Change In Phase Relationship Research Articles

Spatiotemporal Patterns of Fractional Suspended Sediment Dynamics in Small Watersheds

AbstractUnderstanding suspended sediment dynamics and their driving factors is essential for effective watershed management. In this study, the spatiotemporal patterns of suspended sediment were identified for 11 sub‐watersheds of the Goodwin Creek, Mississippi, USA, for the period 1982–2002 using wavelet transforms. The continuous wavelet transform (CWT) results of streamflow time series showed that a near‐continuous annual periodicity influenced all stations over the study period, yet an overall decline occurred in wavelet spectral power of sediment load during the 1990s. This decline in sediment load is a result of the indirect effect of decreased cultivation on reducing the rate of peak flow and thus fluvial erosion processes. The CWTs of fine sediment (clays and silts) concentration (FSC) time series showed that factors other than land‐use (e.g., ponds, ephemeral gullies, and bed composition) better explain the variations in FSC. A comparison of CWTs of FSC at two stations with different bed composition in their channels showed that sandy channels are less responsive to erosion control measures compared to gravely channels indicating that they are major sources of sediment. A change in phase relationship between flow and FSC for the gravel‐dominated channel was associated with the transition in upland land‐use indicating a change in sediment supply mechanisms. The CWTs of sand concentrations reflected the spatiotemporal impact of bank materials, the growth cycle of riparian vegetation, and in‐channel sand availability on sand dynamics. While CWT‐based analysis is sensitive to input conditions, the method is able to provide valuable outcomes for distinguishing patterns in complex temporal datasets.

Zooming into the Mediterranean outflow fossil moat during the 1.2–1.8 million years period (Early-Pleistocene) — An approach by radiogenic and stable isotopes

The fossil Alvarez Cabral erosive Moat contains hemipelagite, contourite and turbidite facies where oceanography changes in the Mediterranean outflow are archived over the 1.2–1.8Myr time period. Here we used Pb and Sr radiogenic isotopes to trace water masses and sediment source changes, for the first time in twenty glacial–interglacial (G-I) cycles of the Early-Pleistocene interval, and the last Glacial Maximum through Holocene cycle (including the Younger Dryas and Heinrich Stadial-1). A mixing line of Pb isotopes gives reliable low radiogenic 208Pb/204Pb, 206Pb/204Pb, and 206Pb/207Pb typical of Mediterranean Outflow Water (MOW) in one end-member and the signature of high radiogenic isotopes of Atlantic Waters (AW) towards the second end-member. The 87Sr/86Sr isotopes also display two end-members of the mixing line between eolian transport/dust source (0.71) and fluvial transport/weathering source (0.73) previously proposed in the Gulf of Cadiz. Combination of Pb and Sr radiogenic isotopes with O and C stable isotopes of planktonic and benthic foraminifera, and the response of foraminifera benthos over the Early-Pleistocene interval, reveals a direct link between water masses circulation and shifts in G-I. We found a persistent cyclic pattern of MOW circulation and fluvial deposition during glaciations and AW and aeolian influence during interglaciations. On site U1386B/C, the upper-MOW was less ventilated but productive and with high flux of organic flux matter during glacials, while Atlantic Waters were better ventilated, enriched in O, but less productive during interglacials. We infer that shifts in ocean and atmospheric processes in the Gulf of Cadiz were strongly controlled by Earth's obliquity (41kyr-cycle) and 35°NH insolation during the Early-Pleistocene. We propose a correlation in changes in phase-relationship between precession and obliquity.

Periodic change in phase relationship between target and hand motion during visuo-manual tracking task: Behavioral evidence for intermittent control

When one performs visuo-manual tracking tasks, velocity profile of hand movements shows discontinuous patterns even if the target moves smoothly. A crucial factor of this “intermittency” is considerable delay in the sensorimotor feedback loop, and several researchers have suggested that the cause is intermittent correction of motor commands. However, when and how the brain monitors task performance and updates motor commands in a continuous motor task is uncertain. We examined how tracking error was affected by the timing of target disappearance during a tracking task. Results showed that tracking error, defined as the average phase difference between target and hand, varied periodically in all conditions. Hand preceded target at one specific phase but followed it at another, implying that motor control was not performed in a temporally uniform manner. Tracking stability was evaluated by the variance in phase difference, and changed depending on the timing of target-removal. The variability was larger when target disappeared around turning points than that when it disappeared around the center of motion. This shows that visual information at turning points is more effectively exploited for motor control of sinusoidal target tracking, suggesting that our brain controls hand movements with intermittent reference to visual information.

