In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

The influence of immune cross-reaction on phase structure in resonant solutions of a multi-strain seasonal SIR model

Resonance in seasonally forced SIR epidemiological models may lead to stable solutions in which the epidemic period is an integer multiple of the forcing period. We examine the influence of immune cross-protection and cross-enhancement on the epidemic phase relationship of resonance solutions in an annually forced two-strain SIR model. Solutions with epidemics of the two strains in-phase commonly occur for wide ranges of cross-reaction intensity. Solutions with epidemics out-of-phase are less common and limited to narrow ranges of cross-reaction intensity. This is broadly as predicted by the two natural periods of the system. The natural period corresponding to out-of-phase solutions is sensitive to changes in the cross-reaction parameter but the natural period corresponding to in-phase solutions is constant. Bifurcation analysis indicates that the stability of in-phase orbits is controlled by pitchfork and period doubling bifurcations while out-of-phase orbits may also be influenced by Andronov-Hopf bifurcations. In order to develop an intuitive understanding of the epidemiological factors governing the occurrence of different solutions we consider how the susceptible, infected and removed components of the system must interact to form a stable solution. This shows that the impact of cross-reaction is moderated by in-phase structures but amplified by out-of-phase structures. Although the average infection rate over long time periods is not affected by phase structure, this analysis indicates that in-phase epidemic patterns are likely to be more consistent and thus allow more effective health care management.     

Neural Synchronization at Tonic-to-Bursting Transitions

We studied the synchronous behavior of two electrically-coupled model neurons as a function of the coupling strength when the individual neurons are tuned to different activity patterns that ranged from tonic firing via chaotic activity to burst discharges. We observe asynchronous and various synchronous states such as out-of-phase, in-phase and almost in-phase chaotic synchronization. The highest variety of synchronous states occurs at the transition from tonic firing to chaos where the highest coupling strength is also needed for in-phase synchronization which is, essentially, facilitated towards the bursting range. This demonstrates that tuning of the neuron’s internal dynamics can have significant impact on the synchronous states especially at the physiologically relevant tonic-to-bursting transitions.     

S3EPY: a Sparky extension for determination of small scalar couplings from spin-state-selective excitation NMR experiments

S3EPY is a Python extension to the program Sparky written to facilitate the assessment of coupling constants from in-phase/antiphase and spin-state-selective excitation (S³E) experiments. It enables the routine use of small scalar couplings by automating the coupling evaluation procedure. S3EPY provides an integrated graphical user interface to programs which outputs graphs and the table of determined couplings.     

Cities and villages: infection hierarchies in a measles metapopulation

An important issue in the dynamics of directly transmitted microparasites is the relationship between infection probability and host density. We use models and extensive spatio-temporal data for the incidence of measles to examine evidence for spatial heterogeneity in transmission probability, in terms of urban–rural hierarchies in infection rate. Pre-vaccination measles data for England and Wales show strong evidence for urban–rural heterogeneities in infection rate – the proportion of urban cases rises significantly before major epidemics. The model shows that this effect is consistent with a higher infection rate in large cities, though small towns have epidemic characteristics intermediate between town and country. Surprisingly, urban and rural areas of the same population size have a similar propensity for local extinction of infection. A spatial map of urban–rural correlations reveals complex regional patterns of synchronization of towns and cities. The hierarchical heterogeneities in infection persist into the vaccine era; their implications for disease persistence and control are discussed.     

Energy analysis reveals the negative effect of delays in passive movement mirror therapy

Wavelet transform energy analyses of the mean and standard error of the electromyogram (EMG) and electroencephalogram (EEG) of eight subjects were investigated in passive movement mirror therapies with no delay (in-phase) and with delay (out-of-phase) situations in two frequency bands of 7.81–15.62 and 15.62–31.25?Hz. It was found that the energy levels of EEG at electrode C4 in the in-phase situation were lower than those in out-of-phase situations, while the energy levels of flexor and extensor forearm muscle groups were larger. With two exceptions, this pattern could be seen in all other subjects. The difference between the in-phase (D0) and out-of-phase situations (D025 and D05) for the frequency range of 15.62–31.25?Hz was found to be significant at a significance level of 0.05 (paired t-test analysis). The respective elevation and decline of EEG and EGM with regard to the increase of the delay may indicate the necessity for synchronization of passive movement and mirror therapy.     

