Bifurcation and stability analysis in musculoskeletal systems: a study in human stance

Reflexes are important in the control of such daily activities as standing and walking. The goal of this study is to establish how reflexive feedback of muscle length, velocity, and force can lead to stable equilibria (i.e., posture) and limit cycles (e.g., ankle clonus and gait). The influence of stretch reflexes on the behavior and stability of musculoskeletal systems was examined using a model of human stance. We computed branches of fold and Hopf bifurcations by numerical bifurcation analysis of the model. These fold and Hopf branches divide the parameter space, constructed by the reflexive feedback gains, into regions of different behavior: unstable posture, stable posture, and stable limit cycles. These limit cycles correspond to a neural deficiency, termed ankle clonus. We also linked bifurcation analysis to known biomechanical concepts by linearizing the model: the fold branch corresponds to zero ankle stiffness and defines the minimal muscle length feedback necessary for stable posture; the Hopf branch is related to unstable reflex loops. Crossing the Hopf branch can lead to the above-mentioned stable limit cycles. The Hopf branch reduces with increasing time delays, making the subjects posture more susceptible to unstable reflex loops. This might be one of the reasons why elderly people, or those with injuries to the central nervous system, often have trouble with standing and other posture tasks. The influence of cocontraction and force feedback on the behavior of the posture model was also investigated. An increase in cocontraction leads to an increase in ankle stiffness (i.e., intrinsic muscle stiffness) and a decrease in the effective reflex loop gain. On the one hand, positive force feedback increases the ankle stiffness (i.e., intrinsic and reflexive muscle stiffness); on the other hand it makes the posture more susceptible to unstable reflex loops. For negative force feedback, the opposite is true. Finally, we calculated areas of reflex gains for perturbed stance and quiet stance in healthy subjects by fitting the model to data from the literature. The overlap of these areas of reflex gains could indicate that stretch reflexes are the major control mechanisms in both quiet and perturbed stance. In conclusion, this study has successfully combined bifurcation analysis with the more common biomechanical concepts and tools to determine the influence of reflexes on the stability and quality of stance. In the future, we will develop this line of research to look at rhythmic tasks, such as walking.     

Modulation of dynamic parameters of muscle reflex by selective activation of its gamma system

The ability of the gamma system to modify the dynamics of the muscle reflex control system is investigated. The dynamics of the triceps surae muscle in decerebrate cat preparations with intact reflex loops were modulated by contralateral tibial and peroneal nerve stimulation. The parameters of the mathematical models representing the muscle reflex system were estimated by the least squares method. The behaviour of the mathematical models of the system, under various degrees of gamma system stimulation, was then studied in response to disturbance inputs. It is shown that the gamma motor system is an efficient agent for carrying out modifications in the dynamics of the muscle reflex system. The possible functional significance of this phenomenon within the framework of operation of the muscular control system is discussed with reference to optimal adaptive system concepts.     

Stretch-shortening cycle: a powerful model to study normal and fatigued muscle

Stretch-shortening cycle (SSC) in human skeletal muscle gives unique possibilities to study normal and fatigued muscle function. The in vivo force measurement systems, buckle transducer technique and optic fiber technique, have revealed that, as compared to a pure concentric action, a non-fatiguing SSC exercise demonstrates considerable performance enhancement with increased force at a given shortening velocity. Characteristic to this phenomenon is very low EMG-activity in the concentric phase of the cycle, but a very pronounced contribution of the short-latency stretch-reflex component. This reflex contributes significantly to force generation during the transition (stretch-shortening) phase in SSC action such as hopping and running. The amplitude of the stretch reflex component - and the subsequent force enhancement - may vary according to the increased stretch-load but also to the level of fatigue. While moderate SSC fatigue may result in slight potentiation, the exhaustive SSC fatigue can dramatically reduce the same reflex contribution. SSC fatigue is a useful model to study the processes of reversible muscle damage and how they interact with muscle mechanics, joint and muscle stiffness. All these parameters and their reduction during SSC fatigue changes stiffness regulation through direct influences on muscle spindle (disfacilitation), and by activating III and IV afferent nerve endings (proprioseptic inhibition). The resulting reduced stretch reflex sensitivity and muscle stiffness deteriorate the force potentiation mechanisms. Recovery of these processes is long lasting and follows the bimodal trend of recovery. Direct mechanical disturbances in the sarcomere structural proteins, such as titin, may also occur as a result of an exhaustive SSC exercise bout.     

