1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >

Linear and quadratic time-frequency signal representations

In this paper, the use of the reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution. This method creates a modified version of a representation by moving its values away from where they are computed, so as to produce a better localization of the signal components. We first propose a new formulation of this method, followed by a thorough theoretical study of its characteristics. Its practical use for a large variety of known time-frequency and time-scale distributions is then addressed. Finally, some experimental results are reported to demonstrate the performance of this method. >

/pdf/improving-the-readability-of-time-frequency-and-time-scale-nogp1msss6.pdf

Improving the readability of time-frequency and time-scale representations by the reassignment method

This summary is a proposed synthesis of available information for the non-specialist. It does not incorporate all the published data, is inconsistent with some, and reflects the biases of the author. Connexin proteins have a common transmembrane topology, with four alpha-helical transmembrane domains, two extracellular loops, a cytoplasmic loop, and cytoplasmic N- and C-terminal domains. The sequences are most conserved in the transmembrane and extracellular domains, yet many of the key functional differences between connexins are determined by amino-acid differences in these largely conserved domains. Each extracellular loop contains three cysteines with invariant spacing (save one isoform) that are required for channel function. The junctional channel is composed of two end-to-end hemichannels, each of which is a hexamer of connexin subunits. Hemichannels formed by some connexin isoforms can function as well-behaved, single-membrane-spanning channels in plasma membrane. In junctional channels, the cysteines in the extracellular loops form intra-monomer disulfide bonds between the two loops, not intermonomer or inter-hemichannel bonds. The end-to-end homophilic binding between hemichannels is via non-covalent interactions. Mutagenesis studies suggest that the docking region contains beta structures, and may resemble to some degree the beta-barrel structure of porin channels. The two hemichannels that compose a junctional channel are rotationally staggered by approximately 30 degrees relative to each other so that the alpha-helices of each connexin monomer are axially aligned with the alpha-helices of two adjacent monomers in the apposed hemichannel. At present there is a published 3D map with 7.5 A resolution in the plane of the membrane, based on electron cryomicroscopy of 2D crystals of junctional channels formed by C-terminal truncated Cx43. The correspondence between the imaged transmembrane alpha-helices and the known transmembrane amino-acid sequences is a matter of debate. Each of the approximately 20 connexin isoforms produces channels with distinct unitary conductances, molecular permeabilities, and electrical and chemical gating sensitivities. The channels can be heteromeric, and subfamilies among connexins largely determine heteromeric specificity, similar to the specificities within the voltage-dependent potassium channel superfamily. The second extracellular loop contains the primary determinants of the specificity of hemichannel-hemichannel docking (analogous to the tetramerization domain of potassium channels). The 7.5 A map shows that each monomer exposes only two transmembrane alpha-helices to the pore lumen. However the conductance state of the imaged structure and the effects of the C-terminal truncation are unknown, so it is possible that other transmembrane domains contribute to the lumen in other functional states of the channel. In the transmembrane region, SCAM and mutagenesis data suggest that parts of the first three transmembrane alpha-helices are exposed to the lumen. Some of these data are contradictory, but may reflect conformational or isoform differences. There is reason to think that the first part of the N-terminal cytoplasmic domain can line the pore in some conformations. In the extracellular part of junctional channels, the N-terminal portion of the first extracellular loop is exposed to the lumen. The unitary conductances through connexin channels vary over an order of magnitude, from 15 pS to over 300 pS. There is a range of charge selectivities among atomic ions, from slightly anion selective to highly cation selective, which does not correlate with unitary conductance. There appear to be substantial ion-ion interactions within the pore, making the GHK model of assessing selectivities of limited value. Pores formed by different connexins have a range of limiting diameters as assessed by uncharged and charged probes, which also does not correlate with unitary conductance (i.e. some have high conductance but have a narrow limiting diameter, and vice versa). Channels formed by different connexins have different permeabilities to various cytoplasmic molecules. Where it has been assessed, the selectivity