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

Stability of Phase Relationships While Coordinating Arm Reaches with Whole Body Motion

The human movement repertoire is characterized by the smooth coordination of several body parts, including arm movements and whole body motion. The neural control of this coordination is quite complex because the various body parts have their own kinematic and dynamic properties. Behavioral inferences about the neural solution to the coordination problem could be obtained by examining the emerging phase relationship and its stability. Here, we studied the phase relationships that characterize the coordination of arm-reaching movements with passively-induced whole-body motion. Participants were laterally translated using a vestibular chair that oscillated at a fixed frequency of 0.83 Hz. They were instructed to reach between two targets that were aligned either parallel or orthogonal to the whole body motion. During the first cycles of body motion, a metronome entrained either an in-phase or an anti-phase relationship between hand and body motion, which was released at later cycles to test phase stability. Results suggest that inertial forces play an important role when coordinating reaches with cyclic whole-body motion. For parallel reaches, we found a stable in-phase and an unstable anti-phase relationship. When the latter was imposed, it readily transitioned or drifted back toward an in-phase relationship at cycles without metronomic entrainment. For orthogonal reaches, we did not find a clear difference in stability between in-phase and anti-phase relationships. Computer simulations further show that cost models that minimize energy expenditure (i.e. net torques) or endpoint variance of the reach cannot fully explain the observed coordination patterns. We discuss how predictive control and impedance control processes could be considered important mechanisms underlying the rhythmic coordination of arm reaches and body motion.     

Dual-color system for simultaneously monitoring intracellular Ca(2+) and ATP dynamics

Although Ca(2+) regulates energy metabolism through diverse pathways, there have been no methods to monitor both Ca(2+) dynamics and metabolic activity simultaneously. Here we report a novel system for simultaneously monitoring intracellular Ca(2+) and ATP levels using a blue-emitting photoprotein and a red-emitting beetle luciferase. Using this system, we monitored the dynamic changes simultaneously in both intracellular Ca(2+) and ATP levels during chondrogenesis. We have found that both intracellular Ca(2+) and ATP levels oscillated and their oscillations have a nearly antiphase relationship with each other. The dual-color monitoring system is useful for studying the relationship between Ca(2+) dynamics and energy metabolic pathways.     

Activation and inhibition of bimanual movements in school-aged children

The development of motor activation and inhibition was compared in 6-to-12 year-olds. Children had to initiate or stop the externally paced movements of one hand, while maintaining that of the other hand. The time needed to perform the switching task (RT) and the spatio-temporal variables show different agerelated evolutions depending on the coordination pattern (inor anti-phase) and the type of transition (activation, selective inhibition, non selective inhibition) required. In the anti-phase mode, activation perturbs the younger subjects’ responses while temporal and spatial stabilities transiently decrease around 9 years when activating in the in-phase mode. Aged-related changes differed between inhibition and activation in the antiphase mode, suggesting either the involvement of distinct neural networks or the existence of a single network that is reorganized. In contrast, stopping or adding one hand in the in-phase mode shows similar aged-related improvement. We suggest that selectively stopping or activating one arm during symmetrical coordination rely on the two faces of a common processing in which activation could be the release of inhibition.     

