Stability and motor adaptation in human arm movements

In control, stability captures the reproducibility of motions and the robustness to environmental and internal perturbations. This paper examines how stability can be evaluated in human movements, and possible mechanisms by which humans ensure stability. First, a measure of stability is introduced, which is simple to apply to human movements and corresponds to Lyapunov exponents. Its application to real data shows that it is able to distinguish effectively between stable and unstable dynamics. A computational model is then used to investigate stability in human arm movements, which takes into account motor output variability and computes the force to perform a task according to an inverse dynamics model. Simulation results suggest that even a large time delay does not affect movement stability as long as the reflex feedback is small relative to muscle elasticity. Simulations are also used to demonstrate that existing learning schemes, using a monotonic antisymmetric update law, cannot compensate for unstable dynamics. An impedance compensation algorithm is introduced to learn unstable dynamics, which produces similar adaptation responses to those found in experiments.     

A mathematical model of the adaptive control of human arm motions

This paper discusses similarities between models of adaptive motor control suggested by recent experiments with human and animal subjects, and the structure of a new control law derived mathematically from nonlinear stability theory. In both models, the control actions required to track a specified trajectory are adaptively assembled from a large collection of simple computational elements. By adaptively recombining these elements, the controllers develop complex internal models which are used to compensate for the effects of externally imposed forces or changes in the physical properties of the system. On a motor learning task involving planar, multi-joint arm motions, the simulated performance of the mathematical model is shown to be qualitatively similar to observed human performance, suggesting that the model captures some of the interesting features of the dynamics of low-level motor adaptation. Received: 20 September 1994 / Accepted in revised form: 18 November 1998     

Longer moment arm results in smaller joint moment development, power and work outputs in fast motions

Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.     

Quantization of human motions and learning of accurate movements

This paper presents a mathematical model for the learning of accurate human arm movements. Its main features are that the movement is the superposition of smooth submovements, the intrinsic deviation of arm movements is considered, visual and kinesthetic feedback are integrated in the motion control, and the movement duration and accuracy are optimized with practice. This model is consistent with the jerky arm movements of infants, and may explain how the adult motion behavior emerges from the infant behavior. Comparison with measurements of adult movements shows that the kinematics of accurate movements are well predicted by the model. Received: 15 May 1997 / Accepted 5 December 1997     

Discharge patterns in human motor units during fatiguing arm movements

The purpose of this study was to determinewhether short interspike intervals (ISIs of <20 ms) would occurnaturally during voluntary movement and would increase in number withfatigue. Thirty-four triceps brachii motor units from ninesubjects were assessed during a fatigue task consisting of fiftyextension and fifty flexion elbow movements against a constant-loadopposing extension. Nineteen motor units were recorded from thebeginning of the fatigue task; the number of short ISIs was 7.1 ± 4.1% of the total number of ISIs in the first one-third of the task(unfatigued state). This value increased to 11.8 ± 5.9% for thelast one-third of the task (fatigued state). Fifteen motor units wererecruited during the fatigue task and discharged, with 16.4 ± 6.0%of short ISIs in the fatigued state. For all motor units, the number of short ISIs was positively correlated(r² = 0.85) withthe recruitment threshold torque. Short ISIs occurred most frequentlyat movement initiation but also occurred throughout the movement. Theseresults document the presence of short ISIs during voluntary movementand their increase in number during fatigue.

     

The role of GABA in human motor learning

GABA modification plays an important role in motor cortical plasticity. We therefore hypothesized that interindividual variation in the responsiveness of the GABA system to modification influences learning capacity in healthy adults. We assessed GABA responsiveness by transcranial direct current stimulation (tDCS), an intervention known to decrease GABA. The magnitude of M1 GABA decrease induced by anodal tDCS correlated positively with both the degree of motor learning and the degree of fMRI signal change within the left M1 during learning. This study therefore suggests that the responsiveness of the GABAergic system to modification may be relevant to short-term motor learning behavior and learning-related brain activity.     

Coupled motions direct electrons along human microsomal P450 Chains

Protein domain motion is often implicated in biological electron transfer, but the general significance of motion is not clear. Motion has been implicated in the transfer of electrons from human cytochrome P450 reductase (CPR) to all microsomal cytochrome P450s (CYPs). Our hypothesis is that tight coupling of motion with enzyme chemistry can signal "ready and waiting" states for electron transfer from CPR to downstream CYPs and support vectorial electron transfer across complex redox chains. We developed a novel approach to study the time-dependence of dynamical change during catalysis that reports on the changing conformational states of CPR. FRET was linked to stopped-flow studies of electron transfer in CPR that contains donor-acceptor fluorophores on the enzyme surface. Open and closed states of CPR were correlated with key steps in the catalytic cycle which demonstrated how redox chemistry and NADPH binding drive successive opening and closing of the enzyme. Specifically, we provide evidence that reduction of the flavin moieties in CPR induces CPR opening, whereas ligand binding induces CPR closing. A dynamic reaction cycle was created in which CPR optimizes internal electron transfer between flavin cofactors by adopting closed states and signals "ready and waiting" conformations to partner CYP enzymes by adopting more open states. This complex, temporal control of enzyme motion is used to catalyze directional electron transfer from NADPH→FAD→FMN→heme, thereby facilitating all microsomal P450-catalysed reactions. Motions critical to the broader biological functions of CPR are tightly coupled to enzyme chemistry in the human NADPH-CPR-CYP redox chain. That redox chemistry alone is sufficient to drive functionally necessary, large-scale conformational change is remarkable. Rather than relying on stochastic conformational sampling, our study highlights a need for tight coupling of motion to enzyme chemistry to give vectorial electron transfer along complex redox chains.     

