## Abstract

We discuss a new framework for understanding the structure of motor control. Our approach integrates existing models of motor control with the reality of hierarchical cortical processing and the parallel segregated loops that characterize cortical–subcortical connections. We also incorporate the recent claim that cortex functions via predictive representation and optimal information utilization. Our framework assumes that each cortical area engaged in motor control generates a predictive model of a different aspect of motor behavior. In maintaining these predictive models, each area interacts with a different part of the cerebellum and BG. These subcortical areas are thus engaged in domain-appropriate system identification and optimization. This refocuses the question of division of function among different cortical areas. What are the different aspects of motor behavior that are predictively modeled? We suggest that one fundamental division is between modeling of task and body whereas another is the model of state and action. Thus, we propose that the posterior parietal cortex, somatosensory cortex, premotor cortex, and motor cortex represent task state, body state, task action, and body action, respectively. In the second part of this review, we demonstrate how this division of labor can better account for many recent findings of movement encoding, especially in the premotor and posterior parietal cortices.

## INTRODUCTION

Kenji Doya proposed an influential hypothesis that delineated the roles of these different brain structures based on computational principles (Doya, 1999, 2000). Doya suggested that the cerebellum, the BG, and the cerebral cortex are specialized for different types of learning: supervised learning, reinforcement learning, and unsupervised learning, respectively. Doya addressed the way that these different learning rules might shape the roles each motor area played in motor behavior. His view was that the learning rules would lead the cerebellum to form internal models, the BG to play a role in action selection, and the cortex to form representations of state and action. Different versions of this idea of the functions of these different areas have served the field well for many years. However, they were brought together particularly powerfully when they were connected to ideas of optimal feedback control introduced into the field by Emo Todorov and Michael Jordan. The optimal feedback control theory for motor coordination (Todorov & Jordan, 2002) suggested a mathematical approach for motor control, which formalized the relationship between motor commands, task goals, sensory–motor noise, and sensory feedback. In this formulation, motor commands were chosen to achieve task goals based on an estimate of state that combined sensory feedback with the system's prediction of the current state. The task goals are represented as a cost-to-go function. The cost-to-go function ascribes the current state a value that combines how well it leads to achievement of task goals and how much effort will be required to achieve them. Reza Shadmehr and John Krakauer (2008) used Todorov's optimal feedback control framework as the basis for a computational neuroanatomy of motor control. In their scheme, primary motor and premotor cortices generate motor commands, whereas the BG evaluate the cost-to-go function, and the cerebellum predicts upcoming state. In recent years, the term “computational neuroanatomy” mostly refers to algorithm-based quantitative approaches to image processing and 3-D reconstruction associated with the study of neuroanatomy. Here, we use it in the same sense used by Shadmehr and Krakauer (2008) to describe the identification of distinct motor control processes from computational models and their mapping to different brain regions.

In this article, we try to extend these influential theories in two key ways. First, we suggest that each of the cortical areas involved in motor control may be implementing the model described by Shadmehr and Krakauer (2008), based on anatomical evidence that each cortical region forms its own loops with the BG and the cerebellum. Second, we suggest that these different cortical areas may be interacting in ways that are consistent with existing influential perspectives on the cortical hierarchy, which focus on the cortex's role in representing prediction and optimal information utilization (Kanai, Komura, Shipp, & Friston, 2015; Clark, 2013). These two extensions combine to produce a new, coherent model of the neuroanatomy of motor control.

### Multiple Cortical Loops with the BG and the Cerebellum

Compelling anatomical evidence supports the existence of parallel loops connecting cortical areas with both the BG and cerebellum. The loops are characterized by a high degree of topographic specificity (Middleton & Strick, 1997, 2001). Most areas of the cortex receive input from dedicated, separate regions of the BG, and the most prominent input to a given region of the BG derives from the same area of cerebral cortex to which it projects. Most cortical areas have a similar loop with the cerebellum (Bostan & Strick, 2018; Dum & Strick, 2003; Kelly & Strick, 2003; Middleton & Strick, 1997). Neuroanatomical studies have demonstrated that cerebellar output reaches many areas of the cortex, including the posterior parietal cortex (PPC) and regions of pFC (see Bostan, Dum, & Strick, 2013, for a review). The primary somatosensory cortex (S1) has projections to the BG (Künzle, 1977) and the cerebellum (Middleton & Strick, 1998). Gerbella, Borra, Mangiaracina, Rozzi, and Luppino (2016) suggested that cortical regions connected one to another (such as specific sectors of the premotor and parietal cortices) also have convergent projections to the same striatal sectors. However, the figures for individual monkeys suggest that it is a group effect because of interparticipant variability in the projections, and within each monkey, there is only partial overlap in the striatal sectors (e.g., Case 62, Figures 10 and 11). Neuroimaging lacks the resolution to address the different pathways, yet human neuroimaging studies also support the notion that different cortical regions are bidirectionally connected to distinct areas of the cerebellum and the BG (Seitzman et al., 2020; Choi, Yeo, & Buckner, 2012; Buckner, Krienen, Castellanos, Diaz, & Yeo, 2011; Yeo et al., 2011; O'Reilly, Beckmann, Tomassini, Ramnani, & Johansen-Berg, 2010).

