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.

Studies comparing movement-related cortical potentials, post-excitatory inhibition after transcranial magnetic brain stimulation, and PET findings in normal controls and patients with cerebellar degeneration demonstrate plasticity of cerebro-cerebellar interactions and hereby support Thach's theory that the cerebellum has the ability to play a role in building behavioral context-response linkages and to build up appropriate responses from simpler constitutive elements, [THACH].

Several target articles in this BBS special issue address the topic of cerebellar and olivary functions, especially as they pertain to motor earning. Another important topic is the neural interaction between the limbic system and the cerebellum during associative learning. In this commentary we present some of our data on olivo-cerebellar and limbic-cerebellar interactions during eyeblink conditioning. [HOUK et al.; SIMPSON et al.; THACH].

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.

PET studies using classical conditioning paradigms are reported. It is emphasized that PET studies show and not in learning paradigms. The importance of dissociating motor performance and learning deficits in human lesions studies is demonstrated in two exemplary studies. The different role of the cerebellum in adaptation of postural reflexes and learning of complex voluntary arm movements is discussed, [THACH].

For reasons I have never understood, some students of the cerebellum have been unwilling to accept the now overwhelming evidence that the cerebellum exhibits lasting synaptic plasticity and plays an essential role in some forms of learning and memory. With a few exceptions (e.g., target article by SIMPSON et al.) this is no longer the case, as is clear in the excellent target articles on cerebellar LTD and the excellent target review by HOUK et al. [CRÉPEL et al.; HOUR et (...) al.; KANO; LINDEN; SIMPSON et al.; SMITH; VINCENT]. (shrink)

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.

In the behavioral literature on human movement, a distinction is made between the learning of parameters and the learning of new movement forms or topologies. Whereas the target articles by Thach, Smith, and Houk et al. provide evidence for cerebellar involvement in parametrization learning and adaptation, the evidence in favor of its involvement in the generation of new movement patterns is less straightforward. A case is made for focusing more attention on the latter issue in the future. This would directly (...) help to bridge the gap between current neurophysiological approaches to the role of the cerebellum and the behavioral expressions of human motor learning, [HOUK et al.; SMITH; THACH]. (shrink)

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.

In response to several requests from commentators, an unambiguous definition of time-varying joint stiffness is provided. However, since a variety of different operations can be used to measure stiffness, a problem for quantification admittedly still exists. Several commentaries pointed out the advantage of controlling joint stiffness in optimizing the speed-accuracy trade-off known as Fittss law. The deficit in rapid reciprocal movements and the impact on joint stiffness inhibition caused by cerebellar lesions is clarified here, as the target article was apparently (...) misinterpreted by some readers. In response to the challenge that there is little consensus among cerebellar physiologists, several areas of tacit agreement with other theories of cerebellar function are enumerated. An alternative interpretation of studies showing a transient activation of the cerebellum in motor learning is suggested. Finally, the relationship between the command signals generated by supraspinal centers such as the cerebellum and spinal interneuron networks controlling muscle synergies is discussed. (shrink)

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.

Several themes can be identified in the commentaries. The first is that the climbing fibers may have more than one function; the second is that the climbing fibers provide sensory rather than motor signals. We accept the possibility that climbing fibers may have more than one function consequence(s)’ in the title. Until we know more about the function of the inhibitory input to the inferior olive from the cerebellar nuclei, which are motor structures, we have to keep open the possibility (...) that the climbing fiber signals can be a combination of sensory and motor signals. (shrink)

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 views of Houk et al., Smith, and Thach on the role of cerebellum in movement control differ substantially, but all three are flawed by the false reasoning that because information passes from the cerebellum to movements the cerebellum must be a movement controller, or a part of one. The divergent and less than compelling ideas expressed by these leading cerebellar theorists epitomize the fruitlessness of this paradigm, and signal the need for a change. [HOUK et al.; SMITH; THACH].

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.

Thach's target article presents a remarkable overview and integration of animal and human studies on the functions of the cerebellum and makes clear theoretical predictions for both the normal operation of the cerebellum and for the effects of cerebellar lesions in the mature human. Commentary is provided on three areas, namely, spatial navigation, implicit learning, and cerebellar agenesis to elicit further development of the themes already present in Thach's paper, [THACH].

The involvement of nitric oxide in cerebellar long-term depression is supported by the observation that nitric oxide is released by climbing fiber stimulation and by pharmacological tool usage. Two forms of long-term depression should be distinguished by their physiological relevance. [CRÉPEL et al.; LINDEN; VINCENT].

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.

We suggest that the cerebellum generates sensory or estimates based on outgoing motor commands and sensory feedback. Thus, it is not a motor pattern generator (HOUK et al.) but a predictive system which is intimately involved in motor behavior. This theory may explain the sensitivity of the climbing fibers to both unexpected external events and motor errors (SIMPSON et al.), and we speculate that unusual biophysical properties of the inferior olive might allow the cerebellum to develop multiple asynchronous sensory estimates, (...) [HOUK et al.; SIMPSON et al.; THACH]. (shrink)

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.”.

The hypothesis that play behavior is more prevalent in larger-brained animals has recently been challenged. It may be, for example, that only certain brain structures are related to play. Here, we analyze social play behavior with regards to the cerebellum: a structure strongly implicated in motor-development, and possibly also in cognitive skills. We present an evolutionary analysis of social play and the cerebellum, using a phylogenetic comparative method. Social play frequency and relative cerebellum size are positively correlated. Hence, there appears (...) to be a link between the evolutionary elaboration of social play and the cerebellum. (shrink)

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.

We criticize the synaptic theory of long-term memory and the inappropriate usage of physical notions such as in motor control theories. Motor control and motor memory hypotheses should be based on explicitly specified hypothetical control variables that are sound from both physiological and physical perspectives. [HOUK et al.; SMITH; THACH].

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.

This article reviews models of the cerebellum and motor learning, from the landmark papers by Marr and Albus through those of the present time. The unique architecture of the cerebellar cortex is ideally suited for pattern recognition, but how is pattern recognition incorporated into motor control and learning systems? The present analysis begins with a discussion of exactly what the cerebellar cortex needs to regulate through its anatomically defined projections to premotor networks. Next, we examine various models showing how the (...) microcircuitry in the cerebellar cortex could be used to achieve its regulatory functions. Having thus defined what it is that Purkinje cells in the cerebellar cortex must learn, we then evaluate theories of motor learning. We examine current models of synaptic plasticity, credit assignment, and the generation of training information, indicating how they could function cooperatively to guide the processes of motor learning. (shrink)

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.