A qualitative model of a motor circadian rhythm

In Nature it is possible to observe diverse rhythms. Because of their adaptive characteristics, the circadian rhythms are of major importance and have been the subject of numerous experimental and theoretical studies. In this article, we give a presentation of the main results we have obtained about the motor circadian rhythm along some years of collaboration between biologists and mathematicians. We present a mathematical model simulating changes in frequency, synchronization and amplitude of the circadian oscillation during two developmental stages of the crayfish, namely, the juvenile and the adult stages. We report also some work in progress on the simulation of the phase response curve and on a simplified model of the rhythm.     

A qualitative mathematical model of the ontogeny of a circadian rhythm in crayfish

Based on experimental work on the ontogeny of the electroretinogram circadian rhythm in crayfish, we present a mathematical model simulating changes in both frequency and amplitude of the electroretinogram oscillation during several developmental stages until shortly before the adult age. Simultaneously, we propose a hypothetical oscillation in the hormonal release whose frequency is imposed on the electroretinogram oscillation. The model consists of two coupled nonlinear oscillators in which a dynamical response is obtained mainly through an Andronov-Hopf bifurcation. Through the construction of the model, a biological hypothesis about the essential elements underlying the ERG circadian rhythm and their interrelations is formulated and discussed.     

Perturbation of a circadian rhythm by single and periodic signals and its mathematical simulation

Adaptive characteristics of circadian rhythm are based on their capacity to be synchronized by external signals, particularly light signals. The effect of both single and periodic light signals on the electroretinogram (ERG) circadian rhythm in crayfish is studied. In a previous work (Lara-Aparicioet al., Bull math. Biol. 55, 97–110, 1993) we developed a mathematical model simulating the emergence of the ERG circadian rhythm during the ontogeny of the crayfish. In the present work we have tested the familiar wave-shift behaviour of an oscillator with a single limit cycle. Two new facts, not present in a simpler model, now appear, which simulate adequately the experimental results, i.e. the presence of a transient stage and the shape of the perturbed wave which changes according to the characteristics of the external light signals.     

About the Existence of Circadian Activity in Cave Crayfish

Evidence of a circadian clock mechanism was found in the cave crayfish Procambarus cavernicola. Analysis of motor activity recorded in this species during 12 consecutive days in either free running (constant darkness, DD or constant light, LL) or entrainment conditions (12 h of light alternated with 12 h of darkness, 12 : 12 LD) showed a well recognized circadian rhythm. In this rhythm however, the absence of synchronization by periodical external signals was notorious. The comparison between the motor circadian rhythm in cave crayfish and epigeous crayfish Procambarus clarkii (these last studied during juvenile and adult stages), evidenced strong similitude between the motor circadian rhythm of cave crayfish and juvenile epigeous crayfish.     

Pigment dispersing hormone generates a circadian response to light in the crayfish, Procambarus clarkii

Photoreceptor cells have been identified as important structures in the organization of the circadian system responsible for the generation and expression of the electroretinogram (ERG) circadian rhythm. They are the structures where the circadian periodicity is expressed (effectors) and which transform information from external light signals to be conducted to the pacemaker in order to induce adjustments of the rhythm (synchronizers). After isolation, eyestalks perfused in a pigment dispersing hormone (PDH) solution, show significant changes in receptor potential (RP) amplitude and duration. Exogenous PDH injected into intact crayfish induces a migration of retinal shielding pigments to a light-adapted state. A single dose of PDH produces advances or delays in the circadian rhythm of response to light of visual photoreceptors. All these effects depend on the circadian phase of PDH application. Consequently, the determination of the action of exogenous PDH on photoreceptor cells proved to be very helpful in understanding some mechanisms underlying the circadian organization of crayfish.     

