A Leg to Stand On: Computational Models of Proprioception

Journal Pre-proof

A leg to stand on: computational models of proprioception

Chris J. Dallmann, Pierre Karashchuk, Bingni W. Brunton, John C. Tuthill

PII: S2468-8673(21)00036-5 DOI: https://doi.org/10.1016/j.cophys.2021.03.001 Reference: COPHYS 426

To appear in: Current Opinion in Physiology

Received Date: 6 February 2021 Accepted Date: 1 March 2021

Please cite this article as: Chris J. Dallmann, Pierre Karashchuk, Bingni W. Brunton, John C. Tuthill, A leg to stand on: computational models of proprioception, (2021), doi: https://doi.org/10.1016/j.cophys.2021.03.001

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Chris J. Dallmann1,*, Pierre Karashchuk2,*, Bingni W. Brunton3,+, and John C. Tuthill1,+

1Department of Physiology and Biophysics, University of Washington, Seattle, WA, USA 2Neuroscience Graduate Program, University of Washington, Seattle, WA, USA 3Department of Biology, University of Washington, Seattle, WA, USA *Co-ﬁrst authors +Co-senior authors

Abstract bations. A classic example of a proprioceptive perturbation Dexterous motor control requires feedback from proprioceptors, experiment is the use of vibration to artificially excite primary internal mechanosensory neurons that sense the body’s posi- muscle spindle afferents. In humans, muscle vibration creates tion and movement. An outstanding question in neuroscience is the illusory perception that a muscle is being stretched [6]. If a how diverse proprioceptive feedback signals contribute to flexi- person is walking, vibrating their hamstring produces an increase ble motor control. Genetic tools now enable targeted recording in forward walking speed, while vibrating their quadriceps has and perturbation of proprioceptive neurons in behaving animals; little effect on walking kinematics [7] (Figure 1, top left). Dur- however, these experiments can be challenging to interpret, due ing backward walking, however, these effects are reversed, sug- to the tight coupling of proprioception and motor control. Here, gesting that proprioceptive feedback acts in a context-dependent we argue that understanding the role of proprioceptive feedback manner. in controlling behavior will be aided by the development of mul- Longer-term mechanical perturbations have also been used tiscale models of sensorimotor loops. We review current phe- to investigate the dynamics of sensorimotor adaptation. Bässler nomenological and structural models for proprioceptor encoding et al. [8] inverted the sign of feedback signals from the femoral and discuss how they may be integrated with existing models of chordotonal organ in the stick insect leg by surgically crossing posture, movement, and body state estimation. the receptor tendon (Figure 1, bottom left). This manipulation causes a walking stick insect to either “salute” or “drag” her leg, and a standing stick insect to rhythmically wave her tibia. Experimental perturbations probe the role of pro- Over the course of a month, Bässler and colleagues observed that the walking salute and dragging remained unchanged, while the prioceptive feedback in motor control waving movements gradually decreased. This observation sug- All animals possess specialized sensory neurons that monitor the gests that the postural feedback control system recovered, while mechanical consequences of their actions. These sensors, known the control system for leg movement did not. as proprioceptors, are essential for coordinating body movement These examples illustrate several hazards to consider when and maintaining body posture [1, 2]. While it is possible for executing and interpreting proprioceptive perturbation experi- some isolated motor circuits to generate structured output in the ments. First, the effects of proprioceptive feedback on motor absence of proprioceptive feedback, behaviors driven by purely output are often context-dependent, such as during forward and feedforward motor signals are often clumsy and ineffectual [3]. backward walking. Second, proprioceptive signals are typically Understanding how proprioceptive feedback interacts with motor used for controlling both posture and movement, often at the circuits to control the body remains a fundamental problem in same time. An additional challenge of mechanical perturbations neuroscience. is that they often lack specificity, leaving it unclear which specific An effective method to investigate the function of sensory proprioceptor neurons underlie the observed behavior. circuits is to perturb neural activity and measure the effect on an animal’s behavior. For example, activating or silencing neurons Neural perturbation experiments in the mammalian visual cortex [4] or insect optic glomeruli [5] has identified the circuitry and patterns of activity that underlie With the emergence of genetic tools to label and manipulate spe- visually-guided behaviors. However, due to the distributed na- cific cell-types, it has recently become possible to genetically ture of proprioceptiveJournal sensors and their tight coupling with motor Pre-proofactivate or silence specific proprioceptive neurons to assess their control circuits, perturbations to the proprioceptive system can role in behavior. However, such manipulation experiments come be difficult to execute and tricky to interpret. with their own challenges [11]. For example, Agrawal et al. [9] used optogenetics to study a population of second-order proprioceptive neurons in Drosophila that encode extension of the Mechanical perturbation experiments fly’s tibia. Activation of these neurons caused walking flies to Early efforts to understand the behavioral contributions of pro- slow down, suggesting that they may participate in controlling prioceptive feedback relied on lesions and mechanical pertur- walking speed (Figure 1, top right). However, fine-grained kine-