among cytoplasmic molecules is substantial and does not correlate in an obvious manner with the size selectivity data derived from fluorescent tracer studies, suggesting there are chemical specificities within the pore that enhance or reduce permeability to specific cytoplasmic molecules, functionally analogous to the ability of some porins to facilitate transport of specific substrates. For example, heteromeric channels with different stoichiometries or arrangements of isoforms can distinguish among second messengers. The differences in permeability to cytoplasmic molecules have biological consequences; in most cases one connexin cannot fully substitute for another. Voltage and chemical gating mechanisms largely operate within each hemichannel, though there is evidence for inter-hemichannel allosteric effects as well. There are at least two distinct gating mechanisms. One (Vj-gating) is a voltage-driven mechanism that governs rapid transitions between conducting states. Its voltage sensor involves charges in the first several positions of the cytoplasmic N-terminal domain and possibly in the N-terminal part of the first extracellular loop, which may both be exposed to the lumen of the pore in some states. The polarity of Vj-gating sensitivity is connexin-specific, closing with depolarization for some connexins and with hyperpolarization for others. The polarity can be reversed by point mutations at the second position. The lower conductance states induced by Vj-gating correspond to physical restrictions of the pore, and thus restricted or eliminated molecular permeation. Since the channels are not fully closed by Vj-gating, it can be seen as a way to eliminate molecular signaling while leaving electrical signaling operational. A second, independent gating mechanism mediates slow transitions (approximately 10-30 ms) into and out of non-conducting state(s). These transitions can occur in response to voltage ('loop gating'), chemical factors such as pH and lipophiles ('chemical gating'), and the docking of two hemichannels (sometimes called the 'docking gate'). These slow transitions may reflect a common structural change induced by these several effectors (electrical, chemical and homodimerization). Alternatively, they could reflect distinct gating processes responding to one or more of these effectors, that are indistinguishable at the single-channel level and have yet to be resolved mechanistically. The slow or loop gate closes with hyperpolarization. As a result, where Vj-gating closes with depolarization, individual hemichannels can close in response to both polarities of voltage (but only to a subconductance state for the Vj-gating polarity). Because of this, it is difficult to assign a macroscopic voltage sensitivity, or its modification due to mutagenesis, chemical modification or heteromeric interactions, to one or the other of these very distinct voltage-sensitive processes. This distinction can be made reliably only at the single-channel level. The Vj-gating voltage sensor and the loop-gating voltage sensor appear to be independent structures, since the Vj-gating voltage sensitivity can modified without effect on loop gating. For some connexins, certain modifications of the C-terminal domain seem to interfere with the operation of the Vj-gate while leaving loop gating unaffected. In some connexins, but not all, the chemical sensitivity to pH can involve interactions between regions of the C-terminal domain and cytoplasmic loop. Whether these regions exert their effects directly by physically blocking the pore, or by allosteric mechanisms (which may be more consistent with the relatively long time-course of closure) is not clear. For several connexins, truncation of the C-terminal domain eliminates the pH sensitivity, and co-expressing the domain with the truncated connexin restores the pH sensitivity. This has a functional resemblance to the particle-receptor mechanism for N-type inactivation of Shaker channels. What is being protonated is not clear, and may involve cytoplasmic factors, such as endogenous aminosulfonates. For other connexins, the action of pH does not involve the C-terminal domain and seems due to direct protonation of connexin. PKC phosphorylation of serine(s) in the C-terminal domain can affect the substate occupancy of at least one connexin. Phosphorylation of series in the C-terminal domain by MAP kinase appears to facilitate an interaction between it and an unknown receptor domain to eliminate coupling. This process has yet to be studied at the single-channel level. It also has a functional analogy to the particle-receptor model of channel inactivation. Both MAP kinase phosphorylation-induced and pH-induced inhibition can be mediated in truncated connexins by the corresponding free peptide. However, the relation between these two mechanisms are unexplored, as are specific mechanisms of direct endogenous regulation of connexin channel activity. (ABSTRACT TRUNCATED)

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Emerging issues of connexin channels: biophysics fills the gap.