Circadian rhythm in melatonin release as a mechanism to reinforce the temporal organization of the circadian system in crayfish

Melatonin (MEL) is a conserved molecule with respect to its synthesis pathway and functions. In crayfish, MEL content in eyestalks (Ey) increases at night under the photoperiod, and this indoleamine synchronizes the circadian rhythm of electroretinogram amplitude, which is expressed by retinas and controlled by the cerebroid ganglion (CG). The aim of this study was to determine whether MEL content in eyestalks and CG or circulating MEL in hemolymph (He) follows a circadian rhythm under a free-running condition; in addition, it was tested whether MEL might directly influence the spontaneous electrical activity of the CG. Crayfish were maintained under constant darkness and temperature, a condition suitable for studying the intrinsic properties of circadian systems. MEL was quantified in samples obtained from He, Ey, and CG by means of an enzyme-linked immunosorbent assay, and the effect of exogenous MEL on CG spontaneous activity was evaluated by electrophysiological recording. Variation of MEL content in He, Ey, and CG followed a circadian rhythm that peaked at the same circadian time (CT). In addition, a single dose of MEL injected into the crayfish at different CTs reduced the level of spontaneous electrical activity in the CG. Results suggest that the circadian increase in MEL content directly affects the CG, reducing its spontaneous electrical activity, and that MEL might act as a periodical signal to reinforce the organization of the circadian system in crayfish.     

Spontaneous and light-evoked discharge of the isolated abdominal nerve cord of crayfish in vitro reveals circadian oscillations.

We examined the well-known spontaneous discharge (SD) and light-evoked (PD) discharge of the crayfish caudal photoreceptor for the possible existence of a daily rhythm in spike frequency. To do this, we isolated the abdominal nerve cord in vitro and studied its discharge frequency in constant darkness. Single cosinor analysis revealed significant SD and PD circadian rhythms (P < .05) with periods tau = 24.4h and 24.2h, respectively. These oscillations correspond to an endogenous circadian discharge of the caudal photoreceptor that is enhanced by light. The importance of this rhythm in the adaptive behavior of crayfish is discussed.     

Erg circadian rhythm in the course of ontogeny in crayfish

• 1.1. The objective of the present work was to study the ontogeny of the ERG circadian rhythm in crayfish.
• 2.2. Long-term recordings of ERG and shielding retinal pigments position measured from the instar, the second instar, the third instar and the adult crayfish were obtained.
• 3.3. In the youngest animals (1–8 days old) an ultradian rhythm (15min-4hr periods) in the ERG amplitude was detected.
• 4.4. Older animals showed a progressive increment in the period length before they exhibited a circadian pattern. This last appeared, the first time, in 30-day-old animals and showed noticeable differences in the adult crayfish. At the same time, the crayfish began to show photomotor reflex. Later on (140-day-old crayfish) the circadian rhythm attained its final parameters.
• 5.5. The SD was used as a measure of lability in periods. The 4 hr ultradian rhythm and the 22.4 hr circadian rhythm showed the lowest SD indicating that they are the most precise period values.
• 6.6. Our results support the idea that the ERG circadian rhythm results from the coupling among high frequency (ultradian) oscillators, particularly those of 4 hr periods and that the coupling depends on the action of neurosecretions released from the sinus gland.

     

Pigment dispersing hormone modulates spontaneous electrical activity of the cerebroid ganglion and synchronizes electroretinogram circadian rhythm in crayfish Procambarus clarkii

In crayfish, one very well-studied circadian rhythm is that of electroretinogram (ERG) amplitude. The cerebroid ganglion has been considered a plausible site for the circadian pacemaker of this rhythm and for the retinular photoreceptors, as the corresponding effectors. The pigment dispersing hormone (PDH) appears to synchronize ERG rhythm, but its characterization as a synchronizer cue remains incomplete. The main purposes of this work were a) to determine whether PDH acts on the cerebroid ganglion, and b) to complete its characterization as a non-photic synchronizer. Here we show that PDH increases the number of the spontaneous potentials of the cerebroid ganglion, reaching 149.92±6.42% of the activity recorded in the controls, and that daily application of PDH for 15 consecutive days adjusts the ERG circadian rhythm period to 24.0±0.2h and the end of the activity period of the rhythm coincides with the injection of the hormone. In this work, we hypothesized that in crayfish, PDH transmits the "day" signal to the ERG circadian system and acts upon both the presumptive circadian pacemaker and the corresponding effectors to reinforce the synchronization of the system.     

