Synchronization of period-doubling oscillations in vascular coupled nephrons.

The mechanisms by which the individual functional unit (nephron) of the kidney regulates the incoming blood flow give rise to a number of nonlinear dynamic phenomena, including period-doubling bifurcations and intra-nephron synchronization between two different oscillatory modes. Interaction between the nephrons produces complicated and time-dependent inter-nephron synchronization patterns. In order to understand the processes by which a pair of vascular coupled nephrons synchronize, the paper presents a detailed analysis of the bifurcations that occur at the threshold of synchronization. We show that, besides infinite cascades of saddle-node bifurcations, these transitions involve mutually connected cascades of torus and homoclinic bifurcations. To illustrate the broader range of occurrence of this bifurcation structure for coupled period-doubling systems, we show that a similar structure arises in a system of two coupled, non-identical Rössler oscillators.

Excitation block in a nerve fibre model owing to potassium-dependent changes in myelin resistance.

The myelinated nerve fibre is formed by an axon and Schwann cells or oligodendrocytes that sheath the axon by winding around it in tight myelin layers. Repetitive stimulation of a fibre is known to result in accumulation of extracellular potassium ions, especially between the axon and the myelin. Uptake of potassium leads to Schwann cell swelling and myelin restructuring that impacts the electrical properties of the myelin. In order to further understand the dynamic interaction that takes place between the myelin and the axon, we have modelled submyelin potassium accumulation and related changes in myelin resistance during prolonged high-frequency stimulation. We predict that potassium-mediated decrease in myelin resistance leads to a functional excitation block with various patterns of altered spike trains. The patterns are found to depend on stimulation frequency and amplitude and to range from no block (less than 100 Hz) to a complete block (greater than 500 Hz). The transitional patterns include intermittent periodic block with interleaved spiking and non-spiking intervals of different relative duration as well as an unstable regime with chaotic switching between the spiking and non-spiking states. Intermittent conduction blocks are accompanied by oscillations of extracellular potassium. The mechanism of conductance block based on myelin restructuring complements the already known and modelled block via hyperpolarization mediated by the axonal sodium pump and potassium depolarization.

The effect of L-NAME on intra- and inter-nephron synchronization.

Kidney autoregulation involves complicated intra- and inter-nephron synchronization phenomena among oscillatory modes produced, respectively, by the tubuloglomerular feedback (TGF) mechanism and by the myogenic regulation of the afferent arteriolar blood flow. The present study aims at examining to what extent these phenomena are reflected in the overall blood flow to the kidney and how they are affected by intravenous administration of nitro-l-arginine-methyl-ester (L-NAME), a potent NO synthesis inhibitor. Wavelet analysis is applied to detect rhythmic activity at the level of the renal artery and compare the observed fluctuations with blood flow variations recorded from efferent arterioles of individual nephrons. We show that administration of L-NAME increases the gain in both the TGF and the myogenic oscillations, and that both normotensive and hypertensive rats demonstrate reduced stability of the various rhythms. This implies that L-NAME, besides strengthening the gain in the individual feedback mechanisms, also causes more frequent transitions among the various synchronization states. In a broader perspective the purpose of the study is to demonstrate the significance of complex dynamic phenomena in the normal regulation of physiological systems as well as in their response to drugs.

Characterizing multimode interaction in renal autoregulation.

The purpose of this paper is to demonstrate how modern statistical techniques of non-stationary time-series analysis can be used to characterize the mutual interaction among three coexisting rhythms in nephron pressure and flow regulation. Besides a relatively fast vasomotoric rhythm with a period of 5-8 s and a somewhat slower mode arising from an instability in the tubuloglomerular feedback mechanism, we also observe a very slow mode with a period of 100-200 s. Double-wavelet techniques are used to study how the very slow rhythm influences the two faster modes. In a broader perspective, the paper emphasizes the significance of complex dynamic phenomena in the normal and pathological function of physiological systems and discusses how simulation methods can help to understand the underlying biological mechanisms. At the present there is no causal explanation of the very slow mode. However, vascular oscillations with similar frequencies have been observed in other tissues.

Non-invasive study of nerve fibres using laser interference microscopy.

