Studies on human finger tapping neural networks by phase transition curves

Generally, the phase resetting experiments can be used to investigate the behaviors of the stable biological oscillators (e.g. circadian rhythms, biochemical oscillators, pacemaker neurons, bursting neurons). Winfree found that there are two types of phase transition curves (PTC) in the phase resetting experiments of biochemical oscillations. The one is the curve with an average slope of unity (Type 1) and is obtained for the small magnitude of perturbation. The other curve is that with a zero average slope (Type 0) and is obtained for the large magnitude of perturbation. Previously, we explained these results mathematically by the homotopy theory. In this paper, some properties of the human finger tapping neural network are studied psychologically using PTC on the basis of above theoretical results: assuming that an oscillatory neural network controls the human finger tapping, we performed two kinds of phase resetting experiments on the finger tapping. In the first experiment, we showed that the PTC was available to estimate the degree of functional interaction between the finger tapping neural network and that which controls another task. Three tasks (rapid key-pushing, rapid voicing and pattern discrimination) were chosen as the perturbation of the phase resetting experiment. Analyzing shapes of PTCs, it was found that the interaction with the key-pushing network was the largest, and that with the pattern recognition network was the smallest of the three. In the second experiment, we modified the first task as perturbation of the phase resetting experiments to investigate further the interactions between the left and the right hand motor systems. Consequently the following results were revealed. First, shapes of PTCs are very different according as subject's experiences of finger tapping. Second, the type of PTC for some subjects changes from Type 0 to Type 1 by learning. Third, the PTC tends to become Type 0 for shorter tapping periods. Fourth, neither changes of motor loads (the necessary force to push the key) nor an alternation of the tapping hand and the key-pushing hand affects the shape of PTCs.     

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     

MEG responses during rhythmic finger tapping in humans to phasic stimulation and their interpretation based on neural mechanisms

 The phase-resetting experiment was applied to human periodic finger tapping to understand how its rhythm is controlled by the internal neural clock that is assumed to exist. In the experiment, the right periodic tapping movement was disturbed transiently by a series of left finger taps in response to impulsive auditory cues presented randomly at various phases within the tapping cycle. After each left finger tap, the original periodic tapping was reestablished within several tapping cycles. Influences of the disturbance on the periodic right finger tapping varied depending on the phase of the periodic right finger tapping at which each left finger tap was made. It was confirmed that the periodic tapping was disturbed not by the auditory cues but by the left finger taps. Based on this fact, in this paper each single left tap was considered as the stimulus, and the phase of the periodic tapping of the right index finger when the left tap was executed as the phase of the stimulus. Responses of the neural activities (magnetoencephalography, MEG), the tapping movement, and the corresponding muscle activities (electromyography) were simultaneously measured. Phase-resetting curves (PRCs) representing the degree of phase reset as a function of the phase of the stimulus were obtained both for the left sensorimotor cortex MEG response and for the right index finger tapping response. The shapes of both PRCs were similar, suggesting that the phase reset of the left sensorimotor cortex activities and that of the finger tapping rhythm were the same. Four out of eight subjects showed type-0 reset in Winfree's definition, and the others showed type-1 reset. For general limit-cycle oscillators, type-0 reset is obtained for relatively strong perturbations and type 1 for weak perturbations. It was shown that the transient response of MEG to the single left tap stimuli in type-0 subjects, where the phase was progressively reset, were different from those in type-1 subjects. Based on detailed analysis of the differences, a neural network model for the phase reset of the tapping rhythm is proposed. Received: 10 February 2000 / Accepted in revised form: 15 January 2002     

Phase plane description of crayfish swimmeret oscillator

Crayfish swimmeret system shows rhythmic, coordinated behavior when the command fibers are stimulated chronically by electrical pulses, and the oscillating frequency becomes faster with increasing stimulus frequency. This behavior is organized by the distributed neural oscillators in the abdominal ganglia. We investigated the dynamics of the neural oscillators which are controlled by command fibers. Phase resetting experiment technique was used for this purpose; a temporary cessation of commanding pulses, which was regarded as suppressive perturbation for the neural oscillator, was applied to the chronically stimulated oscillator, and phase transition curves (PTCs) were measured. For the short cessation of command pulses, type 1 PTCs were obtained. With increasing cessation length, the PTC shifted downward, and finally changed into type 0. We also measured PTCs for temporarily increased stimulus frequency, which was an excitatory perturbation for the neural oscillator and increased the frequency of the oscillation transiently. For the short excitatory perturbation, the PTCs were also type 1 and shifted upward. PTCs changed their shapes from type 1 into type 0, as increasing the perturbation length. These shapes of the PTCs contain important information about the properties of the neural oscillator. Analyzing these PTCs, we present a phase plane diagram which describes the character of the command control of the neural oscillator.     

