory and excitatory inputs. Relatedly, we find that the integration window of ETATonic is much shorter (< 10 ms) than comparable measures reported previously (Lesica and Stanley, 2004, Alitto et al., 2005, Wang et al., 2007). The most obvious explanation for these differences is that our in vitro experiments allowed us to directly test the contribution of higher frequency current to thalamic AP generation, beyond the temporal resolution possible in previous approaches using sensory rather than current stimulation. Another possible explanation for the fast timescale we observe in ETATonic is that our manipulations imposed a particularly stringent separation of spiking modes: here, we pharmacologically reduced or inactivated IT through direct current injection to induce tonic spiking, while previous studies used ISI criteria to infer the presence of tonic spikes without experimental manipulation of IT.
Decomposing ETABurst into slow ETACa and fast ETANa features (Fig. 3) revealed that events with different AP counts encoded distinct combinations of stimuli (Fig. 3C), and more causally, were driven by different levels of depolarization from the LTS (Fig. 3D). Previous studies of model bursting neurons suggested that burst size may encode a variety of stimulus features (Elijah et al., 2015, Kepecs and Lisman, 2003, Kepecs et al., 2002) but this possibility had not been tested experimentally on at the single neuron level. Our approach recalls the theoretical work of (Kepecs and Lisman, 2003) using covariance analysis. While both approaches find that events with different AP counts project to different regions of a reduced two-dimensional stimulus space, our dimensionality reduction approach identifies a temporal sequence of stimuli—a slow, biphasic oscillation followed by high-frequency excitation—rather than (Kepecs and Lisman, 2003)’s combination of orthogonal stimulus features. Moreover, we also observed that AP timing depended on high-frequency inputs, whereas (Kepecs and Lisman, 2003) rather reported that AP times within bursts were robust to noise. In general, it appears that models capturing the fast dynamics we observe experimentally are elusive, as we have not yet been able to reproduce high-frequency selectivity in standard bursting models (e.g. (McCormick and Huguenard, 1992)).
We found that current oscillations showing greater similarity to ETACa evoked bursts with greater numbers of APs (Fig. 3). The filtering properties of ETACa capture thalamic sensitivity to slow background changes in membrane potential and large depolarizations which might arise from synchronous inputs, consistent with circuit-level observations in the visual thalamus: (Butts et al., 2010) found that high spike count responses are evoked by stimuli more similar to the ETA; relatedly, (Gaudry and Reinagel, 2008) showed that burst size can encode sensory information, and that larger bursts are preceded by stronger inhibitory stimuli, while (Lesica et al., 2006) correlated the degree of inhibition present in the ETA with bursting in in vivo data and membrane potential in a model. Here, we directly show that the slow selectivity of ETACa arises from IT and that stimuli which best match this waveform trigger larger LTSs and bursts with more APs, linking stimulus encoding to the underlying bursting mechanism.
Encoding of the slow feature ETACa depended on the overall statistical context of the stimulus, as changes in standard deviation (σ) changed the fundamental forms of both the ETAs (Fig. S5) and the corresponding IO relations (Fig. 5) (see also (Wolfart et al., 2005)). This context sensitivity may arise because different σ values explore substantially different subthreshold voltage ranges, with different levels of IT availability (Jahnsen and Llinas, 1984b). Indeed, our finding that slow sCa predicts LTS size (Fig 4D, inset) and associated AP count supports a scenario where the low-frequency channel encodes the local σ in the number of APs per spiking event. This idea is consistent with the observed σ-dependent increase in burstiness (Fig. S5). Conceptually, this finding is similar to how bursts can encode slope in a model neuron (Kepecs et al., 2002), albeit by an entirely different biophysical mechanism.
The most striking finding we report here is that during bursting and LTS generation, thalamic neurons remain selective for very fast inputs, enabling the AP times within bursts to accurately convey fine temporal details. This greatly increases the information content of thalamic bursts beyond “AP-count” codes where stimulus encoding is limited to the size of the burst (Lesica and Stanley, 2004, Gaudry and Reinagel, 2008, Elijah et al., 2015, Butts et al., 2010). Existing analyses of precise AP times within visually evoked thalamic bursts have not explored the role of specific stimulus selectivity within bursts, demonstrating rather that shorter initial ISIs in a burst are correlated with larger burst AP count (Gaudry and Reinagel, 2008) or duration (Butts et al., 2010), reflecting the fact that larger LTSs drive more APs separated by shorter intervals. In contrast, we show here that intraburst AP times can convey specific high-frequency information, distinct from burst size.
