Feeling anxious can hinder how well someone performs a task, a phenomenon that is sometimes called “choking under pressure”. Anxiety may also impair a person’s ability to learn a new manual task, like juggling or playing the piano; however, it remains unclear exactly how this happens.

People learn manual tasks more quickly if they can practice first, and the more someone varies their movements during these trial runs, the faster they learn afterwards. Yet, anxiety can affect movement; for example, anxious people often make repetitive motions like hand-wringing or fidgeting. There is also evidence that very anxious people may learn less from the outcomes of their actions.

To understand how anxiety may affect the learning of manual tasks, Sporn et al designed experiments where people learned to play a short sequence of notes on a piano. The main experiment involved 60 participants and was split over two phases. In the first ‘exploration’ phase, participants had to play the piano sequence using any timing they liked and were encouraged to explore different rhythms. In the second ‘learning’ phase, participants were rewarded with a higher score the closer they got to playing the notes with a certain rhythm, without being told that this was their specific goal.

To see how anxiety affected performance, the participants were split into three groups. One group were told in the initial exploration phase that they would give a public talk after they completed the piano task, which reliably made them more anxious. A second group were told about the anxiety-inducing public speaking only during the learning phase; while a third group – the controls – were not aware of any public speaking task.

People in the second group could learn the rhythm as well as the controls. Participants who were made anxious during the exploration phase, however, scored fewer points and were less likely to learn the piano sequence in the second phase. They also varied their movements less in the first phase.

As a follow-up, Sporn et al. repeated the experiment with 26 people but without the initial exploration phase. This time the anxious participants were less able to learn the piano sequence and scored fewer points. This suggests that the initial exploration in the previous experiment had enabled later anxious participants to succeed in the learning phase despite being anxious.

Finally, Sporn et al. also used a technique called electroencephalography (or EEG for short) to record brain activity and observed differences in participants with and without anxiety, particularly when they received their scores. The EEG signals showed that anxiety altered rhythmic patterns of brain activity called “sensorimotor beta oscillations”, which are known to be involved in both movement and learning.

Anxiety involves anticipatory changes in physiological and psychological responses to an uncertain future threat (Grupe and Nitschke, 2013; Bishop, 2007). Previous studies have established that trait anxiety interferes with prefrontal control of attention in perceptual tasks, whereas state anxiety modulates the amygdala during detection of threat-related stimuli (Bishop, 2007; Bishop, 2009). An emerging literature additionally identifies the dorsomedial and dorsolateral prefrontal cortex (dmPPC and dlPFC) and the dorsal anterior cingulate cortex (dACC) as central brain regions modulating sustained anxiety, both in subclinical and clinical populations (Robinson et al., 2019).

Computational modeling work has started to examine the mechanisms through which anxiety might impair learning, revealing that individuals with high trait anxiety do not correctly estimate the likelihood of outcomes during aversive or reward learning in uncertain environments (Browning et al., 2015; Huang et al., 2017; Pulcu and Browning, 2019). In the area of motor control, research has shown that stress and anxiety have detrimental effects on performance (Baumeister, 1984; Beilock and Carr, 2001). These results have been interpreted as anxiety interferring with information-processing resources, and as a shift towards an inward focus of attention and an increase in conscious processing of movement (Eysenck and Calvo, 1992; Pijpers et al., 2005). The effects of anxiety on motor learning are, however, often inconsistent, and a mechanistic understanding of these effects is still lacking. Delineating mechanisms through which anxiety influences motor learning is important to ameliorate the impact of anxiety in different settings, including in motor rehabilitation programs.

Motor variability could be one component of motor learning that is affected by anxiety; it is defined as the variation of performance across repetitions (van Beers et al., 2004), and is affected by various factors including sensory and neuromuscular noise (He et al., 2016). As a form of action exploration, movement variability is increasingly recognized to benefit motor learning (Todorov and Jordan, 2002; Wu et al., 2014; Pekny et al., 2015), particularly during reward-based learning, with discrepant effects in motor adaptation paradigms (He et al., 2016; Singh et al., 2016). These findings are consistent with the vast amount of research on reinforcement learning that demonstrates increased learning following initial exploration (Sutton and Barto, 1998; Olveczky et al., 2005).

Yet contextual factors can reduce variability. For instance, an induced anxiety state leads to ritualistic behavior, characterized by movement redundancy, repetition, and rigidity (Lang et al., 2015). This finding resembles the reduction in behavioral variability and exploration that manifests across animal species during phasic fear in reaction to certain imminent threats (Morgan and Tromborg, 2007). On the basis of these results, we set out to test the hypothesis that state anxiety modulates motor learning through a reduction in motor variability.

A second component that could be influenced by anxiety is the flexibility to adapt to changes in the task structure during learning. Individuals who are affected by anxiety disorders exhibit an intolerance of uncertainty, which contributes to excessive worry and emotional dysregulation (Ouellet et al., 2019). Turning to non-clinical populations, computational studies have established that highly anxious individuals exhibit difficulties in estimating environmental uncertainty both in aversive and reward-based tasks (Browning et al., 2015; Huang et al., 2017; Pulcu and Browning, 2019). Failure to adapt to volatile or unstable environments thus impairs learning of action-outcome contingencies in these settings. Accordingly, in the context of motor learning, and more specifically, in reward-based motor learning, we proposed that an increase in anxiety would affect individuals’ estimation of uncertainty about the stability of the task structure, such as the rewarded movement.

On the neural level, we posited that changes in motor variability are driven by activity in premotor and motor areas. Support for our hypothesis comes from animal studies demonstrating that variability in the primate premotor cortex tracks behavioral variability during motor planning (Churchland et al., 2006). Further evidence supports the hypothesis that changes in variability in single-neuron activity in motor cortex drive motor exploration during initial learning, and reduce it following intensive training (Mandelblat-Cerf et al., 2009; Santos et al., 2015). In addition, the basal ganglia are crucial for modulating variability during learning and production, as shown in songbirds and, indirectly, in patients with Parkinson’s disease (Kao et al., 2005; Olveczky et al., 2005; Pekny et al., 2015).

In the present study, we analyzed sensorimotor beta oscillations (13–30 Hz) as a candidate brain rhythm associated with the modulation of motor exploration and variability. Beta oscillations are modulated with different aspects of performance and motor learning (Herrojo Ruiz et al., 2014; Bartolo and Merchant, 2015; Tan et al., 2014), as well as in reward-based learning (HajiHosseini et al., 2012). Increases in sensorimotor beta power following movement have been proposed to signal greater reliance on prior information about the optimal movement (Tan et al., 2016), which would reduce the impact of new evidence on the update of motor commands. We therefore tested the additional hypothesis that changes in sensorimotor beta oscillations mediate the effect of anxiety on belief updates and the estimation of uncertainty driving reward-based motor learning. Crucially, in addition to assessing sensorimotor brain regions, we were interested in prefrontal areas because of prior work in clinical and subclinical anxiety linking the prefrontal cortex (dmPFC and dlPFC) and the dACC to the maintenance of anxiety states, including worry and threat appraisal (Grupe and Nitschke, 2013; Robinson et al., 2019). Thus, beta oscillations across sensorimotor and prefrontal electrode regions were evaluated.

Traditionally, the primary focus of research on oscillations was on power changes, although there is a renewed interest in assessing dynamic properties of oscillatory activity, such as the presence of brief bursts (Poil et al., 2008). Brief oscillation bursts are considered to be a central feature of physiological beta waves in motor-premotor cortex and the basal ganglia (Feingold et al., 2015; Tinkhauser et al., 2017; Little et al., 2018). Accordingly, we assessed both the power and burst distribution of beta oscillations to capture dynamic changes in neural activity that were induced by anxiety and their link to behavioral effects. To test our hypotheses, we recorded electroencephalography (EEG) in three groups of participants while they completed a reward-based motor sequence learning paradigm, with separate phases for motor exploration (without reinforcement) and reward-based learning (using reinforcement). We manipulated anxiety by informing participants about an upcoming public speaking task (Lang et al., 2015). Using a between-subject design, the anxiety manipulation targeted either the motor exploration or the reward-based learning phase. Analysis of the EEG signals aimed to assess anxiety-related changes in the power and burst distribution in sensorimotor and prefrontal beta oscillations in relation to changes in behavioral variability and reward-based learning.

Sixty participants completed our reward-based motor sequence learning task, consisting of three blocks of 100 trials each over two phases (Figure 1): an initial motor exploration (block1, termed exploration hereafter) and a reward-based learning phase (block2 and block3: termed learning hereafter). The rationale for including a motor exploration phase in which participants did not receive trial-based feedback or reinforcement was based on findings indicating that initial motor variability (in the absence of reinforcement) can influence the rate at which participants learn in a subsequent motor task (Wu et al., 2014). If state anxiety reduces the expression of motor variability during the exploration phase, subsequent motor learning would be affected.