Modelling circadian rhythms of protein KaiA, KaiB and KaiC interactions in cyanobacteria

Cyanobacteria are the simplest organisms known that exhibit circadian rhythms. The mechanism of circadian rhythm generation in cyanobacteria is different from eukaryotes. Based on the recent experiments about the interaction of KaiA, KaiB, and KaiC proteins with the generation of circadian rhythms in vitro, we developed a mathematical model to describe post-translational oscillations and the possible chemical reactions involved in the circadian clock mechanism of cyanobacteria. In this model, a series of differential equations, with linear kinetics for binding of proteins, Michaelis - Menten kinetics for enzymatic processes and a term including an explicit delay for dissociation of the KaiA/KaiB/phospho-KaiC complex, are proposed describing the dynamics of the chemistry. It is demonstrated that the mathematical system can lead to circadian oscillation within a range of parameter values.     

Melatonin modulates the ERG circadian rhythm in crayfish

One of the most important functions modulated by melatonin is the synchronization of circadian rhythms. In crayfish (Procambarus clarkii), we have obtained evidence that the amplitude of the electrical response to light of the retinal photoreceptors the receptor potential, is modified by the action of melatonin and that the magnitude of this action depends on the circadian time of melatonin application. In contrast, the electroretinogram (ERG) circadian rhythm can be synchronized by either single or periodic melatonin application. In this work we hypothesized that, in crayfish, melatonin acts on effectors and on pacemaker of ERG circadian rhythm as a non-photic synchronizer. Melatonin could be a hormone that sends a signal of darkness to the ERG circadian system.     

Synchronization by light of the circadian rhythm of motor activity in the crayfish

Abstract

We have studied the pattern for resetting the circadian rhythm in the spontaneous motor activity of the crayfish. Spontaneous motor activity was recorded continously at a constant temperature and under free running conditions in complete darkness. The effect of single light pulses applied at different circadian times, on the circadian rhythm of motor activity was measured in both transient stage and steady state. The results led us to construct a phase‐transition curve and phase‐response curve which were analyzed to obtain information about the oscillators which underlie the circadian rhythm of motor activity.     

Pigment dispersing hormone modulates spontaneous electrical activity of the cerebroid ganglion and synchronizes electroretinogram circadian rhythm in crayfish Procambarus clarkii

In crayfish, one very well-studied circadian rhythm is that of electroretinogram (ERG) amplitude. The cerebroid ganglion has been considered a plausible site for the circadian pacemaker of this rhythm and for the retinular photoreceptors, as the corresponding effectors. The pigment dispersing hormone (PDH) appears to synchronize ERG rhythm, but its characterization as a synchronizer cue remains incomplete. The main purposes of this work were a) to determine whether PDH acts on the cerebroid ganglion, and b) to complete its characterization as a non-photic synchronizer. Here we show that PDH increases the number of the spontaneous potentials of the cerebroid ganglion, reaching 149.92 ± 6.42% of the activity recorded in the controls, and that daily application of PDH for 15 consecutive days adjusts the ERG circadian rhythm period to 24.0 ± 0.2 h and the end of the activity period of the rhythm coincides with the injection of the hormone. In this work, we hypothesized that in crayfish, PDH transmits the “day” signal to the ERG circadian system and acts upon both the presumptive circadian pacemaker and the corresponding effectors to reinforce the synchronization of the system.     

The Circadian Rhythm of Cardiac Frequency in Crayfish: a Multioscillator System?

