Optimal control of self-organized dynamics in cellular signal transduction

• Published in: Mathematical and computer modelling of dynamical systems Vol. 13; no. 5; pp. 487 - 502
• Main Authors: Slaby, O., Sager, S., Shaik, O. S., Kummer, U., Lebiedz, D.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.10.2007
• Subjects: AMS Subject Classifications: 37N25; 49J15; 90C11; Bang-bang control; Biochemical oscillations; Circadian clock; Direct multiple shooting; Inverse problems; Mixed-integer optimal control; Self-organization; Signal transduction
• ISSN: 1387-3954; 1744-5051
• DOI: 10.1080/13873950701243969

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.