A model based on this notion of parallel segregated loops of different cortical areas with the BG and the cerebellum was first presented by James Houk, who refers to it as a distributed processing module (DPM; Houk et al., 2007; Houk, 2001, 2005). According to Houk, a given area of the cortex together with its subcortical loop(s) forms a DPM and the different distributed modules communicate with each other through cortico-cortical connections. Cognitive neuroscientist Takashi Hanakawa suggested a model similar to the DPM model to explain how the premotor cortex (PM) can serve as a gateway between motor and cognitive networks (Hanakawa, 2011). The Hanakawa model is consistent with the model we present below, although our focus is on the roles of premotor and parietal cortices in task–body integration where the Hanakawa model focuses on motor–cognitive integration.

Recent findings of direct connections between the BG and the cerebellum (Quartarone et al., 2020; Bostan & Strick, 2018) add complexity to the view of parallel segregated loops. However, one prominent theory proposes that the newly found connections are part of an integrated network that balances the relative influence of the BG and the cerebellum without changing their respective roles (Bostan & Strick, 2018; Taylor & Ivry, 2014). More controversially, there are recent reports of actual reward processing in the cerebellum (Medina, 2019) based on findings of reward signals in cerebellar climbing fibers (Kostadinov, Beau, Blanco-Pozo, & Häusser, 2019; Heffley et al., 2018). This may challenge the canonical view of the cerebellar role in motor control and learning. However, it is also possible that the reward signals reflect upstream influences of reward on kinematics (Lixenberg, Yarkoni, Botschko, & Joshua, 2020). Another suggestion is that some climbing fibers play a homeostatic role and do not affect motor learning (Tang et al., 2017). A final alternative is that reward signals in the cerebellum are found more laterally in the cerebellum and thus reflect internal modeling of reward that is not directly connected to movement (Sendhilnathan, Semework, Goldberg, & Ipata, 2020; Heffley & Hull, 2019; Tsutsumi et al., 2019). Considering other recent results showing that climbing fibers provide predictive signals about movement parameters (Streng, Popa, & Ebner, 2018), the canonical view is still widely accepted (Apps et al., 2018; Sokolov, Miall, & Ivry, 2017).

It is also worth considering recent findings suggesting that basal ganglionic dopamine signals do not necessarily reflect reward prediction error (Cox & Witten, 2019). These findings are in line with an increasingly prominent hypothesis that direct and indirect pathways in the BG circuit respectively calculate parallel and separate evaluations of action selection and outcome evaluation (Nonomura et al., 2018; Stephenson-Jones et al., 2016; Stephenson-Jones, Kardamakis, Robertson, & Grillner, 2013). This would explain why neurons associated with the direct pathway would not be sensitive to reward. This hypothesis is consistent with findings that the activity of substantia nigra dopaminergic neurons not associated with reward is strongly associated with movement selection and movement vigor (da Silva, Tecuapetla, Paixão, & Costa, 2018).

### Cortical Function

The cerebral cortex has a laminar organization, and certain aspects of the laminar organization are preserved across most of the cortex. This includes many aspects of the distribution of neurons appearing in each layer; it includes aspects of the structure of interlaminar connections and also includes the layers producing local and projection efferents (Shipp, 2007). The similarity in the connectivity patterns of the cortical layers, as well as the patterns of input and output from thalamus and other subcortical structures, has long been taken to imply that different cortical areas employ similar cortical algorithms (Douglas & Martin, 2004; Mumford, 1991, 1992) and that the cerebral cortex, like the cerebellum and BG, is specialized for a particular computation that is applied in different contexts (Doya, 1999).

However, recent findings highlighting the heterogeneity across cortical areas mean that the computation performed may vary with the context (Palomero-Gallagher & Zilles, 2019). The variability in the neurochemistry of the different cortical areas and the variation in the width of the different cortical layers (Zilles & Amunts, 2010), as well as the variability of the patterns of lateral connectivity (Sirosh, Miikkulainen, & Choe, 1996), suggest that the cortical algorithm varies in ways that match specific processing demands in each area of the cortex (Barbas, 2015). To take a familiar example, the target of thalamic input, Layer IV, is unusually thick in the visual cortex. This makes sense, because this input brings the visual input to the visual cortex. In contrast, Layer IV is nonexistent in the motor cortex. Thalamic input to the motor cortex, which represents the output of the BG and the cerebellum, projects to other layers. Thus, processing in the two areas will be different despite the many similarities between them.

