DAN GCaMP6f fluorescence typically exhibited brief transients following cue onset and immediately before first-lick onset (Figure 2A), as observed in previous studies (Coddington and Dudman, 2018; da Silva et al., 2018; Dodson et al., 2016; Howe and Dombeck, 2016; Schultz et al., 1997). However, during the timed interval, we observed slow ‘ramping up’ of fluorescence over seconds, with a minimum after the cue-aligned transient and maximum just before the lick-related transient. The relatively fast intrinsic decay kinetics of GCaMP6f (t_1/2 <100 ms at 37°; Helassa et al., 2016) should not produce appreciable signal integration over the seconds-long timescales of the ramps we observed.

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SNc DAN signals during self-timing.

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Baseline SNc DAN signals.

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DAN signals recorded at SNc, DLS and VTA.

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We asked whether this ramping differed between trials in which the animal moved relatively early or late. Strikingly, when we averaged signals pooled by movement time, we observed systematic differences in the steepness of ramping that were highly predictive of movement timing (Figure 2B–C). Trials with early first-licks exhibited steep ramping, whereas trials with later first-licks started from lower fluorescence levels and rose more slowly toward the time of movement. The fluorescence ramps terminated at nearly the same amplitude, regardless of the movement time. Ramping dynamics were not evident in control tdTomato signals (Figure 2C), indicating that the ramping in the GCaMP6f signals was not an optical artifact. The quantitative relationship between GCaMP6f dynamics and movement time will be addressed in a subsequent section of this paper.

In addition to ramping dynamics, average DAN GCaMP6f signals were correlated with first-lick timing even before cue-onset, with higher baseline fluorescence predicting earlier first-licks (Figure 2B–C). This correlation began before the lamp-off event (the 2 s ‘Baseline’ period before lamp-off; Pearson’s r = −0.63 (95% CI=[-0.92,–0.14]), n = 12 mice) and grew stronger during the ‘Lamp-Off Interval’ between lamp-off and the cue (Pearson’s r = −0.89 (95% CI=[-0.98,–0.68]), n = 12 mice; Figure 2—figure supplement 1A-B). This correlation was independent of the duration of the lamp-off interval (Figure 2—figure supplement 1C). Because dF/F correction methods can potentially distort baseline measurements, we rigorously tested and validated three different dF/F methods, and we also repeated analyses with raw fluorescence values compared between pairs of sequential trials with different movement times (Figure 2—figure supplement 2; see Materials and methods). All reported results, including the systematic baseline differences, were robust to dF/F correction.

In principle, the amplitude of the baseline signal on a given trial n could be related to the animal’s behavior during the baseline interval or the outcome of the previous trial. To test this, we performed four-way ANOVA to compare the main effects of the following factors on the pre-cue signal (averaged for each trial between lamp-off and the start-timing cue, the ‘lamp-off interval’ (LOI), n = 12 mice): (1) presence or absence of spontaneous licking during the LOI; (2) outcome of the previous trial (rewarded or unrewarded); (3) upcoming movement time on trial n (categorized as <3.3 s or >3.3 s to provide a simple binary proxy for movement time); and (4) session number (to account for signal variability across animals and daily sessions). Although the effects of LOI-licking and previous trial outcome were statistically significant (F(1,18282) = 10.7, p = 0.008, η_p²=5.9·10^–4 and F(1,18282) = 281.2, p = 7.5·10^–47, η_p²=0.015, respectively), the upcoming movement time had an independent, statistically significant effect (F(1,18282) = 63.4, p = 5.9·10^–6, η_p²=0.0035). This raises the possibility of an additional source of variance in baseline dopaminergic activity that is independent from previous trial events, but potentially influences the upcoming movement time on that trial.

We found similar ramping dynamics in SNc DAN axon terminals in the dorsolateral striatum (DLS; Figure 2—figure supplement 3A-B) at a location involved in goal-directed licking behavior (Sippy et al., 2015). Ramping was also present in GCaMP6f-expressing DAN cell bodies in the ventral tegmental area (VTA, Figure 2—figure supplement 3C), reminiscent of mesolimbic ramping signals described in goal-oriented navigation tasks (Howe et al., 2013; Kim et al., 2019).

To determine if these movement timing-related signals are available to downstream targets that may be involved in movement initiation, we monitored dopamine release in the DLS with two complementary florescent dopamine sensors (dLight1.1 and DA_2m) expressed broadly in striatal cells (Figure 3 and Figure 2—figure supplement 3D-E). The decay kinetics of the two extracellular dopamine sensors differ somewhat (Patriarchi et al., 2018; Sun et al., 2020), which we confirmed (dLight1.1 t_1/2~75 ms, DA_2m t_1/2~125 ms; Figure 3—figure supplement 1), yet both revealed similar timing-related ramping dynamics on average (Figure 3 inset). These combined data argue that the seconds-long dopaminergic ramping signals were not artifacts of sluggish temporal responses of the various fluorescent sensors and were ultimately expressed as ramp-like increases in dopamine release in the striatum.

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Striatal dopamine indicator signals.

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The systematic ramping dynamics and baseline differences were not observed in the tdTomato optical control channel nor in any of the other movement-control channels, at least on average (Figure 4), making it unlikely that ramping dynamics resulted from optical artifacts. Nevertheless, because DANs show transient responses to salient cues and movements (Coddington and Dudman, 2018; da Silva et al., 2018; Dodson et al., 2016; Howe and Dombeck, 2016; Schultz et al., 1997), it is possible that fluorescence signals could reflect the superposition of dopaminergic responses to multiple task events, including the cue, lick, ongoing spurious body movements, and hidden cognitive processes like timing. For example, accelerating spurious movements could, in principle, produce motor-related neural activity that ramps up during the timed interval, perhaps even at different rates on different trials.

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Movement control signals.

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We thus derived a nested generalized linear encoding model of single-trial GCaMP6f signals (Engelhard et al., 2019; Park et al., 2014; Runyan et al., 2017), a data-driven, statistical approach designed to isolate and quantify the contributions of task events (timing-independent predictors) from processes predictive of movement timing (timing-dependent predictors; Figure 5A–B and Figure 5—figure supplement 1A-D). The model robustly detected task-event GCaMP6f kernels locked to cue, lick and EMG/accelerometer events, but these timing-independent predictors alone were insufficient to capture the rich variability of GCaMP6f signals for trials with different first-lick times, especially the timing-dependent ramp-slope and baseline offset (n = 12 mice, Figure 5C and Figure 5—figure supplement 1E-G). In contrast, two timing-dependent predictors robustly improved the model: (1) a baseline offset with amplitude linearly proportional to first-lick time; and (2) a ‘stretch’ feature representing percentages of the timed interval (Figure 5B–C and Figure 5—figure supplement 1E). The baseline offset term fit a baseline level inversely proportional to movement time, and the temporal stretch feature predicted a ramping dynamic from the time of the cue up to the first-lick, whose slope was inversely proportional to first-lick time. Similar results were obtained for SNc DAN axon terminals in the DLS, VTA DAN cell bodies, and extracellular striatal dopamine release (Figure 5—figure supplement 1H).

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DAN signal encoding model.

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We note that the stretch feature of this GLM makes no assumptions about the underlying shape of the dopaminergic signal; it only encodes percentages of timing intervals to allow for temporal ‘expansion’ or ‘contraction’ to fit whatever shape(s) were present in the data. In particular, the stretch feature cannot produce ramping unless ramping is present in the signal and temporally scales with the length of the interval. Because this feature empirically found a ramp (although not constrained to do so), the stretch aspect indicated that the underlying ramping process took place at different rates for trials with different movement times, at least on average.

In contrast to the GCaMP6f model, when the same GLM was applied to the tdTomato control signal, the timing-independent predictors (which could potentially cause optical/mechanical artifacts—the cue onset, first-lick, and EMG/accelerometer signal) improved the model, but timing-dependent predictors did not (Figure 5C and Figure 5—figure supplement 1F-H). In addition, separate principal component (PC) analysis revealed ramp-like and baseline-offset-like components that explained as much as 93% of the variance in DAN signals during the timing interval (mean: 66%, range: 16–93%), but similar PCs were not present when tdTomato control signals were analyzed with PCA (mean variance explained: 4%, range: 1.6–15%, Figure 5—figure supplement 2).

