# Principles of Synergetics

Since Hermann Haken wrote his book Synergetics several (successful) attempts have been made to apply his formalism to systems that can be described by rate equations. Haken himself applied his concept mainly to laser theory and proceeded to show the general capability of his approach to describe any system that is characterized by physically distinguishable states and natural transition probabilities between these states as well as a control parameter that can induce such transitions (Haken, 1990). Rate equations are the next step to transfer the concept of cellular automata from Wolfram (2002) (see chapter 1.1) into a mathematical formalism. We introduce time and probability to generate dynamics from the single elementary cells that ultimately form the pattern.

In this way it is inferred that the concept of cellular automata can describe biological systems by computational power as stated by Wolfram. A computer that is equipped with the capability of calculating rate equations and modelling states according to a given algorithm might eventually compute the evolution of our biosphere by iterative generation of each single step in this process. This simulation can be done with rate equations modeling the development of cellular automata.

For a simulation of the biosphere’s evolution, formal constraints might be added to that concept, such as the fact that organisms need a special environment and food supply and that their living space is limited. However, on the molecular level these constraints, which appear according to the competition in the biosphere, might arise as a product of the calculation itself as growth leads to limitation.

Such approaches to simulate complex systems generally deliver qualitative results as the outcome depends crucially on the exact values of single transfer steps and the initial conditions. Both cannot be computed with absolute accuracy but deviate in such ways that the system becomes inpredictable after a few cycles. Such models can make complexity understandable in general or they can show the development of selfsimilarity. However, any attempt is far from a quantitative description of evolution as it is observed in our biosphere. One example is the well known “game of life”. Here the constraints of the system - typically the size of the system, the growth dynamics that depend on size, possible food supply factors or predators and their interaction strength - determine the final “phenotype” of the structure.

The limited space but more likely the structure and the composition of the earth at the beginning of this “game of life” should of course, set the initial conditions.

This concept, the concept of the “game of life”, is well known and therefore represents a generalized description formalism that can be used to imitate the generation and decay of reactive oxygen species (ROS) in plants, the interaction of ROS with other chemical compounds, ROS networking and its impact on the resulting plant morphology. The approach is straightforward. Therefore it appears surprising that only few attempts have been made to use time dependent “cellular automata”, which are able to describe the dynamical development of any system, to describe and model biological systems. We provide examples for the general application of rate equations to biological systems: the simulation of the PS II dynamics after light absorption is shown in chapter 2.6 for excitation energy transfer (EET) in light-harvesting complexes, and in chapter 2.7 for electron transfer (ET) processes in the thylakoid membrane.

Haken pointed out how novel and synergetic approaches can be used to better understand the function of the human brain. This approach is useful to find the link that connects complex systems to the general interaction of single compounds and to entities in macroscopic systems, a link that is still not completely understood. We intend to shift the focus to novel ideas and approaches and believe that ROS in photosynthetic organisms paves the road for further concepts that in their turn might help develop new experiments that are suitable to elucidate currently unknown topics, such as the missing links between ROS driven communicating networks. It might be of higher relevance to understand such links between communicating networks than the single steps inside the networks. The accurate quantitative output of a product like this is dependent on exact parameter settings and simply cannot be predicted with absolute accuracy.

This book transfers the very general concepts developed in Haken’s book Synergetics to the specific application of its formalism to signaling networks driven by ROS. It elucidates some mechanisms of coupled top down and bottom up signaling. These ideas are embedded into an overview of basic principles of photophysics and photobiology, lightharvesting, charge transfer and primary processes of photosynthesis and nonphotochemical quenching in plants and cyanobacteria. Therefore, the reader can identify and compare the proposed ideas with a large review of the current state of knowledge in the discipline. The recent knowledge of ROS monitoring, generation, decay and signaling in plant cells and cyanobacteria is presented in the following chapters alongside a number of novel reaction schemes for the production of secondary ROS and inter-organelle signaling.

Understanding the role of reactive oxygen species is a key factor for efficient strategies to target basic research on primary plant metabolism and crop enhancement. Furthermore, the understanding of deleterious effects and protection from ROS is of high interest in diagnostics and therapy of many diseases and can have further biomedical applications, for example ROS play a distinct role in carcinogenesis and ROS form the main therapeutic substrates in photodynamic therapy. Cells control ROS levels by tuning generation and scavenging mechanisms. It was recently shown that cancer cells seem to be characterized by even more sensitive fine adjustment of ROS levels as they contain higher contents of antioxidants and a more stable ROS concentration (Liou and Storz, 2010). Therefore control of ROS is an attractive target for therapeutic concepts in cancer treatment.

Underlying mechanisms such as enhanced metabolic action as well as changes in cellular signaling are key factors in the development of novel therapeutic concepts. While findings on plant cells are not easily transferable to mammalian cells, the suggested strategies are generalized to emphasize medical applications. The book focuses on the stimulation of new ideas for research strategies and experiments that help develop biological and medical progress.