A synergetic theory of environmentally-specified and learned patterns of movement coordination

Rhythmic movement patterns have served as a model case for developing a synergetic theory of biological coordination. In part I of this work we extended the approach to environmentally-specified and learned movement patterns on the level of the collective variable relative phase. Here we show that an identical strategy may be applied to the same problem at the level of the component oscillators. Coordinative patterns and their dynamics are derived from the coupled component dynamics and their interaction with the environment. Thus, behavioral patterns are shown to arise in a purely self-organized fashion. New directions for further research (e.g. dynamics of action-perception systems) follow from the oscillator theory. Finally the relationship between our approach and other kinds of analyses of temporal order (e.g. phase resetting) is addressed.     

A dynamic theory of coordination of discrete movement

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.     

A synergetic theory of quadrupedal gaits and gait transitions

We present a theoretical analysis of the patterns of interlimb co-ordination in the gaits of quadrupedal locomotion. Introducing as collective variables a set of relative phases that describe the co-ordination patterns, we classify gaits by their symmetry properties, which can be expressed as invariances under groups of transformations. We define dynamics of the collective variables, on which we impose symmetry restrictions. The stable observable gait patterns correspond to atractors of these dynamics. A non-trivial consequence of this theoretical viewpoint is that gait transitions can take the form of non-equilibrium phase transitions that are accompanied by loss of stability. We show how various types of such phase transitions involving hysteresis, slowing down and fluctuation enhancement can occur. Also the difference between smooth and abrupt transitions is given theoretical foundation. While existing experimental evidence is consistent with the theory developed here, we propose new experimental measures that can serve to test the present theoretical framework. Finally, the influence of underlying symmetries of the dynamics on the nature of the gait patterns and their stability is analyzed. For example, breaking of a front-hind symmetry can lead to a change from absolute to relative co-ordination in the sense of von Holst (1939, Ergebnisse der Physiologie 42, 228). Also, differential stability of straight and reverse gaits results from thus lowering the symmetry.     

Learning and recall in a dynamic theory of coordination patterns

A dynamic theory of learning and recall of coordination patterns is developed in the context of relative timing skills. Characterizing the coordination patterns in such skills by the collective variable, relative phase, we choose a model system in which the intrinsic pattern dynamics as well as the influence of environmental and memorized information are well understood from previous experimental and theoretical work. To describe learning we endow memorized information with dynamics which is determined by a phenomenological strategy. Similarly, additional degrees of freedom must be introduced to understand recall. As such recall variables we choose the relative strengths with which each memorized pattern acts on the pattern dynamics and model their dynamics phenomenologically. The resulting dynamical system that resembles models used in pattern recognition theory is shown to adequately describe the learning and recall processes. Moreover, due to the operational character of the theory, several predictions emerge that are open to experimental test. In particular, we show under which conditions phase transitions occur in the dynamics of the coordination patterns during learning and during recall. Considering different time scales and their relations we demonstrate how these phase transitions can be identified and observed. Other predictions include the influence of the intrinsic pattern dynamics on the recall process and the existence of history and hysteresis effects in recall. We discuss different forms of forgetting and differentiation of memorized information. The results show how a new theoretical view of learning and recall as change of behavioral dynamics can lead to a different understanding of these processes by providing testable predictions.     

A model of coordination of sperm flagella movement

The periodicity of bulls and humans' spermatozoa motion is investigated. The period of their motion is divisible by 24 and 15 turns of spermatozoa heads respectively. The interrelation of the observed periodicity with the ultrastructure of gamete tails is pre-supposed. A model of mitochondrial coordination of sperm flagella movement is proposed.     

Sensory and intrinsic coordination of movement

A recently generalized theory of perceptual guidance (general tau theory) was used to analyse coordination in skilled movement. The theory posits that (i) guiding movement entails controlling closure of spatial and/or force gaps between effectors and goals, by sensing and regulating the tau s of the gaps (the time-to-closure at current closure rate), (ii) a principal way of coordinating movements is keeping the tau s of different gaps in constant ratio (known as tau-coupling), and (iii) intrinsically paced movements are guided and coordinated by tau-coupling onto a tau-guide, tau g, generated in the nervous system and described by the equation tau g = 0.5 (t-T 2/t) where T is the duration of the body movement and t is the time from the start of the movement. Kinematic analysis of hand to mouth movements by human adults, with eyes open or closed, indicated that hand guidance was achieved by maintaining, during 80 85% of the movement, the tau-couplings tau alpha-tau r and tau r-tau g, where tau r is tau of the hand-mouth gap, tau alpha is tau of the angular gap to be closed by steering the hand and tau g is an intrinsic tau-guide.     

A mathematical theory of visual hallucination patterns

Neuronal activity in a two-dimensional net is analyzed in the neighborhood of an instability. Bifurcation theory and group theory are used to demonstrate the existence of a variety of doublyperiodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity. It is suggested that these simple geometric patterns are the cortical concomitants of the form constants seen during visual hallucinosis.To Heinrich Klüver in memoriamSupported in part by NIHTG 2037     

Activity and movement patterns of Octopus dofleini

Four individual Octopus dofleini were followed over a fifteen day period in their underwater habitat by sonic tracking. Octopuses had small home ranges (250 m²maximum) which were stable over the two weeks of observation. These ranges overlapped those of other octopuses extensively, and animals did not keep a constant distance from one another, which suggests they were solitary and non‐social. Activity was slightly higher at night, and was not correlated with changes in other environmental variables. The O. dofleini made frequent short hunting trips (mode 0.5 hours), tending to have more and longer excursions at night. Octopuses are predators who appear to have flexible activity and, in the short term, restricted home range areas.     

