Dopaminergic manipulations affect the modulation and meta-modulation of movement speed: evidence from two pharmacological interventions

A body of research implicates dopamine in the average speed of simple movements. However, naturalistic movements span a range of different shaped trajectories and rarely proceed at a single constant speed; instead, speed is reduced when drawing “corners” compared to “straights” (i.e., speed-modulation), and the extent of this slowing down is dependent upon the global shape of the movement trajectory (i.e., speed-meta-modulation) – for example whether the shape is an ellipse or a rounded square. By employing two pharmacological intervention studies – individuals with Parkinson’s both ON and OFF dopaminergic medication (N = 32) and members of the general population on a D2 receptor blocker (haloperidol) versus placebo (N = 43) – we implicate dopamine in speed, speed-modulation and speed-meta-modulation. Our findings move beyond vigour models implicating dopamine in average movement speed, and towards a conceptualisation that involves the modulation of speed as a function of contextual information.


Introduction
Dopamine is robustly associated with the speed, or 'vigour', of movements 1-9 but naturalistic fluid movements -such as the movements recorded in human handwriting, or when a rat navigates a maze -do not simply proceed at a single, constant, speed. Rather, humans and non-human animals continuously modulate speed according to the curvature of their movements: speeding up along straights and slowing down for corners. 10,11 This phenomenon of adapting movement speed to curvature is mathematically described by a set of scale-invariant power laws 11 and is robust across species [12][13][14] and effectors 10,[15][16][17] . Speedmodulation of this sort is thought to be a fundamental principle of biological motion but the role of dopamine in speed-modulation is unknown.
Recent advances have shown that speed can also be said to be 'meta-modulated'. 11 That is, the extent to which one slows down for corners and speeds up for straights is dependent on the global shape of one's movement trajectory: If you were drawing a rounded square you would barely modulate your speed (i.e., your speed-modulation value -or the gradient of the slope between your movement speed and current curvature -would be low), whereas speed is dramatically modulated when drawing shapes such as ellipses with fewer, and tighter, 'corners'. 11,[18][19][20][21] This means that you would adapt your speed differently to a specific curvature value based on the global shape you are drawing. This observation -that the number of corners in a shape influences the degree to which one slows down for said corners and speeds up for straights -has been mathematically formalised as a spectrum of power laws 11 . If a 'corner' is defined as a curvature oscillation per two π of angular displacement, then a shape with two 'corners' (an ellipse) is defined as having an angular frequency of two, a shape with four corners (a rounded square) has an angular frequency of four, and so on. Speed-modulation (the gradient of the slope between speed and curvature) is modulated as a function of angular frequency -the higher the angular frequency the lower the speed-modulation.
Although fluid, naturalistic movements nearly always require both speed-modulation and speed-metamodulation, little is known of the role of dopamine in either of these processes. A number of existing theories link dopamine and movement speed [22][23][24][25] , however they do not paint a clear picture of the relationship between dopamine, speed-modulation and speed-meta-modulation. The opportunity costs model 22 , for example, proposes that (tonic) dopamine signals average reward availability, with increased dopamine signalling higher reward availability and thus enhancing the vigour of movements by increasing the opportunity cost of sloth. This model predicts that movements will be less vigorous under low dopamine conditions (e.g., OFF Parkinson's medication, or under haloperidol -a dopamine antagonist). In line with this, many studies have shown less vigorous movement -long reaction times on button press paradigms 26 and slow simple reaching arm movements 5, 7, 23 -under low dopamine conditions. It is, however, unclear how this translates to more complex, naturalistic movements. Consider the example of drawing an ellipse: the opportunity cost of sloth is uniform and unrelated to curvature or global trajectory -it is no more costly to move slowly at corners versus straights. Similarly, it is no more costly to move slowly for low angular frequency (e.g., an ellipse) compared to high angular frequency (e.g., a rounded square) shapes. Therefore, it could be argued that the opportunity costs model 22 would predict that low dopamine conditions should result in a uniform reduction in the average speed of movement with no change to speed-modulation or speed-meta-modulation (i.e., no modulation as a function of curvature or global trajectory). On the other hand, one could argue that curvature and vigour are related such that straights require more vigorous movements than corners (because straight movements are executed at a higher speed 11,[18][19][20][21], and shapes with more, and less tight, corners (high angular frequency shapes) require more vigorous movement in general (because they tend to be drawn faster 18 ). Thus, low dopamine conditions, which reduce vigour, might disproportionately affect straights and high angular frequency shapes because the requisite movements demand more vigour. Under this interpretation, in addition to the effects on speed, the opportunity costs model predicts an effect of dopaminergic manipulation on speed-modulation and speed-meta-modulation.
Existing models, therefore, do not provide clear, unequivocal predictions of the effects of dopaminergic drugs, or of naturally occurring disruptions of the dopamine system (as in Parkinson's), on natural movements that include speed-modulation and speed-meta-modulation. Here, we investigate the role of dopamine in speed, speed-modulation and speed-meta-modulation. We do so by employing a shapes tracing task in two pharmacological intervention studies in which we study people with Parkinson's both ON and OFF dopaminergic medication and members of the general population on a D2 receptor blocker (haloperidol) versus placebo.