Figure 1

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Prior to the experimental task, we recorded 3 min of EEG at rest with eyes open in each participant. Next, on a digital piano, participants played two different sequences of seven and eight notes during the exploration and learning phases, respectively (Figure 1B). The sequence patterns were designed so that the key presses would span a range of four neighboring keys on the piano. Participants were explicitly taught the tone sequences prior to the start of the experiment, yet precise instructions about the timing or loudness (keystroke velocity, Kvel) were not provided. The rationale for selecting two different sequences for the exploration and learning phases was to avoid carry-over effects of learning or a preferred performance pattern from the exploration period into the reward-based learning phase (following Wu et al., 2014).

During the initial exploration phase, participants were informed that they could freely change the pattern of temporal intervals between key presses (inter-keystroke intervals, IKIs) and/or the loudness of the performance in every trial, and that no reward or feedback would be provided. During learning, performance-based feedback in the form of a 0–100 score was provided at the end of each trial. Participants were informed that the overall average score would be translated into monetary reward. They were directly instructed to explore the temporal or loudness dimension (or both) and to use feedback scores to discover the unknown performance objective (which, unbeknownst to them, was related to the pattern of IKIs). The task-related dimension was therefore timing, whereas keystroke velocity was the non-task related dimension.

The performance measure that was rewarded during learning was the vector norm of the pattern of temporal differences between adjacent IKIs (see 'Materials and experimental design'). Different combinations of IKIs could lead to the same rewarded norm of IKI-difference values, and therefore to the same score. Participants were unaware of the existence of these multiple solutions. The multiplicity in the mapping between performance and score could lead participants to perceive an increased level of volatility in the environment (changes in the rewarded performance over time). This motivated us to assess their estimation of volatility during reward-based learning and its modulation by anxiety. In addition, we investigated whether higher initial variability would lead to higher scores during subsequent reward-based learning, independently of changes in variability during this latter phase. If initial exploration improves learning of the mapping between the actions and their sensory consequences (even without external feedback), then participants could learn better from performance-related feedback during the learning phase regardless of their use of variability in this phase. Alternatively, it could be that participants who also use more variability during learning discover the hidden goal by chance.

Participants were pseudo-randomly allocated to either a control group or to one of two experimental groups (Figure 1C): anxiety during exploration (anx1); and anxiety during the first block of learning (anx2). We measured changes in heart-rate variability (HRV) and heart-rate (HR) four times throughout the experimental session: resting state (3 min, prior to performance blocks); block1; block2; and block3. In addition, the state subscale from the State-Trait Anxiety Inventory (STAI, state scale X1, 20 items; Spielberger, 1970) was assessed four times: prior to the resting state recording and also immediately before the beginning of each block, and thus after the induction of anxiety in the experimental groups. The HRV index and STAI state anxiety subscale were able to dissociate in each experimental group between the phase targeted by the anxiety manipulation and the initial resting phase (within-group effects, see statistical results in Figure 2). In addition, significant between-group differences in HRV (not in STAI) further confirmed the specificity of the HRV changes in the targeted blocks (statistical details in Figure 2). These results confirmed that the experimental manipulation succeeded in inducing physiological and psychological responses within each experimental group that were consistent with an anxious state during the targeted phase, as reported previously (Feldman et al., 2004).

Figure 2

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Statistical analysis of behavioral and neural measures focused on the separate comparison between each experimental group and the control group (contrasts: anx1 – controls, anx2 – controls). See 'Materials and methods'.

Behavioral results

Lower initial task-related variability is associated with poorer reward-based learning

All groups of participants demonstrated significant improvement in the achieved scores during reward-based learning, confirming that they effectively used feedback to approach the hidden target performance (changes in average score from block2 to block3 — anx1: p=0.008, non-parametric effect size estimator for dependent samples, ${\mathrm{\Delta }}_{dep}$ = 0.93, 95% confidence interval, termed simply CI hereafter, CI = [0.86, 0.99]; anx2: p=0.004, ${\mathrm{\Delta }}_{dep}$ = 0.83, CI = [0.61, 0.95]; controls: p=0.001, ${\mathrm{\Delta }}_{dep}$ = 0.92, CI = [0.72, 0.98]).

Assessment of motor variability was performed separately in the task-related temporal dimension and in the non-task-related keystroke velocity dimension. Temporal variability—and similarly for Kvel variability—was estimated using the across-trials coefficient of variation of IKI (termed cvIKI hereafter; Figure 3A–B). This index was computed in bins of 25 trials, which therefore provided four values per experimental block. We hypothesized that in the total population, a higher degree of task-related variability during the exploration phase (that is, playing different temporal patterns in each trial), and therefore higher cvIKI, would improve subsequent reward-based learning, as this latter phase rewarded the temporal dimension. A non-parametric rank correlation analysis across the 60 participants revealed that participants who achieved higher scores in the learning phase exhibited a larger across-trials cvIKI during the exploration period (Spearman $\rho =0.45,P=0.003$; Figure 3C).

Figure 3

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A similar result was obtained when excluding anx1 participants from the correlation analysis, supporting the hypothesis that in the subsample of 40 participants who did not undergo the anxiety manipulation during exploration there was a significant association between the level of task-related variability and the subsequent score ($\rho =0.41,P=0.04$). No significant rank correlation was found between the scores and cvKvel ($P>0.05$).

We also assessed whether the degree of cvIKI during learning was associated with the average score and found an inverted pattern: there was a significant negative non-parametric rank correlation between the cvIKI index and the mean score ($\rho =-0.44,P=0.002$; Figure 3D). No significant effect was found for the cvKvel parameter ($P>0.05$).

Notably, the amount of variability in timing and keystroke velocity used by participants was not correlated (cvIKI and cvKvel during initial exploration: $\rho =0.021,P=0.788$, and during learning: ${\displaystyle \rho =-0.030,P=0.844}$). This indicates that in our task, participants could vary the temporal and velocity dimensions separately. On the other hand, however, the generally lower cvKvel values in all blocks and groups further indicate that participants may not have been able to substantially vary this dimension. Finally, the degree of cvIKI during the learning and exploration phases were not correlated ($\rho =0.029,P=0.848$). These findings suggest that achieving higher scores during reward-based learning in our paradigm cannot be accounted for by a general tendency towards more exploration throughout all experimental blocks. In fact, larger sustained task-related variability during learning was detrimental to maintaining the performance close to the inferred target (Figure 3D).

Anxiety during initial exploration reduces task-related variability and impairs subsequent reward-based learning

Next, we assessed pair-wise differences in the behavioral measures between the control group and each experimental group (anx1 and anx2) separately. Participants who were affected by state anxiety during initial exploration (anx1) achieved significantly lower scores in the subsequent reward-based learning phase relative to control participants (Figure 4A: $P<0.05$ after controlling the false discovery rate [FDR] at level $q=0.05$ due to multiple comparisons, termed $P_{FDR}$ thereafter; $\mathrm{\Delta }=0.78,CI=[0.54,0.92]$). By contrast, in the anx2 group scores did not statistically differ from the scores in the control group ($P_{FDR}>0.05$). A planned comparison between both experimental groups demonstrated significantly higher scores in anx2 than in anx1 ($P_{FDR}<0.05,\mathrm{\Delta }=0.67,CI=[0.51,0.80]$).

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During the initial exploration block, anx1 used a lower degree of cvIKI than the control group (Figure 4B; $P_{FDR}<0.05;\mathrm{\Delta }=0.67,CI=[0.52,0.85]$). There was no between-groups (anx1, controls) difference in cvKvel (Figure 4C; $P_{FDR}>0.05$). Performance in anx2 in this phase did not significantly differ from performance in the control group, either for cvIKI or for cvKvel ($P_{FDR}>0.05$).

Subsequently, during the learning blocks, there were no significant between-group differences in cvIKI or cvKvel ($P_{FDR}>0.05$). In each group, there was a significant drop in the use of temporal variability from the first to the second learning block, corresponding to a transition from exploration to the exploitation of the rewarded options (significant drop in cvIKI from block2 to block3 in control, anx1, and anx2 participants; $P_{FDR}<0.05$; effect size — ${\mathrm{\Delta }}_{dep}=0.77,CI=[0.53,0.87]$ in controls; ${\mathrm{\Delta }}_{dep}=0.55,CI=[0.50,0.61]$ in anx1; ${\mathrm{\Delta }}_{dep}=0.83,CI=[0.62,0.94]$ in anx2). This outcome further indicated that all groups successfully completed the reward-based learning task, although anx1 participants achieved lower scores than the reference control group.

