A unified theory of the control of actin and myosin in nonmuscle movements

A theory is advanced that all nonmuscle movements involving actin and myosin are controlled by Ca⁺⁺ flows across membranes as determined by chemical and electrical processes at those membranes. The mechanisms of amoeboid motion, cytoplasmic streaming, and other movements are discussed, and their underlying chemical control reactions are analyzed. Several predictions and experimental tests are suggested. This theory links motility with recent findings on excitable membranes and cyclic AMP.     

A kinematic theory of rapid human movements

 This paper proposes a kinematic theory that can be used to study and analyze rapid human movements. It describes a synergy in terms of the agonist and antagonist neuromuscular systems involved in the production of these movements. It is shown that these systems have a log-normal impulse response that results from the limiting behavior of a large number of interdependent neuromuscular networks, as predicted by the central limit theorem. The delta log-normal law that follows from this model is very general and can reproduce almost perfectly the complete velocity patterns of an end-effector. The theory accounts for the invariance and rescalability of these patterns, as well as for the various observations that have been reported concerning the change in maximum and mean velocities, time to maximum velocity, etc., under different experimental conditions. Movement time, load effects, and control strategies are discussed in a companion paper. Received: 15 February 1993/Accepted in revised form: 15 September 1994     

On the theory of amoeboid movements

It is shown how the application of the principle of maximum energy transformation, discussed in previous papers, leads to expressions which give the probability of occurrence of a pseudopod of a given size and duration in function of other physical constants of the amoeba.     

A control model of human tongue movements in speech

Tongue movements during speech production have been investigated by means of a simple yet realistic biomechanical model, based on a finite elements modeling of soft tissues, in the framework of the equilibrium point hypothesis (-model) of motor control. In particular, the model has been applied to the estimation of the “central” control commands issued to the muscles, for a data set of mid-sagittal digitized tracings of vocal tract shape, r ecorded by means of low-intensity X-ray cineradiographies during speech. In spite of the highly non-linear mapping between the shape of the oral cavity and its acoustic consequences, the organization of control commands preserves the peculiar spatial organization of vowel phonemes in acoustic space. A factor analysis of control commands, which have been decomposed into independent or “orthogonal” muscle groups, has shown that, in spite of the great mobility of the tongue and the highly complex arrangement of tongue muscles, its movements can be explained in terms of the activation of a small number of independent muscle groups, each corresponding to an elementary or “primitive” movement. These results are consistent with the hypothesis that the tongue is controlled by a small number of independent “articulators”, for which a precise biomechanical substrate is provided. The influence of the effect of jaw and hyoid movements on tongue equilibrium has also bee n evaluated, suggesting that the bony structures cannot be considered as a moving frame of reference, but, indeed, there may be a substantial interaction between them and the tongue, that may only be accounted for by a “global” model. The reported results also define a simple control model for the tongue and, in analogy with similar modelling studies, they suggest that, because of the peculiar geometrical arrangement of tongue muscles, the central nervous system (CNS) may not need a de tailed representation of tongue mechanics but rather may make use of a relatively small number of muscle synergies, that are invariant over the whole space of tongue configurations. Received: 27 August 1996 / Accepted in revised form: 25 February 1997     

Cortical control of reaching movements

Recent studies provide further support for the hypothesis that spatial representations of limb position, target locations, and potential motor actions are expressed in the neuronal activity in parietal cortex. In contrast, precentral cortical activity more strongly expresses processes involved in the selection and execution of motor actions. As a general conceptual framework, these processes may be interpreted in terms of such formalisms as sensorimotor transformation and ‘internal models’.     

The control of oscillatory movements of the forearm

The patterns of EMG activity in the biceps and triceps muscles were recorded during horizontal oscillatory movements of the forearm. Subjects showed increased frequency of oscillation as they voluntarily reduced movement amplitude. EMG burst duration was significantly correlated with wavelength of oscillation in every case. In almost half the cases burst intensity was also positively correlated with wavelength. Subjects seemed to be using one or both these methods to control amplitude. A model was developed in three stages which satisfactorily accounted for the data.     

Various characteristics of the control of cyclic movements

It was shown by studying control forces and phasic trajectories during oscillation of human forearm, locomotion and rocking of the body on the support that there was an image of accomplished movement in the central nervous system. This image seems to be realized by linear connected displacements of the muscle tension level and threshold of tonic stretch reflex. During the control process, velocity of the threshold and tension level is similarly transformed to that of the body part. The piece constant similarity coefficient is regulated centrally. The main result of such control is moving of the body along energy optimal trajectories.     