1 Mechanical Neural

Muscle vibration Optogenetic stimulation Walking speed Walking speed -1 -1 1 m s 10 mm s Short term

5 s 0.5 s

Inverted feedback Genetic ablation Slow walking Walking

FeCO 1

0.6 LF Saluting Dragging 0 RF LH RH RF LF 0 -0.6 Flexor 0 1 tendon RH Fast walking Rest Long term DTX DTX

3-6 days 1

0.6 LF Waving Recovered Lumbar spinal cord 0 RF 0 -0.6 0 RH 1

Figure 1: Examples of experimental perturbations used to probe the role of proprioceptive feedback in motor control. Top left: Vibration of hamstring muscles in humans stimulated muscle spindles, leading to an increase in walking speed [7]. Bottom left: Inverting sensory feedback from the femoral chordotonal organ of a stick insect front leg by crossing the receptor tendon (arrow) led to saluting or dragging of the leg during walking and waving during rest (front leg in the air, other legs on the ground). The normal rest posture of the front leg (extended in air) recovered after a few days, but saluting and dragging during walking remained unchanged [8]. Top right: Optogenetic stimulation of second-order proprioceptive neurons in tethered Drosophila walking on a treadmill caused a decrease in walking speed. Trace shows mean of multiple animals [9]. Bottom right: Genetic ablation of hindlimb muscle spindles in the mouse lumbar spinal cord caused inter-limb coordination deficits only during fast walking. 3D plots show timing (phase) of right hindlimb (RH), right forelimb (RF), and left forelimb (LF) relative to left hindlimb (LH) for gait cycles with (gray) and without (green) muscle spindles [10]. matic analysis of leg joints revealed that the same perturbation when the perturbation impacts multiple feedback loops at dif- produced reflexive flexion of the tibia whenever the leg was un- ferent levels of the nervous system. For example, activating or loaded, not just during walking. Thus, the decrease in walking silencing proprioceptors may alter postural reflexes that inter- speed was likely driven by the fly’s reaction to a perceived ex- fere with an ongoing behavior, such as walking. In other cases, tension of her tibia, rather than a disruption to walking speed changes to motor output produced by genetic perturbations may control. only become visible in specific behavioral contexts. Finally, Another recent study used intersectional genetic methods to removing proprioceptive feedback can lead to general deficits test the role of local proprioceptive feedback in rodent loco- to motor coordination that alter an animal’s ability or desire to motion. When Takeoka et al. [10] expressed Diphtheria toxin perform certain behavioral tasks. (DTX) in muscle spindlesJournal that innervate the front or rear legs Pre-proof of adult mice, they observed only subtle changes in spontaneous walking gait. The inter-limb coordination deficits produced by How models can help these ablations became apparent only when mice were forced to run at high speeds on a motorized treadmill (Figure 1, bottom Our thesis is that the design and interpretation of such perturba- right). tion experiments would benefit from the integration of models These examples illustrate how it can be misleading to infer a for proprioceptive sensing with theoretical frameworks for motor direct, causal relationship between neural activity and behavior control. Because of the tight feedback between proprioceptive

