The effects of multiple reflex pathways on the oscillations in neuro-muscular systems

Summary A model of mammalian neuro-muscular systems described previously (Ouztöreli and Stein, 1975) has been extended to include multiple reflex pathways, as have been shown to exist in primates, including man (Milner-Brown et al., 1975). A number of general mathematical properties of the extended system are described. In the final section, using computer solutions, it is shown that the presence of multiple reflex pathways can effectively reduce the tendency for oscillation which will exist if high reflex gain were concentrated in a single pathway. High loop gain is desirable for good control in any negative feedback system, so the presence of multiple reflex pathways could improve reflex control, while limiting the magnitude of tremor or other unwanted oscillations in neuromuscular systems.This work was partly supported by the National Research Council of Canada (Grant NRC-A4345) and by the Medical Research Council of Canada (Grant MRC-MA 3307) through the University of Alberta.     

Activity analysis of neural networks

In a series of articles (Leung et al., 1973, 1974; Ogztöreli, 1972, 1975, 1978, 1979; Stein et al., 1974) we have investigated some of the physiologically significant properties of a general neural model. In these papers the nature of the oscillations occuring in the model has been briefly analyzed by omitting the effects of the discrete time-lags in the interaction of neurons, although these time-lags were incoporated in the general model. In the present work we investigate the effects of the time-lags on the oscillations which are intrinsic to the neural model, depending on the structural parameters such as external inputs, interaction coefficients, self-inhibition, self-excitation and selfadaptation coefficients. The numerical solution of the neural model, the computation of the steady-state solutions and the natural modes of the oscillations around the steady-state solutions are described.This work was partly supported by the Natural Sciences and Engineering Research Council of Canada under Grant NRC-A-4345 through the University of Alberta     

Tremor and other oscillations in neuromuscular systems

A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.     

Analysis of a model for antagonistic muscles

In the present work a linear model for a pair of antogonistic muscles is analysed. Each constituent muscle in this model is identical to ones considered previously (Stein and Ouztöreli, 1976). Analytical properties of the antagonistic muscles and dynamics of the system are described and some numerical results are discussed. The natural modes of the system are determined by a fourth order polynomial, which most commonly has one pair of conjugate complex roots and two negative real roots. The filtering of neural inputs through the active state properties of the muscle increases the order of the system to fifth order for these inputs.This work was partly supported by the National Scientific and Engineering Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MT-3307 through the University of Alberta     

Untersuchungen zur Linearität des okulomotorischen Systems

The oculomotor system, as far as horizontal voluntary eyemovements are concerned, is analyzed by way of average gain and phase frequency plots based on sinusoidal and random noise inputs. On account of the non-linear properties of the system, it is not possible to obtain an overall-transfer-function, but nevertheless frequency-responses are sufficiently appropriate to demonstrate the system-performance using different types of signals. Frequencyresponses are significantly different for sinusoidal and random inputs, because of the interference of the saccadic component. On the other hand, gain and phase, to a certain extent, turn out to be independent of the amplitude of the input.

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Im Rahmen des Sonderforschungsbereichs BIONACH.     

Modeling of a simple motor task in man: intentional arrest of an ongoing movement

Normal subjects and cerebellar patients were instructed to arrest “as soon as possible” a ballistically initiated flexion movement of the forearm. The intentional actions consist essentially of a downward torque, the peak value of which has almost a constant latency (about 200 msec) from the beginning of the movement. A variable number of oscillations precede the arrest of the movement, the characteristics of which depend on the initial velocity of the flexion and on the mass with which the forearm is loaded. The motor commands responsible for the intentionally produced downward torque are controlled centrally as to leave the ratio between the peak values of the angular velocity which precede and follow the peak of the torque almost constant, under all conditions. To describe the oscillations a simple analytical model was proposed which includes the mechanical as well as the reflex factors, the latter under the form of a delayed velocity term. The satisfactory fitting of this model to the experimental findings permitted to establish the following points:

1. The oscillations are sustained by both a mechanical and a reflex stiffness. The contribution of the reflex loop is however quantitatively dominant since it accounts for about 75% of the inertial torque. It is fairly constant over the range of frequency of the oscillations considered.
2. Under the imposed experimental conditions angular velocity appears to be the parameter of the movement which is predominantly sensed and fed back by the reflex loop.