One traditional view of the cortical structure is that the cortex is essentially a tool for representation: Each area of the cortex represents different aspects of reality based on the inputs it receives and the sensory–motor receptive fields of its neurons (Penfield & Boldrey, 1937). Thus, information from various sensory receptors flows forward and accumulates progressively to create a full picture of the real-world scene (Marr, 1982). A more recent view looks at the brain as a dynamical system. The dynamical systems perspective predicts that “the evolution of neural activity should be best captured not in terms of movement parameter evolution, but in terms of the dynamical rules by which the current state causes the next state” (Shenoy, Sahani, & Churchland, 2013). Although some find this view to explicitly contrast with a representational view, it can also be viewed as a framework of constraints on neural representations and their dynamics (Churchland, Cunningham, Kaufman, Ryu, & Shenoy, 2010). Under this logic, even if we accept the representational view, the representations must be structured so that their dynamics interact meaningfully with the dynamics of the real world being represented (Michaels, Dann, & Scherberger, 2016; Churchland et al., 2010, 2012). Structural and neurochemical variations between cortical regions may reflect differences in the aspects of reality being represented (Palomero-Gallagher & Zilles, 2019). These differences would certainly include differences in the time constants of the dynamics as well as the relative importance of prediction and reliability of new information. It may also reflect the dimensionality of the predictive space.

Karl Friston and colleagues have been developing a related approach suggesting that cortical representation is essentially predictive (e.g., Kanai et al., 2015; Clark, 2013; Bastos et al., 2012; Friston, 2010). In this view, cortex mimics the dynamics of the represented world to represent future sensory stimulation. In their view, motor commands are characterized as predictive representations of proprioceptive input (Adams, Friston, & Bastos, 2015). Importantly, parallel segregated loops are a key property of the canonical circuits for predictive coding suggested by Friston and colleagues (Bastos et al., 2012). Incorporating the dynamical and predictive accounts of cortical function and the parallel loops described above into the Shadmehr and Krakauer (2008) scheme leads to a multilayer model described in the next section.

## A REVISED MODEL FOR NEUROANATOMY OF MOTOR CONTROL

Here, we consider the different aspects of reality that might be dynamically represented in different cortical areas. We address two orthogonal dissociations: body versus task and state versus action. What the body is actually doing we call body-state. Our motor commands and our active efforts to move the body we call body-action. Similarly, task-state and task-action represent the movement within the task space. Let us consider again the example of driving discussed earlier. In this situation, body-state is the configuration of our body (hands resting on the wheel, right foot pressing the gas pedal), whereas body-action is the movement of our limbs (moving the hands to rotate the steering wheel and changing the pressure applied by the foot to the pedals). Task-state is the configuration of the car within the task (the car is driving 60 mph in the right lane), and task-action is the movement of the car within the task (taking a turn, accelerating, or breaking).

In many situations, these different predictive dynamical representations are highly correlated. When we reach to a visual target, task-state encodes origin, target, and cursor position; task-action is the movement of the cursor to the target; and body-action is the movement of the hand. In the absence of “experimenter trickery” (such as the well-studied visuomotor perturbations), these naturally represent the same direction. Neuronal coding might be quite similar in different cortical areas (e.g., cells with similar directional tuning [Mahan & Georgopoulos, 2013]). This connects to the familiar credit assignment problem (Wolpert & Landy, 2012), as an error can be assigned to different representations of the body and the task. The system relies on various cues, priors, and heuristics to resolve the source of its errors (Wei & Körding, 2009; Berniker & Körding, 2008), although the computational details are still being explored (Gaffin-Cahn, Hudson, & Landy, 2019; Parvin, McDougle, Taylor, & Ivry, 2018; McDougle et al., 2016).

The differences between the different representations become clearer in the context of a more complex task. For instance, we consider pool or billiards (Haar & Faisal, 2020; Haar, van Assel, & Faisal, 2020). In preparing and making a shot (Figure 1), task-state encodes ball locations and movement and the pocket into which you want to sink the ball. Task-action is defined on the table: how the cue stick hits the white ball and the effect it should have and how the white ball should hit the target ball to push it toward the pocket. In contrast, body-state describes your posture and the way you are holding the cue stick, whereas body-action is the movement you make to take the shot.

Figure 1.