Influence of photoperiod duration and light–dark transitions on entrainment of Per1 and Per2 gene and protein expression in subdivisions of the mouse suprachiasmatic nucleus

The circadian clock located within the suprachiasmatic nuclei (SCN) of the hypothalamus responds to changes in the duration of day length, i.e. photoperiod. Recently, changes in phase relationships among the SCN cell subpopulations, especially between the rostral and caudal region, were implicated in the SCN photoperiodic modulation. To date, the effect of abrupt, rectangular, light-to-dark transitions have been studied while in nature organisms experience gradual dawn and twilight transitions. The aim of this study was to compare the effect of a long (18 h of light) and a short (6 h of light) photoperiod with twilight relative to that with rectangular light-to-dark transition on the daily profiles of Per1 and Per2 mRNA (in situ hybridization) and PER1 and PER2 protein (immunohistochemistry) levels within the rostral, middle and caudal regions of the mouse SCN. Under the short but not under the long photoperiod, Per1, Per2 and PER1, PER2 profiles were significantly phase-advanced under the twilight relative to rectangular light-to-dark transition in all SCN regions examined. Under the photoperiods with rectangular light-to-dark transition, Per1 and Per2 mRNA profiles in the caudal SCN were phase-advanced as compared with those in the rostral SCN. The phase differences between the SCN regions were reduced under the long, or completely abolished under the short, photoperiods with twilight. The data indicate that the twilight photoperiod provides stronger synchronization among the individual SCN cell subpopulations than the rectangular one, and the effect is more pronounced under the short than under the long photoperiod.

Photoperiod alters phase difference between activity onset in vivo and mPer2::luc peak in vitro

Photoperiod is a significant modulator of behavior and physiology for many organisms. In rodents changes in photoperiod are associated with changes in circadian period and photic resetting of circadian pacemakers. Utilizing rhythms of in vivo behavior and in vitro mPer2::luc expression, we investigated whether different entrainment photoperiods [light:dark (L:D) 16:8 and L:D 8:16] alter the period or phase relationships between these rhythms and the entraining light cycle in Per2::luc C57BL/6J mice. We also tested whether mPer2::luc rhythms differs in anterior and posterior suprachiasmatic nucleus (SCN) slices. Our results demonstrate that photoperiod significantly changes the timing of the mPer2::luc peak relative to the time of light offset and the activity onset in vivo. In both L:D 8:16 and L:D 16:8 the mPer2::luc peak maintained a more stable phase relationship to activity offset, while altering the phase relationship to activity onset. After the initial cycle in culture, the period, phase, and peaks per cycle were not significantly different for anterior vs. posterior SCN slices taken from animals within one photoperiod. After short-photoperiod treatment, anterior SCN slices showed increased-amplitude Per2::luc waveforms and posterior SCN slices showed shorter-duration peak width. Finally, the SCN tissue in vitro did not demonstrate differences in period attributable to photoperiod pretreatment, indicating that period aftereffects observed in behavioral rhythms after long- and short-day photoperiods are not sustained in Per2::luc rhythms in vitro. The change in phase relationship to activity onset suggests that Per2::luc rhythms in the SCN may track activity offset rather than activity onset. The reduced amplitude rhythms following long-photoperiod treatment may represent a loss of coupling of component oscillators.

Point:Counterpoint: Respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism

Blood pressure and heart periods fluctuate at respiratory frequencies in healthy humans. Some researchers ([8][1], [23][2]) explain this as a cause-and-effect relation: blood pressure changes trigger baroreflex-mediated R-R interval changes. Here I make the case that respiratory sinus arrhythmia is

Phase differences between SCN neurons and their role in photoperiodic encoding; a simulation of ensemble patterns using recorded single unit electrical activity patterns

