Control and optimization of complex biological systems

Healthy and stable state of complex biological systems lies in the narrow region between chaos and frozen state. The cause of chaos is often small initial change in starting conditions, quickly spreading and leading to system wide changes. For example, few microbial pathogens can quickly lead the host to the serious illness and even death. By the definition, an attractor in a certain dynamical system is a set of physical properties toward which this system tends to evolve, regardless of the starting conditions. It is not easy to control chaos and move system from attractor back to the stable state. This is even more difficult in case of hyperchaos with more attractors. Existing control strategies are passive; modify control parameters and wait until system lends in a future, hopefully stable state. At there is a clear need for more efficient control strategy, we propose the optimization of the matrix representing an evolution operator of the system under the control. Matrix elements are system state functions, and function variables are control parameters. Eventually, optimizing this matrix with respect to some goals can help to drive system back to stability. On the case of Samoyed dog lady attacked by methicillin-resistant and multi-species bacterial pathogens, we were able to identify the chaotic system with at least three attractors; two of them leading the system into the illness, and one driving it back to the healthy state. Consecutively, we established the matrix of its evolution operator and discussed some ways of the matrix optimization, in a hope our approach might help to develop therapies that are more efficient. Not of the less importance, we hope our experience with integrative therapy including standard therapeutics, herbal extracts and homeopathic remedies could help a clinician confronted with a similar case.