Modeling Two-Oscillator Circadian Systems Entrained by Two Environmental Cycles

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these “conflicting zeitgeber” protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as “phase jumps” and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a “conflicting zeitgeber experiment” incorporates only two phase relationships between zeitgebers

Diurnos ou Noturnos? Discutindo padrões temporais de atividade

The identification of nocturnality or diurnality in animals is thought to be simple and obvious when one is characterizing behavioral aspects. However, this distinction may be difficult both in nature and under laboratory artificial conditions. The physiological mechanisms that define diurnal and nocturnal animals are being studied and reports of animals which display a change from day- to nightactivity are increasing. This may reveal a fundamental aspect of the temporal organization, especially in mammalsA classificação de um animal como diurno ou noturno parece, à primeira vista, extremamente simples quando se caracteriza o comportamento geral. Entretanto, tal distinção não é tão evidente nem na natureza e nem nas condições artificiais de laboratório. Atualmente, os mecanismos fisiológicos que definem mamíferos diurnos e noturnos estão sendo investigados em diversos níveis biológicos. Relatos de animais com fases diferentes de atividade em laboratório e em campo estão aumentando, podendo revelar um aspecto fundamental da organização temporal, especialmente em mamífero

Forced Desynchronization of Activity Rhythms in a Model of Chronic Jet Lag in Mice

We studied locomotor activity rhythms of C57/Bl6 mice under a chronic jet lag (CJL) protocol (ChrA6/2), which consisted of 6-hour phase advances of the light-dark schedule (LD) every 2 days. Through periodogram analysis, we found 2 components of the activity rhythm: a short-period component (21.01 ± 0.04 h) that was entrained by the LD schedule and a long-period component (24.68 ± 0.26 h). We developed a mathematical model comprising 2 coupled circadian oscillators that was tested experimentally with different CJL schedules. Our simulations suggested that under CJL, the system behaves as if it were under a zeitgeber with a period determined by (24-[phase shift size/days between shifts]). Desynchronization within the system arises according to whether this effective zeitgeber is inside or outside the range of entrainment of the oscillators. In this sense, ChrA6/2 is interpreted as a (24 - 6/2 = 21 h) zeitgeber, and simulations predicted the behavior of mice under other CJL schedules with an effective 21-hour zeitgeber. Animals studied under an asymmetric T = 21 h zeitgeber (carried out by a 3-hour shortening of every dark phase) showed 2 activity components as observed under ChrA6/2: an entrained short-period (21.01 ± 0.03 h) and a long-period component (23.93 ± 0.31 h). Internal desynchronization was lost when mice were subjected to 9-hour advances every 3 days, a possibility also contemplated by the simulations. Simulations also predicted that desynchronization should be less prevalent under delaying than under advancing CJL. Indeed, most mice subjected to 6-hour delay shifts every 2 days (an effective 27-hour zeitgeber) displayed a single entrained activity component (26.92 ± 0.11 h). Our results demonstrate that the disruption provoked by CJL schedules is not dependent on the phase-shift magnitude or the frequency of the shifts separately but on the combination of both, through its ratio and additionally on their absolute values. In this study, we present a novel model of forced desynchronization in mice under a specific CJL schedule; in addition, our model provides theoretical tools for the evaluation of circadian disruption under CJL conditions that are currently used in circadian research.Fil: Casiraghi, Leandro Pablo. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Oda, Gisele A.. Universidade de Sao Paulo; BrasilFil: Chiesa, Juan José. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Friesen, W. Otto. University of Virginia; Estados UnidosFil: Golombek, Diego Andres. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología. Laboratorio de Cronobiología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Field and Laboratory Studies Provide Insights into the Meaning of Day-Time Activity in a Subterranean Rodent (Ctenomys aff. knighti), the Tuco-Tuco