A stochastic theory of phase transitions in human hand movement

The order parameter equation for the relative phase of correlated hand movements, derived in a previous paper by Haken et al. (1985), is extended to a time-dependent stochastic differential equation. Its solutions are determined close to stationary points and for the transition region. Remarkably good agreement between this theory and recent experiments done by Kelso and Scholz (1985) is found, and new predictions are offered.     

A model relating patterns of human jaw movement to biomechanical constraints

After testing the effects of the ways in which several different ligaments and bony constraints would influence movements of the human mandible in three dimensions, a mathematical model based on constraints due to the articular eminences, temporomandibular ligaments and sphenomandibular ligaments has been constructed. The effects of these constraints on jaw movements during opening and lateral movements are analysed. The model predicts the observed translation of the human condyle during jaw opening and Bennett shift during lateral jaw movements. The model is refined to account for observed irregular movements of the condyle during opening and to predict a locus for the instantaneous centre of rotation. The model can also be used to predict the new position taken up by any point on the mandible after the jaw has been opened and/or moved laterally a given amount.     

Is it possible to transfer learned coordination of head and forepaw movements in dogs

Dogs were trained for tonic forelimb flexion fixed to a lever in order to hold a cup with meat during eating, when the head was bent down to a foodwell. Before learning, the forelimb flexion is accompanied by the anticipatory lifting of the head bent down to the foodwell; following lowering of the head leads to an extension of the flexed forelimb. Simultaneous holding of the flexed forelimb and lowered head is achieved by learning. During the original learning, the innate head-forelimb coordination was rearranged into the opposite one. After the initial instrumental learning, the "working" forelimb was changed to test whether a transfer of the learned head-forelimb coordination would occur. It was shown that the execution of the instrumental reaction by the untrained forelimb was impossible, because the innate coordination between the head and this forelimb persisted. It could also be rearranged by learning. The involvement of the motor cortex in the unilateral rearrangement of the innate head-forelimb movement coordination is discussed.     

Risk sensitivity and theory of mind in human coordination

What humans do when exposed to uncertainty, incomplete information, and a dynamic environment influenced by other agents remains an open scientific challenge with important implications in both science and engineering applications. In these contexts, humans handle social situations by employing elaborate cognitive mechanisms such as theory of mind and risk sensitivity. Here we resort to a novel theoretical model, showing that both mechanisms leverage coordinated behaviors among self-regarding individuals. Particularly, we resort to cumulative prospect theory and level-k recursions to show how biases towards optimism and the capacity of planning ahead significantly increase coordinated, cooperative action. These results suggest that the reason why humans are good at coordination may stem from the fact that we are cognitively biased to do so.     

Whisker motor cortex ablation and whisker movement patterns

Previous studies, based on qualitative observations, reported that lesions of the whisker motor cortex produce no deficits in whisking behavior. We used high-resolution optoelectronic recording methods to compare the temporal organization and kinematics of whisker movements before and after unilateral lesions of whisker motor cortex in rats. We now report that while the lesion did not abolish whisking, it significantly disrupted whisking kinematics, coordination, and temporal organization. Lesioned animals showed significant increases in the velocity and amplitude of whisker protractions contralateral to the lesions, as well as a reduction in the synchrony of whisker movements on the two sides of the face. There was a marked shift in the distribution of whisking frequencies, with reduction of activity in the 5-7 Hz bandwidth and increased activity at < 2 Hz. Disruptions of the normal whisking pattern were evident on both sides of the face, and the magnitude of these effects was proportional to the extent of the cortical ablation. We suggest that the observed deficits reflect an imbalance in cortical inputs to a brainstem central pattern generator.     

Approaches to resolving cephalopod movement and migration patterns

Cephalopod movement occurs during all phases of the life history, with the abundance and location of cephalopod populations strongly influenced by the prevalence and scale of their movements. Environmental parameters, such as sea temperature and oceanographic processes, have a large influence on movement at the various life cycle stages, particularly those of oceanic squid. Tag recapture studies are the most common way of directly examining cephalopod movement, particularly in species which are heavily fished. Electronic tags, however, are being more commonly used to track cephalopods, providing detailed small- and large-scale movement information. Chemical tagging of paralarvae through maternal transfer may prove to be a viable technique for tracking this little understood cephalopod life stage, as large numbers of individuals could be tagged at once. Numerous indirect methods can also be used to examine cephalopod movement, such as chemical analyses of the elemental and/or isotopic signatures of cephalopod hard parts, with growing interest in utilising these techniques for elucidating migration pathways, as is commonly done for fish. Geographic differences in parasite fauna have also been used to indirectly provide movement information, however, explicit movement studies require detailed information on parasite-host specificity and parasite geographic distribution, which is yet to be determined for cephalopods. Molecular genetics offers a powerful approach to estimating realised effective migration rates among populations, and continuing developments in markers and analytical techniques hold the promise of more detailed identification of migrants. To date genetic studies indicate that migration in squids is extensive but can be blocked by major oceanographic features, and in cuttlefish and octopus migration is more locally restricted than predictions from life history parameters would suggest. Satellite data showing the location of fishing lights have been increasingly used to examine the movement of squid fishing vessels, as a proxy for monitoring the movement of the squid populations themselves, allowing for the remote monitoring of oceanic species.