In mammals, a major circadian pacemaker is located in the suprachiasmatic nuclei (SCN), at the base of the anterior hypothalamus. The pacemaker controls daily rhythms in behavioral, physiological and endocrine functions and is synchronized to the external light–dark cycle via the retinohypothalamic tract. The SCN are also involved in photoperiodic processes. Changes in day-length are perceived by the SCN, and result in a compression or decompression of the SCN ensemble pattern, which appears to be effectuated by changes in phase relationship among oscillating neurons. By simulation experiments, we have previously shown that the duration of the single unit activity pattern is of minor importance for the broadness of the population activity peak. Instead, the phase distribution among neurons is leading to substantial differences in the broadness of the population pattern. We now show that the combination of (i) changes in the single unit activity pattern and (ii) changes in the phase distribution among oscillating neurons is also effective to encode photoperiodic information. Moreover, we simulated the ensemble waveform of the SCN with recently recorded single unit electrical activity patterns of mice under long and short photoperiods. We show that these single unit activity patterns cannot account for changes in the population waveform of the SCN unless their phase distribution is changed. A narrow distribution encodes for short photoperiods, while a wider distribution is required to encode long photoperiods. The present studies show that recorded patterns in single unit activity rhythms, measured under long and short day conditions, can be used in simulation experiments and are informative in showing which attributes of the neuronal discharge patterns leads to the capacity of the SCN to encode photoperiod.

A weak pulsed magnetic field affects adenine nucleotide oscillations, and related parameters in aggregating Dictyostelium discoideum amoebae

A model eukaryotic cell system was used to explore the effect of a weak pulsed magnetic field (PMF) on time-varying physiological parameters. Dictyostelium discoideum cells (V12 strain) were exposed to a pulsed magnetic field (PMF) of flux density 0.4 mT, generated via air-cored coils in trains of 2 ms pulses gated at 20 ms. This signal is similar to those used to treat non-uniting fractures. Samples were taken over periods of 20 min from harvested suspensions of amoebae during early aggregation phase, extracted and derivatised for HPLC fluorescent assay of adenine nucleotides. Analysis of variance showed a significant athermal damping effect ( P<0.002, n=22) of the PMF on natural adenine nucleotide oscillations and some consistent changes in phase relationships. The technique of nonlinear dielectric spectroscopy (NLDS) revealed a distinctive effect of PMF, caffeine and EGTA in modulating the cellular harmonic response to an applied weak signal. Light scattering studies also showed altered frequency response of cells to PMF, EGTA and caffeine. PMF caused a significant reduction of caffeine induced cell contraction ( P<0.0006, n=19 by paired t-test) as shown by Malvern particle size analyser, suggesting that intracellular calcium may be involved in mediating the effect of the PMF.

Cardiorespiratory interactions during fixed-pace resistive breathing

We tested the hypothesis that the arterial baroreflex was important in the origin of respiratory sinus arrhythmia (RSA) under conditions of normal and resistive breathing. That is, mechanical effects of breathing [indicated by instantaneous lung volume (ILV)] would directly influence left ventricular stroke volume (LVSV), which in turn would influence systolic arterial blood pressure (SABP), causing variation in R-R interval through the baroreflex. Eight healthy young subjects (four men and four women) were monitored in the supine position while breathing with a fixed frequency (0.2 Hz) and tidal volume for 15 min through each of three resistances (R0, R1, and R2) producing inspiratory (-) and expiratory (+) pressures of +/- 1.6, +/- 5.4, and +/- 16.6 cmH2O, respectively. LVSV was estimated by stroke distance [(SDist); by Doppler ultrasound]. There were no differences across R0, R1, and R2 for the mean values of R-R interval, SDist, or SABP. Cross-spectral analysis showed that, at R0, each value of R-R interval, SDist, and SABP lagged ILV by approximately 80 degrees. At R1 and R2, phase was reduced from ILV to SDist and R-R interval, and the transfer magnitude for SDist (R2 only), SABP, and R-R interval increased. The transfer magnitude from SDist to SABP significantly increased as a function of resistance breathing, whereas that from SABP to R-R interval significantly decreased. There were no changes in phase relationships from SDist to SABP to R-R interval. Thus the magnitude of RSA (ILV to R-R interval) was increased, but the transfer through the arterial baroreflex (SABP to R-R interval) was reduced. Although factors other than the arterial baroreflex are probably involved in the genesis of RSA, the constant phase relationship across the levels of breathing resistance among SDist, SABP, and R-R interval suggests an important functional link caused by mechanical effects of breathing.