A game of billiards as a model for state and action representations. The task-state would encode mostly the locations of the white ball, the red (target) ball, and the pocket that you want to sink the ball to. The task-action would be the action on the table—the cue stick should hit the white ball in a certain position with a certain angle, spin, and speed, and the white ball should hit the target ball and push it toward the pocket. The body-state would be the player's posture and the way they hold the cue stick, and the body-action would be the movement that they perform to move the cue stick.

Figure 1.

A game of billiards as a model for state and action representations. The task-state would encode mostly the locations of the white ball, the red (target) ball, and the pocket that you want to sink the ball to. The task-action would be the action on the table—the cue stick should hit the white ball in a certain position with a certain angle, spin, and speed, and the white ball should hit the target ball and push it toward the pocket. The body-state would be the player's posture and the way they hold the cue stick, and the body-action would be the movement that they perform to move the cue stick.

Our model combines Houk's DPM model with Shadmehr and Krakauer's scheme based on optimal control theory. That is, we propose a multilayer model where at the center of each layer is a cortical region. For each cortical region, activity is affected by a loop through the BG that incorporates expected costs and rewards into its dynamics. The dynamics of each region is also affected through connections with an area of the cerebellum that does predictive error correction: It predicts and corrects persistent errors in the cortical representation of dynamics. This is consistent with the suggestion by Frens and Donchin (2009) that state estimation is actually computed in the deep cerebellar nuclei and with the findings of Gao et al. (2018) showing that ongoing movement representation in the cortex is dependent on the cerebellum. Together, the different cortical regions represent a predictive representation of both state and action (Figure 2).

Figure 2.

A multilayer model for motor control. In each layer (marked by different colored dots and arrows), a cortical region is making a loop with a designated area in the BG for expected costs and rewards as well as another loop with an area of the cerebellum for forward modeling and state estimation. Each layer represents a different function over the two fundamental divisions of task versus body and state versus action. Bidirectional communication between these different layers takes place in the cortex.

Figure 2.

A multilayer model for motor control. In each layer (marked by different colored dots and arrows), a cortical region is making a loop with a designated area in the BG for expected costs and rewards as well as another loop with an area of the cerebellum for forward modeling and state estimation. Each layer represents a different function over the two fundamental divisions of task versus body and state versus action. Bidirectional communication between these different layers takes place in the cortex.

This view fits naturally with the proposal that the cortex is a tool for predictive estimation and dynamic representation. It elaborates the proposal by suggesting that what distinguishes the different areas of the cortex is that they emphasize different parts of reality with different dynamics. For the motor system, we propose that premotor, primary motor, somatosensory, and posterior parietal cortices all predictively represent the ongoing reality and dynamics of our motor behavior but with different emphases. We hypothesize that the primary motor cortex (M1) and S1 are concerned with the bodily aspects of movement whereas the PM and PPC emphasize movement inside the construct of our current task. At the same time, the frontal areas (M1 and PM) are associated more strongly with action for both body and task, whereas the parietal areas (S1 and PPC) are concerned with body-state or task-state. The idea that M1, S1, PM, and PPC have differential functions in body state and task conditions was suggested before (Cisek & Kalaska, 2010), but using different terms and not in the framework of optimal control.

In our model, activity in M1 and PM determines eventual motor output, and the interactions between them creates body-action and task-action chosen in concert. The activity in these areas at any time is determined in part by the ongoing dynamics of task and body actions. However, it is also influenced by the current state of the task and the body, and these are predicted by the parietal cortex. All of these dynamics must be shaped with the aim of achieving task goals. The parietal cortex must ensure that predictions of body-state reflect known dynamics of the body and ongoing sensory input. It must also ensure that predictions are updated in concert with predictions of task-state. Predictions of task-state must reflect known task dynamics.