Results
Participants comprised individuals with Parkinson's both ON and OFF dopaminergic medication (Study 1; N=32) and members of the general population on a D2 receptor blocker (haloperidol) versus placebo (Study 2; N=43). In both studies, participants completed a tracing task in which they used a stylus and touch screen device to trace a range of shapes ( Fig. 1) for 10 full cycles (where a cycle is a complete start point to start point trace of the shape) per trial. The shapes were strategically chosen on the basis that they span a wide spectrum of angular frequencies and thus enable us to index differences in speed-modulation across the angular frequency spectrum. For each trial of the experiment, we recorded x and y coordinates and calculated indices of speed, speed-modulation (the gradient of the relationship between speed and curvature) and speedmeta-modulation (the gradient of the relationship between speed-modulation and angular frequency).
Analyses in the main text were conducted on subsets of the data in which participants had valid trials for at least the shapes with the highest and lowest angular frequency values (Study 1: 4/5 and 4; Study 2: 4/3 and 4). Analyses conducted on full datasets are reported in Supplementary Materials A-D. In the subsequent sections we report dopaminergic effects on speed, speed-modulation and speed-meta-modulation, combining insight from both studies.   [27][28][29] and that working memory capacity can serve as a proxy for this, with low working memory capacity indicating low dopamine synthesis capacity 30,31 . This literature argues for an inverted-U function for the relationship between baseline dopamine and the effects of dopaminergic drugs on performance 32 . To enable us to explore any baseline dependent effects of the drug we asked participants in Study 2 to complete a working memory task 33 whilst under placebo. We predicted that, if there is an inverted-U-shaped relationship between dopamine and speed we would see that the effect of haloperidol is moderated by estimated striatal dopamine synthesis capacity such that individuals with low striatal dopamine synthesis capacity move slower under haloperidol relative to placebo because their (already sub-optimally low) dopamine levels are further reduced by haloperidol. In contrast, individuals with high striatal dopamine synthesis capacity should show speeding effects of the drug because their sub-optimally high levels of dopamine are reduced by haloperidol, thus bringing them closer to the optimal level of dopamine for speedy movements. Including our proxy for striatal dopamine synthesis capacity (i.e., working memory score) as a covariate in our mixed model revealed that the main effect of drug state was indeed moderated by estimated striatal dopamine synthesis capacity (F(1,1600)=42.04, p<.001; Fig. 2).
The interaction between drug state and estimated striatal dopamine synthesis capacity was unpacked by calculating the drug effect for each participant (mean speed under placebo minus mean speed under haloperidol) and plotting this against estimated baseline striatal dopamine synthesis capacity. Results are plotted in Fig. 5 (top-left). Positive values on the y-axis indicate that participants' movements were slowed by haloperidol administration, and negative values indicate that participants moved faster under haloperidol than placebo. Our data revealed a negative linear relationship between drug effect and estimated striatal dopamine synthesis capacity which cut the x-axis, indicating opposing drug effects in low versus high striatal dopamine synthesis capacity groups. That is, a haloperidol-induced reduction in dopamine caused participants with low striatal dopamine synthesis capacity to move slower, and those with high striatal dopamine synthesis capacity to move faster. These results suggest that the drug effect on speed is dependent on estimated striatal dopamine synthesis capacity.

