Circadian phase entrainment via nonlinear model predictive control

Abstract

SUMMARYA 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 h. Research in chronobiology indicates that 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 mammalian circadian model. The integration of MPCbased light pulses, coupled with environmental light:dark cycles, allows the circadian system to recover phase differences within 1.5 days}a fraction of the natural open-loop simulated mammalian recovery time. Accelerated phase entrainment may alleviate disorders caused by circadian rhythms that are out of phase with the environment, and improve performance.

Synchrony and entrainment properties of robust circadian oscillators

“…Such results support the hypothesis that, in general, natural light/dark cycles are not optimized to reset large phase differences (Bagheri et al 2007). Instead, organisms may have evolved to efficiently reset small phase differences since rapid transit across multiple time zones is a recent innovation.…”

“…Circadian synchrony and entrainment N. Bagheri et al S23 means of resetting the organisms' phase (Bagheri et al 2007). Through MPC, we were able to eliminate an induced phase difference between an organism (whose biological clock is modelled as a single deterministic oscillator) and the natural 24 hour light/dark environment.…”

“…Once the controlled state trajectories converge to within 15% of the reference state trajectories, the system is considered to have recovered its phase in T r Z min k ½jeðkÞj N % 0:15 hours. For further details concerning the development and implementation of MPC as applied to circadian networks, the reader is referred to Bagheri et al (2007).…”

Biological switches and clocks

“…Tyson et al molecular mechanism that has provided a challenging problem for mathematical modellers (Emberly & Wingreen 2006;Mehra et al 2006;Mori et al 2007;van Zon et al 2007). Many crucial properties of circadian physiology, such as temperature compensation, synchronization and phase resetting, are inherently dynamical in nature and require precise theoretical descriptions to be understood and managed (Ruoff 1992;Rand et al 2004;Stelling et al 2004;Ruoff et al 2005b;Kurosawa & Iwasa 2005;Bagheri et al 2007;Hong et al 2007). In this special issue, Bagheri et al (2008) used systems-theoretic tools (mathematical control theory) to explore the phase response characteristics of a noisy circadian clock model, in order to understand how populations of oscillators entrain one another to generate a robust rhythm and how the rhythm re-synchronizes to an external 24 hours light-dark cycle from an initial 8 hours phase shift (say, flying between Chicago and Paris).…”

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).…”