Detailed analyses of the trial-by-trial changes in scores and performance using a Bayesian learning model and their modulation by anxiety are reported below. General performance parameters, such as the average performance tempo or the mean keystroke velocity did not differ between groups, either during initial exploration or learning ($P>0.05$). Participants completed sequence1 in 3.0 (0.1) seconds on average, between 0.68 (0.05) and 3.68 (0.10) s after the GO signal (non-significant differences between groups, $P>0.05$). During learning, they played sequence2 with an average duration of 4.7 (0.1) s, between 0.72 (0.03) and 5.35 (0.10) s (non-significant differences between groups, $P>0.05$). The mean learned solution was not significantly different between groups, either during the first or second learning block ($P>0.05$; Figure 4—figure supplement 1; but see trial-by-trial changes below).

These outcomes demonstrate that in our paradigm, state anxiety reduced task-related motor variability when induced during the exploration phase and this effect was associated with lower scores during subsequent reward-based learning. State anxiety, however, did not modulate task-related motor variability or the scores achieved when induced during reward-based learning. Finally, the different experimental manipulations did not affect the mean learned solution in each group.

State anxiety during reward-based learning reduces learning rates if there is no prior exploration phase

Because anx2 participants performed at a level that was not significantly different from that found in control participants during learning, we asked whether the unconstrained motor exploration during the initial phase might have counteracted the effect of anxiety during learning blocks. Alternatively, it could be that the anxiety manipulation was not salient enough in the context of reward-based learning. To assess these alternative scenarios, we performed a control behavioral experiment with new experimental (anx3) and control groups (N = 13 each, see sample size estimation in 'Materials and methods'). Participants in each group performed the two learning blocks 2 and 3 (Figure 1C), but without completing a preceding exploration block. In anx3, state anxiety was induced exclusively during the first learning block, as in the original experiment. We found that the HRV index was significantly reduced in anx3 relative to controls during the manipulation phase ($P_{FDR}<0.05,\mathrm{\Delta }=0.72,CI=[0.62,0.83]$), but not during the final learning phase (block3, $P_{FDR}>0.05$). STAI state subscale scores rose during the anxiety manipulation in anx3 (but not in controls) relative to the initial scores (within-group effect, $P_{FDR}<0.05,\mathrm{\Delta }=0.68,CI=[0.59,0.78]$).

Overall, the anx3 group achieved a lower average score (and final monetary reward) than control participants ($P=0.0256;\mathrm{\Delta }=0.64,CI=[0.50,0.71]$). In addition, anx3 participants achieved significantly lower scores than control participants during the first learning block ($P_{FDR}<0.05,\mathrm{\Delta }=0.68,CI=[0.54,0.79]$, Figure 4D), but not during the second learning block ($P_{FDR}>0.05$). Notably, however, the degree of cvIKI or cvKvel did not differ between groups ($P_{FDR}<0.05$, Figure 4E–F). The mean performance tempo, loudness and the mean learned solution during learning did not differ significantly between groups, as in the main experiment ($P>0.05$). Thus, removal of the initial exploration phase led to the impairment of reward-based learning by the anxiety manipulation, and this effect was not associated with a change in the use of task-related variability or in general average performance parameters.

Bayesian learning modeling reveals the effects of state anxiety on reward-based motor learning

To assess our hypotheses regarding the mechanisms underlying participants’ performance during reward-based learning, we used several versions of a Bayesian learning model, which were based on the two-level hierarchical Gaussian filter for continuous input data (HGF; Mathys et al., 2011; Mathys et al., 2014). The HGF was introduced by Mathys et al., 2011 to model how an agent infers a hidden state in the environment (a random variable), $x_1$, as well as its rate of change over time ($x_2$, environmental volatility). This corresponds to a perceptual model, which is further coupled with a response model to generate responses based on those inferred states. In the two-level HGF, beliefs about those hierarchically related hidden states ($x_1,x_2$) are continuous variables evolving as Gaussian random walks coupled through their variance. Their value (${\displaystyle x_i,i=1,2}$) at trial ${\displaystyle k}$ will be normally distributed around their previous value at trial ${\displaystyle k-1}$ . Thus, the posterior distribution of beliefs about these states is fully determined by the sufficient statistics ${\displaystyle {\mu }_i}$ (mean) and ${\displaystyle {\sigma }_i}$ (variance, representing estimation uncertainty). Beliefs are updated given new sensory input via prediction errors (PEs). In some implementations of the HGF, the series of sensory inputs are replaced by a sequence of outcomes, such as reward value in a binary lottery (Mathys et al., 2014; Diaconescu et al., 2017) or electric shock delivery in a one-armed bandit task (de Berker et al., 2016). In these cases, similarly to the case of sensory input, an agent can learn the causes of the observed outcomes and thus the likelihood that a particular event will occur. In our study, the trial-by-trial input observed by the participants was the series of feedback scores (hereafter input refers to feedback scores). Crucial to the HGF is the weighting of the PEs by the ratio between the estimation uncertainty of the current level and the lower level, or the inverse ratio when using precision (inverse variance or uncertainty of a distribution). Further details are provided in the 'Materials and methods'.

Different implementations of the HGF have recently been used in combination with neuroimaging data to investigate how the brain processes different types of hierarchically-related prediction errors (PEs) within the framework of predictive coding (Diaconescu et al., 2017; Weber et al., 2019). The HGF can be fit to the behavioral data from each individual participant, thus providing dynamic trial-wise estimates of belief updates that depend on hierarchical PEs weighted by precision (precision-weighted PE or pwPE). In predictive coding models, precision is viewed as crucial for representing uncertainty and updating the posterior expectations about the hidden states (Sedley et al., 2016). In the HGF, time-varying pwPEs reflect how participants learn stimulus-outcome or response-outcome associations and their changes over time (Mathys et al., 2014; Diaconescu et al., 2017).

Here, we adapted the HGF to model participants’ estimation of quantity $x_1$, which represented their beliefs about the expected reward (input score, normalized 0–1) for the current trial. Beliefs about ${\displaystyle x_1}$ on trial ${\displaystyle k}$ were thus determined by the expectation of reward ${\displaystyle {\mu }_1^k}$ (mean of the posterior distribution of ${\displaystyle x_1}$) and the uncertainty about this estimate (variance, ${\displaystyle {\sigma }_1^k}$). The model also estimated participants' beliefs about environmental volatility ${\displaystyle x_2}$, related to changes in the reward tendency and determined by (${\displaystyle {\mu }_2^k,{\sigma }_2^k}$) on trial ${\displaystyle k}$. The belief trajectories about the external states $x_1$ and $x_2$ generated by the model were further used to estimate the most likely response corresponding with those beliefs. A schematic illustrating the model structure and the belief trajectories is shown in Figure 5.

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Assessment of the HGF for simulated responses revealed that the expectation of volatility (change in reward tendency) was higher in agents that modulated their performance to a greater extent across trials and thereby observed a broader range of feedback scores (see different examples for simulated performances in Figure 5—figure supplement 1).

Table 1

	Prior mean	Prior variance
log($\kappa$)	log(1)	0
${\omega }_1$	log-variance of 1:20 input scores: −3.04	16
${\omega }_2$	–4	16
log(${\pi }_u^0$)	negative log-variance of 1:20 input scores: 3.04	4
${\mu }_1^0$	value of the first input score: 0.21	variance of 1:20 input scores: 0.05
log(${\sigma }_1^0$)	log-variance of 1:20 input scores: −3.04	1
${\mu }_2^0$	1	0
log(${\sigma }_2^0$)	log(0.01)	1
${\beta }_0$	individual mean of behavioral parameter	4
${\beta }_1$	0	4
${\beta }_2$	0	4

We implemented eight versions of the HGF with different response models. The response model defines the mapping from the trajectories of perceptual beliefs onto the observed responses of each participant. We were interested in how HGF quantities on the previous trial explained changes in performance on the subsequent trial. To assess that relationship, we considered two scenarios characterized by the choice of a different performance measure in the response model. The performance measures used were: (1) the trialwise coefficient of variation of consecutive IKI values (cv across sequence positions; termed ${\mathrm{cvIKI}}_{\mathrm{trial}}$ to dissociate it from the measure of across-trials variability, cvIKI); (2) the trialwise performance tempo (mean of IKI within the trial across sequence positions, termed ${\mathrm{mIKI}}_{\mathrm{trial}}$; here we used the logarithm of this measure in milliseconds, $\log ({\mathrm{mIKI}}_{\mathrm{trial}})$, as in Marshall et al. (2016). Accordingly, we constructed two families of models describing the link between a participant’s inferred perceptual quantities on the previous trial $k-1$ and their changes from trial $k-1$ to $k$ in one of those performance measures:

