Circadian Phase Entrainment via Nonlinear Model Predictive Control

Unpublished AIChE shall not be responsible for statements or opinions contained in papers or in its publications. 1 A nonlinear model predictive control algorithm is developed to investigate the phase resetting properties of robust nonlinear biological oscillators; in particular, those of the circadian rhythm. This pacemaker is an autonomous biochemical oscillator with a free-running period close to 24 hours. Research in chronobiology indicates that a light stimuli may delay or advance the phase of the oscillator, allowing it to synchronize physiological processes and entrain to the environment. In this paper, a closed-loop optimal phase tracking control algorithm is developed and applied to a Drosophila circadian model. Through use of nonlinear MPC, optimal phase entrainment is investigated and compared to natural phase resetting via light:dark cycles. A well-studied example of a biological oscillator is the circadian clock. The term circa-(about) diem (a day) describes a biological event that repeats every 24-hours. Such rhythms are possessed by most organisms, acting as a biological clock. They are observed at all cellular levels since oscillations in enzymes and hormones affect cell function, cell division, and cell growth [1]. Circadian rhythms serve to impose internal alignments between different biochemical and physiological oscillations. Their ability to anticipate environmental changes enables organisms to organize their physiology and behavior such that they occur at biologically advantageous times during the day [1]. An inability to entrain circadian phase to the environment or anticipate change causes many functional disorders. Circadian disorders include non-24-hour sleep-wake syndrome (often due to blindness), rapid time-zone change syndrome (jet lag), work-shift syndrome (impaired sleep and alertness due to unusual work times), advanced or delayed phase sleep syndrome, and irregular sleep-wake pattern syndrome [2]. Such disorders are often caused by circadian oscillators that are out of phase with the environment, and thereby hinder one's performance. Many researchers have studied the clock in an attempt to both understand and resolve existing phase discrepancies. Daan and Pittendrigh, for instance, discussed light-induced phase shifts as a function of circadian time and the role phase response curves play in achieving entrainment [3]. Watanabe et al. confirmed Daan and Pitten-drigh's work through experimental procedures proving that the basis for phase adjustment involves rapid resetting of both advance and delay components of the phase response curve [4]. Boulos et al. performed similar experiments establishing bright light treatment as a means to accelerate cir-cadian re-entrainment following transmeridian travel [5]. Despite the decades of …