Exogenous and Endogenous Influences on Rhythms after Sudden Time Shift

When subjects are following their usual nychthemeral habits, the observed rhythms result from the interaction of a circadian ‘clock’ with rhythmic external influences. These major external influences can be removed by spending 24 h under constant conditions. The endogenous rhythms thus revealed, in temperature and urinary excretion, have mostly an earlier phasing than nychthemeral rhythms and adapt more slowly to time shift, usually by a phase delay. It appears undesirable for the rhythms of shift workers to be entrained to time shifts, and means of retaining the usual phasing are discussed.     

On Robust Stability And Sensitivity Of Circadian Rhythms

We develop an approach to robustness analysis of circadian rhythms from the viewpoints of (local) robust stability of periodic trajectories and their period‐sensitivity, based on mathematical models. Our attention is directed to the core molecular model generating circadian rhythms in Drosophila, proposed by Goldbeter [1], for our approach to be illustrated. We consider two cases when the circadian rhythms are subjected to periodic forcing by light/dark (LD) cycles and when the circadian rhythms are under continuous darkness (DD). First, we propose conditions/algorithms for (local) robust stability, and show that the circadian rhythms generated by the core molecular model are (locally) robustly stable, in both LD and DD cases. Second, in DD case, we derive a formula of period sensitivity, and assess effects of (infinitesimal) parameter‐variations on the period of the circadian rhythms.     

哺乳动物生物钟的数学建模及研究进展

由于数学模型在整合实验数据和分析基因调控网络的动力学方面的独特优势,近年来数学模型在生物节律研究领域越来越受到人们的重视.哺乳动物昼夜节律是由位于视觉交叉上颌的神经元控制的,其中的每个神经元都含有一个内在的生物钟,关键的问题是具有广泛周期分布的神经元振子之间如何达到相同步.在分子水平上结合数学方法中的网络分析与控制的观点构建生物网络,然后用非线性动力学的相关知识进行理论分析和数值模拟,是研究生命现象的一个有效途径.本文从系统生物学的研究思路,对生物钟的数学建模及其动力学研究做了一个综述,并对其今后的研究热点进行了展望.     

Using a circadian rhythms model to evaluate shift schedules

As long as the need for shiftwork exists, so will the demand for an optimal scheduling strategy that balances the needs of both industry and the shiftworker. One aim is for schedules that require workers to be on duty during the times that they are most naturally alert and awake. Czeisler et al. (1982) developed a set of circadian rhythm based guidelines intended to aid in designing such shiftwork schedules. This paper takes research one step further by testing such empirical criteria in a mathematical setting. The two-oscillator model of free-run human circadian rhythms developed by Kronauer et al. (1982) was modified to represent the circadian rhythms of a shiftworker on a pre-selected shiftwork schedule. Numerical simulations were used to compare the circadian rhythms produced from a variety of shiftwork schedules to the free-run rhythms. Shift schedules that resulted in circadian rhythms closest to the free-run rhythms were identified as preferred schedules. The numerical results supported Czeisler's findings (1982), indicating the best shift schedules adopt a slow, forward-shifting rotation pattern, rotate shifts after 2-week periods and allow an average of 2 days off per week.     

Using a circadian rhythms model to evaluate shift schedules

As long as the need for shiftwork exists, so will the demand for an optimal scheduling strategy that balances the needs of both industry and the shiftworker. One aim is for schedules that require workers to be on duty during the times that they are most naturally alert and awake. Czeisler et al. (1982) developed a set of circadian rhythm based guidelines intended to aid in designing such shiftwork schedules. This paper takes research one step further by testing such empirical criteria in a mathematical setting. The two-oscillator model of free-run human circadian rhythms developed by Kronauer et al. (1982) was modified to represent the circadian rhythms of a shiftworker on a pre-selected shiftwork schedule. Numerical simulations were used to compare the circadian rhythms produced from a variety of shiftwork schedules to the free-run rhythms. Shift schedules that resulted in circadian rhythms closest to the free-run rhythms were identified as preferred schedules. The numerical results supported Czeisler's findings (1982), indicating the best shift schedules adopt a slow, forward-shifting rotation pattern, rotate shifts after 2-week periods and allow an average of 2 days o^ff per week.     

Dissecting circadian performance rhythms: implications for shiftwork

Safety on shift systems will depend, at least in part, on the adjustment of shiftworkers' circadian (c.24h) rhythms in performance capabilities which will in turn depend on their underlying control. In the present study three volunteers lived on a 30h ‘day’ and performed a range of tasks every 2h (while awake) to allow estimates of the relative magnitude of the endogenous (body clock) and exogenous (masking) components of their rhythms to be made. Performance rhythms were found to differ considerably in this respect with, for example, speed on a 4–choice serial reaction time task appearing to be largely endogenously determined while that on a 5–target Sternberg task was more dependent on exogenous (i.e., 30h) factors. This implies that performance measures may adjust at very different rates to one another to night work, and hence that the optimal form of shift system may vary according to the precise demands of the shiftworker's task.     