Removal of Parkinson's medication and administration of haloperidol reduces speed-modulation
To investigate effects on speed-modulation we carried out LMMs with speed-modulation values -the gradient of the regression line between instantaneous movement speed and the curvature being drawn -as the dependent variable. Here a main effect of drug state would comprise evidence that manipulating dopamine impacts speed-modulation. An interaction between drug state and shape would be evidence of a drug effect on speed-meta-modulation; as such, in this section we focus on main effects and discuss interactions between drug state and shape in the next section.
In addition to effects on speed, we observed that removal of Parkinson's medication (Study 1) affected speedmodulation. Our LMM with drug state, shape and dosage as fixed effects revealed a main effect of drug state  which again cuts the x-axis, indicating opposing drug effects in low versus high striatal dopamine synthesis capacity groups. That is, a reduction in dopamine caused participants with low striatal dopamine synthesis capacity to move with reduced speed-modulation, and those with high striatal dopamine synthesis capacity to move with increased speed-modulation. Thus, as is the case for speed, the drug effect on speed-modulation is dependent on estimated striatal dopamine synthesis capacity. Our Introduction highlighted that a possible prediction from the opportunity costs model is that a reduction in vigour following dopaminergic manipulation will disproportionately affect high speed movements that require more vigour. This would predict a greater effect of the drug on parts of the trajectories that are executed at higher speeds (i.e., straights relatives to corners), and may account for reductions in speedmodulation values. To interrogate the data for evidence in support of this, we analysed the average of the

Administration of haloperidol reduces speed-meta-modulation, but Parkinson's medication does not.
To test whether the removal of Parkinson's medication (Study 1) would reduce the meta-modulation of movement speed, we calculated a speed-meta-modulation index by regressing angular frequency against speed-modulation values and calculating the gradient of the regression line. Here, a larger gradient magnitude would indicate a greater difference in speed-modulation across the angular frequency spectrum.
This variable was submitted to a LMM with drug state and dosage as fixed effects. There was no significant effect of drug state on speed-meta-modulation, nor drug state by dosage interaction (p>.05; Supp Mats E). This is supported by the lack of a drug state by shape interaction in the speed-modulation LMM described above for Study 1 (p>.05; Supp Mats E). As such, in Study 1 we did not find evidence supporting a role for dopamine in speed-meta-modulation.
This indicated that, under haloperidol, participants did not utilise a range of speed-modulation values across the angular frequency spectrum as would be seen in appropriate speed-meta-modulation. Instead, the extent to which speed was modulated as a function of curvature was similar across all shapes, thus reducing the gradient of the relationship between angular frequency shape and speed-modulation value. This is supported by the presence of a drug state by shape interaction in the speed-modulation LMM described above for Study 2 (F(1,1642)=11.45, p<.001). Therefore, in Study 2, we find evidence for reduced speed-meta-modulation in low dopamine conditions. As was the case for movement speed and speed-modulation, the effect of haloperidol on speed-metamodulation was baseline dopamine dependent; a significant interaction between drug state and estimated striatal dopamine synthesis capacity (F(1,53)=10.95, p=.002) was observed. To aid interpretation, we plotted the relationship between the drug effect and striatal dopamine synthesis capacity (Fig. 5, bottom). The drug effect (y-axis) was calculated as the speed-meta-modulation value under haloperidol minus the speed-metamodulation value under placebo. Note that for speed and speed-modulation (Fig. 5, top-left and top-right) the drug effect was instead calculated as placebo minus haloperidol because more positive speed and speedmodulation values indicate higher speed and greater speed-modulation. Given that more positive speedmeta-modulation values actually indicate less speed-meta-modulation (i.e., flatter slopes for the negative relationship between angular frequency and speed-modulation), the drug effect was calculated as haloperidol minus placebo to ensure that, in line with the other two dependent variables, positive values on the y-axis indicate reduced speed-meta-modulation under haloperidol and negative values indicate increased speedmeta-modulation.   Our Introduction highlighted that a possible prediction from the opportunity costs model is that a reduction in vigour following dopaminergic manipulation will disproportionately affect shapes at higher angular frequencies because these tend to be drawn at a higher speed and may therefore require more vigour. To interrogate the data for evidence in support of this we further explored the drug state by shape interaction in the speed-modulation LMM for Study 2 by running the same LMM (excluding shape) on subsets of the data for each shape. This revealed that the 'flattening of the curve' between angular frequency and speedmodulation (i.e., reduced speed-meta-modulation) under low dopamine conditions was driven by larger drug effects for the lower angular frequency shapes than the higher angular frequency shapes (shape 4/3:

Discussion
In line with the vigour literature, our results showed that low dopamine conditions (removal of Parkinson's medication and administration of haloperidol relative to placebo) reduced movement speed. In addition, dopaminergic drugs independently affected speed-modulation by reducing participants' ability to modulate movement speed according to curvature. Finally, we also found an independent effect of dopaminergic drugs on speed-meta-modulation: haloperidol reduced participants' ability to titrate their speed-modulation such that it was appropriately suited to the global trajectory (the angular frequency of the shape). This latter effect was seen in members of the general population but not for individuals with Parkinson's; we speculate below that this may be due to the incorporation of estimated baseline striatal dopamine synthesis capacity in the general population study. Together these results implicate dopamine in average movement speed, speedmodulation and speed-meta-modulation, and show that dopamine's role in movement speed is broader than that which is conceptualised in current models linking dopamine and movement.
Existing models, such as the opportunity costs models, do not provide clear unequivocal predictions for the effects of dopaminergic manipulation on naturalistic movement. Nevertheless, our Introduction highlighted two possible predictions that can be made from the opportunity costs model. One prediction is that low dopamine conditions should be associated with speed reductions but with no effects on speed-modulation and speed-meta-modulation. Our results clearly diverge from this prediction and thus show that this interpretation of the opportunity costs model does not align with empirical evidence. A second prediction is that dopaminergic manipulation will affect speed, speed-modulation and speed-meta-modulation because reductions in vigour will disproportionately affect high speed movements that require more vigour. More specifically, this would predict a greater effect of the drug on trajectories that are executed at higher speeds (straights vs. corners) and shapes that are executed at higher speeds (high angular frequency shapes). We did not find any evidence to support these predictions. That is, our data did not show that drug state disproportionately affected higher speed movements, or that drug state disproportionately affected speed or speed-modulation values for high, as opposed to low, angular frequency shapes. Our results, cannot, therefore, easily be conceptualised under current formulations of the opportunity costs model.
We next consider whether our results might be consistent with other popular models in the literature.
Bayesian theories 34,35 propose that (tonic) dopamine signals the precision with which incoming information is stored and represented. Under high dopamine -signalling high precision -an individual is thought to be more confident in their representation of incoming sensory information compared to their prior beliefs, and thus more heavily relies on incoming sensory data; conversely, low dopamine promotes a reliance on prior beliefs. Whilst Bayesian theories have not made explicit predictions about our task, one can consider tracing as a task that requires a balance between priors and incoming evidence. One has priors, learned through previous experience, that influence our typical speed of movement 36 but as we trace around the outline of a shape we encounter changes in curvature that demand deviations from these priors. Thus, if we assume that reduced speed-modulation and meta-modulation can occur due to an overweighting of the prior (typical speed) relative to the incoming (trajectory) information, then our results could be considered consistent with Bayesian theories of dopamine and movement. Bayesian theories do not, however, provide a comprehensive account of all of our results because they do not make clear predictions about average movement speed.
A more recent theory -the rational inattention account 37 -merges opportunity cost and Bayesian models by proposing that dopamine signals average reward availability and that this 'pays the cognitive costs' (e.g., attention costs) of increasing precision. This is consistent with evidence that dopamine plays a role in both motivational and cognitive control of behaviour 38 . By merging both approaches, the rational inattention account predicts that low dopamine conditions will be associated with reductions in speed, speed-modulation and speed-meta-modulation.
Although our data can be considered consistent with the rational inattention account this, nevertheless, leaves unanswered questions about the exact mechanisms by which dopamine affects speed-modulation and speedmeta-modulation. The rational inattention account 37 argues that dopamine 'pays the cognitive costs' of increasing the precision with which incoming information (e.g., trajectory information) is stored and represented but the exact nature of these 'cognitive costs' are yet to be determined. Mikhael and colleagues suggest attention as a candidate cost. If this were the case, in the context of our study, the hypothesis would be that in low dopamine conditions speed-modulation (and speed-meta-modulation) is reduced because participants attend less to changes in trajectory curvature because of a reluctance to pay the cognitive costs of selective attention. An alternative account has been forwarded by Manohar and colleagues 39 who propose that, by signalling reward, dopamine permits more aggressive error correction. Thus, in our case, in low dopamine conditions, participants may attend to the changes in curvature but would nevertheless fail to appropriately modulate their speed due to a (presumably implicit) reluctance to pay the energetic costs of error correction. Further studies are required that specifically aim to tease apart whether, in low dopamine conditions, participants were less likely to attend to curvature changes, or whether they simply failed to adapt their movements to accommodate them.