Mathematically, our model is based on that of Shadmehr and Krakauer (2008) but extends its dimensionality. That is, for Shadmehr and Krakauer, there was only one cortical/subcortical loop, whereas our model considers multiple loops. This means that our definitions of state must be expanded to reflect the state in each of the loops simultaneously and the interactions between them. Thus, superficially, the “internal model” of the dynamics as a linear function of motor commands is the same:
$xˆt+1t=Axˆtt+But$
(1)
$yˆt=Hˆxˆt$
(2)
where u(t) is the motor command and $yˆt$ is the expected sensory consequence. $xˆtt$ represents the predicted state at time t given current and previous sensory feedback. However, in our model, the dimensionality of the state vector is increased to include the hypothesized states of the different cortical representations:
$xˆ=xBAxTAxBSxTSBA=Body ActionTA=Task ActionBS=Body StateTS=Task State$
(3)
The body-action and task-action here are not the descending motor command u but the cortical representations of action in the body space and in the task space, which play a role in determining u but are distinct from it and are also influenced by dynamics of the entire system. Matrix A represents the dynamics of the state. Its block diagonal reflects the dynamics of each cortex separately, whereas the off-diagonal blocks describe the cortico-cortical interactions:
$A=ABADBA←TADBA←TS0DTA←BAATA0DTA←TSDBS←BA0ABSDBS←TS0DTS←TADTS←BSATS$
(4)
The single motor command u influences each cortical representation differently, and B captures these different effects:
$B=BBABTABBSBTS$
(5)
Again, as reality is unified, the state of the different cortical areas must be combined to generate a single sensory vector of sensory predictions, $yˆ$. For simplicity, we take the sensory feedback to only include proprioceptive and visual components, y = $ypyv$, although in principle, it probably also affects other modalities including auditory and haptic. The relative contributions of the different cortices to the prediction of sensory feedback are determined by the Matrix H in Equation 2:
$H=Hp,BAHp,TAHp,BSHp,TSHv,BAHv,TAHv,BSHv,TS$
(6)
In addition to Equations 1 and 2 above that describe internal representation of state dynamics and input prediction, the model includes a Kalman gain equation, updating the belief state at time t + 1, given the acquired sensory information. Here, again, our equation is identical to that of Shadmehr and Krakauer:
$xˆt+1t+1=xˆt+1t+Kt+1yt+1−yˆt+1$
(7)
However, in our model, the Kalman gain includes separate blocks from the physical dimensions of the sensory consequences to the neural dimensions:
$Kt+1=KBA,pKBA,vKTA,pKTA,vKBS,pKBS,vKTS,pKTS,v$
(8)
In addition, in the “cost-to-go” function:
$ut=−Gtxˆtt−1$
(9)
the Matrix G would not be in sensory dimensions (v, p) but in neural dimensions:
$Gt=GBAGTAGBSGTS$
(10)

Importantly, the state-versus-action dissociation here is not simply sensory versus motor. The state representation of the body (xBS) is more than its sensory state. Even in the absence of any sensory feedback, there is a representation of the current state of the body (posture, fatigue, etc.) and the future states the body can transition toward. The task-state representation (xTS) is even more distinct from a sensory representation as it accounts for all abstract rules of the task, like driving on the right or left side of the road. Similarly, the body-versus-task dissociation addressed here is different than the common dissociation of intrinsic versus extrinsic coordinate frames (e.g., Haar, Dinstein, Shelef, & Donchin, 2017; Wiestler, Waters-Metenier, & Diedrichsen, 2014; Buneo & Andersen, 2006; Kalaska, Scott, Cisek, & Sergio, 1997). In fact, both body and task can be represented in either coordinate frame or in both. Indeed, there is evidence for both intrinsic and extrinsic coordinate frames in the different cortices discussed (e.g., Wu & Hatsopoulos, 2006, 2007). Nevertheless, in the primary sensorimotor cortices, those representations, in any coordinate frame, would always be of the body and not the task (e.g., the hands on the steering wheel and not the car on the road). Similarly, in the PM and the PPC, those representations, in any coordinate frame, would always be of the task and not the body.

The representations of the body's state and action are not at all independent, of course; the extent to which they interact is attested by the strong connectivity between M1 and S1 (Equation 4). However, although they are both fundamentally representing the same thing—the position of the body and its movement—they represent different aspects of that same thing. M1 is focused on the world of our possible movements, whereas S1 is focused on what effect our movements and the world around us will have on our body. Accordingly, limb perturbation should be processed first in S1 (body-state) and then in M1 (body-action) and PPC (task-state), as the change in the body-state affects both body-action and task-state. Only then will processing pass to PM (task-action), which is affected by body-action and task-state but not directly by body-state (see Equation 4). Indeed, an examination of the relative timing of perturbation-related activity across sensory and motor cortices showed this timing gradient (Omrani, Murnaghan, Pruszynski, & Scott, 2016). Moreover, the authors found that, when the same perturbation is applied with and without task context, the earliest and biggest difference in the neural response is in the PPC, as the task is not experimentally defined and might not be the same in all trials. Thus, the same change in body-state does not induce a consistent change in task-state.

As discussed, Hanakawa (2011) presented a model, similar to ours, describing the role of PM in mediating between motor and prefrontal-cognitive cortices. Under the combined framework, we can imagine that pFC could represent our ongoing plans, strategies, and desires. These should guide the task-action, which later guide the body-action. Caminiti et al. (2017) also emphasize the importance of task-related processing in higher level areas but focus on the relationship of the task/body system with higher-order processing of reward, motivation, and attention in ways that are reminiscent of Hanakawa's model but do not focus on the relative role of motor and premotor cortices.