Encoding of high-frequency inputs showed gain scaling (Fairhall et al., 2001, Mease et al., 2013, Maravall et al., 2007), such that the information per AP was held constant regardless of stimulus contrast (Fig. 5), as can arise from intrinsic spike generation in cortical neurons (Mease et al., 2013). Here, gain scaling is transiently gated by selectivity for low frequencies, as the LTS creates a window for adaptive encoding of fast features. Given the similar intrinsic properties of thalamic relay neurons across different nuclei and sensory systems (Jahnsen and Llinas, 1984a, Landisman and Connors, 2007) this fast encoding may be a generic scheme across levels of thalamic hierarchy (e.g. primary versus higher-order) and sensory modalities. For example, such a fast encoding channel may be an intrinsic mechanism supporting the extreme temporal precision of primary thalamic neurons’ responses to whisker stimuli in vivo (Petersen et al., 2008).
The multiplexed encoding we report is well-matched to the variety of excitatory and inhibitory inputs which converge on thalamic relay neurons. Although the exact anatomical origin of inputs is nucleus-specific, a general input scheme is the combination of fast “driver” and slow “modulatory” excitatory inputs of brainstem and/or cortical origin, along with slow inhibitory inputs mainly from other thalamic nuclei (Sherman and Guillery, 2006). We used near-white noise current to sample minimally biased models of feature selectivity (Rieke et al., 1997); this general thalamic input scheme predicts that the spectral properties of synaptic inputs to POm neurons in vivo likely favor high- and low-frequency inputs from different sources, as we detail below.
For POm neurons, these inputs are relatively well-characterized and include inhibitory input from within the thalamus as well as modulatory excitatory input from cortical layer 6 (Reichova and Sherman, 2004, Mease et al., 2014, Crandall et al., 2015), and fast driving input from both the brainstem and cortical layer 5B (L5B) (Groh et al., 2013, Groh et al., 2008, Reichova and Sherman, 2004, Mease et al., 2016c). In the multiplexing framework, inhibitory and layer 6 modulatory inputs could set the resting membrane potential and thereby control the availability of IT and ETA shape (see also (Lesica et al., 2006)). L5B and brainstem inputs to POm are integrated within an approximate 50 ms window in vivo (Groh et al., 2013) and could provide the strong excitation needed to trigger an LTS; in this case, POm burst size may encode the degree of synchrony of L5B inputs (Groh et al., 2008) or the coincidence of L5B and brainstem inputs (Groh et al., 2013).
Stimuli triggering an LTS also “unlock” a fast encoding channel of transient sensitivity to high frequencies. Specific to POm, the timescales of ETATonic and ETANa (Figs. 2, ,4)4) correspond well to the fast rise (0.5 ms) and decay (1.2 ms) times of the glutamatergic “driver” EPSCs from cortical L5B (Groh et al., 2008), suggesting that POm’s encoding of L5B inputs could also preserve fine L5B spiking structure, e.g. high-frequency bursts (de Kock and Sakmann, 2008). In fact, the LTS-dependent selectivity (Fig. 4) and intrinsic adaptive gain control (Fig. 5D) for high-frequency inputs may well match to the rapid synaptic gain control from short-term depression at L5B-POm synapses (Groh et al., 2008). Although these synapses depress strongly and rapidly, gain scaling could adjust thalamic excitability to normalize L5B input regardless of depression state. For example, the initial L5B spike would trigger large glutamate release at the L5B-POm synapse, thus activating IT and the initiation of a POm LTS. Subsequent L5B spikes within the next ~50 ms would trigger only small EPSCs due to synaptic depression, but our results predict that such spikes could still induce additional POm APs during the transient window of enhanced high-frequency selectivity.
The thalamus is an active and dynamic processor of information en route to the cortex. We find intrinsic properties alone allow thalamic neurons to 1) simultaneously transmit information on different timescales to the cortex, and 2) differentially adapt encoding of this information. In this multiplexed encoding scheme, the timing and size of bursts could reflect low-frequency input synchrony of the presynaptic network, while the timing of spikes could faithfully relay individual presynaptic spike times to the cortex. However, it remains an open question to what degree this information–particularly the fine-scale “intraburst” information—is indeed transmitted to the cortex and is relevant to sensory processing or behavior.
