Ambient light at night causes desynchronization of rhythms in the sleep–wake switching model

The purpose of this study is to analyze the influence of the shape of the daily illumination profile on the synchronization of rhythms in the sleep–wake state switching model. Normally, the alternation of sleep and wakefulness of a person is synchronized with his circadian rhythm and with the 24-hour rhythm of illumination. There is, however, a lot of experimental evidence of a violation of this synchronism, both in the form of phase failures (for example, during air travel) and in the form of long-term mismatch of rhythms (for example, during shift work in production). Mathematical models of the process of switching between sleep and wakefulness also demonstrate the desynchronization of rhythms and are successfully used to optimize work schedules. At the same time, the influence of a number of factors on this process has not been sufficiently studied, including the nature of changes in illumination during the day. Methods. An analysis of the six-dimensional model under study shows that, in terms of nonlinear dynamics, the problem is reduced to finding and interpreting resonance regions on a three-dimensional torus. For the specific purposes of our work, it turned out to be convenient to estimate the ratio of three periods (24 hours, the circadian period, and the current duration of the sleep–wake cycle) by numerically integrating the model equations on a grid of parameter values using parallel computing technology. The main result of our work is that the presence of round-the-clock low-intensity illumination (that is, the addition of a zero-frequency signal to the daily light cycle) causes the circadian rhythm to desynchronize with respect to the daily one in a significant range of parameters. We have proposed an explanation of this effect based on the structure of the mathematical model. Conclusion. Our results raise at least two serious questions, the first of which is related to the physiological interpretation of one of the main variables of the model, sleep homeostasis, and the second is to refine the assumptions that are used in the model description of the photoreceptor response. In any case, there are interesting prospects for further research.