Features of Circadian Rhythms Relevant for the Design of Shift Schedules

The first part of this paper reviews properties of circadian rhythms when free-running in constant conditions, or in situations where zeitgebers are insufficient for entrainment. The second part deals with problems of entrainment by natural and artificial zeitgebers, with phase controlling effects of sleep and the timing of meals, and with the need to differentiate between entraining and masking effects. The third part discusses phase shifts of circadian rhythms, especially the dependence of the rate of re-entrainment on the direction of the shift, and the splitting of the circadian system into parts which are shifted in opposite directions (re-entrainment by partition). The relevance of these features of circadian rhythms for the design of shift-work schedules is discussed.     

No interference of task complexity with circadian rhythmicity in a constant routine protocol

Time course in task performance has been studied extensively. In particular, the investigation of circadian rhythmicity in task performance that varied in complexity. However, these studies disclosed heterogeneous outcomes. This could be the result of confounding exogenous factors, the use of diverse tasks, as well as accumulating sleepiness interfering with the underlying circadian drive. The present study varied task demands systematically within a single task and a dual task, using a constant routine protocol to examine the unmasked influence of the endogenous circadian oscillator on the periodicity of performance. Moreover, the subjects were divided into an early-start and a late-start group to estimate the potential interaction of circadian rhythmicity with the duration of prior wakefulness. The results revealed a distinct congruence in the circadian rhythms of all performance measures, with which prior wakefulness (<?40?h) did not interact. Also, single-task as well as dual-task complexity did not interfere with circadian rhythmicity. In conclusion, when sufficiently controlled for masking exogenous factors, task complexity is removed from the underlying circadian rhythms.     

No interference of task complexity with circadian rhythmicity in a constant routine protocol

Time course in task performance has been studied extensively. In particular, the investigation of circadian rhythmicity in task performance that varied in complexity. However, these studies disclosed heterogeneous outcomes. This could be the result of confounding exogenous factors, the use of diverse tasks, as well as accumulating sleepiness interfering with the underlying circadian drive. The present study varied task demands systematically within a single task and a dual task, using a constant routine protocol to examine the unmasked influence of the endogenous circadian oscillator on the periodicity of performance. Moreover, the subjects were divided into an early-start and a late-start group to estimate the potential interaction of circadian rhythmicity with the duration of prior wakefulness. The results revealed a distinct congruence in the circadian rhythms of all performance measures, with which prior wakefulness (< 40 h) did not interact. Also, single-task as well as dual-task complexity did not interfere with circadian rhythmicity. In conclusion, when sufficiently controlled for masking exogenous factors, task complexity is removed from the underlying circadian rhythms.     

Alteration of circadian rhythm in shift-working ambulance personnel. Monitoring of salivary cortisol rhythm.

In order to investigate the relationship between internal desynchronization and clinical intolerance to shift work, a set of circadian rhythms including salivary cortisol rhythm were monitored in seven shift-working ambulance personnel. Oral temperature, grip strength of both hands, subjective assessment of drowsiness, fatigue and attention were recorded approximately every four hours except during sleep, for seven days. Self-sampling of salivary cortisol, which was suitable evaluation of endocrine rhythm in field studies, was also tried in this study. cosinor (cosine curve fitting) method and power spectral analysis were used for time series data analysis. The internal desynchronizations between rhythms of physiological variables and sleep-wake cycle were observed in shift-working ambulance personnel. The incidence of internal desynchronization seemed to be higher in intolerant subjects, although the difference between tolerant and intolerant subjects did not reach a statistically significant level. The peak time of salivary cortisol rhythm during a twenty-four hour shift was phase-advanced as intolerant to shift work showed apparently an atypical circadian pattern of salivary cortisol with an abnormal peak at 21.00 h. In this subject, the clinical intolerance to shift work seemed to be associated with internal desynchronization of circadian rhythms. The present study confirmed the internal desynchronization of the circadian rhythm in physiological rhythms like oral temperature and grip strengths, and was in favour of the hypothesis of an internal desynchronization and clinical intolerance to shift work. The clinical implication of impairment of salivary cortisol rhythm remains to be further investigated.     