Biological oscillators can be stopped—Topological study of a phase response curve

Many biological oscillators are stable against noise and perturbation (e.g. circadian rhythms, biochemical oscillators, pacemaker neurons, bursting neurons and neural networks with periodic outputs). The experiment of phase shifts resulting from discrete perturbation of stable biological rhythms was developed by Perkel and coworkers (Perkel et al., 1964). By these methods, they could get important insights into the entrainment behaviors of biological rhythms. Phase response curves, which are measured in these experiments, can be classified into two types. The one is the curve with one mapping degree (Type 1), and the other is that with zero mapping degree (Type 0) (Winfree, 1970). We define the phase response curve mathematically, and explain the difference between these two types by the homotopy theory. Moreover, we prove that, if a Type 0 curve is obtained at a certain magnitude of perturbation, there exists at least one lower magnitude for which the phase response curve cannot be measured. Some applications of these theoretical results are presented.     

华南浅海相泥盆系吉维特阶和弗拉阶四射珊瑚组合特征

中泥盆世吉维特晚期(更精确的说是在中吉维特期末)发生的生物更替事件使大量的头贝、全部的泡沫珊瑚亚目以及大多数的绳珊瑚科和内板珊瑚科惨遭灭绝。晚泥盆世弗拉期出现了许多新生分子,诸如Micto-phyllum,Wapitiphyllum,Pseudozaphrentis,Peneckiella等。根据珊瑚的不同组合特征可以鉴别出它们的地质时代。华南自上而下可划分出4个四射珊瑚组合,分别为上泥盆统弗拉阶(Frasnian):4)Disphyllum-Wapitiphyl-lum组合(牙形类gigas或rhenana带和hassi-jamieae带),3)Mictophyllum-Pseudozaphrentis组合(牙形类asymmetricus带);中泥盆统吉维特阶(Givetian):2)Endophyllum-Sunophyllum组合(牙形类varcus带的中部和下部之上段),1)Stringophyllum-Paramixogonaria组合(牙形类hemiansatus带-varcus带最下部)。     

Rhythmic cortical neurons increase their oscillations and sculpt basal ganglia signaling during motor learning

The function and modulation of neural circuits underlying motor skill may involve rhythmic oscillations (Feller, 1999 ; Marder and Goaillard, 2006 ; Churchland et al., 2012 ). In the proposed pattern generator for birdsong, the cortical nucleus HVC, the frequency and power of oscillatory bursting during singing increases with development (Crandall et al., 2007 ; Day et al., 2009 ). We examined the maturation of cellular activity patterns that underlie these changes. Single unit ensemble recording combined with antidromic identification (Day et al., 2011 ) was used to study network development in anesthetized zebra finches. Autocovariance quantified oscillations within single units. A subset of neurons oscillated in the theta/alpha/mu/beta range (8–20 Hz), with greater power in adults compared to juveniles. Across the network, the normalized oscillatory power in the 8–20 Hz range was greater in adults than juveniles. In addition, the correlated activity between rhythmic neuron pairs increased with development. We next examined the functional impact of the oscillators on the output neurons of HVC. We found that the firing of oscillatory neurons negatively correlated with the activity of cortico‐basal ganglia neurons (HVC_Xs), which project to Area X (the song basal ganglia). If groups of oscillators work together to tonically inhibit and precisely control the spike timing of adult HVC_Xs with coordinated release from inhibition, then the activity of HVC_Xs in juveniles should be decreased relative to adults due to uncorrelated, tonic inhibition. Consistent with this hypothesis, HVC_Xs had lower activity in juveniles. These data reveal network changes that shape cortical‐to‐basal ganglia signaling during motor learning. © 2013 Wiley Periodicals, Inc. Develop Neurobiol 73: 754–768, 2013     

