Changes in the phase response curve of the circadian clock to a phase-shifting stimulus.

Experiments were conducted in hamsters to determine whether the phase response curve (PRC) to injections of the short-acting benzodiazepine triazolam is a fixed or a labile property of the circadian clock. The results indicated that (1) both the shape and the amplitude of the PRC to triazolam generated on the first day of transfer from a light-dark cycle (LD 14:10) to constant darkness (DD) (i.e., PRCLD) were different from those of the PRC generated after many days in DD (PRCDD); and (2) the phase-shifting effects of triazolam on the activity rhythms of hamsters transferred from LD 14:10 or 12:12 to DD changed dramatically within the first 8-9 days spent in DD. In an attempt to accelerate the resynchronization of the circadian clock of hamsters subjected to an 8-hr advance in the LD cycle, triazolam was given to the animals at a time selected on the basis of the characteristics of PRCLD. The activity rhythms of five of eight triazolam-treated animals were resynchronized to the new LD cycle within 2-4 days after the shift, whereas those of most of the control animals were resynchronized 21-29 days after the shift. These findings suggest that attempts to use pharmacological or nonpharmacological tools to phase-shift circadian clocks under entrained conditions should take into account information derived from PRCs generated at the time of transition from entrained to free-running conditions.     

A pacemaker cell pair model based on the phase response curve

A pacemaker cell pair model and the dynamic interaction between the two pacemaker cells is described in this paper. It is an extension of our single pacemaker cell model, in which we studied its response to repetitive external depolarization stimulations. This model is a simple model based on the two most important functional properties of the cardiac pacemaker cells: its intrinsic pacemaker cycle length, which is an `internal' parameter of the cell, and the phase response curve (PRC), which is an `overall collective' function. The PRC contains all the `information' about the possible interactions of the pacemaker cell with the outside world (interaction with surrounding cells, external stimulus, etc.). First, we examined the properties and solutions of 1:1 synchronization between two pacemaker cells. We found that in order to achieve synchronization between two pacemaker cells, there should be limitations on the PRC parameters, which depend on the cells intrinsic cycle lengths. Next, we investigated the 2:1 entrainment state between two interacting pacemaker cells. We found that there is not necessarily a unique solution for this state as there was for the 1:1 state. Finally, we ran our computer model to investigate the properties of more complex patterns of entrainment between two pacemaker cells. As a result of our analytical study, we unveil two new important parameters, which are fully defined as a function of the PRC parameters: (1) the `accelerator factor' which describes the tendency of a pair of interacting pacemaker cells to synchronize at a common cycle length, which is closer to the faster cycle of the pair; (2) the `degree of coupling', which describes the range of the 1:1 synchronization and the `strength' of the interaction between a pair of interacting pacemaker cells. Those two interaction parameters arise as helpful `tools' for the understanding of synchronization and mutual entrainment mechanisms between pacemaker cells. Therefore, this study establishes the PRC as an important determinant and a useful approach for the understanding of the dynamic interaction of pacemaker cells among themselves and with the outside world. Received: 12 May 1997 / Accepted in revised form: 22 April 1998     

Synchronization of two coupled pacemaker cells based on the phase response curve

In this paper, the synchronization of a pair of pacemaker cells as Sino-Atrial (SA) and Atrio-Ventricullar (AV) nodes have been studied and a new approach for synchronization, based on the concept of Phase Response Curve (PRC), has been proposed. The paper starts with presenting the necessary and sufficient conditions for synchronization in terms of the PRC parameters. Such conditions are time dependent and thus, the paper proceeds with deriving some sufficient conditions, which are not time dependent. The time-delay between the firing time of SA node and when it reaches the AV node is also considered. When the conditions for spontaneous synchronization are not valid, the synchronization is achieved by applying pulses to the AV or the SA nodes or to both of the nodes, depending on the accessibility. The subject has been investigated and sufficient conditions were achieved for all three cases. In each case, the dynamical equations of coupled pacemakers have been determined and the stability analyses of delay dynamical equations between discharges of two pacemakers were performed. The number of excitation pulses and the time intervals for applying them to accessible pacemaker(s) were obtained and eventually some numerical examples were simulated to approve the accuracy of the theoretical results and conditions.     

