Sensitivity to prediction error in reach adaptation 3 4

16 It has been proposed that the brain predicts the sensory consequences of a movement and compares it to 17 the actual sensory feedback. When the two differ, an error signal is formed, driving adaptation. How 18 does an error in one trial alter performance in the subsequent trial? Here, we show that the sensitivity to 19 error is not constant, but declines as a function of error magnitude. That is, one learns relatively less from 20 large errors as compared to small errors. We performed an experiment in which humans made reaching 21 movements and randomly experienced an error in both their visual and proprioceptive feedback. 22 Proprioceptive errors were created using force fields, and visual errors were formed by perturbing the 23 cursor trajectory to create a visual error that was smaller, the same size, or larger than the proprioceptive 24 error. We measured single trial adaptation and calculated sensitivity to error, i.e., the ratio of the trial-to25 trial change in motor commands to error size. We found that for both sensory modalities, sensitivity 26 decreased with increasing error size. A reanalysis of a number of previously published psychophysical 27 results also exhibited this feature. Finally, we asked how the brain might encode sensitivity to error. We 28 reanalyzed previously published probabilities of cerebellar complex spikes (CS) and found that this 29 probability declined with increasing error size. From this we posit that a CS may be representative of the 30 sensitivity to error, and not error itself, a hypothesis which may explain conflicting reports about CSs and 31 their relationship to error. 32 33 34 Introduction 35 How we perceive the world is at the core of how we behave. As we make a movement, sensory 36 inputs from multiple modalities converge in our brain to create an understanding of the results of that 37 movement. Theory suggests movements may be planned using a forward model, which generates a 38 prediction of our sensory feedback based on the outgoing motor command (Wolpert et al., 1995). If a 39 movement has an unexpected sensory consequence, an error is experienced. Error feedback is rich in 40 nature, and can include the size, relevance, direction, sensory modality and other details about the error. 41 Despite the large number of studies on adaptation (Shadmehr and Mussa-Ivaldi, 1994;Smith et al., 42 2006;Pekny et al., 2011), little is known about how we adapt to a single error, nor how individual sensory 43 prediction errors are processed and combined. Of particular interest are visual and proprioceptive errors, 44 which arguably play the greatest role in control of movement. Here, we will explore the question of how 45 learning from error depends on error size and sensory modality. 46 In models of adaptation, it is generally assumed that learning scales linearly with error size 47 (Thoroughman and Shadmehr, 2000;Scheidt et al., 2001;Cheng and Sabes, 2006;Smith et al., 2006;van 48 Beers, 2009). This implies that sensitivity to error is constant as a function of error size. However, 49 experiments suggest that the brain alters sensitivity to error based on its uncertainty about its predictions 50 relative to its uncertainty about observations (Korenberg and Ghahramani, 2002;Burge et al., 2008). For 51 example, when visual feedback about the consequences of a movement is blurry, one is less likely to 52 change their motor commands as compared to when it is sharp (Izawa and Shadmehr, 2008). Even when 53 the quality of the sensory feedback is kept constant, the brain appears to modulate sensitivity to error as a 54 function of error size. For example, Robinson et al. (Robinson et al., 2003) found that adaptation to 55 saccadic errors declined as the error size increased. Additionally, in reaching tasks, both Fine and 56 Thoroughman (2006) and Wei and Kording (Wei and Kording, 2009) reported that trial-to-trial learning 57 from a force perturbation of increasing size or a visual perturbation of increasing size showed rapid 58 saturation, respectively. That is, learning did not increase linearly with error size. 59 From a neurophysiological perspective, it is also unclear how the brain encodes error sensitivity. 60 Error-dependent adaptation of movements is generally thought to require integrity of the cerebellum 61 (Martin et al., 1996;Maschke et al., 2004;Smith and Shadmehr, 2005;Rabe et al., 2009). Complex spikes 62 that are generated by climbing fiber inputs onto Purkinje cells of the cerebellum are considered to be the 63 biological representation of an error signal (Kitazawa et al., 1998). However, when the probability of a 64 complex spike was measured in response to various error sizes, the probability was high for small errors 65 but decreased for larger errors (Soetedjo et al., 2008). This result is inconsistent with the idea that 66 complex spikes encode an error, and instead indicates that error size may play a role in plasticity of 67 Purkinje cells. 