This paper presents the results of a laser interference microscopy study of the morphology and dynamical properties of myelinated nerve fibres. We describe the principles of operation of the phase-modulated laser interference microscope and show how this novel technique allows us to obtain information non-invasively about the internal structure of different regions of a nerve fibre. We also analyse the temporal variations in the internal optical properties in order to detect the rhythmic activity in the nerve fibre at different time scales and to shed light on the underlying biological processes. We observe pronounced frequencies in the dynamics of the optical properties and suggest that the oscillatory modes have similar origin in different regions, but different strengths and mutual modulation properties.

Multimode dynamics in a network with resource mediated coupling.

The purpose of this paper is to study the special forms of multimode dynamics that one can observe in systems with resource-mediated coupling, i.e., systems of self-sustained oscillators in which the coupling takes place via the distribution of primary resources that controls the oscillatory state of the individual unit. With this coupling, a spatially inhomogenous state with mixed high and low-amplitude oscillations in the individual units can arise. To examine generic phenomena associated with this type of interaction we consider a chain of resistively coupled electronic oscillators connected to a common power supply. The two-oscillator system displays antiphase synchronization, and it is interesting to note that two-mode oscillations continue to exist outside of the parameter range in which oscillations occur for the individual unit. At low coupling strengths, the multi-oscillator system shows high dimensional quasiperiodicity with little tendency for synchronization. At higher coupling strengths, one typically observes spatial clustering involving a few oscillating units. We describe three different scenarios according to which the cluster can slide along the chain as the bias voltage changes.

Giant glial cell: new insight through mechanism-based modeling.

The paper describes a detailed mechanism-based model of a tripartite synapse consisting of P- and R-neurons together with a giant glial cell in the ganglia of the medical leech (Hirudo medicinalis), which is a useful object for experimental studies in situ. We describe the two main pathways of the glial cell activation: (1) via IP(3) production and Ca(2 +) release from the endoplasmic reticulum and (2) via increase of the extracellular potassium concentration, glia depolarization, and opening of voltage-dependent Ca(2 +) channels. We suggest that the second pathway is the more significant for establishing the positive feedback in glutamate release that is critical for the self-sustained activity of the postsynaptic neuron. This mechanism differs from the mechanisms of the astrocyte-neuron signaling previously reported.

New insights offered by a computational model of deep brain stimulation.

Deep brain stimulation (DBS) is a standard neurosurgical procedure used to treat motor symptoms in about 5% of patients with Parkinson's disease (PD). Despite the indisputable success of this procedure, the biological mechanisms underlying the clinical benefits of DBS have not yet been fully elucidated. The paper starts with a brief review on the use of DBS to treat PD symptoms. The second section introduces a computational model based on the population density approach and the Izhikevich neuron model. We explain why this model is appropriate for investigating macroscopic network effects and exploring the physiological mechanisms which respond to this treatment strategy (i.e., DBS). Finally, we present new insights into the ways this computational model may help to elucidate the dynamic network effects produced in a cerebral structure when DBS is applied.

Using wavelet analysis to detect the influence of low frequency magnetic fields on human physiological tremor.

The influence of extremely low frequency magnetic fields (ELF-MFs) on human physiological processes and, in particular, on motor activity is still not established with certainty. Using the wavelet-transform approach, changes in the characteristics of human finger micromovement are studied in the presence of a low intensity MF centred at the level of the head. Different approaches to nonstationary signal analysis involving real as well as complex wavelet functions are considered. We find evidence that ELF-MFs lead to more regular postural tremor and more homogeneous energy distribution.

Unraveling cell processes: interference imaging interwoven with data analysis.

The paper presents results on the application of interference microscopy and wavelet-analysis for cell visualization and studies of cell dynamics. We demonstrate that interference imaging of erythrocytes can reveal reorganization of the cytoskeleton and inhomogenity in the distribution of hemoglobin, and that interference imaging of neurons can show intracellular compartmentalization and submembrane structures. We investigate temporal and spatial variations of the refractive index for different cell types: isolated neurons, mast cells and erythrocytes. We show that the refractive dynamical properties differ from cell type to cell type and depend on the cellular compartment. Our results suggest that low frequency variations (0.1-0.6 Hz) result from plasma membrane processes and that higher frequency variations (20-26 Hz) are related to the movement of vesicles. Using double-wavelet analysis, we study the modulation of the 1 Hz rhythm in neurons and reveal its changes under depolarization and hyperpolarization of the plasma membrane. We conclude that interference microscopy combined with wavelet analysis is a useful technique for non-invasive cell studies, cell visualization, and investigation of plasma membrane properties.

Two-mode chaos and its synchronization properties.