In our model, each of the different cortical areas has projections to the BG to account for the different costs and rewards associated with each type of representation. In essence, it follows the model of Nakahara, Doya, and Hikosaka (2001), which suggests that parallel cortico-BG loops learn different coordinates with different costs and rewards. We suggest those are not coordinates but representations of task versus body and state versus action. For instance, Yeo, Franklin, and Wolpert (2016) discuss the fact that one consequence of movement is its effect on the quality of sensory information. They show the need to account for sensory costs in the framework of optimal feedback control. Following this logic, BG interactions with sensory cortices may relate to optimizing our behavior to maximize the relevant sensory precision.

Inherent in this perspective is an approach to simultaneous representation of state and action. Because each cortical area is representing a particular aspect of reality, inherent in that representation is the implied representation of the dynamics of that aspect of reality. That is, a state representation contains in it, necessarily, an understanding of which states can arise from which other states. In addition, the dynamics of state are influenced by ongoing action so that the precentral areas must influence the postcentral state representations. Similarly, a central part of action representation is the way that one action flows into the next (or leads to the holding of a posture). The dynamics of movement are only as much informed by the ongoing dynamics of state as ongoing state dynamics are informed by knowledge of ongoing actions.

Generally speaking, the dynamics of both body and task are high dimensional, nonlinear, and changing over time. Thus, generally speaking, the predictive representations of every cortical area will be fraught with error. In this sense, if the cerebellum engages in error-driven learning, it can serve each of the cortical areas by learning to predict the errors in its predictive representation. This is precisely the interaction between the cerebellum and cortex hypothesized by Doya (2000). In this view, the cerebellum will play a different role when it corrects for the errors in different cortical representations. However, although the form of the errors will depend on the domain being represented and the model that has developed, the computations underlying the cerebellar circuitry will be the same.

The proposed roles of M1 and S1 in representing body-action and body-state, respectively, are straightforward. We use new terminology to describe the commonly accepted roles of these areas. As such, we do not need to take a position on classical debates regarding coordinate systems (muscles vs. movements). From our perspective, this is a discussion of how body-action is encoded: important in itself but at a level of description that is not our focus. The roles of the PPC and the PM in task-state and task-action representation, respectively, require further discussion. There is much less clarity about their roles, and more work needs to be done to show how our perspective fits in with previous ideas. In the next section, we demonstrate how our perspective helps make sense of the literature.

There are several schools of thought about the role of PPC. One common view is that the PPC serves as a sensorimotor interface for visually guided movements (e.g., Buneo & Andersen, 2006). As such, it is involved mostly in sensory–motor mapping and motor planning (Andersen & Buneo, 2002; Cohen & Andersen, 2002). Perhaps, the leading alternative view is that the PPC is a state estimator, as was originally suggested by Daniel Wolpert and colleagues (Wolpert & Ghahramani, 2000; Wolpert, Goodbody, & Husain, 1998) and later integrated into the current model of computational neuroanatomy for motor control (Shadmehr & Krakauer, 2008). Other possibilities have also been put forward. They include high-order sensory–motor information integration in support of high-level motor functions (e.g., Fogassi & Luppino, 2005) and conscious motor intentions (e.g., Desmurget & Sirigu, 2012). We believe that thinking in the abstracted terms of task-state representation will help clarify this extensive literature and subsume alternative perspectives within a single framework.

Gréa et al. (2002) reported that a patient with bilateral PPC damage had no difficulty reaching to targets in their central fixation, but when the target jumped at reach onset, the participant could not correct for it and continued to reach to the original target location. Desmurget et al. (1999) produce similar results on healthy participants using a single-pulse TMS at reach onset. This phenomenon is a classic example for a deficit in task-state representation. The participant simply could not adjust to the sudden change in the task-state. A study by Funamizu, Kuhn, and Doya (2016) produced similar results using optogentics in mice. Mice express learning in a task by increased anticipatory licking as they approached their goal, even in the absence of external cues. Thus, the mice are expressing their estimation of task-state. The authors showed that silencing of the PPC prevented this ability to evaluate task-state. When the PPC is intact, it encodes task-state continuously; for example, it encodes changing target position even while the body is not yet moving (Reid & Dessing, 2018).