$\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}={\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}-{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}-1}$

${\displaystyle \mathrm{\Delta }\mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{m}\mathrm{I}\mathrm{K}{\mathrm{I}}_{\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}{)}^{\mathrm{k}}=\mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{m}\mathrm{I}\mathrm{K}{\mathrm{I}}_{\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}^{\mathrm{k}})-\mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{m}\mathrm{I}\mathrm{K}{\mathrm{I}}_{\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}^{\mathrm{k}-1})}$

Variable ${\mathrm{cvIKI}}_{\mathrm{trial}}$ was chosen because it is tightly linked to the variable associated with reward: higher differences in IKI values between neighboring positions lead not only to a higher vector norm of IKI patterns but also to a higher coefficient of variation of IKI values in that trial (and indeed ${\mathrm{cvIKI}}_{\mathrm{trial}}$ was positively correlated with the feedback score across participants, nonparametric Spearman ${\displaystyle \rho =0.69,P<{10}^{-5}}$). Alternatively, we considered the scenario in which participants would speed or slow down their performance without altering the relationship between successive intervals. Therefore, we used a performance measure related to the mean tempo, mIKI. We did not choose a performance measure associated with keystroke velocity because our results in the previous sections demonstrate that participants did not consistently modulate cvKvel across trials—either because they realized that this parameter was non-task-related or because they were not able to substantially vary the loudness of the key press. Similarly to Marshall et al. (2016), in each family of models we defined four types of response models to explain the performance measure as a linear function of relevant HGF perceptual parameters on the previous trial, such as the expectation of reward (${\mu }_1$) or volatility (${\mu }_2$) and the pwPEs on these estimates (labeled ${ϵ}_1$ and ${ϵ}_2$, respectively; see Equation 14 and Equation 15). One example is illustrated here:

$\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}={\beta }_0+{\beta }_1{\mu }_1^{k-1}+{\beta }_2{ϵ}_1^{k-1}+\zeta$

where ${\beta }_0$ represents a constant value (intercept) and $\zeta$ is a Gaussian noise variable. Details on the alternative models are provided in the 'Materials and methods' section.

In each model, the feedback scores and the performance measure at each trial $k$ were used to update model parameters, and the log model-evidence was used to optimize the model fit (Diaconescu et al., 2017; Soch and Allefeld, 2018). More details on the modeling approach can be found in the 'Materials and methods' section and in Figure 5.

Between-group comparison focused on four variables, the mean trajectories of perceptual beliefs (${\mu }_1$ and ${\mu }_2$, means of the posterior distributions for $x_1$ and $x_2$; Figure 5), and the uncertainty about those beliefs (variance of the posterior distributions, ${\sigma }_1$ and ${\sigma }_2$; note that the inverse variance is the precision, termed ${\pi }_1$ and ${\pi }_2$, corresponding with the confidence placed on those beliefs). As indicated above, volatility estimates are related to the rate of change in reward estimates, and accordingly we predicted a higher expectation of volatility ${\mu }_2$ for participants exhibiting more variation in ${\mu }_1$ values. In addition, the perceptual model parameters ${\omega }_1$ and ${\omega }_2$, which characterize the learning style of each participant (see Figure 5—figure supplement 2), and the parameters ${\beta }_0,{\beta }_1,{\beta }_2,\zeta$, characterizing the response model, were contrasted between groups.

Random Effects Bayesian Model Selection (BMS) was used to assess at the group level (N = 60) the different models of learning (Stephan et al., 2009); code freely available from the MACS toolbox, (Soch and Allefeld, 2018). First, the models were grouped into two families corresponding with each performance measure ($\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$ and $\mathrm{\Delta }\log ({\mathrm{mIKI}}_{\mathrm{trial}})$). The log-family evidence (LFE) was calculated from the log-model evidence (LME). BMS then determined which family of models provided more evidence. In the winner family, additional BMS determined the final optimal model. BMS provided stronger evidence for the family of models defined for $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$, with an exceedance probability of 1, and an expected frequency of 0.9353 (similar values in experimental and control groups). Next, among all four models in that family, the winning model (exceedance probability 1, model frequency 0.8614) explained the performance measure $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$ as a linear function of the pwPE relating to reward, ${ϵ}_1$, and volatility, ${ϵ}_2$, on the previous trial:

(2) $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}={\beta }_0+{\beta }_1{ϵ}_1^{k-1}+{\beta }_2{ϵ}_2^{k-1}+\zeta$

The ${\beta }_0$ and ${\beta }_1$ coefficients were significantly different than zero in each experimental and control group ($P_{FDR}<0.05$, controlled for multiple comparisons arising from three group tests; Figure 5—figure supplement 3). On average, ${\beta }_0$ was positive, and ${\beta }_1$ was negative. By contrast, ${\beta }_2$ was positive in the control group yet negative in the anx1 and anx2 groups ($P_{FDR}<0.05$). Because pwPEs directly modulate the update in the expectation of beliefs, these findings imply that smaller pwPEs relating to reward on the previous trial (smaller update in the expectation of reward at $k-1$) were associated in all groups with increases in ${\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}$ for the next trial. On the other hand, a negative ${\beta }_1$ also indicates that larger pwPE for reward on the previous trial decreased changes in the performance variable on the following trial. In addition, exclusively in control participants, there was a positive association between larger pwPE relating to volatility at $k-1$ (greater update in the expectation on volatility on the last trial) and a follow-up increment in ${\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}$. In anx1 and anx2 participants, however, trials of larger pwPE driving updates on volatility were followed by reduced changes in trial-wise temporal variability. The results imply that a larger increase in the expectation of volatility on the previous trial promoted larger subsequent changes in the relevant performance variable in control participants (Figure 5—figure supplement 4), whereas in anx1 and anx2, it led to reductions in task-related behavioral changes (Figure 5—figure supplement 5).

The HGF and the winning response model provided a good fit to the behavioral data from each group, as shown in the examination of the residuals (Figure 5—figure supplement 6). Further, there were no systematic differences in the model fits across groups (trial-averaged residuals were compared between each experimental and control group with permutation tests; $P>0.05$ in both comparisons; $P=0.1598$ for anx1 and control groups; $P=0.5646$ for anx2 and control groups). The low mean residual values further indicate that the model captured the fluctuations in data well (trial-averaged residuals and SEM: $0.0004[0.00095]$ in controls; $-0.001[0.0013]$ in anx1; and $0.0003[0.0003]$ in anx2).

Using the winning model, we next evaluated between-group differences in the mean trajectories of perceptual beliefs and their uncertainty throughout learning (Figure 6A–C). Participants in the anx1 relative to the control group had a lower estimate of the mean tendency for $x_1$ ($P_{FDR}<0.05,\mathrm{\Delta }=0.75,CI=[0.59,0.89]$). This indicates a lower expectation of reward in the current trial. Note that this outcome could be anticipated from the behavioral results shown in Figure 4A. The expectation on log-volatility was significantly smaller in anx1 than in control participants ($P_{FDR}<0.05,\mathrm{\Delta }=0.71,CI=[0.60,0.81]$). This quantity was also partly reduced in the anx2 group relative to the control group ($P_{FDR}<0.05,\mathrm{\Delta }=0.69,CI=[0.53,0.75]$). In addition, the uncertainty about environmental volatility, ${\sigma }_2$, was larger in the anx1 and anx2 participants when compared to control participants (control relative to anx1, $P_{FDR}<0.05$, $\mathrm{\Delta }=0.71,CI=[0.65,0.89]$; control relative to anx2, $P_{FDR}<0.05$, $\mathrm{\Delta }=0.65,CI=[0.52,0.86]$). Because larger estimation uncertainty on the current HGF level contributes toward larger steps in the update equations for that level (due to larger precision weights on the PEs, Equation 5), this last outcome suggests that anx1 and anx2 participants updated their estimates of environmental volatility with larger steps (albeit in a negative direction as indicated by the negative slope of the underlying trends in Figure 6C, reducing ${\mu }_2$). No differences between anx2 and control participants in the ${\mu }_1$ estimates were found. Neither did we obtain between-group differences in ${\sigma }_1$.