Phase Resetting Curves Allow for Simple and Accurate Prediction of Robust N:1 Phase Locking for Strongly Coupled Neural Oscillators

Existence and stability criteria for harmonic locking modes were derived for two reciprocally pulse coupled oscillators based on their first and second order phase resetting curves. Our theoretical methods are general in the sense that no assumptions about the strength of coupling, type of synaptic coupling, and model are made. These methods were then tested using two reciprocally inhibitory Wang and Buzsáki model neurons. The existence of bands of 2:1, 3:1, 4:1, and 5:1 phase locking in the relative frequency parameter space was predicted correctly, as was the phase of the slow neuron's spike within the cycle of the fast neuron in which it occurred. For weak coupling the bands are very narrow, but strong coupling broadens the bands. The predictions of the pulse coupled method agreed with weak coupling methods in the weak coupling regime, but extended predictability into the strong coupling regime. We show that our prediction method generalizes to pairs of neural oscillators coupled through excitatory synapses, and to networks of multiple oscillatory neurons. The main limitation of the method is the central assumption that the effect of each input dies out before the next input is received.     

Diaphragmatic defects in children of consanguineous parents

Summary It is known from the literature that total loss of the short arm causes complete Turner's signs (Hoo, 1975; Therman and Patau, 1974). Partial deletions of the short arm of the X chromosome are in some cases compatible with fertility (Fraccaro et al., 1977; Hoo, 1979), but in other cases they cause a significant ovarial insufficiency with Turner's signs (Giraud et al., 1974) or gonadal dysgenesis (Petrinelli et al., 1978). A common sign for all the patients having the Xp-wwith the break point in the dark band (p113-p21) seems to be a short stature. The presence of other clinical signs is rather irregular. In this work, a 25-year-old female patient having a Xp deficiency in region p21 (46,X,del(X) (qterp21:)) with short stature, primary amenorrhea, sterility, and clear Turner's is described.     

Phase locking of biological clocks

Radial isochron clocks (RICs) and their response to external signals and coupling with other RICs are studied. RICs are derived as phase approximations to self-sustained oscillators. Their response to single impulses (phase resetting) and to repetitive impulses is determined. This response may be harmonic or chaotic. Finally, the effect of coupling between clocks is studied. Simple coupling is shown to exhibit rhythm splitting like that observed in fish and small mammals. New phase locking results for general weakly coupled RIC systems are also derived.Supported in part by the National Science Foundation under grants MCS-80-15359 (FCH) and MCS-79-02505 (JPK)     

Information transmission in non-visual fingertip matching along a horizontal track in the median plane

Non-visually triggered arm movements over a horizontal table at shoulder height were analysed by an Information Theory approach according to a method suggested by Sakitt et al. (1983) and Sakitt (1980). The movement track was along the subject's median line and was indicated by a vertical metal ridge fixed to the table. The observer passively moved the subject's left index finger along the left side of the ridge to the target position. The blindfolded subject then had to move his right index finger along the right side of the ridge to match the left finger position. Direct contact between the two fingers was prevented by the ridge. We compared our results, which involve the transmission of information through the arm and shoulder joints of both arms, whith those of Sakitt et al. which involved just one elbow joint. We supplemented our experimental results with simulations and show that the value for the transmitted information, obtained using the method of analysis suggested by Sakitt et al., is very dependent upon the number of trials, and number and spacing of the targets. Sakitt et al. suggest that the Information Theory approach permits easy comparison between different tasks and different observers. Our results suggest that comparisons should be made with caution.     

Potassium stimulated calcium dependent release of immunoreactive somatostatin from incubated rat hypothalamus

S omatostatin (somatotropin release inhibiting factor, SRIF) is present in the median eminence of the hypothalamus in high concentration (K ronheim et al., 1976), is visualized in nerve endings (H ökfelt et al., 1974) and has been found to be concentrated in the synaptosome fraction of hypothalamic homogenates (E pelbaum et al., 1977; B erelowitz et al., 1978), suggesting a true neurosecretory role. To further explore this possibility we have studied the release of immunoreactive SRIF from the incubated rat hypothalamus (B radbury et al., 1974: R otsztein et al., 1977), basally and in response to depolarising concentrations of potassium, and have assessed the calcium dependence of this release.     