Task-state representation requires high-level effector-invariant components in the neural responses during hand and arm movements for general task properties like the task goal or task rule (e.g., proreach vs. antireach, or reach vs. grasp). This invariance in the representation of task properties will be matched by a lack of sensitivity to kinematic components that are not related to the task. On the other hand, body-action and body-state representations should reflect kinematics. Task-action representations might include both kinematic and effector-invariant properties as well as kinematic and effector-dependent properties. Indeed, effector-invariant representation of reach versus grasp was found in the PPC and PM but not in M1 and S1 (Gallivan, McLean, Flanagan, & Culham, 2013). At the same time, effector-invariant representation of reaching movement direction (in joint coordinates) was found in M1, S1, and PM, but not in the PPC (Haar, Dinstein, et al., 2017). The study of motor variability also supports this framework. In measurements made without feedback, where movement variability is dominated by planning noise (Dhawale, Smith, & Ölveczky, 2017), we demonstrated that individual movement variability magnitudes are best predicted by cortical neural variability in the PPC (Haar, Donchin, & Dinstein, 2017). Thus, the variability in the PPC is variability in the task-state domain.

Because most motor control experimental paradigms involve visual feedback, many of the examples above could also be explained simply as if the PPC is representing the visual feedback in the task. Yet, there are examples like Funamizu et al. (2016), where mice are expressing their estimation of task-state in the absence of external cues, but silencing of the PPC prevented this ability, which supports the idea that the PPC is involved in task-state estimation, regardless of specific sensory input. The Heed et al. (2018) fMRI study, which was mentioned above, used tactile stimulation (and not visual) and thus provides another support.

Another recent review has also managed to incorporate a broad group of approaches to the PPC within a consistent framework (Medendorp & Heed, 2019). They argue that different areas of the PPC show different behaviors because they represent the world along two key axes. The first—the rostrocaudal axis—separates representation of body from that of the environment. The second—the mediolateral axis—separates representations of different “action classes.” This review thus addresses an aspect of PPC function explicitly outside the scope of our review: the functional subdivisions within the PPC; their work is fully complementary to our own. For instance, they emphasize that PPC activity is highly dependent on task and context and represents those aspects of body and environment that are relevant to task performance. We suggest a generalization of their approach where rostral PPC reflects the projection of the self into the task—the representation of our ability to have direct effects in the task—rather than an explicit representation of the body, which is more properly the role of S1.

We propose that the role of the PM is to represent task-action. Only a few studies in the existing literature can speak to this question. Most often, PM is studied in tasks involving direct reach to target. In these tasks, task-action representation is simple and consistent with both task-state and body-action. Nevertheless, some studies show dissociation between body-action representation in M1 and task-action representation in PM. For instance, Schwartz, Moran, and Reina (2004) used a motor illusion to separate monkeys' perception of arm movements from their actual movements during figure drawing. Trajectories constructed from cortical activity of the monkeys showed that the actual movement (body-action) was represented in M1, whereas the visualized trajectories (task-action) were found in the ventral PM.

In patients with stroke performing imitation movements, deficits were found to be associated with PM lesions. Imitations were equally impaired when cued by an actor's arm movement or by a cursor, suggesting abstract body-independent movement representation (task-action) in PM (Wong, Jax, Smith, Buxbaum, & Krakauer, 2019). Further support for this dissociation can be found in the result of a study (Saberi-Moghadam, Ferrari-Toniolo, Ferraina, Caminiti, & Battaglia-Mayer, 2016) showing that, when target jumps caused a sudden change in motor intention, this led to earlier changes in PM activity than in M1. In this task, information at the task level was driving the change in motor intention so task-level representation changes drive changes at the body level. We predict that tasks where the perturbation is at the body level and not the task level (for instance, a perturbation of the hand that is not reflected in the cursor) should drive changes that arise first in M1.

More support for task-action representation in the PM can be found in the results of Pastor-Bernier and Cisek (2011), which show that directional tuning of neurons in PM modulated after changes in rewards associated with targets in the preferred direction of the neuron. This modulated tuning reflects a change in the task-action associated with the same task state. Pearce and Moran (2012) used a complex obstacle-avoidance task and showed that PM activity is modulated both by task demands and by the particular strategy being used. They looked at the activity of the PM neurons during trials differing both in the target direction and in the obstacle opening directions and showed that the same neurons show directional selectivity both to the target direction and to the obstacle opening direction. This dual directional selectivity is a good example for task-action representation in the PM. Finger sequencing is another task where the task and body representations differ: The task-action is the sequence, whereas the body-action is individual finger movements. Indeed, a recent fMRI study by Yokoi, Arbuckle, and Diedrichsen (2018) found that, after intense practice on finger sequences, activity patterns in PM and PPC encoded the task (the different movement sequences), whereas the activity patterns in M1 and S1 could be fully explained by the body action/state: a linear combination of patterns for the constituent individual finger movements.