Adaptive Lipschitz Observer Design for a Mammalian Model

This paper deals with observer designs for a proposed mathematical model of circadian rhythms which exist in almost every living organism. A 7th order model for mammalian circadian rhythms which captures the main dynamic features is considered in this paper. A recent result of one‐sided Lipschitz observer design in the literature is applied to this mammalian model to show a possibility of reducing measurements for circadian models in system biology. The mammalian model presented may contain an uncertainty parameter. An adaptive design of the Lipschitz observer is then applied to deal with this case. Besides detailed designs of both observers, detailed analysis is also performed for nonlinear functions in the mammalian model to show that the Lipschitz observers can indeed be applied. Several simulation studies of the proposed observers are carried out with the results shown in this paper.     

Individual differences in circadian rhythm parameters and short-term tolerance to shiftwork: a follow-up study

The relationship between individual differences in the phase and amplitude of circadian rhythms and tolerance to shiftwork has been the subject of several studies. Those studies recorded circadian rhythms and shiftwork tolerance at approximately the same time. The present study aimed to examine the predictive relationships between the amplitude, phase, and mesor of 24 h rhythms obtained before exposure to shiftwork, and subsequent indices of tolerance measured after one and three years of shiftwork. The results revealed some stable relations between the various rhythm parameters and subsequent tolerance measures. Workers who had a higher mesor of positive moods, and a lower mesor of negative moods and fatigue, before entering shiftwork tended to tolerate shiftwork better. Further, those whose heart rate rhythm showed an earlier acrophase had better subsequent sleep quality scores, while those with a smaller amplitude of their temperature, negative mood and fatigue rhythms showed better night-shift tolerance.     

A Review of: “Influencing Organisational Change—The Role of the Personnel Specialist”. By CHARLES E. MARGHRISON. (London: Institute of Personnel Management, 1978.) [Pp. 219.] £5.25.

This study attempted to determine circadian rhythms in metabolic responses to submaximal and maximal workloads by concentrating on repeated observations of a male subject over 16 weeks. Altogether 36 experimental tests were undertaken on a cycle ergometer, six at each of the times, 0200, 0600, 1000, 1400, 1800 and 2200 hours. The work test comprised two consecutive 5-min periods at 82 and 147 W, followed immediately by an incremental workload to exhaustion. Significant circadian rhythms were found at rest pre-exercise for pulse rate (f_h), VO₂, V_E and rectal temperature (T_r) (p<0·001), with f_H leading the others in phase and T_t lagging significantly behind V_E (p<0·05). The circadian cycle in V_E persisted at both submaximal steady rates, with the VO₂ significant at the higher rate only when uncorrected for body weight. There was no evidence of a circadian variation in ‘muscular efficiency’. No significant rhythms were found in metabolic measures at maximal exercise or during recovery, indicating no time of day effect in the physiological capacity for exercise. The circadian variation in T_r persisted in phase and amplitude under maximal conditions and during recovery, indicating that the thermal load induced by a set exercise regime is independent of time of day.     

Circadian Rhythm Amplitude and Individual Ability to Adjust to Shift Work

The magnitude of the circadian acrophase adjustment (Δφ) following a phase shift of socio-ecologtc synchronisers (Δψ) such as results from shift work varies from subject to subject. According to Aschoff (1976) the ability to adjust φ rapidly could be negatively related to the amplitude of certain circadian rhythms. To test this hypothesis the correlation coefficient (r) between the mean rhythm amplitude A and the acrophase shift Δφ after the first night shift was calculated for several variables from estimates of chronobiological time series analyses (single cosinor) in two groups of selected shift workers. Statistically significant negative correlations (ranging from ?0.53 to ?0.63) between A and Δφ were observed in the circadian rhythms of oral temperature, peak expiratory flow and urinary 17-OHCS, but not for grip strength, urinary K ⁺ and Na ⁺ A low amplitude of certain circadian rhythms could thus be considered as a measure of individual ability to adjust to shift work easily. It is posssible that other chronobiological characteristics may be found which will increase the value of this type of measure.     

Memory Based Performance Measures in Studies of Shiftwork

The phase of the circadian rhythm in performance efficiency on a given task is known to be influenced by the memory load involved. Two experiments were performed to determine whether memory load also influences the rate at which rhythms adapt to the phase-shifts involved in (a) transmeridian flight and (b) a long period of nightwork. In the first study, high and low memory load versions of a performance test were given to a 25 y old female subject experiencing a 5h eastward change in time-zone. Differences were found both in the initial phase of the two versions of the test and in the rate at which this phase adapted to the new time. In the second study, two young male subjects, working 21 consecutive night shifts, were given high and low memory load versions of the performance test, and a calculations test, every 4 h around the clock. The results were similar to those of the first study: a cosinor analysis revealed that despite periods of arhythmicity there were large differences between the rate of adaptation of the phases of the performance rhythms of high and low memory versions of the test, and also between the rhythms of temperature and performance. It is concluded that it is wrong to speak of a single ‘performance rhythm’, and that performance tests in shiftwork and jet-lag studies should thus simulate some aspect of the ‘real’ task under consideration.     