Synchronization and signal transmission in protoplasmic strands of Physarum

The importance of endoplasmic streaming in the synchronization of contraction activites in plasmodial strands of Physarum was investigated under experimental conditions allowing simultaneous observation of the endoplasmic flow in the middle part of a strand mounted as a trapeze and the measurement of isometric contraction activities of the arms of the trapeze, as well as of the activities of the strand portion connecting the arms. The correlation of longitudinal and radial contraction activities in different regions of a trapeze was examined. Whereas the arms and the middle part of a trapeze contract synchronously in a longitudinal direction (in-phase behaviour), an antiphase correlation appeared when comparing the longitudinal contraction activity of the arms and the radial activity of the middle part. This result is interpreted to mean that the middle part is able to perform isotonic contractions which induce radial dilatation of the strands. No clear-cut correlation between longitudinal and radial activities could be found when measuring simultaneously both activities in one and the same arm of a trapeze by combining tensiometry and cinematography. Protoplasmic shuttle streaming within a strand mounted as a trapeze is found to run regularly out of one arm through the middle part into the other arm, and vice versa. There is no correlation between the time points of streaming reversal and a certain stage of contraction cycles as presented by the contraction curves of the arms. However, there is a good correlation between the points of streaming reversal and the phase deviations of the longitudinal contraction activities of the arms. The importance of these phase deviations for the control of streaming reversal, i.e., for the generation of hydrostatic pressure differences in a system working with phase synchrony, is discussed. The role of endoplasmic streaming as a pacemaker for synchronization phenomena of contraction activities is stressed. The possibility is discussed that shuttle streaming of endoplasm acts as a mechanical coupling within the regulation phenomena resulting in spatial monorhythmicity.Partly presented at the Cell Motility workshop, 8^th European Muscle Conference, Heidelberg 17.–20. September 1979     

The El Niño southern oscillation and malaria epidemics in South America

A better understanding of the relationship between the El Ni?o Southern Oscillation (ENSO), the climatic anomalies it engenders, and malaria epidemics could help mitigate the world-wide increase in incidence of this mosquito-transmitted disease. The purpose of this paper is to assess the possibility of using ENSO forecasts for improving malaria control. This paper analyses the relationship between ENSO events and malaria epidemics in a number of South American countries (Colombia, Ecuador, French Guiana, Guyana, Peru, Suriname, and Venezuela). A statistically significant relationship was found between El Ni?o and malaria epidemics in Colombia, Guyana, Peru, and Venezuela. We demonstrate that flooding engenders malaria epidemics in the dry coastal region of northern Peru, while droughts favor the development of epidemics in Colombia and Guyana, and epidemics lag a drought by 1 year in Venezuela. In Brazil, French Guiana, and Ecuador, where we did not detect an ENSO/malaria signal, non-climatic factors such as insecticide sprayings, variation in availability of anti-malaria drugs, and population migration are likely to play a stronger role in malaria epidemics than ENSO-generated climatic anomalies. In some South American countries, El Ni?o forecasts show strong potential for informing public health efforts to control malaria.     

Coupled oscillations in food webs: balancing competition and mutualism in simple ecological models

As in other oscillating systems, oscillations of consumer resource pairs in ecological systems may be coupled such that complex behavior results. The form of that coupling may determine the nature and extent of this behavior. Two biologically significant forms of coupling are here investigated: first, where consumers consume each other's resources (CR coupling, representing competition between the two consumers), and second, where the resources are in competition with one another (RR coupling, potentially representing indirect mutualism between the two consumers). Interestingly, CR coupling leads to in-phase synchrony of the oscillations, whereas RR coupling leads to antiphase synchrony. With either form of coupling, if the coupling remains weak, synchronous behavior is generated in the two systems. At strong levels of coupling, when the two forms act simultaneously, a balance between competition and mutualism is generated, which is manifest differently at different levels of resource coupling.     

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.     

Novel strategies for sensitivity enhancement in heteronuclear multi—dimensional NMR experiments employing pulsed field gradients

Summary Novel strategies for sensitivity enhancement in heteronuclear multidimensional spectra are introduced and evaluated theoretically and experimentally. It is shown that in 3D sequences employing several Coherence Order Selective Coherence Transfer (COS-CT) steps, enhancement factors of up to 2 can be achieved. This sensitivity enhancement is compatible with the use of heteronuclear gradient echoes, yielding spectra with excellent water suppression. HNCO and HCCH-TOCSY pulse sequences are proposed and experimentally tested. These experiments employ recently developed coherence order selective pulse sequence elements, e.g., COS-INEPT and planar TOCSY for antiphase to in-phase transfers 2F^-S₂S^- or in-phaseaCOS-CT for in-phase transfer F^-S^-, and the well-known isotropic TOCSY mixing sequences for homo- and heteronuclear in-phase transfer.This work has been presented in part at the 35th ENC, April 10–15, 1994, Asilomar, CA, U.S.A.     