Last, a recent study by Martínez-Vázquez and Gail (2018) looked at the LFP-directed interaction between PM and PPC during movement planning and execution. They found that, during movement planning, the direction of the interaction is from the PPC to the PM, and during movement execution, there is a flip in the direction of the interaction that flips back after execution. These findings are again consistent with our model. During planning, PM receives information from PPC regarding task-state to plan task-action. During execution, PPC receives information from PM regarding ongoing task-action to update task-state.

## CONCLUDING REMARKS

Shadmehr and Krakauer's (2008) proposal for a neuroanatomy for motor control, presented a decade ago, highlighted the cortical loops with the BG and the cerebellum and suggested that they serve for computing costs and for system identification, respectively. We present a new model inspired by that scheme that emphasizes parallel loops connecting different cortical areas with these subcortical regions. This aspect of our model draws inspiration from Houk's DPM model (Houk, 2001) and is supported by compelling anatomical evidence (Middleton & Strick, 1997, 2001). In our model, we address the notion that each area of the cortex represents reality in a different way with different emphases. We suggest that the primary somatosensory and motor cortices represent, respectively, the state and action of the body, whereas the PPC and PM represent the state and action of the task, respectively.

Although it is largely accepted that the BG and the cerebellum form parallel segregated loops with different cortical regions, there is an alternative view of a funnel-like organization from wide areas of the cortex through the subcortical regions onto a small area of the cortex (Allen & Tsukahara, 1974; Kemp & Powell, 1971). Recent findings suggest caveats to the parallel segregated loops framework (Aoki et al., 2019) but still support it. If this ongoing controversy ultimately shows that the parallel segregated loops are a poor model for BG and cerebellar connectivity to the cortex, our proposed model will be undermined.

Ultimately, we wish to emphasize that this model is only a limited cartoon and makes no attempt to capture the full complexity of the cortical hierarchy in motor control or its subcortical connections. Some of these simplifications have been addressed above. Nevertheless, our model advances the paradigm within which we think about and study the motor cortices. It points the way forward toward a developing understanding of the task/body dimension and the need to distinguish the complex relationships of each cortical area to its subcortical support and develop a fuller understanding of each of the parallel loops.

In models of this sort, precise anatomical definitions of the BG and cerebellum are left somewhat vague. This is true for the Shadmehr and Krakauer (2008) model, for the models of Houk (2001) and Hanakawa (2011), and also for our own model. However, the basic idea is that parallel loops with the BG will include parallel instantiations of the direct pathway, the indirect pathway, and the hyperdirect pathway (Nambu, Tokuno, & Takada, 2002). Similarly, in the cerebellum, the idea is that the full cerebellar microcircuit is involved where cortical input drives mossy fibers originating in the pons as well as climbing fiber input originating in the inferior olive and that the output of the circuit will be from the dentate nucleus via the thalamus (Raymond, Lisberger, & Mauk, 1996).

Indeed, this class of models further schematizes the motor system because the models generally do not address subdivisions of the PM and PPC and often leave out other nonprimary motor areas such as SMA, pre-SMA, and cingulate motor area. The idea that the entire PM or the entire posterior parietal cortex performs a unique function is controversial (e.g., Rizzolatti, Cattaneo, Fabbri-Destro, & Rozzi, 2014). The models also fail to address recent findings showing direct connections of the BG to the cerebellum (Quartarone et al., 2020; Bostan & Strick, 2018) and ignore entirely the spinal cord, red nucleus, thalamus, and other subcortical motor areas. These models have, however, helped guide thinking about the interrelations of parts of the motor system and have been an integral part of some of the most inspiring work in our field.

One direction for future work would be the one laid out by King, Hernandez-Castillo, Poldrack, Ivry, and Diedrichsen (2019). These authors used a battery of motor, sensory, and cognitive tasks to produce a detailed map of cerebellar function. However, the tasks they selected do not allow dissociation of task-level and body-level aspects of the task. As a result, their data cannot be used to directly test our hypothesis. A similar study with specifically designed tasks would be an ideal test of our model. Another possibility for testing the dissociation of task and body representations in PM and M1 would be the use of brain–computer interfaces. Using such interfaces, we can define a task that is driven directly by activity in PM. We predict that we could ask patients to imagine doing the task with different bodily effectors and, thus, create a situation in which we can see that premotor activity is directly related to the task whereas M1 activity is related to the imagined movement of the body.

## Acknowledgments

We thank Ilan Dinstein, Liad Mudrik, Daniel Glaser, Alex Gail, and Reza Shadmehr for helpful discussions about the article. S. H. is supported by the Royal Society – Kohn International Fellowship (NF170650). Work on this review was partially supported by DFG grant TI-239/16-1.

Reprint requests should be sent to Shlomi Haar, Department of BioEngineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, or via e-mail: s.haar@imperial.ac.uk.

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