Data were also presented on the performance of the motor task by patients who underwent surgical ablations of the cerebellar cortex. Comparison of these results with those of normal subjects strongly supports the hypothesis that cerebellar-related activities are instrumental in determining the sensitivity of the stretch reflex to angular velocity.     

Physiological changes in central neuronal pathways contributing to the generation of a reflex reversal

1. In the stick insect Carausius morosus the properties of the neuronal network governing the femur-tibia joint depend on the behavioral state of the animal. In the inactive animal flexion of the femur-tibia joint results in the generation of a resistance reflex, while in the active animal the same stimulus induces the so-called active reaction, the first part of which is a reflex reversal.
2. Recordings from motoneurons innervating the extensor tibiae muscle indicated that their time course of activity during the active reaction is due to inputs from intercalated pathways. We therefore investigated the role of identified nonspiking interneurons that transmit sensory information from the chordotonal organ onto the extensor motoneurons in the inactive animal. We can show that (i) the nonspiking interneurons received altered inputs whereas (ii) they provided qualitatively the same synaptic drive onto leg motoneurons.
3. From our results it is clear that (i) neuronal pathways contributing to the generation of the resistance reflex are also involved in the generation of the reflex reversal in the same control loop, (ii) thereby adopting the same principle of information processing (parliamentary principle), because both, supporting and opposing pathways contribute to the generation of the motor output.

     

The role of structural symmetry in linearizing ocular reflexes

This work presents a simulation study using an anatomically relevant model of the vestibulo-ocular reflex (VOR). The aim is to explore the functional properties of a bilateral structure in the premotor circuits of the oculomotor system. The major conclusions using sinusoidal inputs are: A bilateral structure in a sensory-motor system improves its linear range beyond expected central limits, if provided with symmetric interconnections. Given a bilateral (push-pull) sensory arrangement, non-linear sensor characteristics are actually advantageous. The greatest improvement in linear range of the reflex (here VOR) relies on intact sensors on both sides. In the case of a single sensor (unilateral head velocity input), or unmatched bilateral sensors, this study predicts a decrease in the linear range and the appearance of a variable bias. These implications are compatible with available data and can be tested in a clinical invironment.     

The contribution of sensory inputs to the pattern generation of breathing

Current concepts of the basic neural control system and its modulation by afferent inputs are reviewed. It is emphasized that, in analogy with locomotion, the central pattern generator (CPG) for automatic metabolic respiration does not depend on any afferent feedback from receptors sensitive to the movements of the "pump," or the streams of pumped air, for its production of a rhythmic motor output provides the CPG receives some "drive" inputs above threshold and adequate bias. The operation for a variety of reflexes and feedback loops is of fundamental importance, however, for adapting the breathing pattern to the varying requirements for gas exchange to the many behavioural, nonmetabolic demands on the breathing apparatus which are competing with its primary metabolic control functions. The presentation is focussed also on available evidence that the respiratory CPG exerts powerful modulations on the transmission in these reflex pathways controlling the pattern of breathing and adjusting it to the various metabolic and behavioural demands. Mechanisms for "gating," "phasic gain changes," and "phase-dependent reflex reversal" are exemplified.     