Preliminary evaluation of electroencephalographic entrainment using thalamocortical modelling

Abstract: The concept of linked oscillators in biological control systems has long been established. Frequency entrainment is a predominant explanation behind many biological rhythms. In this paper a preliminary examination of electroencephalographic entrainment is made to survey the possibility and methods of achieving signal entrainment at the highest level of neurological organization and function. A model of the thalamocortical system is employed to generate simulated electroencephalographic signals and is tested in various configurations in the search for entrainment under very simple conditions. Additionally, an analysis of the coupled Van der Pol model of the circadian rhythm controller is performed to identify the possibility of affecting that system with a drastically different coupling input signal. We were able to conclude that overall signal shape can have a significant impact on the entrainment characteristics of the system. Due to the nature of the underlying mathematical structure of the model, by examining the circadian rhythm controller, we found that it is unsuitable for entrainment to an incident entraining signal of much higher frequency.     

An algorithm for shift scheduling which considers circadian principles

The principles of circadian rhythms in human beings have been applied to devise a methodology for scheduling shift work in a hospital unit which is operating under several important constraints. Considered here are time off between shifts, number of consecutive work days, number of distinct shifts in any two calendar weeks, number of shifts per week and special staffing for informational and training meetings. It is shown how the method of Czeisler et al. (1982) can be adapted for the more constrained work environment. A set of evaluation scales for circadian theory violations is devised and applied to an example from Togus VA Hospital. Results include the actual schedules together with evaluations on three different aspects of circadian theory: length of cycle on a single shift, rotation involving night shifts and rotation not involving night shifts. Improvements of each of these evaluations with respect to previously published results are obtained.     

The prediction of the adaptation of circadian rhythms to rapid time zone changes

The aim of the study was to find out which factors could explain individual differences in the resynchronization speed of circadian rhythms of salivary melatonin and subjective alertness after transmeridian flights over 10 time zones. The mean age of the 40 female subjects was 33·0 ±6·9 years. The data were gathered by measurements of the circadian rhythms of melatonin excretion and ahertness at 2 h intervals in Helsinki (Finland) two days before westward flight to Los Angeles (USA), where the measurements were repeated on the 2nd day after the flights and on the 2nd day in Finland after return flight. This shift in the acrophases of the two circadian rhythms were used as dependent variables in regression analyses. The predictors used were length of day, marital status, amount of physical exercise, age, neuroticism, extroversion, and eveningness. Age, day length, marital status, and physical exercise explained the acrophase adaptation of the melatonin rhythm after westward flight, and day length, neuroticism, and extroversion after eastward flight. Marital status, neuroticism, and physical exercise explained the variation of the acrophase adjustment of the alertness rhythm after westward flight, and age and eveningness after eastward flight. It is concluded that the amount of daylight and personality are the best predictors of the circadian rhythm adaptation after transmeridian flights.     

Design, optimization and predictions of a coupled model of the cell cycle, circadian clock, DNA repair system, irinotecan metabolism and exposure control under temporal logic constraints

In systems biology, the number of available models of cellular processes has increased rapidly, but re-using models in different contexts or for different questions remains a challenging issue. In this paper, we study the coupling of different models playing a role in the mammalian cell cycle and in cancer therapies. We show how the formalization of experimental observations in temporal logic with numerical constraints can be used to compute the unknown coupling kinetics parameter values agreeing with experimental data. This constraint-based approach to computing with partial information is illustrated through the design of a complex model of the mammalian cell cycle, the circadian clock, the p53/Mdm2 DNA-damage repair system, the metabolism of irinotecan and the control of cell exposure to it. We discuss the use of this model for cancer chronotherapies and evaluate its predictive power with respect to circadian core gene knock-outs.     

Short and Long-term Adjustment of Circadian Rhythms in ‘ Permanent ’ Night Nurses

Two studies are described in which differences were found in the adjustment of the circadian rhythms of full and part-time night nurses to night work. A distinction was drawn between short-term adjustment that takes place over successive night shifts, and long-term adjustment that may take the form either of a permanent ‘flattening’ of the rhythm, or of a facilitation of short-term adjustment. The results from the first study indicated that even when the potential for greater short-term adjustment was controlled for, the full-time staff showed greater adjustment to night work. The second study examined these differences in long-term adjustment in greater detail. No evidence was found of a permanent ‘flattening’ of the full-timers’ circadian rhythms, although they showed clear evidence of adjustment even on the first of a period of successive night shifts. The full-timers also showed more evidence of adjustment from the first to the second night shift. It is suggested that these differences in long-term adjustment may reflect differences in the degree to which the nurses scheduled their lives towards night work.