Consecutive GA pairs stabilize medium-size RNA internal loops

Internal loops in RNA are important for folding and function. Consecutive noncanonical pairs can form in internal loops having at least two nucleotides on each side. Thermodynamic and structural insights into such internal loops should improve approximations for their stabilities and predictions of secondary and three-dimensional structures. Most natural internal loops are purine rich. A series of oligoribonucleotides that form purine-rich internal loops of 5-10 nucleotides, including kink-turn loops, were studied by UV melting, exchangeable proton and phosphorus NMR. Three consecutive GA pairs with the motif 5' Y GGA/3' R AAG or GGA R 3'/AAG Y 5' (i.e., 5' GGA 3'/3' AAG 5' closed on at least one side with a CG, UA, or UG pair with Y representing C or U and R representing A or G) stabilize internal loops having 6-10 nucleotides. Certain motifs with two consecutive GA pairs are also stabilizing. In internal loops with three or more nucleotides on each side, the motif 5' U G/3' G A has stability similar to 5' C G/3' G A. A revised model for predicting stabilities of internal loops with 6-10 nucleotides is derived by multiple linear regression. Loops with 2 x 3 nucleotides are predicted well by a previous thermodynamic model.     

Predicting the magnitude of the reflex response to insertions in ubiquitin

The ability to predict the structural response of a protein to an insertion would be a significant advance for the fields of homology modeling and protein design. However, the effects of insertions on protein conformation are not well understood. Previous work has demonstrated that for two loops in ubiquitin, the primary determinant of the structural adaptation to insertions is the insertion site rather than the sequence of the insertion; this phenomenon was termed the reflex response of loops to insertions. We report herein the analysis of ubiquitin mutants with insertions in two other loops. This study demonstrates that the insertion site is the primary determinant of the response to insertions for these two new loops as well, which further supports the reflex response hypothesis. We also attempted to predict the relative magnitudes of the responses at each site but were unsuccessful. Using the additional data collected in this work, we have refined our predictive hypothesis.     

Spinal and supraspinal effects of activity in ligament afferents.

In this paper available knowledge on effects from joint and ligament afferents on spinal neurones and pathways are briefly reviewed, and possible functional implications discussed. Ligament afferents may contribute to joint stability, muscle coordination and proprioception through direct polysynaptic reflex effects onto ascending pathways and skeletomotoneurones, and/or indirectly via reflex actions on the gamma-muscle spindle system. Theoretical and experimental evidence indicate that ligament afferents, together with afferents from other joint structures, muscles and the skin, provide the CNS with information on movements and posture through ensemble coding mechanisms, rather than via modality specific private pathways. The existence and functional relevance of ligamentomuscular protective reflexes, that are triggered when the ligament is threatened by potentially harmful loads, has been seriously questioned. It seems more likely that peripheral sensory inputs from ligament afferents participate in a continuous control of the muscle activity through feedforward, or preprogramming, mechanisms. In line with these ideas it has been suggested that ligament mechanoreceptors have an important role in muscle coordination and in the reflex regulation of the functional joint stability, by contributing to the preprogramming of the muscle stiffness through reflex modulation of the gamma-muscle spindle system.     