2 and motor circuits at multiple levels, the emergent behavior of Current models of proprioceptors fall into two broad cate- a sensorimotor system depends on how its components are in- gories: phenomenological models and structural models. Phe- tegrated. Therefore, computational simulations are a means to nomenological models reproduce the computational properties generate specific, quantitative predictions about the roles of key of a proprioceptor in abstraction, for instance by deriving a parameters in the system, including sensory delay, gain mod- mathematical function, often a transfer function, from exper- ulation, and encoding nonlinearities. By formalizing how the imentally determined relations between mechanics and neural components contribute to overall behavior, an integrated model activity [18–23]. This function is often derived from recorded can illustrate how different manipulations may produce similar neural activity in response to simple ramp-and-hold or sinusoidal results and aid in the design of experiments to disambiguate stimuli using linear systems theory or non-linear curve fitting. among multiple hypotheses. Phenomenological models are compact and computationally Our overall goal is to guide the design and interpretation efficient, which allows them to be integrated with models of the of experiments to understand the role of proprioceptive neu- motor system. For example, the simple muscle spindle models rons in flexible control of behavior. We first review current by Prochazka and Gorassini [20,21] have been incorporated into approaches to model sensory coding in proprioceptive sensory musculoskeletal models of arms and legs [24–27]. Similarly, neurons. Next, we discuss the role of proprioceptive feedback in the Golgi tendon organs models by Houk and Simon [23] and existing models of posture, locomotion, skilled movements, and Rosenthal et al. [28] have been used in models of the stretch re- body state estimation. Although proprioception plays an impor- flex [18, 29]. A drawback of phenomenological models derived tant role in motor learning, here we focus on innate behaviors from ramp-and-hold or sinusoidal stimuli is that they might per- driven by movement of the limbs, such as walking. We conclude form well for only a narrow subset of stimuli [20,30]. This over- by discussing three obstacles to achieving a systems-level under- fitting is particularly problematic when proprioceptor activity is standing of proprioception: (1) the diversity of proprioceptive context-dependent, such as in muscle spindles. Measuring the sensors, (2) a lack of experimental separability between proprio- responses of proprioceptors to more complex stimuli (e.g., white ceptive and motor circuits, and (3) context-dependent modulation noise or naturalistic limb trajectories) and incorporating nonlin- of proprioceptive feedback for guiding behavior. earities are both likely to produce more generalizable models of spiking responses to sensory stimuli [31, 32]. Unlike abstract phenomenological models, structural models Computational models of sensory coding in pro- derive firing patterns of proprioceptors by approximating their anatomical structure [33–39]. For example, structural models prioceptors of muscle spindles simulate intrafusal muscle fibers and their Proprioceptors are mechanosensory neurons located within mus- interaction with the extrafusal muscle and tendon. In a recent cles, tendons, and joints that convert mechanical forces in the muscle spindle model by Blum et al. [33, 34], the forces of in- body into patterns of neural activity. Proprioceptors can be trafusal muscle fibers are calculated based on measurements of classified into different functional subtypes that encode limb dis- cross-bridge kinetics. Importantly, this knowledge of mechanics placement, load, or their time derivatives [2]. For example, the allows the model to predict varied and complex spindle firing pat- proprioceptors innervating a muscle spindle encode either mus- terns, including history-dependent features. Structural models cle length or a combination of muscle length and its rate of change are more computationally demanding and make more assump- (velocity) [12]. Similarly, proprioceptors in the insect femoral tions about parameters than phenomenological models, but they chordotonal organ encode distinct kinematic parameters, includ- tend to generalize better across conditions because firing patterns ing position, velocity, and acceleration [13, 14]. Recent studies are emergent rather than built-in. Thus, structural models can be have begun to map these functional subtypes onto neuronal cell- particularly effective for proprioceptors with nonlinear tuning, types defined using genetic markers [13, 15]. These tools now such as muscle spindles. enable targeted perturbation experiments to investigate the role of proprioceptor subtypes in specific motor tasks. Due to a combination of neural and mechanical proper- Behavioral functions of proprioceptive feedback ties [16, 17], proprioceptors are tuned to biologically relevant Proprioceptive information is involved in nearly all aspects of stimuli. These same properties can make proprioceptor re- motor control, from rapid recovery after a stumble to searching sponses vary as aJournal function of stimulus history and behavioral Pre-prooffor a light switch with your toes in a dark room while your hands context. Such nonlinearities make proprioceptors different from are bound tightly behind your back. When trying to investigate most engineered sensors, which are designed to directly measure the role of proprioceptive feedback in a specific motor task, it a physical quantity, such as a joint angle or torque. Because sen- is important to consider the impact of perturbing proprioceptive sory neurons constrain the information available for other down- sensors at different levels of the sensorimotor hierarchy. Be- stream computations in the nervous system, the construction of low, we delineate the multiple levels of motor function for which proprioceptor models is an essential first step in quantitative proprioceptive feedback plays an essential role. Although we analysis of sensorimotor loops. discuss posture and movement separately, we note that they are