The aim of this work was to study the humoral regulation of the circadian rhythm of cardiac frequency in crayfish and explore the possibility that isolated heart has a circadian-like oscillation. Sinus glands are the main source of neurohormones in crayfish, and their excision dampens the rhythm, lengthens the period and induces high frequency oscillations. Isolated crayfish hearts show a circadian-like rhythm of frequency with two peaks. These results suggest the participation of several oscillators in the generation and/or expression of the circadian rhythm.     

The Circadian Rhythm of Cardiac Frequency in Crayfish: a Multioscillator System?

The aim of this work was to study the humoral regulation of the circadian rhythm of cardiac frequency in crayfish and explore the possibility that isolated heart has a circadian-like oscillation. Sinus glands are the main source of neurohormones in crayfish, and their excision dampens the rhythm, lengthens the period and induces high frequency oscillations. Isolated crayfish hearts show a circadian-like rhythm of frequency with two peaks. These results suggest the participation of several oscillators in the generation and/or expression of the circadian rhythm.     

Extracellular low pH affects circadian rhythm expression in human primary fibroblasts

Circadian rhythm is a fundamental biological system involved in the regulation of various physiological functions. However, little is known about a nature or function of circadian clock in human primary cells. In the present study, we have applied in vitro real time circadian rhythm monitoring to study human clock properties using primary skin fibroblasts. Among factors that affect human physiology, slightly lower extracellular pH was chosen to test its effects on circadian rhythm expression. We established human primary fibroblast cultures obtained from three healthy subjects, stably delivered a circadian reporter gene Bmal1-luciferase, and recorded circadian rhythms in the culture medium at pH 7.2 and 6.7. At pH 7.2, robust and sustained circadian rhythms were observed with average period length 24.47 ± 0.03 h. Such rhythms were also found at pH 6.7; however, period length was significantly shortened to 22.60 ± 0.20, amplitude was increased, and damping rate was decreased. The effect of exposure to low pH on the period length was reversible. The shortened period was unlikely caused by factors affecting cell viability because cell morphology and MTT assay showed no significant difference between the two conditions. In summary, our results showed that the circadian rhythm expression is affected at pH 6.7 in human primary fibroblasts without affecting cell viability.     

SPONTANEOUS AND LIGHT-EVOKED DISCHARGE OF THE ISOLATED ABDOMINAL NERVE CORD OF CRAYFISH IN VITRO REVEALS CIRCADIAN OSCILLATIONS

We examined the well-known spontaneous discharge (SD) and lightevoked (PD) discharge of the crayfish caudal photoreceptor for the possible existence of a daily rhythm in spike frequency. To do this, we isolated the abdominal nerve cord in vitro and studied its discharge frequency in constant darkness. Single cosinor analysis revealed significant SD and PD circadian rhythms (P <. 05) with periods τ = 24.4h and 24.2h, respectively. These oscillations correspond to an endogenous circadian discharge of the caudal photoreceptor that is enhanced by light. The importance of this rhythm in the adaptive behavior of crayfish is discussed. (Chronobiology International, 18(5), 759–765, 2001)     

Study of circadian activity in the crayfish <Emphasis Type="Italic">Pontastacus Leptodactylus</Emphasis> during their multimonth maintenance in the river water flow

By the method of non-invasive on-line recording and processing of photoplethysmograms of testaceous invertebrates, the circadian rhythm of cardioactivity was studied in crayfish Pontastacus leptodactylus by recording for several month of the heart rate (HR) and stress-index (characteristics of variational pulsometry). The crayfish were kept in the natural running water in regime of the natural illumination alternation (the first group) or at constant artificial illumination of low intensity (the second group). The circadian rhythm was more frequent and more pronounced in crayfish of the first group. The criteria were established to determine the appearance and stabilization of the nocturnal, active rhythm phase: an increase of HR by more than 30% as compared with the daytime rest period and duration of such increase for at least 2.5 h. The stress-index has been shown to be a reliable parameter of the beginning of the nocturnal phase of cardioactivity, while preservation of the typical circadian rhythm can be considered as a bioindicator in the biomonitoring systems of the quality of surface waters.