Both Mikhael and colleagues and Manohar and colleagues suggest motivation-based mechanisms: They do
not argue that dopamine changes one's ability to pay attentional/effort-based costs, only one's motivation to do so. Nevertheless, it is possible that dopamine plays a role in motor ability per se. Dopamine has long been linked to the invigoration of movements 40,41 , is thought to play an important role in generating a range of different movement speeds, 42 and is key in signalling the start and end points of sub-movements. 43 Given the observation that distinct dopamine neurons are involved in reward signalling and self-paced movement 40 (also see Engelhard et al. 44 ) it is feasible that dopaminergic manipulations directly affect participants' ability to physically modulate their actions, independent of their motivation to do so. In other words, participants may be motivated to adapt movement speed as a function of curvature/global trajectory but may be unable to do so, perhaps because they have an inadequate range of movement speeds to choose from, and/or they are unable to signal the start/end points at which the adaptation should occur.
There are a number of possible reasons why the drug effect on speed-meta-modulation was observed only in Study 2 (haloperidol compared to placebo) and not in Study 1 (ON versus OFF dopaminergic medication in Parkinson's). First, in Study 2 we were able to account for baseline striatal dopamine synthesis capacity To summarise, the current studies implicate dopamine in movement speed, speed-modulation and speedmeta-modulation for complex movements, thus extending the theoretical understanding of dopamine function beyond that which is conceptualised in current models of vigour.

Procedure
Participants completed two testing days, one to two days apart, which followed the same protocol but

Shapes tracing task
Participants traced four different shapes of varying angular frequencies (4/5, 4/3, 2, 4). The size of the shapes presented on the device did not exceed 9cm by 9cm. During each trial, participants were asked to trace around the shape on the screen 'as fluidly as possible' in a counter-clockwise direction, using a stylus held in their dominant hand. Participants completed eight blocks, two for each shape, presented in a random order.
Each trial required participants to draw 10 full cycles of the shape, and the x and y coordinates of the stylus were recorded over time. During each block, participants had a total of seven attempts to complete four successful trials. Thus, a maximum of eight successful trials per shape was set, with participants limited to completing up to 14 trials to achieve this number. If participants significantly deviated from the shape (and into a region surrounding the shape which was not displayed to participants) or removed the stylus from the touch-screen (after a 5-second grace period), the trial was not classed as 'successful'. Each trial had a timeout set at 90 seconds.