Postural maintenance during movement: Simulations of a two joint model

Voluntary movements of the upper body are accompanied by anticipatory postural adjustments to the lower body in a standing subject. The long-standing hypothesis is that these anticipatory adjustments serve to counteract the perturbation to the body's center of gravity caused by the voluntary arm movement. This paper presents model simulations investigating the possible roles of anticipatory postural activity that accompanies a rapid, upward arm swing. The model encorporates two (idealized) antagonistic muscle pairs controlling the movements of a double-joint system, with a shoulder joint between the arm and stiff body links, and an ankle joint between the stiff body-leg segment and the ground. Each muscle is represented by a nonlinear viscoelastic element and also includes proprioceptive feedback. Four inputs to the model define the motor control signals for muscle force generation in both the arm and the postural muscle pairs. The neurological component of the model describes consequences of alternate strategies for cocontractions, stretch reflex activity, and anticipatory and synchronous postural activities (or combinations thereof). Simulations with this model show that: (1) none of the postural maintenance schemes considered in these simulations (including varying anticipation) could suppress the initial backward thrust on the body link; (2) the more important destabilizing perturbation is a subsequent forward sway that, left uncountered by postural activity, would eventually leave the body to fall flat on its face; and (3) anticipatory silencing of the postural extensor followed by a brief period of extensor activation (descending control) and synchronous reflex activity (feedback control) appears to be the most likely postural stabilizing strategy that inhibits the continuous forward sway and is consistent with the experimental evidence.     

Bile duct ligation-induced redistribution of canalicular antigen in rat hepatocyte plasma membranes demonstrated by immunogold quantitation

Summary Extrahepatic obstructive cholestasis has been demonstrated to induce a redistribution of domain specific membrane proteins in rat hepatocytes reflecting loss or even reversal of cell polarity. In order to further characterize the redistribution of canalicular antigens, we used the Lowicryl K4M immunogold technique for examination of the effects of bile duct ligation (50 h) on the distribution of antigen in rat hepatocytes at the ultrastructural level and quantitated immuno-gold density in the three domains of the plasma membrane. In normal hepatocytes, antigen was localized almost exclusively in the canalicular domain while the sinusoidal and lateral membranes showed only weak immunoreactivity. Other localizations included organelles compatible with known pathways of biosynthesis and degradation. Bile duct ligation markedly reduced immunolabel in the canalicular and increased it slightly in the sinusoidal domain. The number and staining intensity of immunoreactive sub-canalicular lysosomes and vesicles probably representing endosomes was augmented. Number of immunogold particles per m of plasma membrane were 7.86 vs 2.46 (P<0.005) in the canalicular, 1.16 vs 1.38 (n.s.) in the sinusoidal, and 1.23 vs 1.08 (n.s.) in the lateral domain resulting in a canalicular decrease by 68.7% and a sinusoidal increase of 19.0%. Overall decrease in total plasma membranes was by 29.7% (P<0.05). Thus, our data show that the sinusoidal and lateral domains behave differently. Furthermore, quantitative immunocytochemistry demonstrates a decrease in the canalicular antigen density and suggests a sinusoidal increase. The present data agree with the concept that bile duct ligation results in a loss or even reversal of cell polarity in hepatocytes.This study was supported by the Swiss National Science Foundation grants 3.846.0.87 (to L.L.) and 3.992.0.87 (to P.J.M.)     

Frequency response characteristics of a multi-loop representation of the segmental muscle stretch reflex

This paper continues the investigation of a three-loop representation of the segmental muscle stretch reflex system introduced in a preceding communication. Frequency response characteristics were computed for open-loop conditions, control and disturbance signal inputs under a variety of conditions: (i) in parallel and in series peripheral arrangements of muscle compartments, (ii) various patterns of central connectivity, (iii) various recruitment levels of motor units, (iv) various overall reflex gains, (v) absence or presence of muscle spindle accleration sensitivity. These computations disclosed a number of mechanisms by which the nervous system might improve system stability and behaviour. These mechanisms are discussed with regard to physiological data.     