3 Anatomical Computational

Brain State Brain Controller Spinal estimation cord VNC Brain

Spinal cord, State Controller VNC Other estimation Other measurements modalities Timescale, hierarchy Timescale,

Body-world Proprio- Body-world Body Muscles Actuators interaction ceptors interaction measurements

Figure 2: Anatomical and computational view of proprioceptive feedback in motor control. Left: Proprioceptors from the limbs project to the spinal cord (in vertebrates) and the ventral nerve cord (VNC, in invertebrates), where they transmit sensory signals to distributed circuits for posture and movement control. Right: Proprioceptive signals affect motor control on different timescales through multiple nested feedback loops. Proprioceptive signals are integrated in low- and high-level controllers for posture, movement, and planning. They may also be used to estimate the state of the body. Note that each box represents a computation, not necessarily an anatomically confined circuit. Computations higher up in the hierarchy are more abstract and operate at longer timescales. ultimately integrated behaviors that are not necessarily controlled or they may act across joints to produce a coordinated response independently [40]. that stabilizes a task-level variable, such as the position of the hand while grasping an object [45] or the position of the body’s center of mass while standing [46]. Reflexive control of body posture Proprioceptors from the limbs project to the spinal cord (in ver- A key parameter to achieve stability in negative feedback tebrates) and the ventral nerve cord (in invertebrates), where controllers is the ratio of motor output to sensory input, known they provide excitatory synaptic input to populations of projec- as feedback gain. Tuning feedback gains can be accomplished tion neurons, local interneurons, and motor neurons (Figure 2, in modeling studies by identifying the range of parameters in left). The architecture of these circuits has been extensively stud- which the model is stable or by fitting model predictions to ex- ied [41, 42], although only recently have genetic tools begun to perimental data. In rare cases, gains have also been measured reveal the connectivity of identified cell types [9, 43]. experimentally. In one such experiment, Weiland et al. [47] Behaviors mediated by direct (monosynaptic) or nearly direct measured the gain of the feedback loop that controls the posture feedback from proprioceptors are typically characterized as “re- of the stick insect femur-tibia joint. This experiment was only flexive” because they occur with a shorter latency than voluntary possible because the anatomy of the stretch receptor (femoral movements [44]. In their simplest form, proprioceptive reflexes chordotonal organ) allowed its mechanical stimulation without rapidly (<50 ms) stabilize body posture against external pertur- affecting the surrounding muscles. Today, optogenetic stimula- bations. For example, when a physician taps the tendon near your tion may enable equivalent analyses of reflex loops that cannot knee cap, muscle spindles elicit a compensatory reaction by acti- be manipulated mechanically. vating the quadricepsJournal and inhibiting the antagonistic hamstring. Pre-proof Similarly, when a grasshopper’s tibia is flexed, proprioceptive In addition to their established function in basic postural con- feedback from the femoral chordotonal organ activates the ex- trol, elementary reflex loops also participate in more complex tensor muscle and inhibits the flexor muscle. behaviors that involve multiple joints or limbs [44]. Understand- Such stabilization reflexes can be modeled as negative feed- ing the context-dependent role and tuning of reflexes remains an back controllers, which produce corrective motor output to mini- important direction for future research, and computational mod- mize the error between the sensed posture and a reference posture. els will likely be useful in exploring the underlying circuits and These controllers may act locally to stabilize individual joints, algorithms [48, 49].