Given that ramping and baseline-offset signals were not explained by nuisance movements or optical artifacts, we asked whether DAN GCaMP6f fluorescence could predict first-lick timing on single trials. Using a simple threshold-crossing decoding model (Maimon and Assad, 2006), we found that single-trial GCaMP6f signals were predictive of first-lick time even for low thresholds intersecting the ‘base’ of the ramp, with the predictive value of the model progressively improving for higher thresholds (n = 12 mice: mean R² low = 0.54, mid = 0.71, high = 0.82 (95% CI: low=[0.44,0.64], mid=[0.68,0.75], high=[0.76,0.87]); analysis for one mouse shown in Figure 6A). We will return to this observation in more detail in the upcoming section on single-trial dynamics.

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Movement time decoding model.

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To more thoroughly determine the independent, additional predictive power of DAN baseline and ramping signals over other task variables (e.g., previous trial first-lick time and reward outcome, etc.), we derived a nested decoding model for first-lick time (Figure 6A). In this model, the pre-cue ‘baseline’ was divided into two components: the pre-lamp-off intertrial interval signal (‘ITI’) and the lamp-off to cue interval signal (‘LOI’). All predictors contributed to the predictive power of the model. However, even when we accounted for the contributions of prior trial history, tdTomato artifacts and baseline GCaMP6f signals, GCaMP6f threshold-crossing time robustly dominated the model and absorbed much of the variance explained by baseline dopaminergic signals, alone explaining 10% of the variance in first-lick time on average (range: 1–27%, Figure 6B–D). Alternate formulations of the decoding model produced similar results (Figure 6—figure supplement 1).

Although the threshold-crossing analysis made no assumptions about the underlying dynamics of the GCaMP6f signals on single-trials, in principle, ramping dynamics in averaged neural signals could be produced from individual trials with a single, discrete ‘step’ occurring at different times on different trials. Ramping has long been observed in averaged neural signals recorded during perceptual decision tasks in monkeys, and there has been considerable debate over whether single-trial responses in these experiments are better classified as ‘ramps’ or a single ‘step’ (Latimer et al., 2015; Latimer et al., 2016; Shadlen et al., 2016; Zoltowski et al., 2019; Zylberberg and Shadlen, 2016). It has even been suggested that different sampling distributions can produce opposite model classifications in ground-truth synthetic datasets (Chandrasekaran et al., 2018).

We attempted to classify single-trial dynamics as a discrete stepping or ramping process with hierarchical Bayesian models implemented in probabilistic programs (Figure 6—figure supplement 2A-B). However, like the perceptual decision-making studies, we also found ambiguous results, with about half of single trials best classified by a linear ramp and half best classified by a discrete step dynamic (Figure 6—figure supplement 2C). Nonetheless, three separate lines of evidence suggest that single trials are better characterized by slowly evolving ramps:

First, the relationship of threshold-crossing time to first-lick time is different for the step vs. ramp models when different threshold levels are sampled (Maimon and Assad, 2006), as schematized in Figure 6—figure supplement 3A: Increasing slope of this relationship is consistent with ramps on single trials, but not with a discrete step, which would be expected to have the same threshold-crossing time regardless of threshold level (Figure 6—figure supplement 3B). We found that the slope of this relationship increased markedly as the threshold level was increased, consistent with the ramp model (n = 12 mice: mean slope low = 0.46, mid = 0.7, high = 0.82 (95% CI: low=[0.37,0.54], mid=[0.66,0.73], high=[0.74,0.88]), Figure 6—figure supplement 3C).

Second, if single trials involve a step change occurring at different times from trial-to-trial then aligning trials on that step should produce a clear step on average, rather than a ramp (Latimer et al., 2015). We thus aligned single-trial GCaMP6f signals according to that optimal step position determined from a Bayesian step model fit for each trial and then averaged the step-aligned signals across trials. The averaged signals did not resemble a step function, but rather yielded a sharp transient superimposed on a ‘background’ ramping signal (Figure 6—figure supplement 4A). Step-aligned tdTomato and EMG averages showed a small inflection at the time of the step, but neither signal showed background ramping. This suggests that the detected ‘steps’ in the GCaMP6f signals were likely transient movement artifacts superimposed on the slower ramping dynamic rather than bona fide steps.

Third, the ideal step model holds that the step occurs at different times from trial-to-trial, producing a ramping signal when trials are averaged together. In this view, the trial-by-trial variance of the signal should be maximal at the time at which 50% of the steps have occurred among all trials, and the variance should be minimal at the beginning and end of the interval (when no steps or all steps have occurred, respectively). We thus derived the optimal step time for each trial using the Bayesian step model, and we then calculated variance as a function of time within pools of trials with similar movement times. The signal variance showed a monotonic downward trend during the timed interval, with a minimum variance at the time of movement rather than at the point at which 50% of steps had occurred among trials, inconsistent with the discrete step model (Figure 6—figure supplement 4B).

Taken together, we did not find evidence for a discrete step dynamic on single trials; on the contrary, our observations concord with slow ramping dynamics on single trials. Regardless, our GLM movement-time decoding approaches in Figure 6 did not make any assumptions about underlying single-trial dynamics.

Because dopaminergic ramping signals robustly predicted first-lick timing and were apparently transmitted via dopamine release to downstream striatal neurons, ramping DAN activity may causally determine movement timing. However, because the animals could expect reward within a few hundred milliseconds of the first-lick, it is also possible that the dopaminergic ramps could instead serve as a ‘passive’ monitor of reward expectation without influencing movement initiation. To distinguish these possibilities, we optogenetically activated or inhibited DANs (in separate experiments) on 30% of randomly interleaved trials (Figure 7A and Figure 7—figure supplement 1). For activation experiments, we chose light levels that elevated DAN activity within the physiological range observed in our self-timed movement task, as assayed by simultaneous photometry in the DLS with a fluorescent sensor of released dopamine (dLight1.1, Figure 7—figure supplement 2). DAN activation significantly early-shifted the distribution of self-timed movements on stimulated trials compared to unstimulated trials (12 mice; 2-sample Kolmogorov-Smirnov (KS) Test, D = 0.078 (95% CI: [0.067,0.093]), p = 2.8·10^–26), whereas inhibition produced significant late-shifting compared to unstimulated trials (4 mice; two-sample KS Test, D = 0.051 (95% CI: [0.034,0.077]), p = 3.1·10^–4; Figure 7B and Figure 7—figure supplement 3A). Stimulation of mice expressing no opsin produced no consistent effect on timing (5 mice; two-sample KS Test, D = 0.017 (95% CI: [0.015,0.040]), p = 0.62). The direction of these effects was consistent across all animals tested in each category (Figure 7C). Complementary analysis methods revealed consistent effects (bootstrapped difference in median first-lick times between categories: Δ(activation - no-opsin) = –0.22 s (95% CI=[–0.32 s,–0.12 s]), Δ(inhibition – no-opsin) = +0.19 s (95% CI=[+0.09 s,+0.30 s]), Figure 7C–D; bootstrapped comparison of difference in area under the cdf curves: Δ(activation – no-opsin) = –0.31 dAUC (95% CI=[–0.47 dAUC,–0.15 dAUC]), Δ(inhibition – no-opsin) = +0.23 dAUC (95% CI=[+0.08 dAUC,+0.37 dAUC]), Figure 7—figure supplement 3B; bootstrapped difference in mean first-lick times between categories: Δ(activation – no-opsin) = –0.34 s (95% CI=[–0.49 s,–0.19 s]), Δ(inhibition – no-opsin) = +0.24 s (95% CI=[+0.09 s,+0.39 s]), Figure 7—figure supplement 3C). Similar effects were obtained with activation of SNc DAN axon terminals in the DLS (2 mice, Figure 7—figure supplement 3A-B). Because these exogenous manipulations of DAN activity modulated movement timing on the same trial as the stimulation/inhibition, this suggests that the endogenous dopaminergic ramping we observed during the self-timed movement task likewise affected movement initiation in real time, rather than serving solely as a passive monitor of reward expectation.