Shapes tracing task
Trials with fewer than 2.5 traces were excluded. The first samples of every trial which did not achieve a minimal speed (200 pixels per second), within the 5-second grace period, were removed to address a discontinuity of reported position at trial start. The maximum sampling rate of the tablet was 60Hz, but deviations occurred, thus positional data was resampled using the spline method to achieve a consistent 60Hz. The first ½ π angular displacement of each trial was discounted before data processing. Movement kinematics were calculated for each trial of the experiment using the x and y coordinates recorded over time.

Speed and Speed-modulation
To analyse the shapes tracing task data, effects-coded linear mixed models were employed for movement speed and speed-modulation values with drug state and shape as fixed effects, dosage interacting with drug state, and day, trial number and participant ID as random effects.

Maximum and Minimum Speed Values
Given the possible prediction highlighted in the Introduction that dopaminergic manipulation may disproportionately affect high speed movements, maximum and minimum speed values were analysed using the following LMM: DV ~ Drug State * Shape + Drug State:Dosage + (1|Day) + (1|Trial number) + (1|Participant ID)

Speed-meta-modulation
For speed-meta-modulation, models were run using the following formula: DV ~ Drug State + Drug State:Dosage + (1|Day) + (1|Participant ID) ANOVAs were conducted on the model coefficients to obtain p-values for the fixed effects.

Procedure
Participants completed two testing days, one to four weeks apart, lasting approximately 5.5 hours each.
Following an on-the-day health check involving blood pressure and blood oxygenation levels, participants were administered capsules containing either 2.5mg of haloperidol (a dopamine D2 receptor antagonist) or a placebo, in a double-blind, placebo-controlled, within-subjects design. The orders of the days for haloperidol and placebo were pseudorandomised such that 50% of participants received haloperidol on day 1 and 50% on day 2. Haloperidol dosage and administration times were in line with previous studies in the literature demonstrating behavioural and psychological effects. 28, 64 At 1.75 hours post-tablet intake, participants completed a working memory task, followed by the shapes tracing task 4 hours post-tablet intake. Given that oral haloperidol is reported to be at its peak concentration in the blood plasma between 1.7 and 6.1 hours post-tablet intake on average 65 , both tasks were completed within the peak range of haloperidol blood plasma concentration, ensuring that drug action was likely to occur throughout administration of the tasks. Medical symptoms, blood pressure and mood were monitored before capsule administration, three times throughout the testing day, and at the end of the testing day.

Shapes Tracing Task
The general principles of the shapes tracing task remained the same as in Study 1, with a few exceptions.
Three shapes were presented to participants (4/3, 2, and 4), as opposed to four shapes (Study 1: 4/5, 4/3, 2, and 4) to allow for a greater number of trials for the included shapes. The size of the shapes presented on the device did not exceed 12cm by 12cm. Each shape was traced for a total of 10 trials per shape, as opposed to a maximum of eight trials in Study 1, and each trial consisted of 10 x angular frequency (i.e., 10 x 2π radians of angular displacement) curvature oscillations (in the case of the ellipse and rounded square this is 10 complete traces of the shape). Participants were asked to repeat trials if they deviated from the shape or removed their stylus from the device. Participants could repeat the trial if they felt fluidity was not achieved (e.g., due to deviating from the shape or removing the stylus). The task was programmed and run using MATLAB 2014b 32-bit on a Surface Pro 4, using a touch-screen device to record participants' movements (WACOM Cintiq 22 HD drawing tablet).

Working memory task
Participants completed a visual working memory task, adapted from the Sternberg visual working memory task 33 , programmed using MATLAB 2017b. The task involved 60 experimental trials across five blocks which were completed following 10 practice trials. In each trial, a fixation cross was presented in the centre of the screen (for a variable duration between 500-1000ms), followed by a list of letters (between 5 and 9 consonants depending on the block; 1000ms duration) and a blue fixation cross (3000ms duration). A single letter was then displayed (4000ms) and participants indicated with a keyboard press whether the letter was present in the previously displayed list (1 = yes, 2 = no, 3 = unsure). Accuracy and response time were recorded for each trial.