South American subterranean rodents (Ctenomys aff. knighti), commonly known as tuco-tucos, display nocturnal, wheel-running behavior under light-dark (LD) conditions, and free-running periods >24 h in constant darkness (DD). However, several reports in the field suggested that a substantial amount of activity occurs during daylight hours, leading us to question whether circadian entrainment in the laboratory accurately reflects behavior in natural conditions. We compared circadian patterns of locomotor activity in DD of animals previously entrained to full laboratory LD cycles (LD12∶12) with those of animals that were trapped directly from the field. In both cases, activity onsets in DD immediately reflected the previous dark onset or sundown. Furthermore, freerunning periods upon release into DD were close to 24 h indicating aftereffects of prior entrainment, similarly in both conditions. No difference was detected in the phase of activity measured with and without access to a running wheel. However, when individuals were observed continuously during daylight hours in a semi-natural enclosure, they emerged above-ground on a daily basis. These day-time activities consisted of foraging and burrow maintenance, suggesting that the designation of this species as nocturnal might be inaccurate in the field. Our study of a solitary subterranean species suggests that the circadian clock is entrained similarly under field and laboratory conditions and that day-time activity expressed only in the field is required for foraging and may not be time-dictated by the circadian pacemaker

Symmetric limit-cycle system: Oscillator and <i>zeitgeber</i> reference phases at different coupling strengths.

<p>Steady-state oscillator phases (<i>φ_A</i> and <i>φ_B</i>) are represented by filled squares and circles, respectively; <i>zeitgeber</i> phases (<i>Φ_L</i> and <i>Φ_T</i>) are represented by open squares and circles, respectively (as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0023895#pone-0023895-g002" target="_blank">Fig. 2</a>). In each of the 24 successive horizontal bars <i>Φ_T</i> was increased by 1 h with respect to the phase of <i>zeitgeber</i> L, which was fixed at <i>Φ_L</i> = 12 h. The duration and amplitude of both <i>zeitgebers</i> were fixed. Coupling strengths C were set to: A) 0.0; B) 0.01; C) 0.07; D) 0.15; and E) 0.18. Pittendrigh-Pavlidis model parameters here and in the remaining figures: <i>a</i> = 0.85, <i>b</i> = 0.3, <i>c</i> = 0.8, <i>d</i> = 0.5. <i>T</i> = <i>L</i> = 2.</p

Asymmetrical inter-oscillator coupling in Pittendrigh-Pavlidis systems.

<p>A) Phase difference between oscillators (<i>φ_AB</i>) as a function of the phase difference between <i>zeitgebers</i> (Δ<i>Φ_LT</i>). <i>C_AB</i> = 0.07 and C_BA varies as a fraction of <i>C_AB</i> (see legend inside the figure). B) Oscillator and <i>zeitgeber</i> reference phases for a master-slave configuration, elicited by <i>C_AB</i> = 0.07,<i>C_BA</i> = 0. Oscillator phases (<i>φ_A</i> and <i>φ_B</i>) are represented by filled squares and circles, respectively; <i>zeitgeber</i> phases (<i>Φ_L</i>and <i>Φ_T</i>) are represented by open squares and circles, respectively. In each of the 24 successive horizontal bars <i>Φ_T</i> was increased by 1 h with the phase of <i>zeitgeber</i> L fixed at <i>Φ_L</i> =  12 h. The duration and amplitude of both <i>zeitgebers</i> were fixed. C) For a stronger value of unidirectional coupling <i>C_AB</i> = 0.11 and <i>C_BA</i> = 0, relative coordination (loss of stable entrainment) occurs in lines 9 and 10 (hatched). Pittendrigh-Pavlidis model parameters: <i>T</i> = <i>L</i> = 2.</p

Schematic representation of the dynamics of oscillators and <i>zeitgebers</i>.