Change in phase relationship between SBP and R-R interval during lower body negative pressure

We have investigated the hypothesis that beat-by-beat interaction of systolic blood pressure (SBP) to R-R interval (the spontaneous baroreflex) is dependent on the length of the R-R interval. Data were collected from eight healthy men while heart rate was slow (R-R interval 1,043 +/- 34 ms) and accelerated (R-R interval 804 +/- 18 ms) by application of lower body negative pressure (LBNP greater than or equal to -40 mmHg). Time series data of SBP and R-R interval were searched for spontaneous baroreflex sequences in which R-R interval changed in the same (lag 0), next (lag 1), or next following (lag 2) beat as SBP. This phase relationship was also quantified by cross-spectral analysis. At rest, 85% of all spontaneous baroreflex sequences occurred with no lag (lag 0). With LBNP, there was a significant reduction in the number of lag 0 sequences (26%), whereas lag 1 and lag 2 sequences increased (10-26% and 5-29%, respectively). Cross-spectral phase also changed significantly from -2.3 +/- 6.3 degrees at rest to 70.5 +/- 7.4 degrees during LBNP. These data supported the hypothesis that the lag of a baroreflex event was dependent on the prevailing R-R interval.

The effects of daily injections of l-dihydroxyphenylalanine and 5-hydroxytryptophan in different temporal relationships on thyroid-gonadal interaction in an Indian finch, spotted munia, Lonchura punctulata

Daily injections of l-dihydroxyphenylalanine ( l-DOPA, a dopamine precursor) given 12 hr after 5-hydroxytryptophan (5-HTP, a serotonin precursor) stimulated testicular growth and body weight increase in the spotted munia Lonchura punctulata. Daily injections of the same drugs given 8 hr apart had the opposite effect, inhibiting both testicular growth and body weight gain. These responses were not observed when either of the drugs were given alone, indicating that the effect was due to temporal synergism between serotonergic and dopaminergic functions. The inhibitory effect of daily injections of thyroxine on testicular and body growth were negated by injections of 5-HTP and l-DOPA separated by 12 hr. Conversely, the stimulatory effects of thyroidectomy in maintaining full testicular size and body weight after the breeding seasons were negated by daily injections of 5-HTP and l-DOPA separated by 8 hr. It is concluded that the inverse relationship between seasonal changes in thyroidal and reproductive functions may involve seasonal changes in phase relationships between daily rhythm in serotonergic and dopaminergic activity in the central nervous system.

Spiral waves in excitable media: a model for diverse aspects of organismal development

Conical skeletal elements of various morphologies are a feature common to numerous Lower and Middle Cambrian organisms of problematic affinity, not to mention their occurrence in multiple extant metazoan phyla. In some cases these display helicospiral morphology, sometimes with dextral and sinistral morphs that may have been paired structures in a bilaterally symmetrical body plan. Such paired elements, including spines of coeloscleritophorans, appear to show a spicular substructure with some suggestion of spatial organization comparable to that of phyllotactic systems in vascular plants. These recurring structural themes raise old questions regarding the significance and mode of development of spiral forms and patterns in many organisms, both unicellular and multicellular.Most recent work on phyllotaxis has interpreted patterns of spiral organization as emergent geometrical properties of systems controlled by local reaction-diffusion interactions around the developing plant axis, without recourse to any explicitly spiral process. The term “generative spiral,” for the pattern linking consecutively formed elements, has thus taken on a purely descriptive, rather than mechanistic, meaning. Likewise, helicospiral shells and comparable structures are generally assumed to reflect no truly spiral growth mechanism, but rather, the regular scaling and displacement of a fundamentally concentric, cone-within-cone, accretionary system. Explanations for the common appearance of such forms include the structural strength offered by adherent whorls (though many forms are evolute), and the simplicity of isometric growth (though departures from logarithmic spirals are common).An alternative perspective was suggested initially by discovery of a higher order pattern in the phyllotactic systems of some conifers, wherein the handedness of the generative spiral reverses as each parent axis gives rise to daughters, through the full range of levels in the branching hierarchy. Although this may be explicable in conventional terms, it may also be interpreted as involving a spiral wave of activation passing rhythmically around the plant axis, at or within some critical distance of the apical meristem. Models for such phenomena are provided by several physical systems involving excitable media, the most well known of which is the Belousov-Zhabotinsky reaction, and by some biological systems, such as neural networks or aggregations of slime mold. At nearly the opposite end of the organismic realm, vertebrate teeth, most of which are subtly but fundamentally helicospiral in form, show features that also suggest rotating waves of activity. These include the common presence of an axial canal in the dentin underlying tooth cusps, which could represent the phase singularity of a rotating wave in the layer of odontoblasts responsible for dentin formation, and asymmetries in autoradiographic patterns associated with developing teeth. In such systems it may be generally true that the period of other physiological cycles that modulate secretory activity is not a simple multiple of the period of rotation of the spiral wave. This would result in a regular change in phase relationship, generating helicospiral form. Additional applications of this principle may illumine features as diverse as bovid horns and the handedness of supernumerary appendages in grafting experiments on insects and amphibians. Spiral waves in excitable media also have properties of symmetry and capacity for generating serial structure that make them intriguing candidates for involvement in even earlier stages of metazoan development.