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To understand why anx2 did not substantially differ from the control group in their expectation of reward yet had significantly lower volatility estimates (resembling those of the anx1 group), we looked more closely at Figure 5—figure supplement 1. This figure shows the HGF trajectories for perceptual beliefs and related quantities for a series of simulated responses. The results indicate that lower expectation of volatility can result from a smaller variance in the distribution of observed feedback scores, but also from a behavior characterized by smaller changes from trial to trial in the performance variable ($\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$). Accordingly, as a post-hoc analysis, we tested whether anx2 participants had smaller variance in the distribution of feedback scores when compared to control participants. This was the case (means [SEM]) were 0.064 [0.004] in control participants and 0.052 [0.003] in anx2, $P_{FDR}<0.05$). Anx1 participants also contributed to a similar effect (means [SEM] were 0.051 [0.002], $P_{FDR}<0.05$, smaller in anx1 than in the control group). Furthermore, anx2 participants had, on average, smaller $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$ values than the control group (means [SEM] were 0.005 [0.0011] in controls and 0.0032 [0.0007] in anx2, $P_{FDR}<0.05$). The same results were obtained for the anx1 group (0.0013 [0.0009], $P_{FDR}<0.05$). Thus, anx2 participants achieved high scores, as did control participants, yet they observed a reduced set of scores. In addition, their task-related behavioral changes from trial to trial were more constrained. These smaller trial-to-trial behavioral changes in anx2 indicated a tendency to exploit their inferred optimal performance, leading to consistently high scores. This different strategy of successful performance ultimately accounted for the reduced estimation of environmental volatility in this group, and contrasted with the higher ${\mu }_2$ values obtained in control participants.

As an additional post-hoc analysis, and based on the insights obtained from Figure 5—figure supplement 1, we assessed in the total population whether volatility estimates were associated with the change in performance variable $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$ or with the variance of the distribution of feedback scores. There was only a small yet significant non-parametric correlation between the HGF log-volatility estimates ${\displaystyle {\mu }_2}$ and the variance of the distribution of feedback scores across the 200 trials (Spearman $\rho =0.3029,P<0.0190$, Figure 6—figure supplement 1). This outcome suggests that participants who encountered more variable feedback scores in association with their performance also had a higher expectation of volatility.

Along with the above-mentioned group effects on relevant expectation and uncertainty trajectories, we found significant differences between anx1 and control participants in the perceptual parameter ${\omega }_2$ (mean and SEM values: −5.2 [0.50] in controls, −3.6 [0.49] in anx1; $P_{FDR}<0.05$), but not in ${\omega }_1$ (−4.8 [0.72] in controls, −4.8 [0.52] in anx1; $P>0.05$). Parameter ${\omega }_2$ modulates the rate at which volatility changes, with higher values—as obtained in anx1 participants—leading to sharper and more pronounced steps of update in volatility (Figure 5—figure supplement 2C). This can also be described as a different learning style (Weber et al., 2019). Participants in the anx2 group did not differ from control participants in ${\omega }_1$ (−4.1 [0.47], $P>0.05$) or ${\omega }_2$ (−4.0 [0.74], $P>0.05$).

In the second experiment, in which anx3 participants demonstrated a pronounced drop in scores relative to those of control participants during the anxiety manipulation, we found that on the group level, the winning family of models was also the one associated with the performance parameter $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}$ (model frequency 0.8747 and exceedance probability of 1). Further, the best individual model within that family was the one that explained $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}$ as a function of ${ϵ}_1^{k-1}$ and ${ϵ}_2^{k-1}$ (exceedance probability of 1, and model frequency of 0.9051). Between-group comparisons in relevant model parameters demonstrated that, like anx1 participants in the main study, anx3 participants in this control experiment had a lower estimate of the mean tendency for $x_1$ ($P_{FDR}<0.05,\mathrm{\Delta }=0.80,CI=[0.68,0.95]$; Figure 6D–F), and also had a reduced expectation on environmental volatility ($P_{FDR}<0.05,\mathrm{\Delta }=0.67,CI=[0.55,0.76]$). In addition, the anxiety manipulation led participants to have higher uncertainty about their phasic volatility estimates relative to control participants ($P_{FDR}<0.05,\mathrm{\Delta }=0.65,CI=[0.51,0.77]$). No differences in the uncertainty about estimates for $x_1$ were found. The perceptual parameters ${\omega }_1$ and ${\omega }_2$ did not differ between groups ($P>0.05$; average values of ${\omega }_1$ and ${\omega }_2$ were −4.9 [SEM 0.32] and −3.4 [0.41] in the control group, and −5.6 [0.39] and −4.4 [0.44] in the anx3 group). Last, among all response parameters, ${\beta }_0,{\beta }_1,{\beta }_2,\zeta$, we found that exclusively ${\beta }_2$ (modulating the impact of ${ϵ}_2^{k-1}$ on $\mathrm{\Delta }{\mathrm{cvIKI}}_{\mathrm{trial}}^{\mathrm{k}}$) was significantly different between groups (larger in control participants; $P=0.041,\mathrm{\Delta }=0.68,CI=[0.55,0.76]$). Converging with the main experiment, parameters ${\beta }_0$ and ${\beta }_1$ were on average positive and negative, respectively, in each group.

Electrophysiological analysis

The analysis of the EEG signals focused on sensorimotor and prefrontal (anterior) beta oscillations and aimed to assess separately (i) tonic and (ii) phasic (or event-related) changes in spectral power and burst rate. Tonic changes in average beta activity would be an indication that the anxiety manipulation had an effect on the general modulation of underlying beta oscillatory properties. Complementing this analysis, assessment of the phasic changes in the measures of beta activity during trial performance and following feedback presentation allowed us to investigate the neural processes that drive reward-based motor learning and their alteration by anxiety. These analyses focused either on all channels (tonic changes) or on a subset of channels across contralateral sensorimotor cortices and anterior regions (phasic changes; see statistical analysis details in 'Materials and methods').

State anxiety prolongs beta bursts and enhances beta power during exploration

We first looked at the general averaged properties of beta activity in this phase and their modulation by anxiety. The first measure we used was the standard averaged normalized power spectral density (PSD) of beta oscillations. Normalization of the raw PSD into decibels (dB) was carried out using the average PSD from the initial rest recordings (3 min) as reference. This analysis revealed a significantly higher beta-band power in a small contralateral sensorimotor region in anx1 participants relative to that in control participants during initial exploration ($P<0.025$, two-sided cluster-based permutation test, FWE-corrected; Figure 7—figure supplement 1). In anx2 participants, the beta power in this phase was not significantly different than that in controls (Figure 7—figure supplement 1, $P>0.05$). No significant between-group changes in PSD were found in lower (< 13Hz) or higher (> 30Hz) frequency ranges ($P>0.05$).

Next, we analyzed the between-group differences in the distribution of beta bursts extracted from the amplitude envelope of beta oscillations during initial exploration (Figure 7A). This analysis was motivated by evidence from recent studies suggesting that differences in the duration, rate, and onset of beta bursts could account for the association between beta power and movement in humans (Little et al., 2018; Torrecillos et al., 2018). To identify burst events and to assess the distribution of their duration, we applied an above-threshold detection method, which was adapted from previously described procedures (Poil et al., 2008; Tinkhauser et al., 2017; Figure 7B). In this analysis, we selected epochs locked to the GO signal at 0 s and extending up to 11 s. This interval included the STOP signal at 7 s and—in reward-based learning trials only—the feedback score at 9 s. Bursts extending for at least one cycle were selected. Using a double-logarithmic representation of the probability distribution of burst durations, we obtained a power law and extracted the (absolute) slope, $\tau$, also termed the ‘life-time’ exponent (Poil et al., 2008). Modeling work has revealed that a power law in the burst-duration distribution, reflecting the fact that the oscillation bursts have no characteristic scale, indicates that the underlying neural dynamics operate in a state close to criticality, and thus are beneficial for information processing (Poil et al., 2008; Chialvo, 2010).

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Crucially, because the burst duration, rate, and slope provide complementary information, we focused our statistical analysis of the tonic beta burst properties on the slope or life-time exponent, $\tau$. A smaller slope corresponds to a burst distribution that is biased towards more frequent long bursts.

In all of our participants, the double-logarithmic representation of the distribution of burst duration followed a decaying power-law with slope values $\tau$ in the range 1.4–1.9. The life-time exponents were smaller in the anx1 group than in the control group at left sensorimotor electrodes, corresponding with a long-tailed distribution (1.43 [0.30]; 1.70 [0.15]; $P_{FDR}<0.05,\mathrm{\Delta }=0.81,CI=[0.75,0.87]$). No differences in slope values $\tau$ were found between anx2 and control participants. The smaller life-time exponents in anx1 in sensorimotor electrodes were also reflected in a longer mean burst duration: 182 (10) ms in the anx1 group, 153 (2) ms in control participants (166 [6] ms in anx2 participants). The differences in slope in the distribution of burst duration in anx1 reflected the more frequent presence of long bursts ( $>500$ ms) and the less frequent brief bursts in this group relative to control participants (Figure 7D–E).