A honey bee (Apis mellifera) light phase response curve

The authors report a phase response curve (PRC) for individual honey bees (Apis mellifera) to single 1-h light pulses (1000 lux) using an Aschoff Type 1 protocol (n = 134). The bee PRC is a weak (Type 1) PRC with a maximum advance of 1.5 h between circadian time (CT) 18 and 3 and a maximum delay of 1.5 h between CT 12 and 18. This is the first published honey bee light PRC and provides an important resource for chronobiologists and honey bee researchers. It may also have practical applications for what is an economically important species frequently transported across different time zones.     

Modulation of Hydra attenuata rhythmic activity: phase response curve.

We investigated the effect of photic stimulation on the frequency of Hydra attenuata column contractions. We used positive or negative abrupt light transitions, single or repetitive light or darkness pulses, and alternation of light and darkness periods. The main results are: (a) The frequency of the contraction pulse trains (CPTs) varies transiently in response to an abrupt variation of the light intensity. (b) CPTs in progress can be inhibited by different types of photic stimuli. (c) The response time to a single photic stimulus varies during the inter-CPT interval and depends also on the polarity of the stimulus. (d) The CPTs are entrainable with repetitive light stimulation of various frequencies. (e) Long-lasting variations of the frequency of CPTs occur after the end of a repetitive light stimulation. We suggest that the mechanism responsible for the rhythym of column contractions is quite similar to that on which other biological rhythmic phenomena are based.     

Model of bidirectional interaction between myocardial pacemakers based on the phase response curve

As a basis for the study of sinus rhythm determination, a model is proposed of bidirectionally-coupled oscillators as a system of difference equations based on the phase response curve of sinoatrial pacemaker cells. Solutions corresponding to the one-to-one synchronization of the two pacemakers are obtained, and the relation among those solutions is examined: It is revealed that two different solutions with different cycle length coexist, and the synchronized frequency can be higher or lower than the original intrinsic frequencies of the two pacemaker cells. The experimental results of the cultured cells of cardiac pacemakers are interpreted by the analytical result of the model.     

Melatonin rhythm observed throughout a three-cycle bright-light stimulus designed to reset the human circadian pacemaker.

Exposure to light and darkness can rapidly induce phase shifts of the human circadian pacemaker. A type 0 phase response curve (PRC) to light that has been reported for humans was based on circadian phase data collected from constant routines performed before and after a three-cycle light stimulus, but resetting data observed throughout the entire resetting protocol have not been previously reported. Pineal melatonin secretion is governed by the hypothalamic circadian pacemaker via a well-defined neural pathway and is reportedly less subject to the masking effects of sleep and activity than body temperature. The authors reasoned that observation of the melatonin rhythm throughout the three-cycle light resetting trials could provide daily phase-resetting information, allowing a dynamic view of the resetting response of the circadian pacemaker to light. Subjects (n = 12) living in otherwise dim light (approximately 10-15 lux) were exposed to a noncritical stimulus of three cycles of bright light (approximately 9500 lux for 5 h per day) timed to phase advance or phase delay the human circadian pacemaker; control subjects (n = 11) were scheduled to the same protocols but exposed to three 5-h darkness cycles instead of light. Subjects underwent initial and final constant routine phase assessments; hourly melatonin samples and body temperature data were collected throughout the protocol. Average daily phase shifts of 1 to 3 h were observed in 11 of 12 subjects receiving the bright light, supporting predictions obtained using Kronauer's phase-amplitude model of the resetting response of the human circadian pacemaker. The melatonin rhythm in the 12th subject progressively attenuated in amplitude throughout the resetting trial, becoming undetectable for >32 hours preceding an abrupt reappearance of the rhythm at a shifted phase with a recovered amplitude. The data from control subjects who remained in dim lighting and darkness delayed on average -0.2 h per day, consistent with the daily delay expected due to the longer than 24-h intrinsic period of the human circadian pacemaker. Both temperature and melatonin rhythms shifted by equivalent amounts in both bright light-treated and control subjects (R = 0.968; p<0.0001; n = 23). Observation of the melatonin rhythm throughout a three-cycle resetting trial has provided a dynamic view of the daily phase-resetting response of the human circadian pacemaker. Taken together with the observation of strong type 0 resetting in humans in response to the same three-cycle stimulus applied at a critical phase, these data confirm the importance of considering both phase and amplitude when describing the resetting of the human circadian pacemaker by light.     