Multiplet component separation for measurement of methyl 13C-1H dipolar couplings in weakly aligned proteins

A simple spectral editing procedure is described that generates separate subspectra for the methyl ¹³C-¹H₃ multiplet components of ¹H-¹³C HSQC spectra. The editing procedure relies on co-addition of in-phase and antiphase spectra and yields ¹H-coupled constant-time HSQC subspectra for the methyl region that have the simplicity of the regular decoupled CT-HSQC spectrum. Resulting spectra permit rapid and reliable measurement of ¹H-¹³C J and dipolar couplings. The editing procedure is illustrated for a Ca²⁺-calmodulin sample in isotropic and liquid crystalline phases.     

An accurate mathematical model predicting number of dengue cases in tropics

Dengue fever is a systemic viral infection of epidemic proportions in tropical countries. The incidence of dengue fever is ever increasing and has doubled over the last few decades. Estimated 50million new cases are detected each year and close to 10000 deaths occur each year. Epidemics are unpredictable and unprecedented. When epidemics occur, health services are over whelmed leading to overcrowding of hospitals. At present there is no evidence that dengue epidemics can be predicted. Since the breeding of the dengue mosquito is directly influenced by environmental factors, it is plausible that epidemics could be predicted using weather data. We hypothesized that there is a mathematical relationship between incidence of dengue fever and environmental factors and if such relationship exists, new cases of dengue fever in the succeeding months can be predicted using weather data of the current month. We developed a mathematical model using machine learning technique. We used Island wide dengue epidemiology data, weather data and population density in developing the model. We used incidence of dengue fever, average rain fall, humidity, wind speed, temperature and population density of each district in the model. We found that the model is able to predict the incidence of dengue fever of a given month in a given district with precision (RMSE between 18- 35.3). Further, using weather data of a given month, the number of cases of dengue in succeeding months too can be predicted with precision (RMSE 10.4—30). Health authorities can use existing weather data in predicting epidemics in the immediate future and therefore measures to prevent new cases can be taken and more importantly the authorities can prepare local authorities for outbreaks.     

Self-organization of the heartbeat as coordination among ventricular myocardial cells through mechano-electrical feedback

To elucidate the mechanism of the self-organizing control of heartbeats, models that include the electrical and mechanical processes of heartbeat are proposed. As the mutual interaction between the two processes, mechano-electrical feedback (MEF), mediated by stretch-activated ionic channels, is considered. Analyses of the models show that coordination of beats among myocardial cells is established by MEF even in the absence of electrical coupling. The coordination of heartbeats is found to show in-phase synchronization under normal conditions, while it is out of phase or irregular under mechanically abnormal conditions. It is concluded that coupling by MEF is important for the self-organization of heartbeats. Received: 4 December 1997 / Accepted in revised form: 29 July 1998     

Synchronization in ecological systems by weak dispersal coupling with time delay

One of the most salient spatiotemporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial scales in relation to the rate of dispersal among discrete populations. However, the dependence of synchrony on patterns of among-patch movement across heterogeneous landscapes has been largely ignored. Here, we consider the duration of movement between two predator–prey communities connected by weak dispersal and its effect on population synchrony. More specifically, we introduce time-delayed dispersal to incorporate the finite transmission time between discrete populations across a continuous landscape. Reducing the system to a phase model using weakly connected network theory, it is found that the time delay is an important factor determining the nature and stability of phase-locked states. Our analysis predicts enhanced convergence to stable synchronous fluctuations in general and a decreased ability of systems to produce in-phase synchronization dynamics in the presence of delayed dispersal. These results introduce delayed dispersal as a tool for understanding the importance of dispersal time across a landscape matrix in affecting metacommunity dynamics. They further highlight the importance of landscape and dispersal patterns for predicting the onset of synchrony between weakly coupled populations.