4 Feedback control of locomotion or accuracy. The role of proprioception in this framework is to Walking and other forms of locomotion are characterized by help generate and update an accurate estimate of the state of the rhythmic movements of the body and limbs. The rhythmic body, which in turn determines how the controller initiates and pattern of these movements can, in some cases, be generated refines movements. Unlike the simple negative feedback con- without feedback by intrinsically rhythmic circuits in the spinal trollers discussed above, optimal feedback controllers correct for cord and ventral nerve cord, referred to as central pattern gen- perturbations only to the degree that they interfere with task suc- erators (CPGs) [50, 51]. However, proprioceptive feedback has cess. For example, when throwing a ball to a target, an optimal long been known to regulate phase transitions, stabilize ongoing feedback controller minimizes the variability of hand trajectories movements, and adjust locomotion to changes in the environ- only around the time of release while allowing variability at other ment [52, 53]. times [64]. Several recent models of locomotion control combine feed- Although optimal feedback control can predict many com- forward motor commands from CPGs with proprioceptive feed- mon features of goal-directed movement, it remains unclear how back. Such models have been useful in testing the contribution this strategy may be implemented in the nervous system. It is of each control pathway in producing coordinated movements. typically assumed that feedback control of skilled movements For example, in a CPG model of cat walking, Markin et al. [26] is mediated by higher-order regions, such as cortex in verte- found that the integration of feedback from muscle spindles and brates, but recent experiments suggest that even fast spinal re- Golgi tendon organs is critical for providing body weight sup- flexes can produce sophisticated control reminiscent of optimal port and coordinating the legs’ transitions between stance and feedback [45,66]. In humans and other primates, there is a strong swing phases. Proctor and Holmes [54] modeled cockroach run- tradition of combining mechanical perturbations with computa- ning and found that the integration of feedback from leg joints tional models to understand the sensory inputs and algorithms (roughly corresponding to load feedback from campaniform sen- that underlie feedback control of reaching [67,68]. Recent stud- silla) with a CPG model helps recover the heading direction after ies of primate motor cortex have revealed that neural activity a lateral perturbation. Similarly, feedback from body stretch re- during skilled movements exhibits rotational dynamics that lie ceptors effectively tunes rhythmic CPG patterns for swimming on a low-dimensional manifold [69]. The role of proprioceptive and crawling [55, 56]. In fact, locomotion can be successfully signals in constructing these representations is currently unclear, modeled without CPGs [57–60], emphasizing the functional im- although a recent modeling study showed that recurrent neural portance of integrating proprioceptive feedback in low-level mo- network models trained to control a limb exhibited similar ro- tor circuits. In high-level motor circuits, proprioceptive informa- tational dynamics [70]. These activity patterns have also been tion may be used for planning movement on a longer timescale. modeled using an implementation of a feedback controller in For instance, during walking, a high-level controller may use a spiking neural network [71]. Going forward, these model- proprioceptive feedback to plan desired foot placements, which ing frameworks may also help understand the results of genetic then serve as target inputs to a low-level controller [57, 59]. perturbations to neural circuits that underlie skilled motor be- The use of proprioceptive feedback to drive or fine-tune mo- havior. As optimal feedback control models generally have few tor control of locomotion is ultimately constrained by neural parameters, they may prove particularly useful for providing ex- conduction delays and muscle kinetics. During fast running, for perimental predictions of behavior when combined with models example, proprioceptive feedback might not be fast enough to of proprioceptors. modulate muscle activity on a step-by-step basis [61]. In such situations, stable locomotion can arise from interactions between Body state estimation feedforward control and passive body mechanics [62, 63]. Us- ing direct experimental perturbations of proprioceptive neurons Natural proprioceptive signals are noisy and subject to conduc- has the potential to disambiguate the relative contributions of tion delays, creating problems for continuous feedback control. feedforward and feedback signals in locomotion control, but in- To quantify and manage the uncertainty introduced by noise and terpreting these experiments may require careful modeling of delays, the central nervous system may implement a form of state inputs and outputs at multiple scales. estimation (Figure 2, right), where sensory feedback is combined with a prediction of the body’s state from an internal model—a neural representation of the system that is being controlled [72]. Feedback control ofJournal skilled limb movements Pre-proofThis comparison of sensory feedback against an internal predic- The control of non-rhythmic movements, such as putting on a tion can compensate for sensory delays and make control more sock or dodging a projectile, also critically depends on propri- robust to sensory noise. Robustness to noise makes state esti- oceptive feedback. A particularly useful framework for mod- mation a useful strategy for controlling motor tasks, including eling such goal-directed movements is optimal feedback con- posture [73], reaching [74], and locomotion [75]. For example, in trol [64, 65]. Optimal control posits that the motor system at- a dynamical simulation of posture control during standing, both tempts to minimize a set of cost functions that describe the per- feedback and state-estimation controllers were found to be stable formance criteria of a given task—for example, movement effort against external perturbations without noise, but in the presence