Suppressive control of the crustacean pyloric network by a pair of identified interneurons. I. Modulation of the motor pattern

A pair of identified neuromodulatory neurons, the pyloric suppressor (PS) neurons, can individually and strongly modify the activity of the pyloric network in the stomatogastric nervous system of the lobster Homarus gammarus. The PS neurons are identified by the location of their somata in the inferior ventricular nerve, their axonal projections, and their effects on pyloric network activity in vitro. Discharge of a PS neuron evokes large EPSPs in the pyloric dilator (PD) neurons and a long-lasting cessation of rhythmic activity in the neurons that control movements of the pyloric filter: PD, lateral pyloric (LP), and pyloric (PY). This cessation of rhythmic activity can outlast by several 10s of seconds a brief discharge of PS lasting only a few seconds. The different neurons of the pyloric filter do not exhibit the same sensitivity to the suppressive effects of PS, with the LP neuron being the most sensitive. Tonic discharge in PS induces graded alterations in the pyloric pattern, depending on its firing frequency. At low (less than 5 Hz) discharge frequencies, PS provokes changes in phase relationships and duration of bursting in pyloric neurons. A slight increase in PS frequency suppresses the rhythmic activity of some pyloric neurons, resulting in a switch from a triphasic to a biphasic pattern. At higher (greater than 10 Hz) PS firing frequencies, rhythmic activity in all the pyloric neurons, including the pacemakers (PD, anterior burster), is abolished, except in cells (ventricular dilator, inferior cardiac) controlling the pyloric valve. We conclude that a central pattern generator is not only subject to activating modulatory control, but may also be the target of suppressive inputs that are themselves able to provoke functional reconfigurations of the network.

Effects of light intensity on the circadian temperature and feeding rhythms in the squirrel monkey

The circadian rhythms of body temperature and feeding appear to be timed by separate pacemakers. Tonic administration of light has been used to investigate the response of the pacemaker timing behavioral rhythms; however, the response of the body temperature rhythm has not been similarly examined. This study investigates the circadian timing of the body temperature rhythm under conditions of different light intensity. We simultaneously recorded the patterns of both feeding and body temperature in squirrel monkeys free-running in an environment free of external time cues. In each lighting condition, the periods of the body temperature and feeding rhythms were identical. In constant bright light the rhythm periods were longer than when the animals were exposed to constant dim light. In addition, the variability of the periods was dependent on light intensity. The feeding rhythm period variance of animals in constant bright light was smaller than when in dim light. Conversely, the period of the free-running body temperature rhythm exhibited more variability in bright light than in dim light. Further, in each condition, there were changes in phase angle relationship between feeding and body temperature which were qualitatively similar to those observed in humans, although quantitatively smaller in magnitude. Thus, in the squirrel monkey, tonic light studies reveal that the mean circadian period of the body temperature and feeding rhythms are similar. However, changes in phase relationship, and differential rhythm period stabilities suggest differences in the period of the underlying, tightly coupled pacemakers.

Enzyme patterns in energy metabolism during flower induction in spinach leaves

Abstract. Time series measurements of six enzymes linked to different pathways in energy metabolism [NAD‐ and NADP‐dependent glyceraldchyde‐3‐phosphate dehydrogenase (NAD‐ and NADP‐GPDs), adenylate kinase (AK), malate dehydrogenase (MDH), glucose‐6‐phosphate dehydrogenase (G‐6PDH) and 6‐phosphogluconate dehydrogenase (6‐PGDH)] have been performed in spinach leaves subjected to different photoperiodic treatments, inductive or not of the flowering process. It is shown that the vegetative and the floral states are characterized by specific enzyme patterns, respectively. Among the six enzymes measured, only three of them present a particular behaviour during the early period of flower induction and probably might be specific markers of this physiological change in the leaves. It is concluded that in a C3 plant such as spinach, floral induction in the leaves mostly involves a reorganization of the ‘vegetative’ metabolic network possibly through a change in phase relationships in the different pathways in energy metabolism.

