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Notes: Abstract While living under constant conditions and complete isolation from environmental time cues for about 4 weeks, 9 male subjects exercised on a bicycle ergometer seven times per ‘day’ during two weeks and refrained from physical activities during the other 2 weeks. The freerunning circadian rhythms of wakefulness and sleep and of rectal temperature showed, on the average, no difference between the two sections with regard to the autonomous period and the tendency towards internal desynchronization. Even in the one experiment in which the two rhythms became internally desynchronized, the periods of the rhythms remained unchanged during the time the subject worked on the bicycle. Only in one out of the nine subjects, the autonomous period was considerably longer under the influence of work than without it. The hypothesis is advanced that the period of an autonomous rhythm becomes normally independent of physical workload by way of a compensation mechanism.

Notes: Abstract The sleep-wake cycle and the circadian rhythm of rectal temperature were recorded in subjects who lived singly in an isolation unit. In 10 subjects, the freerunning rhythms remained internally synchronized, 10 other subjects showed internal desynchronization. Times of onset and end of bedrest (“sleep”) were determined in each cycle and referred to the phase of the temperature rhythm. In the synchronized subjects, onset of sleep occurred, on the average, 1.34 h before the minimum of temperature, and end of sleep 6.94 h thereafter, with narrow distributions. The desynchronized subjects had a broad bimodal distribution of sleep onsets (peaks 6.3 and 1.3 h before the minimum); the duration of sleep varied between more than 15 h when sleep began about 10 h before the temperature minimum, and less than 4 h when sleep began several hours after the minimum. The dependence of sleep duration on body temperature is interpreted as a continuing action of the coupling forces between the two rhythms after mutual synchronization is lost.

Notes: Zusammenfassung Durch Einstechen von Wärmequellen und Thermoelementen in die Haut sind an Zeigefingern verschiedener Versuchspersonen Wärmetransportzahlen parallel zur Hautoberfläche nach distal und nach proximal gemessen worden. Die beiden Wärmetransportzahlen nehmen im allgemeinen bei Anwachsen der gleichzeitig registrierten Hautdurchblutung in sehr unterschiedlichem Maße zu, die Haut ist also bezüglich der Wärmetransportzahl stark anisotrop. Diese Anisotropie ist von Person zu Person in ihrer Größe und sogar in ihrer Richtung unterschiedlich.

Notes: Abstract The relative effectiveness of external zeitgebers synchronizing circadian rhythms can be evaluated by mesuring the size of the range of entrainment. The experimental approach to measure entrainment limits is the application of an artificial zeitgeber with slowly and steadily changing period. In human circadian rhythms, an absolute light-dark (LD) cycle with a light intensity during L of 100 lux or less, results in an upper entrainment limit of 26.91±0.24 hours. The same limit is reached in constant illumination when only informations are given to the subjects. Consequently, the LD cycle is effective mainly with its behavioral component characterized by the request of the light-dark alternation to go to rest. In experiments with the same experimental protocol but higher intensity of illumination during L (∼400 lux, i.e., exceeding the threshold beyond which melatonin excretion is suppressed in humans), human circadian rhythms can be synchronized within a much larger range; the upper entrainment limit is, with all overt rhythms measured, beyond 29 hours. This means that bright light has an effect on the human circadian system which is qualitatively different from that of dim light, and which is similar to the effect of light in most animal experiments. This finding has theoretical and practical implications.

Notes: Abstract Under the influence of artificial zeitgebers, human circadian rhythms can be entrained only within limited ranges of periods; different overt rhythms may show different entrainment limits. When the period of a zeitgeber is varied slowly but continuously, entrainment limits can be evaluated precisely. An overt rhythm is synchronized to the zeitgeber only up to a certain day, or period respectively, until it breaks away from the zeitgeber and starts to freerun. The interindividual comparison among different subjects shows that the range of entrainment is positioned nearly symmetrically around the freerunning period. Its width depends strongly on the freerunning period; it increases with lengthening freerunning period. As the consequence, subjects with a freerunning period only slightly shorter than 23 h would fail to become synchronized to the natural 24-h day, whereas subjects with a freerunning period even slightly longer 28 h would become synchronized. In the intraindividual comparison, overt rhythms of different variables show different entrainment limits. For instance, rhythms in urinary excretion of different electrolytes can be dissociated for several days; the same is true with the rhythms of deep body temperature and performance. This temporal separation excludes the possibility of functional interdependencies between the variables under consideration. Consequently, results obtained with this method of fractional desynchronization do not only assist in evaluating properties of the circadian system, but also assist in the search for physiological interconnections between different variables.