It is clear that thalamic bursts and single spikes evoke different responses in the cortex: compared to single spikes, bursting strongly activates cortical networks (Swadlow and Gusev, 2001), evokes larger depolarizations in cortical neurons (Bruno and Sakmann, 2006), and promotes facilitation of cortical sensory responses (Whitmire et al., 2017). However, propagation of more precise burst size information requires that cortical responses scale with thalamic burst size, which has yet to be shown. One possible approach could be combining optogenetic methods with thalamic and cortical recordings (Whitmire et al., 2016, Mease et al., 2016a, Mease et al., 2016b, Whitmire et al., 2017).
The successful transmission of precise temporal information within bursts depends critically on the properties of thalamocortical (TC) connections. TC synapses from POm have submillisecond precision (~0.4 ms jitter) (Lee and Sherman, 2008) and the integration window of cortical neurons can be quite precise (1–10 ms) (Gabernet et al., 2005), suggesting that thalamic intraburst AP timing could in principle persist across the TC synapse. However, the AP-triggering efficacy of cortical EPSPs corresponding to APs within a thalamic burst would be controlled by the depression or facilitation dynamics of the synapse. In the case of POm projections, these dynamics can be target-specific, as (Viaene et al., 2011) report both depressing and facilitating connections to primary and secondary somatosensory cortices, respectively. In the case of strong depression, survival of later thalamic spike times in cortex would likely be contingent on TC convergence onto single cortical neurons (Constantinople and Bruno, 2013, Bruno and Sakmann, 2006), and on strong, precise synchrony across thalamic neurons, which (Whitmire et al., 2016) find is promoted during bursting. Intriguingly, neurons in barrel cortex can encode separate channels of high- and low-frequency information about whisker displacement (Alenda et al., 2010), and our findings suggest that such parallel information streams are present at the level of single thalamic neurons.
Animal protocols followed the guidelines of German animal welfare and were approved by oversight committees at the Technische Universität München and Heidelberg University. In vivo recordings in 6–8 week old thy1-ChR2 (line 18) or wild-type mice (both BL/6 background) of either sex were done as in (Groh et al. 2013). In vitro whole-cell patch clamp recordings were made in brain slices maintained at 33–35 °C as described in (Groh et al. 2008) and (Mease et al. 2013), for Wistar rats (n=8 cells) and BL/6 mice (n=8 cells) of either sex, 20–25 days after birth. Gaussian noise current stimuli were exponentially filtered with temporal correlation of 0.5 or 1.0 ms. We use “spiking event” to refer to a single AP, or a burst of two or more APs. In the latter case, the time of the first AP is taken as the event time. Calculation of Linear-Nonlinear models was as described in (Mease et al. 2013). ETABurst was split into components ETACa and ETANa by fitting an exponential to the fast rising stimulus trajectory immediately preceding the trigger time (Fig. S3). Details are found in Supplemental Experimental Procedures.
Supplemental Figure 1: Categorizing POm spiking events in response to noise current stimulation. Related to Methods and Figure 2
A. Data shown is from one representative “burst mode” recording. Each marker shows a single AP, following ISI versus preceding ISI. ISI thresholds between 10–30 ms effectively segregate four categories of AP, clockwise from upper right: single AP events, initial APs in bursts, intermediate APs in bursts, and final APs in bursts
B. Population mean ± SEM cumulative ISI histograms for burst (black, n=15) and tonic (gray, n=7) spiking modes. In burst mode, mean event rate ± SD was 2.4 ±1.4 Hz, while total AP rate was 5.6±8.3 Hz, and was increased with depolarization to 9.5 ± 8.3 Hz in tonic mode. The two regions of increase in burst mode correspond to long (>100 ms) interburst intervals and short intraburst (<10 ms) intervals, in contrast to a steady increase for intervals between 10 and 100 ms in tonic mode, reflecting unpredictable depolarization driven by the noise stimulus.
C. Mean power spectra of noise stimuli I(t) projected onto tonic and burst ETAs (n=15 burst, n=7 tonic). Dashed line shows baseline from raw I(t).
Supplemental Figure 2: Information theoretic analysis of burst and tonic thalamic spiking modes. Related to Figure 2.