Effects of dim or bright-light exposure during the daytime on human gastrointestinal activity

On the basis of our previous findings that bright-light exposure during the daytime has profound influence on physiological parameters such as melatonin secretion and tympanic temperature in humans, we proposed the hypothesis that bright vs. dim light-exposure during the daytime has a different influence on the activity of the digestive system via the endocrine and/or autonomic nervous system. To examine this hypothesis, we conducted a series of counterbalanced experiments in which subjects stayed the daytime (7:00 to 15:00h) under either a dim (80 lux) or bright (5,000 lux) light condition. We measured gastrointestinal activity using a breath hydrogen (indicative of carbohydrate malabsorption) and an electrogastrography (EGG, indicative of gastric myoelectric activity) test. The results showed the postprandial breath hydrogen excretion during the following nighttime period after daytime exposure to the dim-light condition was significantly higher than under the bright-light condition (p < 0.05). In addition, the spectrum total power of the EGG recorded after taking the evening meal was significantly lower for the dim than bright-light condition (p < 0.05). These results support our hypothesis and indicate that dim-light exposure during the daytime suppresses the digestion of the evening meal, resulting in malabsorption of dietary carbohydrates in it.     

Photic phase response curve in Octodon degus: assessment as a function of activity phase preference

Light exposure during the early and late subjective night generally phase delays and advances circadian rhythms, respectively. However, this generality was recently questioned in a photic entrainment study in Octodon degus. Because degus can invert their activity phase preference from diurnal to nocturnal as a function of activity level, assessment of phase preference is critical for computations of phase reference [circadian time (CT) 0] toward the development of a photic phase response curve. After determining activity phase preference in a 24-h light-dark cycle (LD 12:12), degus were released in constant darkness. In this study, diurnal (n = 5) and nocturnal (n = 7) degus were randomly subjected to 1-h light pulses (30-35 lx) at many circadian phases (CT 1-6: n = 7; CT 7-12: n = 8; CT 13-18: n = 8; and CT 19-24: n = 7). The circadian phase of body temperature (Tb) onset was defined as CT 12 in nocturnal animals. In diurnal animals, CT 0 was determined as Tb onset + 1 h. Light phase delayed and advanced circadian rhythms when delivered during the early (CT 13-16) and late (CT 20-23) subjective night, respectively. No significant phase shifts were observed during the middle of the subjective day (CT 3-10). Thus, regardless of activity phase preference, photic entrainment of the circadian pacemaker in Octodon degus is similar to most other diurnal and nocturnal species, suggesting that entrainment mechanisms do not determine overt diurnal and nocturnal behavior.     

Characterizing dynamic interactions between ultradian glucocorticoid rhythmicity and acute stress using the phase response curve