Neural mechanisms of emesis

Emesis is a reflex, developed to different degrees in different species, that allows an animal to rid itself of ingested toxins or poisons. The reflex can be elicited either by direct neuronal connections from visceral afferent fibers, especially those from the gastrointestinal tract, or from humoral factors. Emesis from humoral factors depends on the integrity of the area postrema; neurons in the area postrema have excitatory receptors for emetic agents. Emesis from gastrointestinal afferents does not depend on the area postrema, but probably the reflex is triggered by projections to some part of the nucleus tractus solitarius. As with a variety of other complex motor functions regulated by the brain stem, it is likely that the sequence of muscle excitation and inhibition is controlled by a central pattern generator located in the nucleus tractus solitarius, and that information from humoral factors via the area postrema and visceral afferents via the vagus nerve converge at this point. This central pattern generator, like those for motor functions such as swallowing, presumably projects to the various motor nuclei, perhaps through interneuronal pathways, to elicit the sequential excitation and inhibition that controls the reflex.     

Function of the anal sphincters following anterior resections of rectum

The purpose of the present work is to evaluate the function of the anal sphincter following anterior resections of the rectum. Our data have shown that the anorectal reflex did not depend on the presence of the rectal mucosa. The external anal sphincter contraction involves a reflex which is initiated by stretch receptors in the levator ani muscle. The internal anal sphincter relaxation is likely a local reflex involving nerve pathways not yet completely defined.     

Long-latency reflexes of the human arm reflect an internal model of limb dynamics

A key feature of successful motor control is the ability to counter unexpected perturbations. This process is complicated in multijoint systems, like the human arm, by the fact that loads applied at one joint will create motion at other joints [1-3]. Here, we test whether our most rapid corrections, i.e., reflexes, address this complexity through an internal model of the limb's mechanical properties. By selectively applying torque perturbations to the subject's shoulder and/or elbow, we revealed a qualitative difference between the arm's short-latency/spinal reflexes and long-latency/cortical reflexes. Short-latency reflexes of shoulder muscles were linked exclusively to shoulder motion, whereas its long-latency reflexes were sensitive to both shoulder and elbow motion, i.e., matching the underlying shoulder torque. In fact, a long-latency reflex could be evoked without even stretching or lengthening the shoulder muscle but by displacing just the elbow joint. Further, the shoulder's long-latency reflexes were appropriately modified across the workspace to account for limb-geometry changes that affect the transformation between joint torque and joint motion. These results provide clear evidence that long-latency reflexes possess an internal model of limb dynamics, a degree of motor intelligence previously reserved for voluntary motor control [3-5]. The use of internal models for both voluntary and reflex control is consistent with substantial overlap in their neural substrates and current notions of intelligent feedback control [6-8].     

Computational reconstruction of the human skeletal muscle secretome

In multicellular organisms, secreted proteins play pivotal regulatory roles in intercellular communication. Proteins secreted by skeletal muscle can act locally on muscle cells through autocrine/paracrine loops and on surrounding tissues such as muscle blood vessels, or they can be released into the blood stream, thus producing systemic effects. By a computational approach, we have screened 6255 products of genes expressed in normal human skeletal muscle. Putatively secreted proteins were identified by sequential steps of sieving, through prediction of signal peptide, recognition of transmembrane regions, and analysis of protein annotation. The resulting putative skeletal muscle secretome consists of 319 proteins, including 78 still uncharacterized proteins. This is the first human skeletal muscle secretome produced by computational analysis. Knowledge of proteins secreted by skeletal muscle could stimulate development of novel treatments for different diseases, including muscle atrophy and dystrophy. In addition, better knowledge of the secretion process in skeletal muscle can be useful for future gene therapy approaches.     

The computer-vibromyography as a biometric progress in studying muscle function

Muscular vibrations were recorded from different relaxed and contracted skeletal muscles in human subjects, with the use of a piezo-electric device. Simultaneous wire-EMG recordings were performed. Spectral analysis of the acceleration curves (vibromyograms) disclosed muscle and function dependent compound frequency patterns. We suggest that the activity of motor units including the action of central reflex loops and oscillatory driving is mainly responsible for the muscular vibrations. Other sources are discussed. Computer-Vibromyography as a mechanical ensemble measurement supplements bioelectric EMG techniques and classical tremor analysis and provides further insights into the function of muscle and motor-system.     