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Optogenetic manipulation of SNc DANs.

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Recent studies have shown that physiological ranges of optogenetic DAN activation (as assayed by simultaneous recordings from DANs) fail to elicit overt movements (Coddington and Dudman, 2018). We likewise found that optogenetic DAN activation did not elicit immediate licking outside the context of the task (Figure 7—figure supplement 4A). Additionally, optogenetic DAN inhibition did not reduce the rate of spontaneous licking outside the context of the task (Figure 7—figure supplement 4B). In both cases, we used the same light levels that had elicited the robust shifts in timing behavior during the self-timed movement task. In other control experiments, we purposefully drove neurons into non-physiological activity regimes during the task by applying higher activation light levels. Over-stimulation caused large, immediate, sustained increases in DLS dopamine (Figure 7—figure supplement 2), comparable in amplitude to the typical reward-related dopamine transients on interleaved, unstimulated trials. These non-physiological manipulations resulted in rapid, nonpurposive body movements and disrupted performance of the task. Together, these results suggest that the optogenetic effects on timing in Figure 7 did not result from direct, immediate triggering or suppression of movement, nor from non-physiological dopamine release due to over-stimulation.

Optogenetic manipulations of DAN activity in the physiological range appeared to modulate the probability of initiating the pre-potent, self-timed movement. Given that endogenous DAN signals increased during the timing interval of the self-timed movement task, we reasoned that the probability of movement should likewise increase over the course of the timed interval. We thus derived a nested probabilistic movement-state decoding model to explore the link between DAN signals and movement propensity (Figure 8A). We applied a GLM based on logistic regression, in which we classified each moment of time as either a non-movement (0) or movement (1) state (Figure 8A–B), and we examined how well various parameters could predict the probability of transitioning from the non-movement state to the movement state. Unlike the decoding model in Figure 6, which considers a single threshold-crossing time, the probabilistic approach takes into account continuous DAN signals. Initial model selection included previous trial history (movement time and reward outcome history) in addition to the DAN GCaMP6f signal, but Bayesian Information Criterion (BIC) analysis indicated that the instantaneous GCaMP6f signal alone was a robustly significant predictor of movement state, whereas previous trial outcomes were insignificant contributors and did not further improve the model (Figure 8—figure supplement 1). We thus only considered the DAN GCaMP6f signal as a predictor in subsequent analyses.

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Movement state decoding model.

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The continuous DAN GCaMP6f signal was indeed predictive of current movement state at any time t, and it served as a significant predictor of movement state up to at least 2 s in the past (Figure 8C). However, the signals became progressively more predictive of the current movement state as time approached t. That is, the dopaminergic signal level closer to time t tended to absorb the behavioral variance explained by more distant, previous signal levels (Figure 8C), reminiscent of how threshold crossing time absorbed the variance explained by the baseline dopaminergic signal in the movement-timing decoding model (Figure 6B–C). This observation is consistent with a diffusion-like ramping process on single trials, in which the most recent measurement gives the best estimate of whether there will be a transition to the movement state (but is difficult to reconcile with a discrete step process on single trials, consistent with the results in Figure 6—figure supplements 3–4).

We applied the fitted instantaneous probabilities of transitioning to the movement state to derive a fitted hazard function for each behavioral session (Figure 8D). The DAN GCaMP6f signals were remarkably predictive of the hazard function, both for individual sessions and on average, explaining 65% of the variance on average (n = 12 mice). Conversely, when the model was fit on the same data in which the timepoint identifiers were shuffled, this predictive power was essentially abolished, explaining only 5% of the variance on average (Figure 8E).

Together, these results demonstrate that slowly evolving dopaminergic signals are predictive of the moment-to-moment probability of movement initiation. When combined with the optogenetics results, they argue that dopaminergic signals causally modulate the moment-to-moment probability of the pre-potent movement. In this view, trial-by-trial variability in the DAN signal gives rise to trial-by-trial differences in movement timing in the self-timed movement task.

A number of studies have reported short-latency (<500 ms) modulations in DAN activity following reward-predicting sensory cues and immediately preceding movements (Coddington and Dudman, 2018; da Silva et al., 2018; Dodson et al., 2016; Howe and Dombeck, 2016; Schultz et al., 1997), similar to the sensory- and motor-related transients we observed within ~500 ms of the cue and first-lick. However, the ramping DAN signals we observed during self-timing were markedly slower, unfolding over seconds and preceding the first-lick by as long as 10 s. Previous studies have reported similarly slow ramping dopaminergic signals in other behavioral contexts, including goal-directed navigation toward rewarded targets (Howe et al., 2013), multi-step tasks leading to reward (Hamid et al., 2016; Howard et al., 2017; Mohebi et al., 2019), and passive observation of dynamic visual cues indicating proximity to reward (Kim et al., 2019). A common feature in these experiments and our self-timed movement task is that trials culminated in the animal’s receiving reward. Thus, parsimony suggests that dopaminergic ramping could reflect reward expectation. However, dopaminergic ramping is generally absent in Pavlovian paradigms, in which animals learn to expect passive reward delivery at a fixed time following a conditioned stimulus (Menegas et al., 2015; Tian et al., 2016; Schultz et al., 1997; Starkweather et al., 2017). One exception is a report of ramping activity in monkey DANs during a Pavlovian paradigm with reward uncertainty (Fiorillo et al., 2003); however, ramping was not subsequently reproduced under similar conditions, either in monkeys (Fiorillo, 2011; Matsumoto and Hikosaka, 2009; Tobler et al., 2005) or rodents (Hart et al., 2015; Tian and Uchida, 2015). Thus, while dopaminergic ramping is likely related to reward expectation, the preponderance of evidence suggests that reward expectation alone is insufficient to cause DAN ramping.

To reconcile these disparate findings, Gershman and colleagues proposed a formal model in which dopaminergic ramping encodes reward expectation in the form of an ‘ongoing’ reward-prediction error (RPE) that arises from resolving uncertainty of one’s position in the value landscape (i.e., one’s spatial-temporal distance to reward delivery/omission). For example, uncertainty is resolved if animals are provided visuospatial cues indicating proximity to reward (Howe et al., 2013; Kim et al., 2019). In contrast, because animals can only imprecisely estimate the passage of time, the animal is uncertain of when reward will be delivered/omitted in Pavlovian tasks. The RPE model holds that this temporal uncertainty flattens the Pavlovian value landscape, thereby flattening dopaminergic ramping to the degree that it is obscured (Gershman, 2014; Kim et al., 2019; Mikhael and Gershman, 2019; Mikhael et al., 2019). Although both our task and Pavlovian tasks involve timing, the key difference may be that the animal actively determines when reward will be delivered/omitted in the self-timed movement task—just after it moves. Certainty in the timing of reward relative to its own movement would resolve the animal’s uncertainty of its position in the value landscape, and may thus explain why dopaminergic ramping occurs prominently in the self-timed movement task, but not in Pavlovian tasks (Hamilos and Assad, 2020). Although the RPE model provides a plausible explanation for our findings, dopaminergic ramping signals are also consistent with broader views of ‘reward expectation’, such as value tracking as animals approach reward (Hamid et al., 2016; Mohebi et al., 2019). In a companion theoretical paper (Hamilos and Assad, 2020), we explore the reward expectation-based computational framework in more detail, including a reconciliation of apparently contradictory DAN signals reported in the context of a perceptual timing task (Soares et al., 2016).

We found that trial-by-trial variability in ramping dynamics explained the precise timing of self-timed licks. However, because the animals could expect reward shortly after the first-lick, the ramping dopaminergic signal might serve as a passive monitor of reward expectation rather than causally influencing the timing of movement initiation. To distinguish these possibilities, we optogenetically manipulated SNc DAN activity. We found that exciting or inhibiting DANs altered the timing of the first-lick on the concurrent trial, in a manner suggesting an increase/decrease in the probability of movement, respectively. This suggests that endogenous DAN signaling could play a causal role in the initiation of reward-related movements in real time—but by what mechanism?