5 of proprioceptive noise, only state-estimation-based control was moves through and interacts with the environment. Therefore, stable [73]. a model that describes the input-output function of a muscle It is typically assumed that state estimation occurs in higher- spindle in a leg muscle may have little in common with a mus- level circuits, such as the cerebellum and parietal cortex in ver- cle spindle in a jaw muscle. Existing models may be tuned to tebrates [72], or the mushroom bodies in insects [76]. But an match the properties of different proprioceptors (e.g. [84]), but intriguing idea is that locomotor CPGs perform computations in most cases, additional physiological data is needed. In addi- equivalent to state estimation and can thus be understood as ob- tion, there remain many proprioceptors for which models do not servers of feedback control rather than just generators of limb currently exist. Historically, there has been a strong focus on motion [77]. This idea suggests that a form of state estimation modeling the activity of mammalian muscle spindles and Golgi may occur at multiple timescales and levels of the sensorimo- tendon organs [18–21, 33–39]. In contrast, computational mod- tor hierarchy (Figure 2, right). Indeed, signals from different els of invertebrate proprioceptors are only beginning to emerge proprioceptor subtypes can converge as early as in second-order (e.g. [22, 85]), despite the growing literature characterizing en- neurons [9, 42, 78, 79]. However, little is known about how cir- coding properties of chordotonal organs, campaniform sensilla, cuits at different levels represent the body and to what degree slit sensilla, and other proprioceptors [86–88]. Models of in- they combine signals from the diverse proprioceptor subtypes. sect proprioceptors would be particularly useful to complement Going forward, one useful role of computational models could be the available genetic tools to experimentally manipulate specific to predict the proprioceptive information available during natural proprioceptive neurons during behavior [86]. movement, for example by combining models of proprioceptors Even where precise proprioceptor models are available, with realistic models of the muscles and limbs [27]. many recent neuromechanical simulations rely on simplified State estimates enabled by proprioceptive feedback are also phenomenological proprioceptor models [24, 26, 27, 84, 89, 90]. used beyond the motor system. Recent work in the Drosophila Whether such simplifications are appropriate may depend on central complex has revealed circuits that encode the body in both the level of system being modeled, and further experimental self-centered and world-centered coordinates [80–82]. Neural and computational analyses are needed to identify constraints on encoding of several key quantities that guide spatial navigation useful approximations. One attractive possibility is that a trans- during walking, including heading in allocentric coordinates and formation of coordinates in the input and output variables may velocity in egocentric coordinates, persist in darkness [83], which help simplify proprioceptor models, as in the case of using force suggests that they rely on proprioceptive signals from the legs. instead of fiber length to model muscle spindle responses [34] or However, it remains unknown precisely which proprioceptive transforming signals between eye, head, or body reference frames signals are used to compute these signals. Computational mod- to model proprioceptive encoding in the cerebellar nuclei [91]. els that predict the proprioceptive information available during More generally, a powerful modeling framework would capture natural movement by simulating both proprioceptors and the me- diverse proprioceptors with a tractable number of tunable pa- chanics of the limbs could help explore which signals are suited rameters, such as location on body, hysteresis, and maximum to extract key quantities like heading and velocity. firing rate. Of course, simulation parameters and code should be openly shared to facilitate reproducibility and reuse. Approaches for systems-level modeling of proprio- Integration of models for proprioception and motor control ception A major challenge in understanding the behavioral functions of We propose that developing multiscale computational models proprioceptive feedback is the lack of experimental separability that span proprioceptive sensing and motor control will make it between proprioceptive and motor circuits across the sensorimo- easier to understand how neural circuits flexibly control the body. tor hierarchy. An integration of models across levels can provide Below, we outline several possible approaches, including devel- unique insights into the control of posture, movement, and state oping tractable models that grapple with proprioceptor diversity, estimation that only emerge when considering these systems as integrating across levels of the sensorimotor hierarchy, and ac- a whole. counting for the roles of sensory delay, noise, and contextual modulation of proprioceptive signals. To study how specific proprioceptive signals contribute to posture control, Prochazka et al. [48] integrated models of mus- Journal Pre-proofcle spindles and Golgi tendon organs into a feedback-controlled Diversity of proprioceptive sensors and their models stimulation of arm and leg muscles. The authors found that posi- A major challenge in modeling proprioceptors is the diversity tive force feedback from Golgi tendon organs, which is generally of sensory neuron subtypes. Unlike sensory systems that are considered unstable, can actually stabilize a muscle’s response to concentrated into specialized organs (e.g. the eye, nose, and increased load if one also incorporates sensory delays and natural ear), proprioceptors are distributed throughout the body. Fur- filtering properties of mammalian muscle. The conclusion that thermore, the receptive field of each proprioceptor is idiosyn- positive force feedback is a stable means to control load-bearing cratic to the tissue in which it is embedded and how that tissue motor tasks would not have been clear in studying the controller