Peripheral factors influencing expression of pressor reflex evoked by muscular contraction

The effect of evoked muscle tension, active muscle mass, and fiber-type composition on the pressor reflex evoked by muscular contraction was examined in decerebrate and anesthetized cats. Muscular contraction was induced by stimulating the L7 and S1 ventral roots with 0.1-ms duration pulses three times motor threshold at various frequencies. The experiments were designed to isolate the variable under study as much as possible and included the use of selectively denervated preparations to limit contractions to specific muscles. It was found that altering the evoked tension by varying the resting muscle length had commensurate effects on the pressor reflex (greater evoked tension caused a larger reflex). In addition it was found that changing the amount of active muscle mass caused similar changes in the reflex (the smaller the muscle mass, the smaller the reflex). Finally, it was found that contrary to other accounts, pressor reflexes could be evoked by activation of the slow-twitch muscle soleus, composed exclusively of red (type I) fibers.     

Effects of Removal of Muscle Receptor Organ Input on the Temporal Structure of Non-Giant Swimming Cycles in the Crayfish, Cherax Destructor

Most studies of the muscle receptor organs (MROs) of decapod crustaceans have focused on their role in local reflex loops. This may not be their only function. We examine their involvement in the regulation of non-giant swimming cycles by removing stretch receptor (SR) input from the MROs in abdominal segments 2-5 of the crayfish Cherax destructor . SR input was left intact in two control groups, one of which had sham surgery and the other no surgery at all. We recorded electromyograms (EMGs) from selected uropod muscles during tailflipping in sequences of non-giant swimming in tethered animals. The removal of SR input had a significant effect. The opener muscle period was shorter in the experimental group than in either of the control groups. This suggests that by using SR afference, crayfish sacrifice speed for increased control of the swimming movement.     

Spasticity and spastic dystonia: the two faces of velocity-dependent hypertonia

BackgroundSpasticity and spastic dystonia are two separate phenomena of the upper motor neuron syndrome. Spasticity is clinically defined by velocity-dependent hypertonia and tendon jerk hyperreflexia due to the hyper-excitability of the stretch reflex. Spastic dystonia is the inability to relax a muscle leading to a spontaneous tonic contraction. Both spasticity and spastic dystonia are present in patients who are at rest; however, only patients with spasticity are actually able to kept their muscles relaxed prior to muscle stretch. The idea that has inspired the present work is that also in patients with spastic dystonia the stretch reflex is likely to be hyper-excitable. Therefore, velocity-dependent hypertonia could be mediated not only by spasticity, but also by spastic dystonia.MethodsTonic stretch reflexes in the rectus femoris muscle were evoked in 30 patients with multiple sclerosis showing velocity-dependent hypertonia of leg extensors and the habituation of the reflex was studied. Moreover, the capability of relax the muscle prior to muscle stretch (spastic dystonia) was also investigated.ResultsA tonic stretch reflex was evoked in all the enrolled patients. 73% of the patients were able to relax their rectus femoris muscle prior to stretch (spasticity). In the overwhelming majority of these patients, the tonic stretch reflex decreased during repeated stretches. In the remaining 27% of the subjects, the muscle was tonically activated prior to muscle stretch (spastic dystonia). In the patients in whom spastic dystonia progressively increased over the subsequent stretches (50% of the subjects with spastic dystonia), the habituation of the reflex was replaced by a progressive reflex facilitation.DiscussionThis study shows for the first time that velocity-dependent hypertonia can be caused by two distinct phenomena: spasticity and spastic dystonia. The habituation of the tonic stretch reflex, which is a typical feature of spasticity, is replaced by a reflex facilitation in the half of the subject with spastic dystonia. These preliminary findings suggest that differentiating the two types of velocity-dependent muscle hypertonia (spasticity and spastic dystonia) could be clinically relevant.     