We next turned to our main goal and asked whether there were between-group differences in the beta oscillatory properties at specific periods throughout the initial exploration trials, above and beyond the general block-averaged changes reported above. The results in Figure 4 establish that state anxiety during the initial exploration phase reduced task-related motor variability, but also subsequently led to impaired reward-based learning. We therefore sought to assess whether the anxiety-related reduction in motor variability during exploration was associated with altered dynamics in beta-band oscillatory activity at specific time intervals during trial performance.

In anx1 participants, the mean beta power increased after completion of the sequence performance and further following the STOP signal, and these changes were significantly more pronounced than in control participants ($P_{FDR}<0.05,\mathrm{\Delta }=0.72,CI=[0.63,0.80]$; Figure 8A). This significant effect was localized to contralateral sensorimotor and right prefrontal channels. As a post-hoc analysis, the time course of the burst rate was assessed separately in beta bursts of shorter ($<300$ ms) and longer ($>500$ ms) duration, following the results from Figure 7 showing a pronounced dissociation between longer and brief bursts in the experimental and control groups. In addition, this split was motivated by previous studies linking longer beta bursts to detrimental performance (e.g. beta bursts longer than 500 ms in the basal ganglia of Parkinson’s disease patients are associated with worse motor symptoms; Tinkhauser et al., 2017).

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The rate of long oscillation bursts displayed a similar time course and topography to those of the power analysis, with an increased burst rate after movement termination and after the STOP signal in anx1 participants relative to control participants ($P_{FDR}<0.05,\mathrm{\Delta }=0.69,CI=[0.61,0.78]$; Figure 8B). By contrast, brief burst events were less frequent in anx1 than in control participants, albeit exclusively during performance ($P_{FDR}<0.05,\mathrm{\Delta }=0.74,CI=[0.65,0.82]$; Figure 8C). No significant effects were found when comparing any of these measures between anx2 and control participants.

Additional post-hoc control analyses were carried out to dissociate the separate effects of anxiety and motor performance on the time course of the beta-band oscillation properties during initial exploration. These analyses demonstrated that, when controlling for changes in motor variability, anxiety alone could explain the findings of larger post-movement beta-band PSD and rate of longer bursts, while also explaining the reduced rate of brief bursts during performance (Figure 8—figure supplement 1). Similar outcomes were found when controlling for changes in the mean total duration of the sequence (Figure 8—figure supplement 2), the variability of the sequence length (the coefficient of variation of sequence duration; Figure 8—figure supplement 3), and mean keystroke velocity (Figure 8—figure supplement 4).

Motor variability did also partially modulate the beta power and burst measures, after excluding anxious participants. This effect, however, had a small effect size and was limited to contralateral sensorimotor electrodes (Figure 8—figure supplement 5). In a last post-hoc analysis, we found that the average beta power following the STOP signal in those same significant sensorimotor electrodes was negatively correlated with the across-trials temporal variability, such that participants with a smaller increase in sensorimotor beta power after the STOP signal had a larger expression of task-related variability in this initial block (Spearman $\rho =-0.4397,P=0.0001$; Figure 8—figure supplement 6).

Reduced beta power and reduced presence of long beta bursts during feedback processing promotes the update of beliefs about reward

During learning, the general average level of PSD did not differ between groups ($P_{FDR}<0.05$; Figure 9—figure supplement 1A–C), neither was there a significant between-group difference in the scaling exponent of the distribution of beta-band oscillation bursts ($P_{FDR}>0.05$, Figure 9—figure supplement 1D–E; mean ${\displaystyle \tau }$ across contralateral and prefrontal electrodes: 1.78 [0.06] in control, 1.61 [0.10] in anx1, 1.70 [0.06] in anx2 group). The lack of significant between-group differences in these measures indicated that during reward-based motor learning, there were no pronounced tonic changes in average beta activity induced by the previous (anx1) or concurrent (anx2) anxiety manipulation.

Figure 4 had established that motor variability (or other motor output variables) did not differ in learning blocks between experimental and control groups, and therefore could not explain the significant and pronounced drop in scores in anx1 participants. Accordingly, we next aimed to assess whether alterations in the beta-band measures over time during trial performance or in feedback processing could account for that effect. In the anx1 group, the mean beta power increased towards the end of the sequence performance more prominently than in control participants, and this effect was significant in sensorimotor and prefrontal channels ($P_{FDR}<0.05,\mathrm{\Delta }=0.67,CI=[0.56,0.78]$; Figure 9A). A significant increase with similar topography and latency was observed in the anx2 group relative to control participants ($P_{FDR}<0.05,\mathrm{\Delta }=0.61,CI=[0.56,0.67]$). An additional and particularly pronounced enhancement in beta power appeared in anx1 and anx2 participants within 400—1600 ms following presentation of the feedback score. This post-feedback beta increase was significantly larger in anx1 than in the control group ($P_{FDR}<0.05,\mathrm{\Delta }=0.65,CI=[0.55,0.75]$; no significant effect in anx2, $P>0.05$).

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Further, we found that the time course of the beta burst rate exhibited a significant increase in anx1 participants relative to that in control participants within 400–1600 ms following feedback presentation, similar to the power results (Figure 9B; $P_{FDR}<0.05,\mathrm{\Delta }=0.82,CI=[0.70,0.91]$). The rate of brief oscillation bursts was, by contrast, smaller in anx1 than in control participants, albeit exclusively during performance and not during feedback processing (Figure 9C; $P_{FDR}<0.05,\mathrm{\Delta }=0.70,CI=[0.56,0.84]$). The significant effects in anx1 participants were observed in left sensorimotor and right prefrontal electrodes. There were no significant differences between anx2 and control groups in the rate of brief or long bursts throughout the trial ($P>0.05$).

To rule out the possibility that the feedback-related changes in beta activity were accounted for by concurrent movement-related artifacts (e.g. larger artifacts in anx1 than in control participants), we performed a control analysis of higher gamma band activity, which has been consistently associated with muscle artifacts in previous studies (Muthukumaraswamy, 2013). This control analysis found no evidence for movement artifacts affecting differently anx1 or control groups (Figure 9—figure supplement 2).

Having established that, relative to control participants, anx1 participants exhibited a phasic increase in beta activity and an increase in the rate of long bursts 400–1600 ms following feedback presentation, we next investigated whether these post-feedback beta changes could account for the altered reward and volatility estimates in the anx1 group (Figure 6). In the proposed predictive coding framework, superficial pyramidal cells encode PEs weighted by precision (precision-weighed PEs or pwPEs), and these are also the signals that are thought to dominate the EEG (Friston and Kiebel, 2009). A dissociation between high (gamma >30 Hz) and low (beta) frequency of oscillations has been proposed to correspond with the encoding of bottom-up PEs and top-down predictions, respectively (Arnal and Giraud, 2012). Operationally, however, beta oscillations have been associated with the change in predictions or expectations ($\mathrm{\Delta }{\mu }_i$) rather than with predictions themselves (Sedley et al., 2016). In the HGF, the update equations for ${\mu }_1$ and ${\mu }_2$ are determined exclusively by the pwPE term in that level, such that the change in predictions, $\mathrm{\Delta }{\mu }_i$, is equal to pwPE (see Equation 14 and Equation 15). Accordingly, we assessed whether the trialwise feedback-locked beta power or burst rate represented the magnitude of pwPEs in that trial that serve to update expectations on reward (${\mu }_1$) and environmental volatility (${\mu }_2$).

For each participant, we assessed simultaneously the effect of ${ϵ}_1$ and ${ϵ}_2$ on the trial-by-trial feedback-locked beta activity by running a multiple linear regression. These two regressors were not linearly correlated with each other (Pearson r coefficient in the total population was 0.1 on average [median = 0.1], and individual correlation p-values were $P>0.05$ in 80% of all participants). For the multiple linear regression analysis, trial-wise estimates of beta power (or burst rate) were averaged within 400–1600 ms following feedback presentation and across the sensorimotor and prefrontal electrodes where the post-feedback group effects were found (Figure 9). The results indicate that ${ϵ}_1$ had a significant negative effect on the measure of beta power (Figure 10; similarly for the rate of long bursts, see Figure 10—figure supplement 1), as ${\beta }_1$ was significantly smaller than zero in each group ($P_{FDR}<0.05$). In addition, the ${\beta }_1$ coefficient was decreased in anx1 relative to the control group ($P_{FDR}<0.05,\mathrm{\Delta }=0.72,CI=[0.57,0.81]$; there were no differences between anx2 and control group). Thus, a reduction in ${ϵ}_1$ contributed to an increase in post-feedback beta power and the rate of long beta bursts. The intercept also significantly differed between anx1 and control groups, with a larger coefficient representing a larger level of post-feedback beta power as found in anx1 ($P_{FDR}<0.05,\mathrm{\Delta }=0.69,CI=[0.55,0.75]$; no differences were obtained in anx2 relative to control participants). The ${\beta }_2$ coefficient modulating the contribution of ${ϵ}_2$ to beta activity was not different than 0 in any group ($P>0.05$). Accordingly, these results provide evidence for a pattern of neural oscillatory modulation that is associated with the updating of beliefs about reward. Furthermore, they link enhanced post-feedback beta activity—as found in anx1—to reduced pwPE about reward.