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

 We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment. Received: 30 December 1994/Accepted in revised form: 27 June 1995     

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.     

Hierarchically coupled ultradian oscillators generating robust circadian rhythms

Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many coupled oscillators predict that the output period should vary as the square root of the number of participating units, thus being inconsistent with the well-established experimental result that ablation of substantial parts of the suprachiasmatic nuclei (SCN), the main circadian pacemaker in mammals, does not eliminate the overt circadian functions, which show no changes in the phases or periods of the rhythms. From these observations, we have developed a theoretical model that exhibits the robustness of the circadian clock to changes in the number of cells in the SCN, and that is readily adaptable to include the successful features of other known models of circadian regulation, such as the phase response curves and light resetting of the phase.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Slow Noise in the Period of a Biological Oscillator Underlies Gradual Trends and Abrupt Transitions in Phasic Relationships in Hybrid Neural Networks

In order to study the ability of coupled neural oscillators to synchronize in the presence of intrinsic as opposed to synaptic noise, we constructed hybrid circuits consisting of one biological and one computational model neuron with reciprocal synaptic inhibition using the dynamic clamp. Uncoupled, both neurons fired periodic trains of action potentials. Most coupled circuits exhibited qualitative changes between one-to-one phase-locking with fairly constant phasic relationships and phase slipping with a constant progression in the phasic relationships across cycles. The phase resetting curve (PRC) and intrinsic periods were measured for both neurons, and used to construct a map of the firing intervals for both the coupled and externally forced (PRC measurement) conditions. For the coupled network, a stable fixed point of the map predicted phase locking, and its absence produced phase slipping. Repetitive application of the map was used to calibrate different noise models to simultaneously fit the noise level in the measurement of the PRC and the dynamics of the hybrid circuit experiments. Only a noise model that added history-dependent variability to the intrinsic period could fit both data sets with the same parameter values, as well as capture bifurcations in the fixed points of the map that cause switching between slipping and locking. We conclude that the biological neurons in our study have slowly-fluctuating stochastic dynamics that confer history dependence on the period. Theoretical results to date on the behavior of ensembles of noisy biological oscillators may require re-evaluation to account for transitions induced by slow noise dynamics.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Production of presumptive humoral haematopoietic regulators in canine cyclic haematopoiesis

Abstract. Conditioned media (CM) were prepared according to previously published techniques from the bone marrow of dogs with cyclic haematopoiesis (CH). CM prepared from day 9 marrows inhibited mouse bone marrow CFU-s proliferation rate while CM from day 10 marrows were stimulatory and also contained an erythroid stimulating factor which appeared to be erythropoietin. In addition a highly significant trend from CM containing CFU-s inhibitory materials to media with CFU-s stimulatory activity was observed through cycles day 1 to 8. These studies further support the concept that CH is due to a defect in factors controlling stem cell proliferation and suggest that a major event occurs in CH dog marrow on days 9 and/or 10 of the cycle. Bone marrow transplantation studies (Dale & Graw, 1974; Weiden et al., 1974; Jones et al., 1975b) have indicated that canine cyclic haematopoiesis (CH) is probably due to a disorder in the multipotential stem cells. Morphological evidence (Scott et al., 1973) and the almost synchronous cycling of CFU-e, CFU-c and diffusion chamber progenitor cells (DCPC) (DUM et al., 1977, 1978a, b) lend support to such a theory. However, efforts to identify the mechanisms controlliig multipotential stem cell proliferation in dogs have been handicapped by the lack of suitable techniques to study these cells in the canine. Recently, Wright and co-workers (Wright & Lord, 1978, 1979; Wright et al., 1979; Lord et al., 1979), on the basis of previous observations (Frindel et al., 1976; Frindel & Guigon, 1977), described the preparation of species non-specific, bone marrow conditioned media (CM) which are capable of influencing the proliferation rate of murine colony forming units-spleen (CFU-s). The studies now reported were designed to determine if CM prepared from canine CH marrow would influence the proliferation rate of murine bone marrow CFU-s. The results indicate that a major event, possibly related to the in vivo control of stem cell proliferation in dogs with CH, occurs on days 9–10 of the cycle; day 1 being the first day when the peripheral blood neutrophil count falls below-1600 mm³.