Phase tracking and restoration of circadian rhythms by model-based optimal control

Abstract

Periodic cellular processes and especially circadian rhythms governed by the oscillating expression of a set of genes based on feedback regulation by their products have become an important issue in biology and medicine. The central circadian clock is an autonomous biochemical oscillator with a period close to 24 h. Research in chronobiology demonstrated that light stimuli can be used to delay or advance the phase of the oscillator, allowing it to influence the underlying physiological processes. Phase shifting and restoration of altered rhythms can generally be viewed as open-loop control problems that may be used for therapeutic purposes in diseases. A circadian oscillator model of the central clock mechanism is studied for the fruit fly Drosophila and show how model-based mixed-integer optimal control allows for the design of chronomodulated pulse-stimuli schemes achieving circadian rhythm restoration in mutants and optimal phase synchronisation between the clock and its environment.

A systems theoretic approach to analysis and control of mammalian circadian dynamics

“…Prior studies have analyzed several of these systems under the lens of control theory including glycolytic oscillators [91], the drosophila circadian clock [27, 91–93], and the light-responsive human clock [28, 29]. Leveraging computational models of the circadian clock and the tools outlined in the prior section, it is possible to formulate feedback controllers for the manipulation of clock phase, clock amplitude, or entrainment.…”

“…Prior studies have formulated these as mixed-integer optimal control problems, yielding a reduction in computational complexity, though this remains prohibitively computationally expensive [91, 93]. Alternate control implementations could be evaluated by comparing the time required to perform phase shifts for a variety of desired shifts and initial conditions.…”

Circadian Phase Control Using Adaptive Synchronization

“…For theoretical description of these rhythms, recent studies have contributed in constructing the mathematical models Gonze et al (2000); Franois (2005); Goldbeter (1995); Becker-Weimann et al (2004). For control theory, several control strategies have been investigated to tackle the phase deviation issue such as nonlinear model predictive control Bagheri et al (2007aBagheri et al ( , 2008, optimal control Shaik et al (2008), and nonlinear output feedback control Tonthat and Ding (2012).…”

Time optimal control of spiking neurons

“…The results might also be relevant for other stimulated oscillators for which a phase reduction can be performed. In the biological context, this could include the heart as stimulated by an artificial pacemaker, or an organisim's circadian rhythm as stimulated by light or chemicals (Forger and Paydarfar 2004;Revell 2005;Shaik et al 2008).…”