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The results revealed several interrelated mechanisms through which state anxiety impairs reward-based motor learning. First, state anxiety reduced motor variability during an initial exploration phase. This was associated with limited improvement in scores during subsequent learning. Second, the smaller change in the expectation of reward throughout time led to a decrease in the expectation of volatility. Along with those results, we observed an overestimation of uncertainty about volatility due to state anxiety, which promoted the drop in the volatility estimate. Additional computational results demonstrated that larger precision-weighted prediction errors relating to reward and volatility had the effect of constraining the trial-to-trial behavioral adaptations in state anxiety. This contrasted with the findings for volatility in control participants, where larger pwPE relating to this quantity promoted behavioral exploration.

On the neural level, anxiety during initial exploration was associated with elevated sensorimotor beta power and a distribution of bursts of sensorimotor beta oscillations with a longer tail (smaller scaling exponent). The latter result indicated a more frequent presence of longer bursts, resembling recent findings of abnormal burst duration in movement disorders (Tinkhauser et al., 2017). The anxiety-induced higher rate of long burst events and higher beta power during initial exploration also manifested in prefrontal electrodes and extended to the following learning phase, where phasic trial-by-trial feedback-locked increases in these measures accounted for the attenuated updating of expectation on reward. These results provide the first evidence that state anxiety induces changes in the distribution of sensorimotor and prefrontal beta bursts, as well as in beta power, which may account for the observed deficits in the update of predictions during reward-based motor learning.

Evidence from our main experiment suggested that the finding of anxiety-related reduced motor variability during exploration was associated with the outcome of subsequently impaired learning from reward. These results validate previous accounts on the relationship between motor variability and Bayesian inference (Wu et al., 2014). In addition, the association between larger initial task-related variability and higher scores during the following learning phase extends results on the faciliatory effect of exploration on motor learning, at least in tasks that require learning from reinforcement (Wu et al., 2014; Pekny et al., 2015; Dhawale et al., 2017; see also critical view in He et al., 2016.

Crucially, state anxiety constrained the total amount of task-related variability only when induced during the initial exploration phase. The lack of between-group differences in cvIKI during learning in both experiments suggests that this measure could not account for the anxiety-related deficits in reward-based learning. Our Bayesian learning model provided additional insight on this aspect. The modelling results suggested that state anxiety can impair learning from reward not only by influencing the posterior distributions of beliefs (expectations and uncertainty) but also by altering how pwPE relating to those beliefs affect behavioral variability. The response model consistently demonstrated in experimental and control groups that smaller pwPEs driving reward updates on the previous trial (leading to decreased expectation of reward) were followed by an increase in task-related motor variability (higher exploration). On the other hand, trials of larger pwPE relating to reward were followed by reduced task-related behavioral changes. By contrast, the effect of pwPE on volatility differed substantially in control and anxiety groups. Although large pwPEs on volatility promoted subsequent larger task-related behavioral changes in control participants, they constrained behavioral exploration in the anx1 and anx2 groups.

Accordingly, state anxiety facilitated the use of task-related variability during reward-based learning only in trials following smaller pwPE reducing volatility estimates. This led participants who were affected by the prior or concurrent state anxiety manipulation to underestimate environmental volatility. Thus, they had the expectation that reward estimates are more stable throughout time. Anx1 and anx2 participants also had larger uncertainty about volatility. This implies that they were less confident about their volatility estimate, and allowed for a greater influence of new information in updating this quantity. This finding is additionally reinforced in anx1 by the result of a larger ${\omega }_2$, reflecting a different learning style that is characterized by sharper and more pronounced steps of update in ${\mu }_2$. The results align well with recent computational work in decision-making tasks, showing that high trait anxiety leads to alterations in uncertainty estimates and adaptation to the changing statistical properties of the environment (Browning et al., 2015; Huang et al., 2017; Pulcu and Browning, 2019.

Notwithstanding the similarities in the anx1 and anx2 groups concerning the expectation of volatility and associated uncertainty, the fact that anx2 participants achieved high scores in the task and were not impaired in learning requires further clarification. Our post-hoc analyses revealed that the drop in ${\mu }_2$ in anx2 could be accounted for by the narrower distribution of scores encountered by this group. In addition, these participants introduced smaller trial-to-trial changes in temporal variability when compared to control participants. Thus, anx2 participants had a tendency to exploit the current motor program more than control participants, suggesting a more conservative approach to success. Anx1 participants also introduced smaller trial-to-trial changes in trial-wise temporal variability (${\displaystyle \mathrm{c}\mathrm{v}\mathrm{I}\mathrm{K}{\mathrm{I}}_{\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}}$), yet their behavioral changes had a slower benefit on reward. In both groups, however, the more pronounced tendency to exploit the current motor program was associated with alterations in how pwPE relating to volatility influenced behavioral changes. Overall, our findings provide the first evidence that computational mechanisms similar to those described for trait anxiety and decision-making underlie the effect of temporary anxious states on motor learning. This might be particularly the case in the context of learning from rewards, such as feedback about success or failure, which is considered one of the fundamental processes through which motor learning is accomplished (Wolpert et al., 2011).

Previous studies manipulating psychological stress and anxiety to assess motor learning showed both a deleterious and a faciliatory effect (Hordacre et al., 2016; Vine et al., 2013; Bellomo et al., 2018). Differences in experimental tasks, which often assess motor learning during or after high-stress situations but not during anxiety induction in anticipation of a stressor, could account for the previous mixed results. Here, we adhered to the neurobiological definition of anxiety as a psychological and physiological response to an upcoming diffuse and unpredictable threat (Grupe and Nitschke, 2013; Bishop, 2007). Accordingly, anxiety was induced using the threat of an upcoming public speaking task (Feldman et al., 2004; Lang et al., 2015), and was associated with a drop in the HRV and an increase in state anxiety scores during the targeted blocks. Although the average state anxiety scores were not particularly high, they were significantly higher during the targeted phases than during the initial resting state phase. Future studies should use more impactful stressors to study the effect of the full spectrum of state (and trait) anxiety on motor learning (Bellomo et al., 2018).

What is the relationship between the expression of motor variability and state anxiety? As hypothesized, state anxiety during initial exploration reduced the use of variability across trials. This converges with recent evidence demonstrating that anxiety leads to ritualistic behavior (repetition, redundancy, and rigidity of movements) that allow the subject to regain a sense of control (Lang et al., 2015). The outcome also aligns well with animal studies in which evidence shows a reduction in motor exploration when the stakes are high (high-reward situations, social context; Kao et al., 2008; Dhawale et al., 2017; Woolley et al., 2014). These interpretations, however, seem to stand in contrast with our findings in anx2 participants, who were affected by the anxiety manipulation during learning but with no significant effect on the total degree of motor variability expressed during this phase. Similar results were obtained in the second experiment, as anx3 and control participants did not differ in the amount of across-trials variability expressed during learning. Bayesian computational modelling clarified these findings demonstrating that anx2 participants used increased exploitation of their current motor program. Also, their trial-to-trial changes in temporal variability were smaller than those in the control group, particularly following large pwPEs that increased the expectation on volatility. This outcome was also found in both anx1 and anx3 participants in the second experiment. Thus, anxiety consistently constrained dynamic trial-to-trial changes in temporal variability—with these changes negatively influenced by pwPEs on volatility. Notably, however, the strategy in anx2 participants of more extensively exploiting the inferred rewarded solution (relative to control participants) was successful, and therefore differs from the learning impairment exhibited by anx1 participants. In the second experiment, removing the initial exploration phase led to impaired reward-based learning in anx3 participants. This group also tended to explore less than controls at the trial level as a function of changes in volatility pwPEs. Thus, the combined evidence suggests that normal use of initial variability in anx2 participants protected their performance from the subsequent impact of the anxiety manipulation. Initial use of variability in anx2 might promote faster learning of the mapping between actions and their asociated outcome, contributing to successful goal-directed exploitation. We interpret these results to indicate that initial unconstrained exploration is important for later subsequent successful motor learning.