One possibility is that endogenous or exogenous DAN signals could increase the animal’s motivation or heighten its expectation of reward, which then secondarily influences reward-related movement. There is some evidence that might support this view. Phillips et al. found that electrical stimulation of the VTA in rats elicited approach behavior for self-delivery of intravenous cocaine; however, the electrical stimulation could have activated non-DAN fibers/pathways via the VTA (Phillips et al., 2003). Hamid et al. found that selective optogenetic stimulation of DANs could shorten the latency for rats to engage in a port-choice task—but only if the rat was disengaged from the task; if the rat was already engaged in task performance, the latency became slightly longer (Hamid et al., 2016).

In contrast to these equivocal findings, a large body of evidence suggests that selective optogenetic stimulation or inhibition of DANs generally does not affect reward-related movements on the same trial. First, we ourselves could not evoke licking (nor inhibit spontaneous licking) outside the context of our self-timed movement task (Figure 7—figure supplement 4). Our mice were thirsty and perched near their usual juice tube, but offline DAN stimulation/inhibition did not alter licking behavior, even though we applied the same optical power that altered movement probability during the self-timed movement task. Numerous studies have also examined the effects of optogenetic modulation of DANs in Pavlovian conditioning paradigms, with the general finding that DAN modulation affects conditioned movements on subsequent trials or sessions—a learning effect—but not on the same trial (Coddington and Dudman, 2018; Coddington and Dudman, 2021; Lee et al., 2020; Maes et al., 2020; Morrens et al., 2020; Pan et al., 2021; Saunders et al., 2018). For example, Lee et al. found that optogenetic inhibition of mouse DANs at the same time as an olfactory conditioned stimulus had no effect on anticipatory licking on the concurrent trial, even though inhibition at the time of reward delivery reduced the probability and rate of anticipatory licking on subsequent trials (Lee et al., 2020). Thus, the preponderance of evidence argues against a simple scheme whereby modulating DAN activity leads to a change in motivation that automatically evokes or suppresses reward-related movements in real time. The fact that we observed robust, concurrent optogenetic modulation of movement timing in our experiment suggests that additional factors were at play for self-timed movements.

One possibility is that during self-timing, exogenous (optogenetic) stimulation of DANs summed with the endogenous ramping DAN signal, leading to supra-heightened motivation to obtain reward. However, when we deliberately over-stimulated DANs—eliciting even higher dopamine signals in the DLS (Figure 7—figure supplement 2)—we observed ‘dyskinetic’ body movements rather than purposive licking. An alternative possibility is that the explicit timing requirement of the self-timed movement task made it particularly responsive to dopaminergic modulation. A long history of pharmacological and lesion experiments suggests that the dopaminergic system modulates timing behavior (Meck, 2006; Merchant et al., 2013). Broadly speaking, conditions that increase/decrease dopamine availability or efficacy speed/slow the ‘internal clock’, respectively (Dews and Morse, 1958; Mikhael and Gershman, 2019; Schuster and Zimmerman, 1961; Malapani et al., 1998; Meck, 1986; Meck, 2006; Merchant et al., 2013). The dopaminergic ramping signals we observed also bear resemblance to Pacemaker-Accumulator models of neural timing, in which a hypothetical accumulator signals that an interval has elapsed when it reaches a threshold level (Gallistel and Gibbon, 2000; Lustig and Meck, 2005; Meck, 2006). To ‘self-time’ a movement also implies that the movement is prepared and pre-potent during the timing period, potentially making the relevant neural motor circuits more sensitive to dopaminergic modulation.

Regardless of the detailed mechanism, our results provide a link between dopaminergic signaling and the initiation of self-timed movements. Although endogenous dopaminergic ramping likely reflects reward expectation, we propose that these reward-related ramping signals can influence the timing of movement initiation, at least in certain behavioral contexts. This framework also provides a link between two seemingly disparate roles that have been proposed for the dopaminergic system—reward/reinforcement-learning on one hand, and movement modulation on the other.

Importantly, we are not suggesting that DANs directly drive movement (like corticospinal or corticobulbar neurons). To the contrary, outside of the context of the self-timed movement task, we could not evoke reward-related movements by activating DANs. Even during the self-timed movement task, DAN stimulation did not elicit immediate movements: first-lick times still spanned a broad distribution from trial-to-trial. Moreover, dopaminergic ramping does not invariably lead to movement. For example, Kim et al. found dopaminergic ramping in the presence of visual cues that signaled proximity to reward, independent of reward-related movements (Kim et al., 2019). Consequently, we propose that when a movement is pre-potent (as in our self-timed movement task), dopaminergic signaling can modulate the probability of initiating that movement. Consistent with this view, we found that the endogenous ramping dynamics were highly predictive of the moment-by-moment probability of movement (as captured by the hazard function), with DAN signals becoming progressively better predictors as the time of movement onset approached.

This view of dopaminergic modulation of movement probability could be related to classic findings from extrapyramidal movement disorders, in which dysfunction of the nigrostriatal pathway produces aberrations in movement initiation rather than paralysis or paresis (Bloxham et al., 1984; Fahn, 2011; Hallett and Khoshbin, 1980). That is, movements do occur in extrapyramidal disorders, but at inappropriate times, either too little/late (e.g., Parkinson’s), or too often (e.g., dyskinesias). Based on the deficits observed in Parkinsonian states (e.g., perseveration), this role may extend to behavioral transitions more generally, for example, starting new movements or stopping ongoing movements (Guru et al., 2020).

We have suggested that the ramping DAN signals in the self-timed movement task could be related to reward expectation coupled with the explicit timing requirement of the task. However, when we averaged DAN signals aligned to ‘spontaneous’ licks during the ITI, we also observed noisy, slow ramping signals building over seconds up to the time of the next lick, with a time course related to the duration of the inter-lick interval (Figure 8—figure supplement 2). This observation raises the possibility that slowly evolving DAN signals may be related to the generation of self-initiated movements more generally—although our highly trained animals may have also been ‘rehearsing’ timed movements between trials and/or expecting reward even for spontaneous licks.

We found that DAN signals predict movement timing via two low-dimensional signals: a baseline offset and a ramping dynamic that ‘stretches’ depending on trial-by-trial movement timing. Intriguingly, similar stretching of neural responses has been observed before self-timed movement in other brain areas in rats and primates, including the dorsal striatum (Emmons et al., 2017; Mello et al., 2015; Wang et al., 2018), lateral interparietal cortex (Maimon and Assad, 2006), presupplementary and supplementary motor areas (Mita et al., 2009), and dorsomedial frontal cortex (DMFC; Remington et al., 2018; Sohn et al., 2019; Wang et al., 2018; Xu et al., 2014). In the case of DMFC, applying dimensionality reduction to the population responses revealed two lower-dimensional characteristics that resembled our findings in DANs: (1) the speed at which the population dynamics unfolded was scaled (‘stretched’) to the length of the produced timing interval (Wang et al., 2018), and (2) the population state at the beginning of the self-timed movement interval (‘setpoint’) was correlated with the timed interval (Remington et al., 2018; Sohn et al., 2019). Recurrent neural network models suggested variation in stretching and setpoint states could be controlled by (unknown) tonic or monotonically-ramping inputs to the cortico-striatal system (Remington et al., 2018; Sohn et al., 2019; Wang et al., 2018). We found that DANs exhibit both baseline (e.g., ‘setpoint’) signals related to timing, as well as monotonically ramping input during the timing interval. Thus, through their role as diffusely-projecting modulators, DANs could potentially orchestrate variations in cortico-striatal dynamics observed during timing behavior. Ramping DAN signals could also be related to the slow ramping signals that have been observed in the human motor system in anticipation of self-initiated movements, for example, readiness potentials in EEG recordings (Deecke, 1996; Libet et al., 1983).