Eye movements and brainstem neuronal responses evoked by cerebellar and vestibular stimulation in chicks

Summary The vestibulo-ocular reflex undergoes adaptive changes that require inputs from the cerebellar flocculus onto brainstem vestibular neurons. As a step toward developing an in vitro preparation in chicks for studying the synaptic basis of those changes, we have elucidated the organization of the pathways through which the flocculus influences vestibulo-ocular movements. Electrical stimulation of the vestibular ampulla evoked brief, contralaterally directed movements in both eyes. Although single current pulses to the flocculus elicited no response, conjunctive stimulation of the flocculus and the vestibular apparatus significantly reduced the vestibularly-evoked movement. Trains of current pulses applied to the flocculus and ampulla evoked eye movements directed toward and away from the side of stimulation, respectively. Recordings from the brainstem revealed neurons that were activated by ipsilateral vestibular stimulation and inhibited by ipsilateral floccular stimulation. Our sample included neurons in the lateral vestibular nucleus, the ventrolateral portion of the medial vestibular nucleus, and the superior vestibular nucleus. Similarities between these findings and those of similar studies in mammals indicate that the chick will provide a good model system for cellular studies of adaptive changes in the vestibulo-ocular reflex.Abbreviations FTN flocculus target neuron - VOR vestibuloocular reflex     

Probing the neuromodulatory gain control system in sports and exercise sciences

The monoaminergic bulbospinal pathways from the brainstem are central to motor functions by regulating the gains of spinal motoneurons and represent, in that respect, probably the primary control system for motoneuron excitability. Yet, the efficiency of this system is few, if not never, assessed in the fields of sports and exercise sciences. In this review paper, we propose a methodological approach intended to assess how this neuromodulatory system affects motoneuron excitability. This approach is based on the use of tendon vibration which can, in certain circumstances, induce the generation of the so-called tonic vibration reflex through the stimulation of muscle spindles. Force and EMG responses to tendon vibration are indeed indicative of how this descending system modulates the gain of the ionotropic inputs from Ia afferents and thus of the strength of the monoaminergic drive. After a brief presentation of the neuromodulatory system and of the mechanisms involved in the generation of the tonic vibration reflex, we address some important methodological considerations regarding the use of the TVR to probe this neuromodulatory gain control system. Hopefully, this paper will encourage sports and exercise scientists to investigate this system.     

Global stability and oscillations in classical Lotka-Volterra loops

The paper considers the classical Volterra system of n ( 3) species in predator-prey relation forming a loop, and derives some global properties of its solutions. Sufficient conditions for global asymptotic stability in terms of parameters are obtained, and also the region of global boundedness in the parameter space is indicated. Lastly a three species system is discussed in detail in relation to its global stability, unboundedness of solutions, existence of periodic and non-periodic oscillations.Work performed under the auspices of G.N.F.M., C.N.R. (Italy) and within the activity of the group Evolution Equations and Applications, M.P.I., (Italy)     

Disease pathways at the Rat Genome Database Pathway Portal: genes in context-a network approach to understanding the molecular mechanisms of disease

Background

Biological systems are exquisitely poised to respond and adjust to challenges, including damage. However, sustained damage can overcome the ability of the system to adjust and result in a disease phenotype, its underpinnings many times elusive. Unraveling the molecular mechanisms of systems biology, of how and why it falters, is essential for delineating the details of the path(s) leading to the diseased state and for designing strategies to revert its progression. An important aspect of this process is not only to define the function of a gene but to identify the context within which gene functions act. It is within the network, or pathway context, that the function of a gene fulfills its ultimate biological role. Resolving the extent to which defective function(s) affect the proceedings of pathway(s) and how altered pathways merge into overpowering the system's defense machinery are key to understanding the molecular aspects of disease and envisioning ways to counteract it. A network-centric approach to diseases is increasingly being considered in current research. It also underlies the deployment of disease pathways at the Rat Genome Database Pathway Portal. The portal is presented with an emphasis on disease and altered pathways, associated drug pathways, pathway suites, and suite networks.

Results

The Pathway Portal at the Rat Genome Database (RGD) provides an ever-increasing collection of interactive pathway diagrams and associated annotations for metabolic, signaling, regulatory, and drug pathways, including disease and altered pathways. A disease pathway is viewed from the perspective of networks whose alterations are manifested in the affected phenotype. The Pathway Ontology (PW), built and maintained at RGD, facilitates the annotations of genes, the deployment of pathway diagrams, and provides an overall navigational tool. Pathways that revolve around a common concept and are globally connected are presented within pathway suites; a suite network combines two or more pathway suites.