Using a simple model with bimodal dynamics, we investigate the intra- and inter-system entrainment of the two different time scales involved in the chaotic oscillations. The transition between mode-locked and mode-unlocked chaos is analyzed for a single system. For coupled oscillators, we demonstrate full and partial synchronization patterns depending on the adjustment between the fast and slow time scales and reveal the embedded structure of the corresponding synchronization regions.

Interference microscopy under double-wavelet analysis: a new approach to studying cell dynamics.

This Letter combines a novel experimental approach to the study of intracellular processes with a newly developed technique for multimode time-series analysis. Experiments are performed on isolated pond snail (Lymnaea stagnalis) neurons. Local variations in the cellular refractive index as detected by laser interference microscopy are related to the processes in the cell. A wavelet analysis shows the presence of several identifiable modes in the membrane and intracellular dynamics, and a double-wavelet analysis reveals nonlinear interactions between the regulatory processes in the form of mutual frequency and amplitude modulations.

Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics.

On the basis of double-wavelet analysis, the paper proposes a method to study interactions in the form of frequency and amplitude modulation in nonstationary multimode data series. Special emphasis is given to the problem of quantifying the strength of modulation for a fast signal by a coexisting slower dynamics and to its physiological interpretation. Application of the approach is demonstrated for a number of model systems, including a model that generates chaotic dynamics. The approach is then applied to proximal tubular pressure data from rat nephrons in order to estimate the degree to which the myogenic dynamics of the afferent arteriole is modulated by the slower tubulo-glomerular dynamics. Our analysis reveals a significantly stronger interaction between the two mechanisms in spontaneously hypertensive rats than in normotensive rats.

Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation.

Biological time series often display complex oscillations with several interacting rhythmic components. Renal autoregulation, for instance, involves at least two separate mechanisms both of which can produce oscillatory variations in the pressures and flows of the individual nephrons. Using double-wavelet analysis we propose a method to examine how the instantaneous frequency and amplitude of a fast mode is modulated by the presence of a slower mode. Our method is applied both to experimental data from normotensive and hypertensive rats showing different oscillatory patterns and to simulation results obtained from a physiologically based model of the nephron pressure and flow control. We reveal a nonlinear interaction between the two mechanisms that regulate the renal blood flow in the form of frequency and amplitude modulation of the myogenic oscillations.

Torus breakdown in noninvertible maps.

We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L(0) coincides with the eigendirection corresponding to vanishing eigenvalue for the noninvertible map. Further parameter changes lead typically to the generation of loops (self-intersections of the invariant manifolds) followed by the transformation of the torus into a complex chaotic set.

Complex phase dynamics in coupled bursters.

The phenomenon of phase multistability in the synchronization of two coupled oscillatory systems typically arises when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components. Alternatively, phase multistability can be caused by variations of the phase velocity along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns in the bursting behavior of a model of coupled pancreatic cells. In particular, we show how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes.

Transitions between beta and gamma rhythms in neural systems.

We study the coexistence of different rhythms in a local network of one inhibitory and two excitatory nerve cells for a wide range of the excitatory synapse strength and of the slow K+-channel conductance. The dynamic features of spike trains in the presence of noise are discussed. It is found that noise can both cause switching between different states and induce coherent firing events.

Phase multistability of self-modulated oscillations.

The paper examines the type of multistability that one can observe in the synchronization of two oscillators when the systems individually display self-modulation or other types of multicrest wave forms. The investigation is based on a phase reduction method and on the calculation of phase maps for vanishing and finite coupling strengths, respectively. Various phase-locked patterns are observed. In the presence of a frequency mismatch, the two-parameter bifurcation analysis reveals a set of synchronization regions inserted one into the other. Numerical examples using a generator with inertial nonlinearity and a biologically motivated model of nephron autoregulation are presented.

Quantitative effects of medium hardness and nutrient availability on the swarming motility of Serratia liquefaciens.

We report the first controlled measurements of expansion rates for swarming colonies of Serratia liquefaciens under different growth conditions, combined with qualitative observations of the organization of the colony into regions of differentiated cell types. Significantly, the results reveal that swarming colonies of S. liquefaciens can have an increasing expansion rate with time. We compare and contrast the expansion rate results with predictions from a recent mathematical model which coupled key hydrodynamical and biological mechanisms. Furthermore, we investigate whether the swarming colonies grow according to a power law or exponentially (for large times), as suggested by recent theoretical results.