In operant tasks in which difficulty is systematically varied over blocks of trials, increased intertrial dopamine in the nucleus accumbens has been associated with higher average reward rate and decreased latency to engage in a new trial, suggesting a link between dopamine and ‘motivational vigor’, the propensity to invest effort in work (Hamid et al., 2016; Mohebi et al., 2019). Intriguingly, we observed the opposite relationship in the self-timed movement task: periods with higher average reward rates had lower average baseline dopaminergic signals and later first-lick times. Moreover, for a given first-lick time (e.g., 3.5–3.75 s), we did not detect differences in baseline (or ramping) signals during periods with different average reward rates, such as near the beginning or end of a session. This difference between the two tasks may be due to their opposing strategic constraints: in the aforementioned experiments, faster trial initiation increased the number of opportunities to obtain reward, whereas earlier first-licks tended to decrease reward acquisition in our self-timed movement task.

The basal ganglia have also been implicated in controlling ‘movement vigor,’ generally referring to the speed, force or frequency of movements (Bartholomew et al., 2016; Dudman and Krakauer, 2016; Panigrahi et al., 2015; Turner and Desmurget, 2010; Yttri and Dudman, 2016). The activity of nigrostriatal DANs has been shown to correlate with these parameters during movement bouts and could promote more vigorous movement via push-pull interactions with the direct and indirect pathways (Barter et al., 2015; da Silva et al., 2018; Mazzoni et al., 2007; Panigrahi et al., 2015). Movement vigor might also entail earlier self-timed movements, mediated by moment-to-moment increases in dopaminergic activity.

If moving earlier is a signature of greater movement vigor, then earlier self-timed movements might also be executed with greater force/speed. We looked for movement-related vigor signals, examining both the amplitude of lick-related EMG signals and the latency between lick initiation and lick-tube contact. We detected no consistent differences in these force- or speed-related parameters as a function of movement time; on the contrary, the EMG signals were highly stereotyped irrespective of the first-lick time (data not shown). It is possible that vigor might affect movement timing without affecting movement kinematics/dynamics—but, if so, the distinction between ‘timing’ and ‘vigor’ would seem largely semantical.

We have posited that dopaminergic ramping reflects reward expectation, a common element of behavioral paradigms that reveal slow dopaminergic ramping. Furthermore, our optogenetic manipulations indicate that dopaminergic signals do not directly trigger movements, but rather act as if modulating the probability of the pre-potent self-timed movement. Taken together, these observations suggest that as DAN activity ramps up, the probability of movement likewise increases. In this view, different rates of increase in DAN activity lead to shorter or longer elapsed intervals before movement, on average. This framework leaves open the question of what makes movement timing ‘probabilistic.’ One possibility is that recurrent cortical-basal ganglia–thalamic circuits could act to generate movements ‘on their own,’ without direct external triggers (e.g., a ‘go!’ cue). By providing crucial modulation of these circuits, DANs could tune the propensity to make self-timed movements—and pathological loss of DANs could reduce the production of such movements. Future experiments should address how dynamic dopaminergic input influences downstream motor circuits involved in self-timed movements.

Adult male and female hemizygous DAT-cre mice (Bäckman et al., 2006; B6.SJL-Slc6a3^{tm1.1(cre)Bkmm}/J, RRID:IMSR_JAX:020080; The Jackson Laboratory, Bar Harbor, ME) or wild-type C57BL/6 mice were used in all experiments (>2 months old at the time of surgery; median body weight 23.8 g, range 17.3–31.9 g). Mice were housed in standard cages in a temperature and humidity-controlled colony facility on a reversed night/day cycle (12 hr dark/12 hr light), and behavioral sessions occurred during the dark cycle. Animals were housed with enrichment objects provided by the Harvard Center for Comparative Medicine (IACUC-approved plastic toys/shelters, e.g., Bio-Huts, Mouse Tunnels, Nest Sheets, etc.) and were housed socially whenever possible (1–5 mice per cage). All experiments and protocols were approved by the Harvard Institutional Animal Care and Use Committee (IACUC protocol #05098, Animal Welfare Assurance Number #A3431-01) and were conducted in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals.

Surgeries were conducted under aseptic conditions and every effort was taken to minimize suffering. Mice were anesthetized with isoflurane (0.5–2% at 0.8 L/min). Analgesia was provided by s.c. 5 mg/kg ketoprofen injection during surgery and once daily for 3 d postoperatively (Ketofen, Parsippany, NJ). Virus was injected (50 nL/min), and the pipet remained in place for 10 min before removal. 200 µm, 0.53 NA blunt fiber optic cannulae (Doric Lenses, Quebec, Canada) or tapered fiber optic cannulae (200 µm, 0.60 NA, 2 mm tapered shank, OptogeniX, Lecce, Italy) were positioned at SNc, VTA, or DLS and secured to the skull with dental cement (C&B Metabond, Parkell, Edgewood, NY). Neck EMG electrodes were constructed from two Teflon-insulated 32 G stainless steel pacemaker wires attached to a custom socket mounted in the dental cement. Sub-occipital neck muscles were exposed by blunt dissection and electrode tips embedded bilaterally.

Viral Injection:

• SNc: 3.16 mm posterior, ±1.4 mm lateral, 4.2 mm ventral

• VTA: 3.1 mm posterior, ±0.6 mm lateral, 4.2 mm ventral

• DLS: 0 mm anterior, ±2.6 mm lateral, 2.5 mm ventral.

Fiber Optic Tips:

• SNc/VTA: 4.0 mm ventral (photometry) or 3.9 mm ventral (optogenetics).

• DLS: 2.311 mm ventral (blunt fiber) or 4.0 mm ventral (tapered fiber)

Animals recovered for 1 week postoperatively before water deprivation. Mice received daily water supplementation to maintain ≥80% initial body weight and fed ad libitum. Mice were habituated to the experimenter and their health was monitored carefully following guidelines reported previously (Guo et al., 2014). Training commenced when mice reached the target weight (~8–9 d post-surgery).

Mice were anesthetized with >400 mg/kg pentobarbital (Somnasol, Henry Schein Inc, Melville, NY) and perfused with 10 mL 0.9% sodium chloride followed by 50 mL ice-cold 4% paraformaldehyde in 0.1 M phosphate buffer. Brains were fixed in 4% paraformaldehyde at 4 °C for >24 hr before being transferred to 30% sucrose in 0.1 M phosphate buffer for >48 hr. Brains were sliced in 50 µm coronal sections by freezing microtome, and fluorophore expression was assessed by light microscopy. The sites of viral injections and fiber optic placement were mapped with an Allen Mouse Brain Atlas.

A custom rig provided sensory cues, recorded events and delivered juice rewards under the control of a Teensy 3.2 microprocessor running a custom Arduino state-system behavioral program with MATLAB serial interface. Digital and analog signals were acquired with a CED Power 1400 data acquisition system/Spike2 software (Cambridge Electronic Design Ltd, Cambridge, England). Photometry and behavioral events were acquired at 1000 Hz; movement channels were acquired at 2000 Hz. Video was acquired with FlyCap2 or Spinnaker at 30 fps (FLIR Systems, Wilsonville, OR). Data were analyzed with custom MATLAB statistics packages.

Mice were head-fixed with a juice tube positioned in front of the tongue. The spout was placed as far away from the mouth as possible so that the tongue could still reach it to discourage compulsive licking (Guo et al., 2014), ~1.5 mm ventral and ~1.5 mm anterior to the mouth. During periods when rewards were not available, a houselamp was illuminated. At trial start, the houselamp turned off, and a random delay ensued (0.4–1.5 s) before a cue (simultaneous LED flash and 3300 Hz tone, 100 ms) indicated start of the timing interval. The timing interval was divided into two windows, early (0–3.33 s in most experiments; 0–4.95 s in others) and reward (3.33–7 s; 4.95–10 s), followed by the intertrial interval (ITI, 7–17 s; 10–20 s). The window in which the mouse first licked determined the trial outcome (early, reward, or no-lick). An early first-lick caused an error tone (440 Hz, 200 ms) and houselamp illumination, and the mouse had to wait until the full timing interval had elapsed before beginning the ITI. Thus there was no advantage to the mouse of licking early. A first-lick during the reward window caused a reward tone (5050 Hz, 200 ms) and juice delivery, and the houselamp remained off until the end of the trial interval. If the timing interval elapsed with no lick, a time-out error tone played (131 Hz, 2 s), the houselamp turned on, and ITI commenced. During the ITI and pre-cue delay (‘lamp-off interval’), there was no penalty for licking.