Notes: Summary Using the physical and mathematical basis given in two foregoing papers, a differential equation is proposed for a model of the biological 24-hour-periodicity. This oscillation equation contains two characteristic non-linearities describing the self-sustaining property and the “circadian rule”. The right side of the equation (“external force”) represents the controlling environmental conditions, mainly the intensity of illumination. Solutions were obtained for different environmental conditions using a digital computer. Under “constant conditions” the solution of the equation describes oscillations self-sustained within a certain range of environmental conditions. In this range the oscillations fulfil the circadian rule, e.g. for light-active organisms: The frequency and the mean value of the oscillation increase with increasing light intensity; with an additional (arbitrary) threshold separating activity time and rest time for describing an activity rhythm, the α∶ρ (activity time ∶ rest time) ratio and the total amount of activity also increase. Under periodically changing environmental conditions five properties of the “Zeitgeber” used (two distinct intensities with twilight transitions) are variable and varied: The range of oscillation of the Zeitgeber, its frequency, its mean value, its L ∶ D ratio (time relation of light time and dark time), and the duration of the twilights. The most important of the examined properties was the phase angle difference between the (forced) oscillation and the (forcing) Zeitgeber. The general result for light-active organisms was: The phase of the oscillation advances relative to the Zeitgeber (in sofar as the oscillation is synchronized) if the period of the Zeitgeber, or its mean value, or its L∶D ratio, or the duration of the twilights increase. In dark-active organisms, the relation between phase angle difference and the mean value or the L∶D ratio is reversed. Exceptions to this general rule exist in the relation between phase angle difference and L ∶ D ratio if the “free running” period of the oscillation deviates too much from the period of a “weak” Zeitgeber (mainly in dark-active organisms) or if the duration of the twilights is too short (especially if the transitions are rectangular). Single exposures to light (or darkness) during constant conditions result in phase shifts depending in direction and amount on the phase of the oscillation at which the disturbance occured. The resulting response curves depend in range and form on the one hand on the time of measuring the phase shifts (either immediately or after several periods — in the steady state — following the disturbance) and, on the other hand, on the intensity of the initial illumination, on the duration, and on the intensity of the exposures, each in a different manner. Moreover, response curves effective in LD conditions deviate from those measured under constant conditions; the reason being the difference in the energy state of the oscillations in the two conditions. Therefore, it is impossible to derive the phase angle difference between the oscillation and a Zeitgeber in self-sustained oscillations from the measurement of response curves alone. The oscillation equation used contains only one free parameter, the frequency coefficient. If this coefficient is changed, the equation describes other biological rhythms. For instance, with a high value it describes the behaviour of single nerve cells, and that not only in cases of spontaneous rhythmicity (e.g. receptor cells) but also in cases of reactions to single or rhythmic stimuli. Moreover, the derived characteristics of the equation — especially the non-linearities — seem to be significant for other biological problems such as control mechanisms.

Notes: Summary The biological 24-hour-periodicity is based upon an endogenous (self-sustained) oscillation which is synchronized with the earth's rotation by periodically changing factors of the environment, primarily by the alternation of light and dark. These external „Zeitgebers” affect the phase of the endogenous oscillation. Theoretically, there are four different simple types of phase-control; all complicated types are combinations of these four types. In model experiments the behaviour of an oscillation in each of the four cases of phase-control is clearly demonstrated. The comparison of model experiments and biological experiments suggests that in organisms a specific combination-type of phase-control occurs. In this combination-type, a change in frequency is always positively correlated with a change in average level of the oscillation. Both parameters of the oscillation increase in light-active organisms and decrease in dark-active organisms with increasing light-intensity (“circadian rule”). In organisms both parameters are coupled by means of non-linear elements. The differential equation describing the 24-hour-periodcity is characterized by certain non-linearities. One of these makes the oscillation self-sustained and simultaneously couples the frequency of the oscillation to the average level, in the sense postulated by the circadian rule. The magnitude of the non-linearity is such that the resulting oscillation is intermediated between a harmonic and a relaxation type of oscillation, but has more characteristics of a harmonic oscillation. A second non-linearity which also couples frequency and level positively concerns the energy of recoil. All general properties of the biological 24-hour-periodicity can be reproduced by the described oscillator model. Some special properties (e.g. “pattern”) are more easily understood by the assumption of two coupled oscillators; the second oscillator, following the same general laws described above, is controlled by the first one. The oscillator hypothesis can be applied to biological periodicities with other frequencies; in general, the higher the frequency of a system the more the oscillation tends towards a relaxation type of oscillation.