The Wigner-Ville spectrum has been recently introduced as the unique generalized spectrum for time-varying spectral analysis. Its properties are revised with emphasis on its central role in the analysis of second-order properties of nonstationary random signals. We propose here a general class of spectral estimators of the Wigner-Ville spectrum: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time-frequency representations of deterministic signals with finite energy. Classical estimators like short-time periodograms and the recently introduced pseudo-Wigner estimators are shown to be special cases of the general class. The generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo-Wigner estimators. The effective numerical implementation, by an N-point FFT, of pseudo-Wigner estimators of 2N points is indicated and various examples are given.

/pdf/wigner-ville-spectral-analysis-of-nonstationary-processes-1yhuhybmsn.pdf

Wigner-Ville spectral analysis of nonstationary processes

We have studied the proliferation of rat 208F cells (a derivative of Rat-1 cells) transformed by activated c-Ha- ras , v- fgr , v- raf , v- fms , or v- src oncogenes during cocultivation with an excess of early passage rat embryonic fibroblasts or immortal 208F cells. The total number and size of foci formed by oncogene-transformed 208F cells were strongly reduced by cocultured normal fibroblasts. The extent of growth suppression of transformed foci appears to be dependent on the type of transforming oncogene and on the type of normal fibroblasts rather than on the extent of gap-junctional communication between transformed and normal cells. Total inhibition of fluorescent dye transfer between normal and transformed cells by the 3β- O -hemisuccinate of 18α-glycyrrhetinic acid (18α-carbenoxolone), an inhibitor of gap-junctional communication in human fibroblasts, did not prevent growth inhibition of transformed cells in the cocultivation assay. Since adjacent cells remained electrically coupled in the presence of this inhibitor it is possible that the strongly reduced metabolic cooperation, as indicated by the lack of fluorescent dye transfer, is sufficient for mediating the growth-inhibitory effect of normal fibroblasts. 208F cell-conditioned medium, however, also caused strong growth inhibition of transformed derivatives, suggesting that the effect is in part mediated by release of stable growth inhibitor(s) from 208F cells.

Growth inhibition of oncogene-transformed rat fibroblasts by cocultured normal cells: relevance of metabolic cooperation mediated by gap junctions.

Detection of changes of signal structure by using the Wigner-Ville spectrum

1. The swimming activity of 6 specimens of the Pachon cave form of Astyanax mexicanus was tested with regard to its time control under various light-dark(LD)cycles and constant conditions, and it is compared to that of a river form. 2. In general, activity is entrainable by all applied LDs, but even if the amplitude of a forcing signal increases the signal energies are lower than in the river fish. 3. In case of entrainment the maximum values of surface activity correspond to the dark phases, those of bottom activity to the light phases of a LD. Flexible patterns -as often observed in the river form in the range of resonance about 24 h - are very seldom. Furthermore, disturbances of­ ten occur in the entrainment of one activity form, or one form runs arrhythmic while the other is still entrained. 4. The activity answers to changing environmental conditions are not as uniformly quick as in the river fish. But the system hardly needs a swing-in time to become entrained when a LD starts. 5. After transition from LD to DD (= constant darkness) the entrained rhythms disappear immediately. 6. In no LD with a period length differing from 24 h a circadian rhythm can be observed in addition to the entrained frequency. 7. These results show that the passive system of the river form has developped into an extremely passive one being unable to oscillate and thus has become simplified during regressive evolution. Concerning the circadian oscillator of the epigean ancestor, it was also subjected to regression, but it has not been completely lost. After a LD with a period length about 24 h the circadian oscillator is able to act as a stable system, clearly shown by the freerunning circadian rhythms of surface activity. But out of this range the oscillator is unable to control activity. In DD after all other LDs activity patterns are arrhythmic.