Differential corticostriatal plasticity during fast and slow motor skill learning in mice

BACKGROUND: Motor skill learning usually comprises "fast" improvement in performance within the initial training session and "slow" improvement that develops across sessions. Previous studies have revealed changes in activity and connectivity in motor cortex and striatum during motor skill learning. However, the nature and dynamics of the plastic changes in each of these brain structures during the different phases of motor learning remain unclear. RESULTS: By using multielectrode arrays, we recorded the simultaneous activity of neuronal ensembles in motor cortex and dorsal striatum of mice during the different phases of skill learning on an accelerating rotarod. Mice exhibited fast improvement in the task during the initial session and also slow improvement across days. Throughout training, a high percentage of striatal (57%) and motor cortex (55%) neurons were task related; i.e., changed their firing rate while mice were running on the rotarod. Improvement in performance was accompanied by substantial plastic changes in both striatum and motor cortex. We observed parallel recruitment of task-related neurons in both structures specifically during the first session. Conversely, during slow learning across sessions we observed differential refinement of the firing patterns in each structure. At the neuronal ensemble level, we observed considerable changes in activity within the first session that became less evident during subsequent sessions. CONCLUSIONS: These data indicate that cortical and striatal circuits exhibit remarkable but dissociable plasticity during fast and slow motor skill learning and suggest that distinct neural processes mediate the different phases of motor skill learning.     

Modelling the learning of biomechanics and visual planning for decision-making of motor actions

Recent experiments showed that the bio-mechanical ease and end-point stability associated to reaching movements are predicted prior to movement onset, and that these factors exert a significant influence on the choice of movement. As an extension of these results, here we investigate whether the knowledge about biomechanical costs and their influence on decision-making are the result of an adaptation process taking place during each experimental session or whether this knowledge was learned at an earlier stage of development. Specifically, we analysed both the pattern of decision-making and its fluctuations during each session, of several human subjects making free choices between two reaching movements that varied in path distance (target relative distance), biomechanical cost, aiming accuracy and stopping requirement. Our main result shows that the effect of biomechanics is well established at the start of the session, and that, consequently, the learning of biomechanical costs in decision-making occurred at an earlier stage of development. As a means to characterise the dynamics of this learning process, we also developed a model-based reinforcement learning model, which generates a possible account of how biomechanics may be incorporated into the motor plan to select between reaching movements. Results obtained in simulation showed that, after some pre-training corresponding to a motor babbling phase, the model can reproduce the subjects’ overall movement preferences. Although preliminary, this supports that the knowledge about biomechanical costs may have been learned in this manner, and supports the hypothesis that the fluctuations observed in the subjects’ behaviour may adapt in a similar fashion.     

Backbone dynamics of the human CC chemokine eotaxin: fast motions, slow motions, and implications for receptor binding.

Eotaxin is a member of the chemokine family of about 40 proteins that induce cell migration. Eotaxin binds the CC chemokine receptor CCR3 that is highly expressed by eosinophils, and it is considered important in the pathology of chronic respiratory disorders such as asthma. The high resolution structure of eotaxin is known. The 74 amino acid protein has two disulfide bridges and shows a typical chemokine fold comprised of a core of three antiparallel beta-strands and an overlying alpha-helix. In this paper, we report the backbone dynamics of eotaxin determined through 15N-T1, T2, and [1H]-15N nuclear Overhauser effect heteronuclear multidimensional NMR experiments. This is the first extensive study of the dynamics of a chemokine derived from 600, 500, and 300 MHz NMR field strengths. From the T1, T2, and NOE relaxation data, parameters that describe the internal motions of eotaxin were derived using the Lipari-Szabo model free analysis. The most ordered regions of the protein correspond to the known secondary structure elements. However, surrounding the core, the regions known to be functionally important in chemokines show a range of motions on varying timescales. These include extensive subnanosecond to picosecond motions in the N-terminus, C-terminus, and the N-loop succeeding the disulfides. Analysis of rotational diffusion anisotropy of eotaxin and chemical exchange terms at multiple fields also allowed the confident identification of slow conformational exchange through the "30s" loop, disulfides, and adjacent residues. In addition, we show that these motions may be attenuated in the dimeric form of a synthetic eotaxin. The structure and dynamical basis for eotaxin receptor binding is discussed in light of the dynamics data.     