Time optimality in the control of human movements

In a simulation study the control of maximally fast goal directed movements has been analyzed. For a simple linear model it is shown that the presence of a third input block reduces the movement duration. The time optimal size of the third block depends on the ratio of a neuromuscular time constant (first-order lag) and movement time. As a second step a non-linear muscle model was simulated. By an optimization of input parameters it was found that the time optimal input, as expected, switches between maximal agonist and maximal antagonist activation. As for the linear model, a third phase was required for an optimal movement. It was found that the third phase serves to compensate the slowly decaying antagonist force. Also an input similar to experimentally found activation patterns was simulated. This input contains a silent period between the first two bursts and the second and the third burst have submaximal amplitudes. This input led to a near time optimal movement with a duration 9% larger than the minimal duration but with largely reduced muscle forces. This suggests that a criterion is minimized which also takes into account the effort spent. Including gravity in the model indicates optimality of a silent period between the third phase and a final agonist activity to resist gravity. When assuming different dynamics for agonist and antagonist, the optimal switch times for agonist and antagonist no longer coincide, also after the three block pattern some extra activity is required to obtain a cancellation of the slowly decaying force in agonist and antagonist.     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

Operant control of human eye movements

Saccade and smooth pursuit are the eye movements used by primates to shift gaze. In this article we review evidence for the effects of reinforcement on several dimensions of these responses such as their latencies, velocities or amplitudes. We propose that these responses are operant behaviours controlled by their consequences on performance of visually guided tasks. Studying the conditions under which particular eye movement patterns might emerge from the cumulative effects of reinforcement provides critical insights about how motor responses are attuned to environmental exigencies.     

A kinematic theory of rapid human movements: Part III. Kinetic outcomes

This paper describes the kinematic and kinetic properties of simple rapid movements using a single and unique framework based on a delta-lognormal law (Plamondon 1993a,b, 1995a,b). Predictions concerning isotonic measurements are made using the properties of acceleration profiles, as described by the first time derivative of the delta-lognormal law. Predictions dealing with isometric measurements are directly analyzed using the delta-lognormal law, after demonstrating the experimental equivalence between isometric forces and virtual velocity profiles. The theory is also used to make statistical predictions about the variability of numerous kinematic and kinetic variables. The overall approach can be viewed as if, at some level of representation, the central nervous system were planning, executing and evaluating simple rapid movements in terms of momentum and energy instead of forces. The unifying perspective provided by the theory constitutes a powerful tool with which to study and analyze movements under numerous experimental conditions, using a single analytical law. Received: 13 November 1996 / Accepted in revised form: 6 November 1997     

A neural-network system for control of eye movements: basic mechanisms

This paper presents a neural-network-based system that can generate and control movements of the eyes. It was inspired by a number of experimental observations on the saccadic and gaze systems of monkeys and cats. Because of the generality of the approach undertaken, the system can be regarded as a demonstration of how parallel distributed processing principles, namely learning and attractor dynamics, can be integrated with experimental findings, as well as a biologically inspired controller for a dexterous robotic orientation device. The system is composed of three parts: a dynamic motor map, a push-pull circuitry, and a plant. The dynamics of the motor map is generated by a multi-layer network that was trained to compute a bidimensional temporal-spatial transformation. Simulation results indicate (1) that the system is able to reproduce some of the properties observed in the biological system at the neural and movement levels and (2) that the dynamics of the motor map remains stereotyped even when the motor map is subject to abnormal stimulation patterns. The latter result emphasizes the role of the topographic projection that connects the motor map to the push-pull circuitry in determining the features of the resulting movements.     

A 'top-down' approach to the determination of control coefficients in metabolic control theory

A new approach to the determination of flux and concentration control coefficients in metabolic pathways is outlined. Linear pathways are conceptually divided in two around an intermediate metabolite (or group or metabolites) and the control coefficients of the two parts are derived from the elasticity coefficients of the two parts to the intermediate. Branched pathways are treated similarly, the control coefficients of the branches being derived either from the elasticities of the branches to their common intermediate or from the relative flux changes of the branches. Repeating this analysis around other intermediates in the pathway allows the control coefficients of smaller and smaller groups of enzymes to be determined. In complex systems this approach to describing control may have several advantages over determining the control coefficients of individual enzymes and is a potentially useful complementary approach.     

A mathematical model of the gate control theory of pain

The first test which any theory of pain must pass is that it must be able to explain the phenomena observed in acute pain in humans. This criterion is used to test the major theory of pain at present, the gate control theory of Melzack & Wall (1965, 1982). The theory is explicit enough to be cast in mathematical terms, and the mathematical model is shown to explain the observations considered. It also points up a common misconception on the consequences of the theory, and thus demolishes an argument which has been used against it. A hypothesis of the origin of rhythmic pain is then made, and consequent testable predictions given. This is the first time that the gate control theory has been used to explain any quality of pain. It has important consequences for the treatment of such pain. Finally, the applicability of the gate control theory as an explanation for chronic pain is discussed.