Exogenous and Endogenous Control of Swimming Activity in Astyanax mexicanus (Characidae, Pisces) by Direct Light Response and by a Circadian Oscillator II. Features of Time-Controlled Behaviour of a Cave Population and their Comparison to a Epigean Ancestral Form

The Wigner-Ville spectrum is known to be the unique generalized spectrum for the time-varying spectral analysis of harmonizable processes. This time-frequency representation of a process is based on the covariance function and, for quasi-stationary processes, estimators can be defined by means of local time-averaging. We propose here a general class of such estimators relying on an arbitrary weighting function and discuss their first and second order properties in an unifying way. When specifying the arbitrary function, conventional estimators such as short-time periodograms and pseudo-Wigner estimators are recovered and can be compared. This generalized framework emphasizes the versatility of smoothed pseudo-Wigner estimators, especially for uncoupled time and frequency behaviors : they overcome the uncertainty relations of short-time periodograms which only can improve the performances in one direction of the time-frequency plane at the expense of a loss in the other one.

A general class of estimators for the wigner-ville spectrum of non-stationary processes

Abstract 1. The swimming activity of 6 specimens of an Astyanax mexicanus' river population was tested with regard to its time control under various light-dark(LD)cycles and under constant conditions. 2. Activity is classified into three different forms according to the special experimental arrangement: surface activity, bottom activity and the sum of both (total activity). 3. All applied LD-cycles act as socalled forcing signals (Zeitgeber) and entrain the activity. 4. The maximum values of surface activity correspond to the dark phases of a LD-cycle, those of bottom activity to the light phases. This inversity causes a less strong entrainment of the total activity up to a loss of a significant oscillation in extreme cases. 5. This inverse pattern is kept the more stronger the more the period length of a LD deviates from 24 h. In the range of resonance about 24 h there is a greater flexibility with regard to the phase relation of the maximum values. 6. Activity reacts very sensitive to the differential parameter of the forcing signal. Therefore, no phaseangle difference occurs between forcing and forced signal. Moreover, the system needs no swing-in time to become entrained when starting a LD. 7. After transition from LD to DD (= constant darkness) the forced signal does not die away immediately, but damps out within one or a few cycles with decreasing amplitude and unchanged frequency. 8. In nearly all applied LDs a non-synchronized circadian rhythm can be observed in addition to the entrained frequency, which is dominant. 9. Also, in DD a freerunning circadian rhythm is detectable. 10. We suggest the model that first a passive system with a nearly unlimited range of entrainment controls activity. In contrary to extremely passive systems, it is able to oscillate. Moreover, it acts like a linear system with respect to frequency transfer: In the tested cases, output and input frequency are equal. In addition, activity is under control of an endogenous circadian oscillator. Its effects are overlapped under forcing conditions, but they become obvious under constant conditions. Furthermore, nonstationary processes are features of this circadian rhythm. The proper ties of a passive and a circadian system alone do not explain the flexible patterns in the range of resonance. Therefore, a time-dependent controller is demanded to control the phase relation of the maxima.

Exogenous and Endogenous Control of Swimming Activity in Astyanax mexicanus (Characidae, Pisces) by Direct Light Response and by a Circadian Oscillator I. Analyses of the Time-Control Systems of an Epigean River Population

Wolfgang Martin

Papers

Growth inhibition of oncogene-transformed rat fibroblasts by cocultured normal cells: relevance of metabolic cooperation mediated by gap junctions.

Detection of changes of signal structure by using the Wigner-Ville spectrum

Exogenous and Endogenous Control of Swimming Activity in Astyanax mexicanus (Characidae, Pisces) by Direct Light Response and by a Circadian Oscillator II. Features of Time-Controlled Behaviour of a Cave Population and their Comparison to a Epigean Ancestral Form

A general class of estimators for the wigner-ville spectrum of non-stationary processes

Exogenous and Endogenous Control of Swimming Activity in Astyanax mexicanus (Characidae, Pisces) by Direct Light Response and by a Circadian Oscillator I. Analyses of the Time-Control Systems of an Epigean River Population