The hypothalamic-pituitary-adrenal (HPA) axis is a dynamic oscillatory hormone signalling system that regulates the pulsatile secretion of glucocorticoids from the adrenal glands. In addition to regulation of basal levels of glucocorticoids, the HPA axis provides a rapid hormonal response to stress that is vitally important for homeostasis. Recently it has become clear that glucocorticoid pulses encode an important biological signal that regulates receptor signalling both in the central nervous system and in peripheral tissues. It is therefore important to understand how stressful stimuli disrupt the pulsatile dynamics of this system. Using a computational model that incorporates the crucial feed-forward and feedback components of the axis, we provide novel insight into experimental observations that the size of the stress-induced hormonal response is critically dependent on the timing of the stress. Further, we employ the theory of Phase Response Curves to show that an acute stressor acts as a phase-resetting mechanism for the ultradian rhythm of glucocorticoid secretion. Using our model, we demonstrate that the magnitude of an acute stress is a critical factor in determining whether the system resets via a Type 1 or Type 0 mechanism. By fitting our model to our in vivo stress-response data, we show that the glucocorticoid response to an acute noise stress in rats is governed by a Type 0 phase-resetting curve. Our results provide additional evidence for the concept of a deterministic sub-hypothalamic oscillator regulating the ultradian glucocorticoid rhythm, which constitutes a highly responsive peripheral hormone system that interacts dynamically with hypothalamic inputs to regulate the overall hormonal response to stress.     

Triphasic pattern in the ex vivo response of human proliferative phase endometrium to oestrogens

The aim of this study was to evaluate the ex vivo oestrogen responsiveness of human proliferative phase endometrium using short-term explant cultures. The effects of oestrogen (17beta-E2) on proliferation and the expression of oestrogen-responsive genes known to be involved in regulating endometrial function were evaluated. Three distinct response patterns could be distinguished: (1) the menstrual (M) phase pattern (cycle days 2-5), which is characterised by a complete lack in the proliferative response to 17beta-E2, while an increased expression of AR (2.6-fold, P<0.01), PR (2.7-fold, P<0.01) and COX-2 (3.5-fold, P<0.01) at the mRNA level was observed and a similar upregulation was also found for AR, PR and COX-2 at the protein level; (2) the early proliferative (EP) phase pattern (cycle days 6-10) with 17beta-E2 enhanced proliferation in the stroma (1.7-fold, P<0.05), whereas the expression of AR, PR and COX-2 were not affected at the mRNA and protein levels and ER-alpha mRNA and protein levels were significantly reduced by 17beta-E2; (3) the late proliferative (LP) phase pattern (cycle days 11-14), which is characterised by a moderate stimulation of proliferation (1.4-fold, P<0.05) and PR mRNA expression (1.7-fold, P<0.01) by 17beta-E2. In conclusion, three distinct response patterns to 17beta-E2 could be identified with respect to proliferation and the expression of known oestrogen-responsive genes in human proliferative phase endometrium explant cultures.     

Pulse coupled oscillators and the phase resetting curve

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

Soybean seed growth in response to long-term exposures to differing oxygen partial pressures

Short-term studies have indicated that alterations in the oxygen partial pressure (pO₂) around developing soybean (Glycine max [L.] Merr.) seeds may alter seed growth characteristics. A 2-year field study was undertaken to determine the effects on seed development of long-term exposures of individual pods to either sub-ambient or supra-ambient pO₂. Pod chambers were used through which fixed pO₂ were continuously flowed throughout seed development. No effects on maturity date were observed from exposures to either sub-ambient or supra-ambient pO₂. On the other hand, seed weight was reduced by 0.10 pO₂ in both years of the study implicating an O₂ limitation on seed growth rate at this fairly high pO₂. In 1 of the 2 years, supra-ambient pO₂ resulted in increased seed weight.     

Difference equation model of ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve

A model of extended ventricular parasystole proposed by Moe et al. (1977) was formulated as a system of nonlinear difference equations by using the phase response curve of myocardial pacemakers. A number of ECG patterns of ventricular arrhythmia such as bigeminy, trigeminy etc. were explained from the property of periodic solutions of the equation. Characteristic properties of special kinds of arrhythmia called “concealed bigeminy” and “concealed trigeminy” were derived mathematically by assuming the model, in relation to the equation of the analog neuron model. The present study was considered to be of clinical significance as a theoretical foundation for the study of genesis of cardiac arrhythmias.