Interlimb coordination during stepping in the cat: In-phase stepping and gait transitions

The coordination of step cycles between all 4 limbs during in-phase stepping and during transitions to and from alternate stepping was studied in 12 adult cats during repeated overground stepping trials. The temporal spacing of step cycles of the different limbs was determined from analysis of electromyographic (EMG) activity in a single extensor muscle of each limb. Patterns of coordination of the different limbs were established on the basis of the frequency with which phase values separating step cycles were encountered. Steps in which the phasing of step cycles of the two hindlimbs were closer to true in-phase coordination than true alternation (phase between 270° and 90°) and where similar coupling was found in both the preceding and following steps were defined as steady state conditions. Distinct patterns of coordination of forelimb-forelimb and forelimb-hindlimb step cycles were noted under steady state conditions. During stepping sequences which include transitions either to or from alternate stepping, both gradual and abrupt phase changes were found. The changes in both forelimb-forelimb and forelimb-hindlimb phase relationships were more often gradual than abrupt. Where abrupt changes were encountered in the change in phase relationships between one such limb pair the phase change in the other pair was gradual. Changes in hindlimb-hindlimb phase relationships during transitions were nearly always abrupt. It is concluded that the 4 limbs are coordinated during in-phase stepping according to a few patterns, but that the variability about these patterns makes their association with simple neural circuitry rather speculative. The finding that transitions were most often gradual is interpreted in terms of a state-dependent model of interlimb control, in which the type of transition utilized depends on the strength of neural coupling of step cycles of all 4 limbs at the time that the transition is initiated.

The motor output during turning flight in a hawkmoth, Manduca sexta

Electrical activity was recorded extracellularly from mesothoracic flight muscles and the position of the wings was observed during attempted turning by Manduca sexta in fixed flight. The results show that changes in the phase relationships among the motor neurons to the flight muscles are an important part of the neural code by which this hawkmoth controls its flight direction. The third acillary muscle, previously presumed to function in folding the wing at the end of flight, was phasically active during flight. During turns toward the side from which the recordings were made, the wing was remoted, and the third axillary muscle was excited by one to several impulses just before the main depressor muscle (dorsal longitudinal, DLm). During a turn in the opposite direction, the third axillary muscle fired shortly before or with the elevator muscles. The subalar muscle was excited shortly before the DLm during remotion; during promotion it was excited in phase with the DLm or with both the DLm and the elevator muscles. Large changes in phase relationships also occurred in the basalar muscle. In the third axillary and basalar muscles, transition from one phase relationship to another usually involved firing at twice the wingbeat frequency. This observation suggests that the motor neurons to the direct muscles can be loosely coupled to the neurons supplying either the DLm or the elevator muscles. Phase changes during flight also occurred in decapitated animals stimulated with a touch on one side of the abdomen. Therefore alteration of phase relationships and production of motor patterns which result in a turn do not require signals from the brain.

A mechanism for the production of certain types of very-low-frequency emissions

It has been shown that some types of VLF emissions (hooks, risers, and falling tones) may be the result of cyclotron emission by energetic electrons trapped in the earth's magnetic field. Observational evidence suggests that a relatively intense electromagnetic whistler-mode wave may be necessary to trigger each such emission. An interaction mechanism is proposed by which certain electrons may couple with a wave already propagating along the same line of force. A gyroresonance is established which organizes the electrons so that cyclotron radiation can be coherent. A change in phase relationship occurs for those electrons that have a longitudinal velocity component such that the Doppler-shifted frequency of the whistler wave seen by the electron is equal or nearly equal to the electron gyrofrequency. This condition is met by electrons moving in a direction opposite to the whistler wave and is satisfied only over a certain fraction of the line of force. Observations also show instances of a sudden change in slope of the rising tail of a hook or other VLF emission at the crossing of the spectrums of the emission and a whistler. This change is interpreted as the effect of the encounter of a whistler with the electron stream that changes both energy and pitch angle of the emitting electrons.