Effects of Removal of Muscle Receptor Organ Input on the Temporal Structure of Non-Giant Swimming Cycles in the Crayfish,Cherax Destructor

Most studies of the muscle receptor organs (MROs) of decapod crustaceans have focused on their role in local reflex loops. This may not be their only function. We examine their involvement in the regulation of non-giant swimming cycles by removing stretch receptor (SR) input from the MROs in abdominal segments 2-5 of the crayfish Cherax destructor. SR input was left intact in two control groups, one of which had sham surgery and the other no surgery at all. We recorded electromyograms (EMGs) from selected uropod muscles during tailflipping in sequences of non-giant swimming in tethered animals. The removal of SR input had a significant effect. The opener muscle period was shorter in the experimental group than in either of the control groups. This suggests that by using SR afference, crayfish sacrifice speed for increased control of the swimming movement.     

Considerations on mechanisms of focussed signal transmission in the multi-channel muscle stretch reflex system

This paper presents theoretical considerations on the possibility of topographically ordered signal transmission in the control system of the muscle stretch reflex. It is investigated how correlations between Ia fibres from primary muscle spindle endings in conjunction with an appropriate connectivity of Ia fibres and motoneurones enable the stretch reflex system to trace local routes through the spinal cord. The complex data processing capabilities of the motoneuronal soma-dendritic membrane system are fully taken into account, and it is argued that correlations between inputs to this system may play an important role for signal transmission through the spinal cord.     

Factors affecting thermodynamic stabilities of RNA 3 x 3 internal loops

Internal loops in RNA are important for folding and function. The 3 x 3 nucleotide internal loops are the smallest size symmetric loops with a potential noncanonical base pair (middle pair) flanked on both sides by a noncanonical base pair (loop-terminal pair). Thermodynamic and structural insights acquired for 3 x 3 loops should improve approximations for stabilities of 3 x 3 and larger internal loops. Most natural 3 x 3 internal loops are purine rich, which is also true of other internal loops. A series of oligoribonucleotides containing different 3 x 3 internal loops were studied by UV melting and imino proton NMR. Both loop-terminal and middle pairs contribute to the thermodynamic stabilities of 3 x 3 loops. Extra stabilization of -1.2 kcal/mol was found for a GA middle pair when flanked by at least one non-pyrimidine-pyrimidine loop-terminal pair. A penalty of approximately 1 kcal/mol was found for loops with a single loop-terminal GA pair that has a U 3' to the G of the GA pair. A revised model for predicting stabilities of 3 x 3 loops is derived by multiple linear regression.     

Effects of hypoxia on genioglossus and scalene reflex responses to brief pulses of negative upper-airway pressure during wakefulness and sleep in healthy men.

Hypoxia can depress ventilation, respiratory load sensation, and the cough reflex, and potentially other protective respiratory reflexes such as respiratory muscle responses to increased respiratory load. In sleep-disordered breathing, increased respiratory load and hypoxia frequently coexist. This study aimed to examine the effects of hypoxia on the reflex responses of 1) the genioglossus (the largest upper airway dilator muscle) and 2) the scalene muscle (an obligatory inspiratory muscle) to negative-pressure pulse stimuli during wakefulness and sleep. We hypothesized that hypoxia would impair these reflex responses. Fourteen healthy men, 19-42 yr old, were studied on two separate occasions, approximately 1 wk apart. Bipolar fine-wire electrodes were inserted orally into the genioglossus muscle, and surface electrodes were placed overlying the left scalene muscle to record EMG activity. In random order, participants were exposed to mild overnight hypoxia (arterial oxygen saturation approximately 85%) or medical air. Respiratory muscle reflex responses were elicited via negative-pressure pulse stimuli (approximately -10 cmH(2)O at the mask, 250-ms duration) delivered in early inspiration during wakefulness and sleep. Negative-pressure pulse stimuli resulted in a short-latency activation followed by a suppression of the genioglossus EMG that did not alter with hypoxia. Conversely, the predominant response of the scalene EMG to negative-pressure pulse stimuli was suppression followed by activation with more pronounced suppression during hypoxia compared with normoxia (mean +/- SE suppression duration 64 +/- 6 vs. 38 +/- 6 ms, P = 0.006). These results indicate differential sensitivity to the depressive effects of hypoxia in the reflex responsiveness to sudden respiratory loads to breathing between these two respiratory muscles.