Information Technology Reference
In-Depth Information
Chapter 5
Synchronization of Circadian Neurons
and Protein Synthesis Control
Abstract
The chapter proposes a new method for synchronization of coupled
circadian cells and for nonlinear control of the associated protein synthesis process
using differential flatness theory and the derivative-free nonlinear Kalman Filter. By
proving that the dynamic model of the FRQ protein synthesis is a differentially
flat one its transformation to the linear canonical (Brunovsky) form becomes
possible. For the transformed model one can find a state feedback control input
that makes the oscillatory characteristics in the concentration of the FRQ protein
vary according to desirable setpoints. To estimate nonmeasurable elements of the
state vector the Derivative-free nonlinear Kalman Filter is used. The Derivative-
free nonlinear Kalman Filter consists of the standard Kalman Filter recursion on
the linearized equivalent model of the coupled circadian cells and on computation
of state and disturbance estimates using the diffeomorphism (relations about state
variables transformation) provided by differential flatness theory. Moreover, to
cope with parametric uncertainties in the model of the FRQ protein synthesis
and with stochastic disturbances in measurements, the Derivative-free nonlinear
Kalman Filter is redesigned in the form of a disturbance observer. The efficiency
of the proposed Kalman Filter-based control scheme is tested through simulation
experiments.
5.1
Overview
The chapter studies synchronization of networks of circadian oscillators and control
of the protein synthesis procedure performed by them. Circadian oscillators are
cells performing protein synthesis within a feedback loop. The concentration of
the produced proteins exhibits periodic variations in time. In humans, circadian
oscillators are neural cells which are found in the suprachiasmatic nucleus of the
hypothalamus and which are coupled through the exchange of neurotransmitters.
There are also peripheral circadian oscillators which are responsible for rhyth-
micity in the functioning of various organs in the human body. The peripheral