Shapes tracing task
As in Study 1 the first ½ π angular displacement of each trial was discounted before data processing.
Movement speed (average, maximum and minimum values), speed-modulation values and speed-metamodulation values were calculated for each trial using the x and y coordinates recorded over time, as in Study 1. To meet normality assumptions, a log transform was applied to the movement speed and speedmodulation data. Outliers of each dependent variable were removed, defined as values further than 2 standard deviations away from the mean. Three participants failed to complete both testing days, therefore two haloperidol datasets and one placebo dataset are missing from analyses.

Working memory task
As in previous studies 29, 63 , working memory span was calculated as the percentage of correct responses across all trials. Given evidence that baseline working memory span reliably predicts individual dopamine synthesis capacity 30,31 , baseline striatal dopamine synthesis capacity was taken as the working memory span obtained under placebo. This value was used to explore any baseline dependent effects of the drug, as a body of literature reports that effects of dopaminergic drugs are modulated by striatal dopamine synthesis capacity. [27][28][29] Five participants failed to complete the working memory task at baseline, thus baseline striatal dopamine synthesis capacity could not be estimated and these participants could not be included in analyses incorporating this measure. We note that the correlation between working memory span and dopamine synthesis capacity was not replicated in a recent positron emission tomography (PET) imaging study 66 , but this may be due to the use of a less sensitive radioligand compared to earlier studies (18F-FDOPA rather than 18F-FMT).

Data subsetting
As in Study 1, speed-meta-modulation slopes were calculated from participants who had valid trials for at

Analyses
All analyses were conducted in MATLAB 2022A. All mixed models were run using MATLAB's fitlme function. As in Study 1, all linear mixed models were followed up with an ANOVA on the model coefficients to obtain p-values for the fixed effects. Data and analysis scripts are available online at https://osf.io/vwu5t/?view_only=f1ce99b65142493bb313472f389c2e1f

Speed and Speed-modulation
To analyse the dependent variables speed and speed-modulation, a series of effects-coded linear mixed models were employed. Reported in the main text is a mixed model that incorporated baseline striatal dopamine synthesis capacity as a fixed effect alongside drug state and shape, with day, trial number, and participant ID as random effects. and Supp Mats F (speed-meta-modulation)).

Maximum and Minimum Speed Values
Given the possible prediction highlighted in the discussion that dopaminergic manipulation may disproportionately affect high speed movements, maximum and minimum speed values were analysed using the following LMM: DV ~ Drug State * Shape + Drug State * Striatal Dopamine Synthesis Capacity + (1|Day) + (1|Trial number) + (1|Participant ID)

Speed-meta-modulation
For the speed-meta-modulation data, the following models were run, with (main text) and without When a significant interaction between drug state and striatal dopamine synthesis capacity was found, this was unpacked by assessing the relationship between striatal dopamine synthesis capacity and the drug effect. Following the drug effect calculation, a linear model was then employed with striatal dopamine synthesis capacity as predictor and Drug Effect and DV. To provide evidence in favour of an inverted-U function for the relationship between baseline dopamine and the dependent variable 32 , a negative linear relationship that cuts the x-axis would be expected when plotting the drug effect against estimated striatal dopamine synthesis capacity.

Independence of drug effects
Given the presence of drug effects on all three dependent variables in Study 2, further exploratory analyses were implemented on this dataset to investigate whether the drug effects are independent from each other.
In each case, the control variable (e.g., speed) was included in a model predicting the dependent variable (e.g., speed-modulation), from which the residuals were saved. Models also included day as a random effect, and trial as a random effect for cases in which speed or speed-modulation were the dependent variable. A mixed model testing the effect of drug was run on the resultant residuals, using the corresponding model formula that included striatal dopamine synthesis capacity listed above.

Data and Code Availability
Data and analysis scripts are available online at https://osf.io/vwu5t/?view_only=f1ce99b65142493bb313472f389c2e1f