6 or proprioceptors alone. able to reproduce state-dependent reflex reversal observed during Several recent neuromechanical models of movement con- locomotion [99]. trol have also simulated the dynamic activity of propriocep- Reflex modulation may also play an important role in steer- tors [24, 26, 89, 90, 92]. For example, Goldsmith et al. [89] in- ing, possibly via descending input which modulates sensory feed- tegrated models of proprioceptors into a simulation and robotic back depending on the steering direction. For example, Schilling model of a walking fruit fly. Using feedback signals inspired and Cruse [57] proposed a fully decentralized model of walking by the tuning properties of insect femoral chordotonal neurons control that produces curved walking by adjusting the setpoint of and campaniform sensilla enabled the robot to adapt to continu- local control loops in each leg. Ultimately, we expect that most ous changes in load. These models could eventually be used to behaviors will involve not only a unique set of descending motor study the effects of conduction delays, noise, and modulation of commands, but also bespoke tuning of proprioceptive feedback specific proprioceptive signals on locomotion and skilled limb pathways. movements, and to generate testable predictions for perturbation experiments. We hope that emerging methods for neuromechan- Conclusion ical modeling will make these models easier to construct and Due to advances in genetic targeting of neuronal cell-types, our use [93–95]. ability to perform targeted perturbations in proprioceptive and Systems-level models can also provide insights into how pro- motor circuits is rapidly expanding. As the space of possible prioceptive circuits represent the body and suggest potential roles experiments grows, there is a pressing need for computational for feedback in motor control. For example, Hamlet et al. [55] frameworks to help guide experimental design and interpreta- used a multiscale model of lamprey swimming to investigate tion. Models developed for proprioceptors and motor control at how different proprioceptive signals, encoding the direction and different scales can be integrated to yield new insights about how magnitude of body curvature, may exert different effects on lo- proprioception interacts with motor control to support dexterous comotor speed and energy consumption. In another example, and flexible movements. These biological principles may also Sandbrink et al. [27] recently showed that some proprioceptive inspire the design of novel robotic systems and contribute to our representations naturally arise in a deep neural network trained understanding and treatment of movement disorders. to recognize characters from arm motions given a biologically realistic model of a human arm. Finally, Ache and Dürr [85] modeled the proprioceptive hairs of an insect antenna to predict how Acknowledgements downstream neurons encode antennal movements. These studies illustrate how systems-level models provide a useful framework We are grateful for insightful comments on the manuscript from to investigate the role of proprioceptive feedback in guiding nat- Joshua L. Proctor, Nicholas Szczecinski, and members of the ural movements. Tuthill and Brunton laboratories. CJD was supported by a Re- search Fellowship from the German Research Foundation (DFG DA 2322/1-1). PK was supported by a National Science Foun- Context-dependent modulation dation Graduate Research