Some considerations should be taken into account. Task-related motor variability might be pivotal for learning from reinforcement or reward signals (Sutton and Barto, 1998; Dhawale et al., 2017; Wu et al., 2014), whereas in other contexts, such as during motor adaptation, the evidence is conflicting (He et al., 2016; Singh et al., 2016). An additional consideration is that greater levels of motor variability could reflect both an intentional pursuit of an explorative regime and an unintentional higher level of motor noise, in the latter case similar to that observed in previous work (Wu et al., 2014; Pekny et al., 2015). A recent study established that motor learning is improved by the use of intended exploration, not motor noise (Chen et al., 2017). Our paradigm cannot dissociate intended and unintended exploration. This limitation will be addressed in future work by using a separate initial phase with regular performance to assess motor noise as a measure of unintended exploration.

Another consideration is that our use of an initial exploration phase that did not provide reinforcement or feedback signals was motivated by the work of Wu et al. (2014), which demonstrated a correlation between initial variability (no feedback) and learning curve steepness in a subsequent reward-based learning phase—a relationship previously observed in the zebra finch (Kao et al., 2005; Olveczky et al., 2005; Ölveczky et al., 2011). This suggests that higher levels of motor variability do not solely amount to increased noise in the system. Instead, this variability represents a broader action space that can be capitalized upon during subsequent reinforcement learning by searching through previously explored actions (Herzfeld and Shadmehr, 2014). Accordingly, an implication of our results is that state anxiety could impair the potential benefits of an initial exploratory phase for subsequent learning.

Last, we used a reward-based motor learning paradigm in which different performances could provide the same feedback score. The rationale for using this task was to explore the effect of state anxiety on volatility estimates, as recent work demonstrates that anxiety primarily affects learning in volatile conditions (Browning et al., 2015; Huang et al., 2017). This scenario, however, implied that a high expression of task-related motor variability during learning would be associated with a more volatile perception of the task, which is indeed supported by our correlation results. This could be a confounding factor when explaining the group effects. Importantly, however, further analyses revealed that the total degree of motor variability during learning and the mean learned performance did not differ between groups, suggesting that these are not confounding factors that could explain the reward-based-learning group results. Instead, our findings underscore that computational mechanisms related to how pwPE on reward and volatility influence behavioral changes are the main factors driving the effects of concurrent or prior state anxiety on reward-based motor learning.

At the neural level, an important finding was that anxiety during initial exploration increased the power of beta oscillations and the rate of long beta bursts (long-tailed distribution). The increases in power and the rate of long-lived bursts manifested after completion of the sequence, reflecting an anxiety-related enhancement of the post-movement beta rebound (Kilavik et al., 2012; Kilavik et al., 2013). This effect was observed in a region of contralateral sensorimotor and right prefrontal channels, and could be explained by anxiety alone, despite a small effect of motor variability on the modulation of these neural changes across sensorimotor electrodes. Further, larger sensorimotor beta power at the termination of the sequence performance was associated with a more constrained use of task-related variability. Our analyses did not provide a detailed anatomical localization of the effect, but the findings in sensorimotor regions that partially contribute to changes in motor variability are consistent with the involvement of premotor and motor cortex in driving motor variability and learning, as previously reported in animal studies (Churchland et al., 2006; Mandelblat-Cerf et al., 2009; Santos et al., 2015). The results also converge with the representation in the premotor cortex of temporal and sequential aspects of rhythmic performance (Crowe et al., 2014; Kornysheva and Diedrichsen, 2014).

During learning, an unexpected result was that, in anx2 participants, there was an increase in beta power at the end of the sequence performance but not during feedback processing—and despite the anxiety manipulation successfully affecting the HRV. This outcome, as well as the lack of beta burst effects in this group, seems to be in agreement with the lack of learning impairments when compared with control participants. An additional unexpected result during learning blocks was the presence in anx1 participants of higher rates of long bursts and greater beta power at the end of the trial and during feedback processing, across both sensorimotor and prefrontal electrodes. These phasic changes in beta activity in anx1 participants extended from the previous phase, and the outcome aligns with the finding of prefrontal involvement in the emergence and maintenance of anxiety states (Davidson, 2002; Grupe and Nitschke, 2013; Bishop, 2007). Thus, our results revealed that, in the context of motor learning, anxious states induce changes in sensorimotor and prefrontal beta power and burst distribution. These changes are maintained after physiological measures of anxiety return to baseline, and thus continue to affect relevant behavioral parameters. Anxiety has been shown to modulate different oscillatory bands depending on the context, such as gamma activity in visual areas and amygdala when processing fearful faces (Schneider et al., 2018), alpha activity in response to processing emotional faces (Knyazev et al., 2008) or theta activity during rumination (Andersen et al., 2009). Beta-band oscillations could be particularly relevant to flesh out the effects of anxiety on performance during motor tasks.

Mechanistically, phasic trial-by-trial feedback-locked changes in the sensorimotor beta power and burst distribution were related to the computational alterations in updating expectations on reward found in anx1 participants, and thus explained their poorer performance during reward-based learning. Specifically, a higher rate of long beta bursts and increased power following feedback were associated with a reduced update in the expectation of reward.

The computational quantity that determines the update of expectations in our Bayesian model is the precision-weighted PEs. Here, pwPE relating to reward were inversely related to the rate of long beta bursts and beta power, and were therefore attenuated in anx1 participants because of their enhanced feedback-related beta activity. We found no significant contribution of pwPE relating to volatility to explaining changes in beta activity, suggesting that additional frequency ranges should be considered when linking hierarchical pwPEs to neural oscillations during learning. In the context of the predictive coding hypothesis, PEs (or pwPEs) are hypothesized to be mediated by gamma oscillations, whereas the neuronal signaling of predictions is mediated by lower frequencies (e.g., alpha 8–12 Hz, Friston et al., 2015). Further studies point to beta oscillations as the cortical oscillatory rhythm associated with encoding predictions, although the evidence to date is scarce (Arnal and Giraud, 2012). More recently, beta oscillations have been associated with the change to predictions rather than with predictions themselves (Sedley et al., 2016), which is consistent with our findings as pwPEs were the quantities determining the change to predictions. In line with these results, a post-performance increase in beta power during motor adaptation is considered to index confidence in priors, and thus a reduced tendency to change the ongoing motor command (Tan et al., 2016). More generally, beta oscillations along cortico-basal ganglia networks have been proposed to gate incoming information to modulate behavior (Leventhal et al., 2012) and to maintain the current motor state (Engel and Fries, 2010). Consequently, the phasic increase in beta power and the rate of beta bursts following feedback presentation could represent neural states that impair the encoding of pwPEs and the update of predictions about lower level quantities—reward here—induced by anxiety states. Notably, the modulation of feedback-locked beta activity was not explained by changes in pwPE relating to volatility. We speculate that the effect of reduced reward estimates on the expectation of volatility in the HGF suggests that abnormal increases in beta activity following feedback presentation indirectly influenced volatility estimates, while it had a direct effect on reward expectation.

Our findings show that the assessment of neural activity in sensorimotor regions is crucial to understanding the effects of anxiety on motor learning and to determining mechanisms, above and beyond the role of prefrontal control of attention, in mediating the effects of anxiety on cognitive and perceptual tasks (Bishop, 2007; Bishop, 2009; Eysenck and Calvo, 1992). Our data imply that the combination of Bayesian learning models and analysis of oscillation properties can help us to better understand the mechanisms through which anxiety modulates motor learning. Future studies should investigate how the brain circuits that are involved in anxiety interact with motor regions to affect motor learning. In addition, assessing burst properties across both beta and gamma frequency ranges would further allow us to delineate and dissociate the neural mechanisms responsible for anxiety biasing decision-making and motor learning.

MIDI (performance) and EEG data, as well as new response model scripts, have been deposited in the Open Science Framework Data Repository under the accession code mfe2j.

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Author details

1. Sebastian Sporn

   1. School of Psychology, University of Birmingham, Birmingham, United Kingdom
   2. Department of Psychology, Goldsmiths University of London, London, United Kingdom

   Contribution

   Conceptualization, Investigation, Writing - review and editing

   Competing interests

   No competing interests declared

2. Thomas Hein

   Department of Psychology, Goldsmiths University of London, London, United Kingdom

   Contribution

   Investigation, Writing - review and editing

   Competing interests

   No competing interests declared

3. Maria Herrojo Ruiz

   1. Department of Psychology, Goldsmiths University of London, London, United Kingdom
   2. Center for Cognition and Decision Making, Institute for Cognitive Neuroscience, National Research University Higher School of Economics, Moscow, Russian Federation

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Funding acquisition, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   M.Herrojo-Ruiz@gold.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8948-9444

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