The following questions are discussed: (1) Who determines the nature of “control variables”? (2) Is the “positional monopoly” healthy? (3) Does a descending command alter reflex threshold alone without eoncomitantly altering stiffness? (4) How does the CNS deal with history-dependent effects? (5) Should we abandon the idea that the CNS controls classical Newtonian variables such as muscle length?

A key feature of the lambda model is the hypothesis of a local spring-like muscle-reflex system defined by a central control variable that has units of position. This is intriguing, especially for a study of postural stability in large-scale systems, but it has limited direct application to skilled everyday movements. If movement is considered as a goal-directed, neuro-optimization problem, however, theavailabilityof lambda-like peripheral models (vs. conventional musculoskeletal models) deserves exploration.

It is argued that the equilibrium point model can lead to new insights regarding transition and stability processes in movement coordination. The role of movement control parameters on equifinality and phase-resetting is discussed; not only control but also external control parameters can affect the global dynamical regime.

The historical debate on representation in cognitive science and neuroscience construes representations as theoretical posits and discusses the degree to which we have reason to posit them. We reject the premise of that debate. We argue that experimental neuroscientists routinely observe and manipulate neural representations in their laboratory. Therefore, neural representations are as real as neurons, action potentials, or any other well-established entities in our ontology.

Examination of infant spontaneous and goal-directed arm movements supports Feldman and Levin's hypothesis of a functional hierarchy. Early infant movements are dominated by biomechanical and dynamic factors without external frames of reference. Development involves not only learning to generate these frames of reference, but also protecting the higher-level goal of the movement from internal and external perturbations.

Important similarities exist between the dynamical concepts implicit in Feldman & Levin's extended λ model and those basic to a dynamical systems approach. We argue that careful application of the key concepts of control and order parameters, equilibria, and stability, can relate known facts of neuromuscular processes to the observables of functional, task-specific behavior.

An alternative multi-joint extension to the lambda model is proposed. According to this extension, the activity of a muscle depends not only on the difference between lambda and length of that muscle, but also on the difference between lambda and length of other muscles. This 2-D extension can describe more neurophysiological experiments than the extension proposed in the target article.

Whereas the λ model provides a useful technique to describe complex movements, the focus on control variables in this model limits its potential for interpreting the activity and function of many cells in motor areas of the CNS.

Neurophysiological evidence consonant with F&L's lambda model is reviewed and results of additional experiments are presented. The evidence shows that there are neurons in the motor cortex that respond to selective band widths of passive sinusoidal movements; the additional data show how, with movement, directionally sensitive population vectors can be shown to emerge from the data.

The question of how the brain can construct a stable representation of the external world despite eye movements is a very old one. If there have been some wrong statements of problems (such as the inverted retinal image), other statements are less naive and have led to analytic solutions possibly adopted by the brain to counteract the spurious effects of eye movements. Following the MacKay (1973) objections to the analytic view of perceptual stability, Bridgeman et al. claim that the idea (...) that signals canceling the effects of saccadic eye movements are needed is also a misconception, as is the claim that stability and position encoding are two distinct problems. It must be remembered, however, that what made the theory of “cancellation” formulated by von Holst and Mittelstaedt (1950) so appealing was the clinical observation of perceptual instability following ocular paralysis. Following the concept of corollary discharge, the theory of efference copy had the advantage of simultaneously solving three problems: the stability of the visual world during the saccade, the same visual stability across saccades, and the visual constancy problem of allowing the subject to know where an object in space is. (shrink)

Generation of swing phase limb trajectory over obstacles during locomotion should be a reasonable test for the λ model proposed by Feldman and Levin. The observed features such as lack of simple amplitude scaling of endpoint (toe) trajectories for different obstacle heights, complex shaped toe velocity profiles, and exploitation of passive intersegmental dynamics to control limb elevation cannot be adequately explained by the λ model.

The trade-off between force and length of muscle as adjusted by neural signals is a critical fact in the dynamics of motor control. Whether we call it “length-tension effect,” “feedback-like,” “invariant condition,” or “spring-like” is unimportant. We must not let semantics or details of representation obscure the basic physics of effects introduced by this trade-off in muscle.

The model identifies a spatial coordinate frame within which the sensorimotor apparatus produces movement. Its spatial nature simplifies its coupling with spatial reference frames used concurrently by vision and proprioception. While the positional reference frame addresses the performance of spatial tasks, it seems to have little to say about movements involving energy expenditure as the principle component of the task.

We describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

It is proposed here that the spinal network of proprioceptive feedback from length and force receptors constitutes the mechanism underlying the coordination of activation thresholds for muscles acting about the same and neighboring joints. For the most part, these circuits come between motoneurons and supraspinal signals, invalidating the idea that the activation thresholds constitute control variables for the motor system.

Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

Parameters of the lambda model seem tightly linked to certain characteristics of human performance influenced by weightlessness. This commentary suggests that there is a valuable opportunity to probe the lambda model using the changed environment experienced during space flight. The likely benefits are a better model and a better understanding ofthe consequences of weightlessness for human performance.

The lambda model of servocontrol seems superior to the alpha model in terms of dealing with the mechanical complexities of nonlinear and multiarticular muscles. Both, however, can be trivialized by noting that the “control variable” may simply be the sum of descending influences at propriospinal interneurons in the case of the lambda model or in the muscles themselves in the case of the alpha model. The notion that the brain explicitly computes output in terms of any such control variables may (...) be an engineering metaphor, useful for conceptual understanding but not for generating predictive hypotheses about higher motor circuitry. (shrink)

Feldman and Levin present a model for movement control in which the system is said to seek equilibrium points, active movement being produced by shifting frames of reference in space. It is argued that whatever merit this model might have is limited to an understanding of “the how” and not “the why” we move. In this way the authors seem to be forced into a dualistic position leaving the upper level of the proposed control hierarchy “floating.”.

Understanding of the λ model has greatly increased in recent years as evidenced by most of the commentaries. Some commentators underscored the potential of the model to integrate aspects of different sensorimotor systems in the production of movement. Other commentators focused on not-yet-fully-developed parts of the model. A few persisted in misunderstanding some of its basic concepts, and on these grounds they reject it. In responding to commentaries we continue to elaborate on some fundamental points of the model, especially control (...) variables, the idea of movement production by shifting the positional frame of reference and the hypothesis of biomechanical correspondence in motor control. We also continue to develop our ideas on the intrinsic generation of the frame of reference associated with external space and utilized for the control of arm movement and locomotion. The dynamic principles underlying the model are discussed in light of the dynamical systems approach. (shrink)

The authors report that the reorganization of body configuration during weightlessness is based on an intrapersonal frame of reference such as the configuration of the support surface and the position of the body's center of gravity. These results stress the importance of “knowledge” of the state of internal geometric structures, which cannot be directly signalled by specific receptors responsible for direct dialogue with the physical external world.

The equilibrium-point hypothesis (the λ-model) is superior to all other models of single-joint control and provides deep insights into the mechanisms of control of multi-joint movements. Attempts at associating control variables with neurophysiological variables look confusing rather than promising. Probabilistic mechanisms may play an important role in movement generation in redundant systems.

The problem for the CNS in any particular movement task is to coordinate the various frames of reference appropriate to the task. Control variables are determined by this coordination. The coordination problem varies greatly from task to task, and so no single set of control variables is likely to account for a broad range of movement tasks.

The experiments Feldman and Levin suggest do not definitively test their proposed solution to the problem of selecting muscle activations. Their test of the movement directions that elicit EMG activity can be interpreted without regard to the form of the central commands, and their fast elbow flexion test is based on a forward computation that obscures the insensitivity of the predicted trajectory to the details of the putative commands.

We argue that the concept of a control variable (CV) as described by Feldman and Levin needs to be revised because it does not account for the influence of sensory feedback from the periphery. We provide evidence from the realm of rhythmic movements that sensory feedback can permanently alter the frequency and phase of a centrally generated rhythm.

The lambda model predicts that the command received by each motor nucleus during locomotion is specific for the joint at which its muscle acts and is independent of external conditions. However, investigation of the commands received by motor nuclei during fictive locomotion and of the sensitivity of these commands to feedback from the limb during locomotion indicates that neither condition is satisfied.

Extrapersonal frames of reference for aimed movements are representationally convenient. They may, however, carry associated costs when the movement is executed in terms of the complex coordination of multiple joints they require. Studies that have measured both fingertip and joint paths suggest the motor systems may seek a compromise between simplicity of extrapersonal spatial representation and computational simplicity of multi-joint execution.

Models of central control variables (CVs) that are expressed in positional reference frames and rely on proprioception as the dominant specifier of muscle activation patterns have not yet been shown to be adequate for the description of fast, voluntary movement, even of single joints. An alternative model with illustrative data is proposed.