<p>Time course of oscillator A, <i>zeitgeber</i> L (upper panel), oscillator B and <i>zeitgeber</i> T (lower panel). <i>S</i> and <i>R</i> variables of each oscillator are represented, respectively, by heavy and light lines. <i>Zeitgebers</i> L and T are represented by rectangular pulses with periods  =  24 h. The phase of A, with respect to the acrophase (upper, filled squares) is given by <i>φ_A</i>, that of B (lower, filled circles) is given by <i>φ_B</i>_. The phases of the <i>zeitgeber</i> pulses are indicated by <i>Φ_L</i> (upper, open squares) and <i>Φ_T</i> (lower, open circles). The phase difference between oscillators A and B is represented by <i>φ_AB</i>, while the phase difference between <i>zeitgebers</i> L and T is represented by <i>Φ_LT</i>.</p

Experimental data and model of Pittendrigh and Bruce (1959).

<p>A) Eclosion rhythm of <i>Drosophila</i> populations under 24 h light/dark and temperature cycles. Each horizontal bar corresponds to two successive days. Light/dark cycles are shown by shaded areas and temperature cycles by a continuous curve, the latter being displaced by 2 h in each successive bar. Dark bars indicate the number of flies that eclosed within a 2 h time window. From Pittendrigh and Bruce (1959) with permission. B) Schematic diagram of two coupled A and B oscillators, entrained, respectively by <i>zeitgebers</i> L and T.</p

Period determination in the food-entrainable and methamphetamine-sensitive circadian oscillator(s)

Daily rhythmic processes are coordinated by circadian clocks, which are present in numerous central and peripheral tissues. In mammals, two circadian clocks, the food-entrainable oscillator (FEO) and methamphetamine-sensitive circadian oscillator (MASCO), are "black box" mysteries because their anatomical loci are unknown and their outputs are not expressed under normal physiological conditions. In the current study, the investigation of the timekeeping mechanisms of the FEO and MASCO in mice with disruption of all three paralogs of the canonical clock gene, Period, revealed unique and convergent findings. We found that both the MASCO and FEO in Per1(-/-)/Per2(-/-)/Per3(-/-) mice are circadian oscillators with unusually short (similar to 21 h) periods. These data demonstrate that the canonical Period genes are involved in period determination in the FEO and MASCO, and computational modeling supports the hypothesis that the FEO and MASCO use the same timekeeping mechanism or are the same circadian oscillator. Finally, these studies identify Per1(-/-)/Per2(-/-)/Per3(-/-) mice as a unique tool critical to the search for the elusive anatomical location(s) of the FEO and MASCO.National Science FoundationNational Science Foundation [IOS-1146908]National Mouse Metabolic Phenotyping Centers MICROMouse ProgramNational Mouse Metabolic Phenotyping Centers MICROMouse Program [U24DK076169]Tennessee Valley Healthcare SystemTennessee Valley Healthcare SystemNational Institutes of Health [DK085712]National Institutes of HealthDiabetes Research and Training CenterDiabetes Research and Training Center [DK20593

Nocturnal to Diurnal Switches with Spontaneous Suppression of Wheel-Running Behavior in a Subterranean Rodent.

Several rodent species that are diurnal in the field become nocturnal in the lab. It has been suggested that the use of running-wheels in the lab might contribute to this timing switch. This proposition is based on studies that indicate feed-back of vigorous wheel-running on the period and phase of circadian clocks that time daily activity rhythms. Tuco-tucos (Ctenomys aff. knighti) are subterranean rodents that are diurnal in the field but are robustly nocturnal in laboratory, with or without access to running wheels. We assessed their energy metabolism by continuously and simultaneously monitoring rates of oxygen consumption, body temperature, general motor and wheel running activity for several days in the presence and absence of wheels. Surprisingly, some individuals spontaneously suppressed running-wheel activity and switched to diurnality in the respirometry chamber, whereas the remaining animals continued to be nocturnal even after wheel removal. This is the first report of timing switches that occur with spontaneous wheel-running suppression and which are not replicated by removal of the wheel