Mice learned the task in three stages (Figure 1—figure supplement 1A). On the first 1–4 days of training, mice learned a beginner-level task, which was modified in two ways: (1) to encourage participation, if mice did not lick before 5 s post-cue, they received a juice reward at 5 s; and (2) mice were not penalized for licking in reaction to the cue (within 500 ms). When the mouse began self-triggering ≥50% of rewards (days 2–6 of training), the mouse advanced to the intermediate-level task, in which the training reward at 5 s was omitted, and the mouse had to self-trigger all rewards. After completing >250 trials/day on the intermediate task (usually days 4–7 of training), mice advanced to the mature task, with no reaction licks permitted. All animals learned the mature task and worked for ~400–1,500 trials/session.

The raw frequency of a particular response time in the self-timed movement task is ‘distorted’ by how often the animal has the chance to respond at that time (Anger, 1956). This bias was corrected by calculating the hazard function, which takes into account the number of response opportunities the animal had at each timepoint. The hazard function is defined as the conditional probability of moving at a time, t, given that the movement has not yet occurred (referred to as ‘IRT/Op’ analysis in the old Differential Reinforcement of Low Rates (DRL) literature). The hazard function was computed by dividing the number of first-movements in each 250 ms bin of the first-lick timing histogram by the total number of first-movements occurring at that bin-time or later—the total remaining ‘opportunities’.

Movements were recorded simultaneously during behavior with four movement-control measurements: neck EMG (band-pass filtered 50–2000 Hz, 60 Hz notch, amplified 100–1000x), back-mounted accelerometer (SparkFun Electronics, Boulder, CO), high-speed camera (30 Hz, FLIR Systems, Wilsonville, OR), and tdTomato photometry. All control signals contained similar information, and thus only a subset of controls was used in some sessions.

Fiber optics were illuminated with 475 nm blue LED light (Plexon, Dallas, TX) (SNc/VTA: 50 μW, DLS: 35 μW) measured at patch cable tip with a light-power meter (Thorlabs, Newton, NJ). Green fluorescence was collected via a custom dichroic mirror (Doric Lenses, Quebec, Canada) and detected with a Newport 1401 Photodiode (Newport Corporation, Irvine, CA). Fluorescence was allowed to recover ≥1 d between recording sessions. To avoid crosstalk in animals with red control fluorophore expression, the red channel was recorded at one of the three sites (SNc, VTA, or DLS, 550 nm lime LED, Plexon, Dallas, TX) while GCaMP6f, dLight1.1 or DA_2m was recorded simultaneously only at the other implanted sites.

Raw fluorescence for each session was pre-processed by removing rare singularities (single points > 15 STD from the mean) by interpolation to obtain F(t). To correct photometry signals for bleaching, dF/F was calculated as:

where F₀(t) is the 200 s moving average of F(t) (Figure 2—figure supplement 2A). We tested several other complementary methods for calculating dF/F and all reported results were robust to dF/F method (see Materials and methods: dF/F method characterization and validation). To ensure dF/F signal processing did not introduce artifactual scaling or baseline shifts, we also tested several complementary techniques to isolate undistorted F(t) signals where possible and quantified the amount of signal distortion when perfect isolation was not possible (see Materials and methods: ‘dF/F method characterization and validation’, below, and Figure 2—figure supplement 2C).

dF/F calculations are intended to reduce the contribution of slow fluorescence bleaching to fiber photometry signals, and many such methods have been described (Kim et al., 2019; Mohebi et al., 2019; Soares et al., 2016). However, dF/F methods have the potential to introduce artifactual distortion when the wrong method is applied in the wrong setting. Thus, to derive an appropriate dF/F method for use in the context of the self-timed movement task, we characterized and quantified artifacts produced by four candidate dF/F techniques.

DA_2m was about twice as bright as dLight1.1, and thus generally yielded larger and less noisy dF/F signals. To compare the two extracellular dopamine sensors in the same plot, dF/F was normalized for each signal by the amplitude of its lick-related transient. dF/F was calculated as usual, and then the mean baseline-to-transient peak amplitude was measured for trials with first-licks occurring between 2 and 3 s. Percentage NdF/F is reported as the percentage of this amplitude.

dLight1.1 is an extracellular dopamine sensor derived from the dopamine-1-receptor, and has fast reported kinetics: rise t_1/2 = 9.5 ± 1.1 ms, decay t_1/2 = 90 ± 11 ms (Patriarchi et al., 2018). DA_2m is a new extracellular dopamine indicator derived from the dopamine-2-receptor, which provides brighter signals. DA_2m signals have been reported to decay slowly in slice preparations but are much faster in vivo, presumably because endogenous dopamine-clearance mechanisms are preserved: reported rise t_1/2 ~50 ms, decay t_1/2 ~360 ms in freely behaving mice; decay t_1/2 ~190 ms in head-fixed Drosophila (Sun et al., 2020). To estimate the dopamine-sensor kinetics in our head-fixed mice, we examined the phasic fluorescence transient occurring on unrewarded first-licks (0.5–3.3 s), which showed a stereotyped fast rise and decay with both sensors (Figure 2—figure supplement 3D-E). While the transient was somewhat complex, reminiscent of phasic burst-pause responses sometimes observed for movement-related DAN activity (Coddington and Dudman, 2018; Coddington and Dudman, 2019), we measured the time for average fluorescence to decay from the peak of the transient to half the baseline-to-peak amplitude. We found decay t_1/2~75 ms for dLight1.1 and t_1/2~125 ms for DA_2m (Figure 3—figure supplement 1). Given that the dopaminergic ramping signals in our study evolved over several seconds, the kinetics of both dopamine sensors are thus fast enough that they should not have caused appreciable distortion of the slow ramping dynamics.

The mean SNc GCaMP6f signal during the ‘baseline’ (2 s interval before the lamp-off event) or minimum lamp-off interval (‘LOI’; –0.4 s to 0 s, the cue-time) was compared to the first-lick time for pooled trials in Figure 2C by calculating the Pearson correlation coefficient. There were at least 700 trials in each pooled set of trials (0.75–4 s included).

To test the independent contribution of each task-related input to the photometry signal and to select the best model, we employed a nested fitting approach, in which each dataset was fit multiple times (in ‘nests’), with models becoming progressively more complex in subsequent nests. The nests fit to the GCaMP6f photometry data employed the inputs X^(j) at each j^th nest:

• Null Model: X⁽⁰⁾ = x₀

• Nest 1: X⁽¹⁾ = X⁽⁰⁾+ tdTomato (tdt)

• Nest 2: X⁽²⁾ = X⁽¹⁾+ cue + first-lick

• Nest 3: X⁽³⁾ = X⁽²⁾+ EMG/accelerometer

• Nest 4: X⁽⁴⁾ = X⁽³⁾+ time-dependent baseline offset

• Nest 5: X⁽⁵⁾ = X⁽⁴⁾+ stretch representing percentages of interval

Overfitting was penalized by ridge regression, and the optimal regularization parameter for each nest was obtained by five-fold cross-validation to derive the final model fit for each session. Model improvement by each input was assessed by the percentage loss improvement at the nest where the input first appeared compared to the prior nest. The loss improvement of Nest 1 was compared to the Null Model (the average of the photometry timeseries). The nested model of tdt control photometry signals was the same, except Nest 1 was omitted.

The GLM for each nest takes the form:

where Y is the 1xn vector of the photometry signal across an entire behavioral session (n is the total number of sampled timepoints); X^(j) is the dxn design matrix for nest j, where the rows correspond to the d_j predictors for nest j and the columns correspond to each of the n sampled timepoints of Y; and ϴ is the dx1 vector of fit weights.