Equilibrium point control of a monkey arm simulator by a fast learning tree structured artificial neural network

A planar 17 muscle model of the monkey's arm based on realistic biomechanical measurements was simulated on a Symbolics Lisp Machine. The simulator implements the equilibrium point hypothesis for the control of arm movements. Given initial and final desired positions, it generates a minimum-jerk desired trajectory of the hand and uses the backdriving algorithm to determine an appropriate sequence of motor commands to the muscles (Flash 1987; Mussa-Ivaldi et al. 1991; Dornay 1991b). These motor commands specify a temporal sequence of stable (attractive) equilibrium positions which lead to the desired hand movement. A strong disadvantage of the simulator is that it has no memory of previous computations. Determining the desired trajectory using the minimum-jerk model is instantaneous, but the laborious backdriving algorithm is slow, and can take up to one hour for some trajectories. The complexity of the required computations makes it a poor model for biological motor control. We propose a computationally simpler and more biologically plausible method for control which achieves the benefits of the backdriving algorithm. A fast learning, tree-structured network (Sanger 1991c) was trained to remember the knowledge obtained by the backdriving algorithm. The neural network learned the nonlinear mapping from a 2-dimensional cartesian planar hand position {x, y} to a 17-dimensional motor command space {u ₁, ..., u ₁₇}. Learning 20 training trajectories, each composed of 26 sample points {{x y{,{u ₁, ..., u ₁₇} took only 20 min on a Sun-4 Spare workstation. After the learning stage, new, untrained test trajectories as well as the original trajectories of the hand were given to the neural network as input. The network calculated the required motor commands for these movements. The resulting movements were close to the desired ones for both the training and test cases.     

The role of slow and fast protein motions in allosteric interactions

Allostery is fundamentally thermodynamic in nature. Long-range communication in proteins may be mediated not only by changes in the mean conformation with enthalpic contribution but also by changes in dynamic fluctuations with entropic contribution. The important role of protein motions in mediating allosteric interactions has been established by NMR spectroscopy. By using CAP as a model system, we have shown how changes in protein structure and internal dynamics can allosterically regulate protein function and activity. The results indicate that changes in conformational entropy can give rise to binding enhancement, binding inhibition, or have no effect in the expected affinity, depending on the magnitude and sign of enthalpy–entropy compensation. Moreover, allosteric interactions can be regulated by the modulation a low-populated conformation states that serve as on-pathway intermediates for ligand binding. Taken together, the interplay between fast internal motions, which are intimately related to conformational entropy, and slow internal motions, which are related to poorly populated conformational states, can regulate protein activity in a way that cannot be predicted on the basis of the protein’s ground-state structure.     

Secondary motions of the shoulder during arm elevation in patients with shoulder tightness

An analysis of secondary shoulder motions (humeral rotation, humeral head anterior/posterior translation, scapular tipping, and scapular upward/downward rotation) in subjects with anterior/posterior shoulder tightness provides the opportunity to examine the role of tightness as a means of affecting shoulder motions. Subjects with shoulder tightness (anterior, n = 12; posterior, n = 12) elevated their arms in the scapular plane. Three replicated movements were performed to the maximum motions. Kinematics data were collected by FASTRAK 3D electromagnetic system. To determine if a significant difference of the secondary motions existed between anterior/posterior shoulder tightness, two-factor mixed ANOVA models with the repeated factor of elevation angle (five elevation angles) and the independent factor of group were calculated. The relationships between the self-reported functional scores (Flexilevel Scale of Shoulder Function, FLEX-SF) and abnormal shoulder kinematics were assessed. For humeral head anterior/posterior translation, the subjects with posterior tightness demonstrated anterior humeral head translation (10 mm, p = 0.019) compared to subjects with anterior tightness. The subjects with anterior tightness demonstrated less posterior tipping (2.2°, p = 0.045) compared to subjects with posterior tightness. The humeral anterior translation had moderate relationships with FLEX-SF scores (r = ?0.535) in subjects with posterior tightness. The scapular tipping had moderate relationships with FLEX-SF scores (r = 0.432) in subjects with anterior tightness. In conclusion, the secondary motions were different between subjects with anterior and posterior shoulder tightness. During arm elevation, less scapular posterior tipping and less posterior humeral head translation in subjects with anterior and posterior shoulder tightness, respectively, are significantly related to self-reported functional disability in these subjects.     

Neocortical mechanisms in motor learning

The ability to learn novel motor skills has fundamental importance for adaptive behavior. Neocortical mechanisms support human motor skill learning, from simple practice to adaptation and arbitrary sensory-motor associations. Behavioral and neural manifestations of motor learning evolve in time and involve multiple structures across the neocortex. Modifications of neural properties, synchrony and synaptic efficacy are all related to the development and maintenance of motor skill.     

Modeling investigation of learning a fast elbow flexion in the horizontal plane--prediction of muscle forces and motor units action

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.