Conclusions

The Pathway Portal is a rich resource that offers a range of pathway data and visualization, including disease pathways and related pathway suites. Viewing a disease pathway from the perspective of underlying altered pathways is an aid for dissecting the molecular mechanisms of disease.

     

Ultrastructural observations on the droplets of experimentally-induced goitres in Xenopus laevis with especial reference to the development of uhlenhuth colloid cells

Summary Goitres were induced in tadpoles and young toads of Xenopus laevis Daudin by prolonged immersion in aqueous solutions (0.005% or 0.01% w/v) of potassium perchlorate, potassium thiocyanate, thiourea or propyl-thiouracil. Various categories of single membrane-limited droplets were induced and these are described. Also some of the goitrous cells showed an accumulation of colloid droplets leading to the formation of Uhlenhuth colloid cells. The development and significance of these cells in the amphibian goitres is considered.This work was carried out during the tenure by one of us (R. C.) of a Medical Research Council Scholarship and forms part of a programme of research in amphibian thyroid physiology supported by the Medical Research Council to whom we are indebted for their generous assistance.     

Analysis of the reflexive feedback control loop during posture maintenance

 In previous work it has been shown in posture experiments of the human arm that reflexive dynamics were substantial for narrow-band stochastic force disturbances. The estimated reflex gains varied substantially with the frequency content of the disturbances. The present study analyses a simplified linear model of the reflexive feedback control loop, to provide an explanation for the observed behaviour. The model describes co-activation and reflexive feedback. The task instruction `minimize the displacements' is represented mathematically by a cost function that is minimized by adjusting the parameters of the model. Small-amplitude displacements allow the system to be analysed with a quasi-linear approach. The optimization results clarify the limited effectiveness of reflexive feedback on the system's closed-loop behaviour, which emanates from the time delay present in the reflex loops. For low-frequency inputs less than 5 Hz, boundary-stable solutions with high reflex gains are predicted to be optimal. Input frequencies near the system's eigenfrequency (about 5 Hz), however, would be amplified and result in oscillatory behaviour. As long as the disturbance does not excite these frequencies, boundary stability will be optimal. The predicted reflex gains show a striking similarity with the estimated reflex gains from the experimental study. The present model analysis also provides a clear explanation for the negative reflex gains, estimated for near-sinusoidal inputs beyond 1.5 Hz. Received: 24 January 2000 / Accepted in revised form: 7 July 2000     

Heart rate variability biofeedback as a method for assessing baroreflex function: a preliminary study of resonance in the cardiovascular system

This study describes the use of a biofeedback method for the noninvasive study of baroreflex mechanisms. Five previously untrained healthy male participants learned to control oscillations in heart rate using biofeedback training to modify their heart rate variability at specific frequencies. They were instructed to match computer-generated sinusoidal oscillations with oscillations in heart rate at seven frequencies within the range of 0.01–0.14 Hz. All participants successfully produced high-amplitude target-frequency oscillations in both heart rate and blood pressure. Stable and predictable transfer functions between heart rate and blood pressure were obtained in all participants. The highest oscillation amplitudes were produced in the range of 0.055–0.11 Hz for heart rate and 0.02–0.055 Hz for blood pressure. Transfer functions were calculated among sinusoidal oscillations in the target stimuli, heart rate, blood pressure, and respiration for frequencies at which subjects received training. High and low target-frequency oscillation amplitudes at specific frequencies could be explained by resonance among various oscillatory processes in the cardiovascular system. The exact resonant frequencies differed among individuals. Changes in heart rate oscillations could not be completely explained by changes in breathing. The biofeedback method also allowed us to quantity characteristics of inertia, delay, and speed sensitivity in baroreflex system. We discuss the implications of these findings for using heart rate variability biofeedback as an aid in diagnosing various autonomic and cardiovascular system disorders and as a method for treating these disorders.