Y is the concatenated photometry timeseries taken from trial start (lamp-off) to the time of first-lick. Because of day-to-day/mouse-to-mouse variation (ascribable to many possible sources, for example, different neural subpopulations, expression levels, behavioral states, etc.), each session was fit separately.

The d_j design matrix predictors were each scaled (maximum amplitude 1) and grouped by input to the model. The timing-independent inputs were: 1. Null offset (x₀, 1 predictor), 2. tdt (1 predictor), 3. cue (24 predictors), 4. first-lick (28 predictors), and 5. EMG/accelerometer (44 predictors). The timing-dependent inputs were: 6. timing-dependent baseline offset (1 predictor), 7. stretch (500 predictors).

To reduce the number of predictors, the cue, first-lick and EMG/accelerometer predictors (Figure 5—figure supplement 1C) were composed from sets of basis kernels as described previously (Park et al., 2014; Runyan et al., 2017). The cue basis kernels were spaced 0 to 500 ms post-cue, and first-lick basis kernels were spaced –500 to 0 ms relative to first-lick, the typically-observed windows of stereotypical sensory and motor-related neural responses. For nuisance movements (EMG/accelerometer), events were first discretized by thresholding (Figure 5—figure supplement 1B) and then convolved with basis kernels spanning –500 to 500 ms around the event. This window was consistent with the mean movement-aligned optical artifact observed in the tdt channel. The timing-dependent baseline offset was encoded as a constant offset spanning from lamp-off until first-lick, with amplitude taken as linearly proportional to the timed interval on the current trial. The timing-dependent stretch input was composed of 500 predictors, with each predictor containing 1’s tiling 0.05% of the cue-to-lick interval, and 0’s otherwise (Figure 5—figure supplement 1D). Importantly, the stretch was not constrained in any way to form ramps.

Basis sets were optimized to minimize Training Loss, as calculated by mean squared error of the unregularized model:

Superfluous basis set elements that did not improve Training Loss compared to the Null Model were not included in the final model. Goodness of the training fit was assessed by Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), R², and Training Loss. The optimal, regularized model for each nest/session was selected by five-fold cross-validation in which the regularization parameter, λ_j, was optimized for minimal average Test Loss:

Test Loss for each optimal model was compared across nests to select the best model for each session. Models were refit with the optimal λ_j to obtain the final fit.

Model error was simulated 1,000x by redrawing ϴ coefficients consistent with the data following the method described by Gelman and Hill, 2006, and standard errors were propagated across sessions. The absolute value of each predictor was summed and divided by the total number of predictors for that input to show the contribution of the input to the model (Figure 5—figure supplement 1G). To simulate the modeled session’s photometry signal for each nest j, Yfit was calculated as ϴX^(j) and binned by the time of first-lick relative to the cue. The error in the simulation was shown by calculating Yfit_sim = ϴ_simX^(j) for 300 simulated sets of ϴ_sim.

Unsmoothed ramping intervals for photometry timeseries were subjected to PCA and reconstructed with the first three principal components (PCs). To derive a PCA fit matrix with ramping intervals of the same number of samples, the length of each trial was scaled up by interpolation to the maximum ramping interval duration (5,700 samples):

Following PC-fitting, datasets were down-sampled to produce a fit of the correct time duration. Trials where the ramping interval was <0.1 s were excluded to exclude noise from down-sampling.

A nested, generalized linear model was derived to predict the first-lick time on each trial in a session and to quantify the contribution of previous reward history and photometry signals to the prediction. The model was of the form:

where y is the first-lick time, b is a vector of fit coefficients and x is a vector of predictors. The nested model was constructed such that predictors occurring further back in time (such as reward history) and confounding variables (such as tdt photometry signals) were added first to determine the additional variance explained by predictors occurring closer to the time of first-lick, which might otherwise obscure the impact of these other variables. The predictors, in order of nesting, were:

• Nest 0: b0 (Null model, average log-first-lick time)

• Nest 1: b1 = b0 + first lick time on previous trial (trial ‘n-1’)

• Nest 2–5: b2 = b1 + previous trial outcome (1,0)*

• Nest 6: b3 = b2 + median photometry signal in 10 s window before lamp-off (‘ITI’)

• Nest 7: b4 = b3 + median photometry signal from lamp-off to cue (‘lamp-off interval’)

• Nest 8: b5 = b4 + tdt threshold crossing time**

• Nest 9: b6 = b5 + GCaMP6f threshold crossing time**

where all predictors were normalized to be in the interval (0,1).

* Outcomes included (in order of nest): Reaction (first-lick before 0.5 s), Early (0.5–3.333 s), Reward (3.333–7 s), ITI (7–17 s). No-lick was implied when all four outcomes were encoded as zeros.

** Details on threshold-crossing time and alternative models included in Materials and methods: ‘Derivation of threshold and alternative decoding models’.

To exclude the sensory- and motor-related transients locked to the cue and the first-lick events in the threshold-crossing nests, the ramping interval was conservatively defined as 0.7 s post-cue up until 0.6 s before first-lick, and the minimum ramping interval for fitting was 0.1 s. Thus, for a trial to be included in the model, the first lick occurred between 1.4 s to 17 s (end of trial).

Initial model goodness of fit was assessed by R², mean-squared loss and BIC. Models were five-fold cross-validated with ridge regression at each nest to derive the final models, as described above. 95% confidence intervals on model coefficients were calculated by two-sided t-test with standard errors propagated across sessions.

The probability of each single-trial SNc GCaMP6f signal belonging to a ramp vs. step model class was determined via Hierarchical Bayesian Model fitting with probabilistic programs written in the novel probabilistic programming language, Gen.jl, which is embedded in the Julia Programming Language (Cusumano-Towner et al., 2019). The top of the model hierarchy was the model class (linear ramp vs. step function) and the lower level was the respective parameterization of the two model classes (described below).

The probability of the step vs. ramp model class was inferred with data-driven inference. The best fit (step or ramp and parameterization) for each trial was calculated across 20 iterations (Gen Traces) of hierarchical modeling with 50 rounds of probabilistic refinement (computation via Gen Importance Resampling) per iteration (in model testing, models typically converged to their steady-state probability of model class within only 30 rounds of refinement, but 50 rounds were used conservatively to reduce the likelihood of suboptimal classifications).

The multi-threshold procedure described above was also employed to determine whether single-trial ramping dynamics were more consistent with a continuous ramp vs. discrete step dynamic on single-trials. The threshold-crossing time for each trial was regressed against its first-lick time, and the slope of this relationship was reported, as well as the variance explained.

For discrete step single-trial dynamics to produce ramping on average, the time of the step across trials must be distributed throughout the trial interval (importantly, a peri-motor step occurring consistently just before first-lick cannot give rise to continuous ramping dynamics on average). As such, the variance in the GCaMP6f signals across trials for similar first-lick times should be minimal near the time of the cue (when few trials have stepped) and near the time of the first-lick (when all of the trials have stepped). This predicts an inverted-U shaped relationship of signal variance across trials vs. position in the timing interval.

To compare variance across trials equitably, trials were first aligned to the cue and pooled by first-lick time in pools of 1 s each (1–2 s, 2–3 s, etc.), truncated at the earliest first-lick time within the pool. The variance in GCaMP6f signals across trials within a pool was quantified in 10% percent increments of time from the cue up to the earliest first-lick time in the pool (i.e., 1–2 s pool truncated at 1 s, divided into 100 ms increments). Measuring variance by percent of elapsed time within pool allowed pooling of trials across the entire session. The shape of the variance vs. percent of timed interval elapsed was compared to the inverted-U shape prediction to assess for discrete step dynamics.