68 In addition to errors having different sizes, errors can occur in multiple modalities. The most 69 commonly used adaptation paradigms rely on visual error alone (i.e., a visuomotor rotation) or visual and 70 proprioceptive error concurrently (i.e., a force field). Behavioral studies suggest that learning from visual 71 and proprioceptive errors may occur independently (Krakauer et al., 1999;Pipereit et al., 2006;Bock and 72 Thomas, 2011). Furthermore, a recent study of people with cerebellar damage demonstrated that 73 adaptation in these two paradigms relied on different regions of the cerebellum (Rabe et al., 74 2009;Donchin et al., 2012). Thus it is important to consider the relative contributions of visual and 75 proprioceptive error, and understand how the two interact. 76 Here we performed an experiment to measure sensitivity to error, defined as the ratio of the 77 change in motor output from trial 1 n− to trial 1 n+ , to the error experienced in trial n . We aimed to 78 understand the role of error size and modality on sensitivity to error, in a way which unified the results of 79 past studies. To do so, we performed a one trial learning experiment in which we varied errors in vision, 80 proprioception, and size of discrepancy throughout the same task. Our results demonstrate that, 81 regardless of sensory modality, sensitivity to error declines with increasing error size. Furthermore, 82 discrepancy between modalities does not significantly modulate error sensitivity, thus learning from each 83 modality may occur independently. Finally, we show that the relationship between sensitivity and error 84 size is similar to the relationship between the probability of a complex spike and error size. This suggests 85 that the occurrence of a complex spike may be a reflection of sensitivity to error, and not the error itself. 86 87 Methods 88 Ten subjects (age 25.8 ± 3.7 years, 4 male) participated in the experiment. The protocol was 89 approved by the Johns Hopkins Institutional Review Board and all subjects provided written consent. All 90 subjects were healthy, right hand dominant and naive for the purpose of the experiment. Subjects held the 91 handle of a robotic manipulandum with their right hand below an opaque horizontal screen that prevented 92 view of their arm (Fig. 1A). An elastic force helped guide their hand to the start position, indicated by a 93 6x6mm green square. Once the hand was within 1 cm of the start box, a cursor indicating current hand 94 position was turned on. After stopping within the start box, a target box (6x6mm square) appeared at 8cm 95 distance and the start box disappeared. There was only a single target, always located 8 cm above the 96 start position. Subjects were required to make a ballistic movement through the target box (a shooting 97 movement), crossing through the target between 150 and 250 ms after the movement start, at which point 98 a ”pillow” force field cushioned and slowed their movement and the robot brought the hand back to the 99 target box. The cursor indicating hand position remained on until the hand was returned to the target box. 100 Subjects then received feedback regarding their movement. Feedback consisted of the target box turning 101 red, blue or “exploding,” indicating that the movement was too fast, too slow, or accurate and correctly 102 timed, respectively. For every target explosion, subjects gained a point towards their score. Subjects 103 were instructed to score as many points as possible. 104 The experiment lasted approximately 90 minutes. There were 10 blocks with 80 movements in 105 each. The experiment began with a warm-up period of 40 movements through a null field to acquaint the 106 subjects with the apparatus. 107 Perturbations 108 Subjects were exposed to 11 different perturbation types, each applied in both the left and right 109 directions. In each block, all of the possible 22 perturbation types appeared once in a random order (Fig. 110 1B). Thus not only was the overall experiment balanced, but each individual block as well. The 111 perturbation trials consisted of a force perturbation and a visual perturbation. The force perturbation was 112 caused by a velocity dependent curl force field that applied force perpendicular to the direction of 113 movement, 114 0 0 B B   =   −   f x 115 where x is hand velocity. There were three possible force perturbation sizes, causing a small 116 proprioceptive error ( B = ±6.5 N.s/m), a medium proprioceptive error ( B = ±13 N.s/m) or a large 117 proprioceptive error ( B = ±19.5 N.s/m) to the left or right. Fig. 1C shows sample hand trajectories for 118 rightward perturbations. For the small or medium force perturbation one of five possible visual gains 119 were applied to the cursor trajectory. The visual gain, , g scaled the lateral deviation of the hand from the 120 straight line to the target by 0, 0.5, 1, 1.5, or 2. Thus, the lateral trajectory taken by the cursor, x c , had 121 either smaller, the same, or larger error than the lateral trajectory taken by the hand, x h : 122