A. Ievent, information per spiking event in tonic and burst modes as a function of time bin dt, calculated using repeated presentations of the same 5 s noise stimulus (see Methods)(Brenner et al., 2000b, Fairhall et al., 2006). Values plotted in A–C are population means ± SEM (n=7 neurons, burst mode; n=4 neurons, tonic mode; 4 neurons had both burst and tonic mode recordings and 3 additional neurons were recorded from only in burst mode).
B. As in A, but shown as Ievent multiplied by tonic spiking or bursting rate during the repeated stimulus to give information/unit time.
C. Ifract, the fraction of information captured by the LN model for burst (black) and tonic (gray) as a function of time bin dt used for calculating model’s information capture and responses to repeated stimulus presentation. Ifract of 1 would indicate that the LN model captures all of the information the spike train encodes about the stimulus.
Supplemental Figure 3: Manipulation of IT reduces bursting and simplifies ETA. Related to Figure 2.
A. Wash in of 50 μM mibrefradil abolishes the LTS response to current steps, indicating decreased availability of the T-type calcium channel underlying thalamic bursting. Similar results were seen in two neurons.
B. ISI histograms corresponding to control burst (black, −70 mV), tonic (gray, −48 mV), and mibrefradil (red, −70 mV) noise stimulations in an example POm recording. For tonic and mibrefradil cases, membrane potential was held constant by injection of a constant current.
C. ETAs for the three conditions in B. Mibrefradil reduces slow components of the ETA and increases the amplitude of the fast component.
D. IO relations for the three conditions in B. Mibrefradil increases the slope of the IO relation nearly two-fold and shifts it to favor larger stimulus values, similar to the tonic condition. Slopes fit to log-linear portions of IO relations were 1.25, 2.20, and 2.25 (units of log10 event probability/σ2) for burst, tonic, and mibrefradil conditions, respectively.
A. An example burst ETA (black) from one POm neuron is decomposed into fast sodium (gray) and slow calcium (blue) ETAs. The sodium ETA was found by fitting a single exponential to the rising phase of the fast feature; the calcium ETA is the slow component that remains when the rising (exponential fit) and falling (raw data) phases of the fast sodium ETA are subtracted from the burst ETA. For the calculations shown in Figs. 3 and S4, this procedure was repeated independently for burst mode ETAs from all neurons.
B. ETABurst, split by AP count for a representative neuron, showing an increase in slow and decrease in fast (inset) components as AP count increases.
C. Trade-off between slow calcium and fast sodium components as a function of burst size. Small markers show mean sCa |event (black) and sNa |event (gray) for individual neurons. Open markers show grand population mean (n=15) presented as mean ± SD.
D. Information IETA captured about the stimulus by ETACa (left) or ETANa (right) as a function of stimulus binning and AP count. Information was calculated as the Kullback-Leibler divergence between the event-triggered stimulus and the prior stimulus distributions. Data presented as mean ± SD.
Supplemental Figure 5: Different adaptive characteristics of sodium and calcium feature selectivity. Related to Figure 5.
A. Mean AP or event responses as a function of time, n=4 neurons, bin size=500 ms, dotted lines indicate standard deviation.
B. Event size proportion as a function of time relative to stimulus switch, population mean. The higher variance σ2 condition increased total AP rate by a factor of three due to both spiking events occurring more frequently, and an increase in the average number of APs per event.
C. Mean ± SD cumulative ISI histograms for low (black) and high (gray) σ conditions.
D–G. Burst mode ETAs in raw stimulus units for low and high σ conditions separated into slow calcium (D) and fast sodium (E) components, and the same ETAs scaled to unit σ (F,G). Population means shown (n=4). The increase in stimulus σ increased the amplitudes of both ETACa and ETANa but this change in shape nearly disappeared from ETANa when the relative change in σ was divided out, while ETACa retained a decreased hyperpolarizing component and a faster depolarizing component.
Funding was provided by DFG Collaborative Research Center 1158 (RAM, AG), National Institutes of Health Institutional Grant for Neurobiology T32 GM07108–35 and The Grass Foundation (RAM), DFG Collaborative Research Center 1134 and CellNetworks Cluster of Excellence EXC 81 (TK), and National Science Foundation EF-0928251 (ALF). We thank Arthur Konnerth, Bert Sakmann, and Bernhart Meyer for lab space and support at the Technische Universität München.
Author Contributions: All authors contributed to research design and the final manuscript. RAM and AG performed research, analyzed data, and wrote an initial draft of the manuscript.
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