To test whether optogenetic manipulations during the self-timing task were in the physiological range, we assessed the magnitude of the effect of activation on dopamine release in the DLS by simultaneous photometry recordings with optical activation (Figure 7—figure supplement 2). In two DAT-cre mice, we expressed ChrimsonR bilaterally in SNc DANs and the fluorescent dopamine indicator dLight1.1 bilaterally in DLS neurons. SNc cell bodies were illuminated bilaterally (ChrimsonR 550 nm lime or 660 nm crimson, 0.5–5 mW) on 30% of trials (10 Hz, 10 or 20 ms up-time starting at cue onset and terminating at first-lick). dLight1.1 was recorded with 35 µW 475 nm blue LED light at DLS. To avoid crosstalk between the stimulation LED and the photometry recording site, the brief stimulation up-times were omitted from the photometry signal and the missing points filled by interpolation between the adjacent timepoints.

In a few preliminary sessions, we also explored whether we could evoke short-latency licking (i.e., within a few hundred milliseconds of the stimulation) if light levels were increased above the physiological range for DAN signals. Rather than eliciting immediate licking, higher light levels produced bouts of rapid, nonpurposive limb and trunk movements throughout stimulation, and task execution was disrupted. The animals appeared to have difficulty coordinating the extension of the tongue to touch the lick spout. Simultaneous DLS dopamine detection showed large, sustained surges in dopamine release throughout the period of stimulation, with an average amplitude comparable to that of the reward transient (Figure 7—figure supplement 2, right). This extent of dopamine release was never observed during unstimulated trials. Consequently, to avoid overstimulation in activation experiments, we kept light levels well below those that generated limb and trunk movements.

To determine whether optogenetic stimulation directly elicited or prevented licking, licking behavior was first tested outside the context of the self-timed movement task on separate sessions in the same head-fixed arena but with no cues or behavioral task. Opsin-expressing mice were tested before any exposure to the self-timed movement task (‘Naive’) as well as after the last day of behavioral recording (‘Expert’). In ChR2 control sessions, stimulation (5 mW 425 nm light, 3 s duration, 10 Hz, 20% duty cycle) was applied randomly at the same pace as in the self-timed movement task. stGtACR2 control sessions were conducted similarly (12 mW 425 mW light, 3 s duration, constant illumination); but to examine if inhibition could block ongoing licking, we increased the baseline lick-rate by delivering juice rewards randomly (5% probability checked once every 5 s).

SNc DANs were optogenetically manipulated in the context of the 3.3 s self-timed movement task. To avoid overstimulation, light levels were adjusted to be subthreshold for eliciting overt movements as described above, and mice were not stimulated on consecutive days.

The difference in the distribution of trial outcomes between stimulated and unstimulated trials on each session was quantified in four ways.

1. 2-Sample Unsigned Kolmogorov-Smirnov Test.

2. Difference in empirical continuous probability distribution function (cdf). The difference in the integral of the stimulated and unstimulated cdf (dAUC) was calculated for each session from 0.7 to 7 s. Effect size was quantified by permutation test, wherein the identity of each trial (stimulated or unstimulated) was shuffled, and the distribution of dAUCs for the permuted cdfs was calculated 10,000x. Results were reported for all sessions.

3. Difference in mean movement time. Movement times on stimulated and unstimulated trials were pooled and the distribution of movement time differences was determined by non-parametric bootstrap, in which a random stimulated and unstimulated trial were drawn from their respective pools 1,000,000x, and the difference taken. The mean of each session’s bootstrapped distribution was compared across sessions by the 1,000,000x bootstrapped difference of the mean between sessions of different categories.

4. Difference in median movement time. Same as above but with median.

The probability of transitioning to a movement state, s_t = 1, at time = t was decoded with a logistic generalized linear model of the form:

where X_t is a vector of predictors for the timepoint, t, and b is the vector of fit coefficients. The vector of predictors was comprised of the GCaMP6f signal at every timepoint (the current time, t) as well as the signal history, represented as 200 ms-wide signal averages moving back in time from t. Previous trial history (n-1^th and n-2^th first-lick times and reward/no-reward outcomes) did not contribute significantly to the model during model selection and were thus omitted (see Model Selection, below).

Movement state, s_t, was defined as a binary variable, where s_t=0 represented all timepoints between the cue up until 160 ms before the first-lick detection (to exclude any potential peri-movement responses), and s_t=1 represented the timepoint 150 ms before the first-lick. Because there were many more s_t=0 than s_t=1 samples in a session, s_t=0 points were randomly down-sampled such that states were represented equally in the fit. To avoid randomly sampling a particular model fit by chance, each dataset was fit on 100 randomly down-sampled (bootstrapped) sets, and the average fit across these 100 sets was taken as the model fit for the session.

GCaMP6f signals were smoothed with a 100 ms gaussian kernel and down-sampled to 100 Hz. The GCaMP6f predictors were then nested into the model starting with those furthest in time from the current timepoint, t:

• Nest 0: b0 (Null model)

• Nest 1: b1 = b0 + mean GCaMP6f 1.8:2.0 s before current time = t

• Nest 2: b2 = b1 + mean GCaMP6f 1.6:1.79 s before current time = t

• Nest 3: b3 = b2 + mean GCaMP6f 1.4:1.59 s before current time = t

• Nest 4: b4 = b3 + mean GCaMP6f 1.2:1.39 s before current time = t

• Nest 5: b5 = b4 + mean GCaMP6f 1.0:1.19 s before current time = t

• Nest 6: b6 = b5 + mean GCaMP6f 0.8:0.99 s before current time = t

• Nest 7: b7 = b6 + mean GCaMP6f 0.6:0.79 s before current time = t

• Nest 8: b8 = b7 + mean GCaMP6f 0.4:0.59 s before current time = t

• Nest 9: b9 = b8 + mean GCaMP6f 0.2:0.39 s before current time = t

• Nest 10: b10 = b9 + GCaMP6 f signal at current time = t

Nesting the predictors from most distant in time to most recent permitted observation of the ability of more proximal signal levels to absorb the variance contributed by more distant signal history.

The fitted hazard function was then found as the average probability of being in the movement state across all trials in the session as calculated from the average model fit. Because s_t = 0 states were significantly downsampled during fitting, this rescaled the fit hazard. Thus, to return the fit hazard to the scale of the hazard function calculated from the behavioral distribution, both the fit hazard and true hazard function were normalized on the interval (0,1), and the goodness of fit was assessed by R² comparison of the fit and true hazard functions. This metric was similar between individual session fits as well as the grand-average fit across all animals and sessions.

To guard against overfitting, this procedure was repeated on the same datasets, except the datasets were shuffled before fitting to erase any non-chance correlations between the predictors and the predicted probability of being in the movement state.

All custom behavioral software is available at https://github.com/harvardschoolofmouse/HSOMbehaviorSuite (Hamilos, 2021a, copy archived at swh:1:rev:5a9b981afb658cfc05277b1a257e1733f274c9a2). All custom analysis tools are available with sample datasets at https://github.com/harvardschoolofmouse/eLife2021 (Hamilos, 2021b, copy archived at swh:1:rev:fa4b2cdfd6d6a55b82124f86d2599faebccd4eee).

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We thank D Chicharro, JG Mikhael, SJ Gershman, J Drugowitsch, K Reinhold, S Panzeri, R Bliss and EN Brown for discussions on analytical methods; J Tenenbaum, C Wong, and A Lew for their instruction and advice pertaining to probabilistic programming in Gen; V Berezovskii, J LeBlanc, T LaFratta, O Mazor, P Gorelik, J Markowitz, A Lutas, KW Huang, L Hou, SJ Lee and NE Ochandarena for technical assistance; and B Sabatini, C Harvey, SR Datta, M Andermann, L Tian and W Regehr for reagents. The work was supported by NIH grants UF-NS108177 and U19-NS113201, and NIH core grant EY-12196. AEH was supported by a Harvard Lefler Predoctoral Fellowship and a Stuart HQ & Victoria Quan Predoctoral Fellowship at Harvard Medical School. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

All experiments and protocols were approved by the Harvard Institutional Animal Care and Use Committee (IACUC protocol #05098, Animal Welfare Assurance Number #A3431-01) and were conducted in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals. Surgeries were conducted under aseptic conditions with isoflurane anesthesia, and every effort was taken to minimize suffering.

© 2021, Hamilos et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.