Optimal control of self-organized dynamics in cellular signal transduction

Abstract

We demonstrate how model-based optimal control can be exploited in biological and biochemical modelling applications in several ways. In the first part, we apply optimal control to a detailed kinetic model of a glycolysis oscillator, which plays a central role in immune cells, in order to analyse potential regulatory mechanisms in the dynamics of associated signalling pathways. We demonstrate that the formulation of inverse problems with the aim to determine specific time-dependent input stimuli can provide important insight into dynamic regulations of self-organized cellular signal transduction. In the second part, we present an optimal control study aimed at target-oriented manipulation of a biological rhythm, an internal clock mechanism related to the circadian oscillator. This oscillator is responsible for the approximate endogenous 24 h (latin: circa dies) day-night rhythm in many organisms. On the basis of a kinetic model for the fruit fly Drosophila, we compute switching light stimuli via mixed-integer optimal control that annihilate the oscillations for a fixed time interval. Insight gained from such model-based specific manipulation may be promising in biomedical applications.

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.…”

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

“…free switching of ports in Simulated Moving Bed processes, [18,34], timedependent tray selection in batch distillation processes [32], unconstrained energy-optimal operation of subway trains [36], a simple F-8 flight control problem [20,32], optimal transit path determination for a submarine vessel [30], and phase resetting in biological systems [22,40,38]. Path-constrained arcs.…”

Reconciling periodic rhythms of large-scale biological networks by optimal control

“…Several approaches have been developed to control cyclic rhythms. Slaby et al [27] and Shaik et al [28] applied model-based optimal control to find appropriate strength and timing of light stimulus to suppress or restore the circadian rhythms of the Drosophila model. In these studies, light-sensitive parameters were taken as control variables a priori, i.e.…”