Fellowship. BWB was supported by An important characteristic of proprioception is that its effects on the Washington Research Foundation and the Air Force Office motor control are not fixed, but can be tuned by the nervous sys- of Scientific Research grants FA9550-19-1-0386 and FA9550- tem under different behavioral contexts. Modeling experimental 18-1-0114. JCT is a New York Stem Cell Foundation – Robert- results with such context-dependent changes requires informa- son Investigator and was additionally supported by the Searle tion about interactions across multiple levels, further motivating Scholar Program, the Pew Biomedical Scholar Program, the systems-level models. McKnight Foundation, and National Institute of Health grants A clear example of such a top-down modulation is the case of R01NS102333 and U19NS104655. reflex reversal, in which a reflex changes sign depending on the behavioral state of the animal. For instance, stimulating neurons in the femoral chordotonal organ in the stick insect leads to either Recommended reading extension or flexion of the tibia depending on whether the leg Papers of particular interest, published within the period of re- is in stance or swing [96]. Although there have been detailed view, have been highlighted as: studies of the circuitsJournal that mediate reflex reversal [97], this phe- Pre-proof* of special interest nomenon is not commonly built into models for sensorimotor ** of outstanding interest control. One notable exception is the recent model by Goldsmith et al. [49], which investigated different perturbations in a neu- * Agrawal et al. [9]: This study investigates how second-order romechanical model and found that reflex reversal may be due neurons in the Drosophila ventral nerve cord process proprio- to inhibition of the flexion-tuned position- and velocity-sensitive ceptive information from the fly leg. Optogenetic stimulation neurons. In another example, Bacqué-Cazenave et al. [98] built paired with kinematic analyses reveals that different subtypes a neuromechanical model of the crayfish leg circuitry which was of second-order neurons mediate diverse behaviors, including

7 reﬂexive control of limb posture. provide the main information.

* Takeoka and Arber [10]: This study finds that genetic ablation ** Goldsmith et al. [49]: This study formulates a neurome- of proprioceptive feedback in mice leads to broad alterations in chanical model of an insect leg joint to explain reflex reversal gait timing, limb movement trajectory, and intra- and interlimb by inhibition of the proprioceptors of the femoral chordotonal coordination with no significant behavioral adaptation over time. organ. It is one of the few studies providing a quantitative model Interestingly, removal of proprioceptive feedback from either the for reflex reversal. front or rear legs has only subtle effects on slow walking but disrupts interlimb coordination at high speeds.

** Sandbrink et al. [27]: In this study, the authors integrate a References phenomenological model of the muscle spindle into a muscu- [1] U. Proske and S. C. Gandevia, “The proprioceptive senses: loskeletal model of the human arm to explore how proprioceptive their roles in signaling body shape, body position and move- signals form representations of the body at diﬀerent levels of the ment, and muscle force,” Physiological Reviews, vol. 92, central nervous system. pp. 1651–1697, 2012.

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