Chemical Organisation Theory

Abstract

Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory consists of two parts. The first part introduces the concept of a chemical organization as a closed and mass-maintaining set of components. This concept allows to map a complex (reaction) network to the set of organizations, providing a new view on the system's structure. The second part connects dynamics with the set of organizations, which allows to map a movement of the system in state space to a movement in the set of organizations.Our world is changing, qualitatively and quantitatively. The characteristics of its dynamics can be as simple as in the case of a friction-less swinging pendulum, or as complex as the dynamical process that results in the creative apparition of novel ideas or entities. We might characterize the nature of a dynamical process according to its level of novelty production. For example, the friction-less swinging pendulum implies a process where the novelty is only quantitative. Whereas the process of biological evolution is highly creative and generates qualitative novelties, which then spread in a quantitative way.Fontana and Buss [1] called processes and systems that display the production of novelty, constructive (dynamical) processes and constructive (dynamical) systems, respectively. Constructive systems can be found on all levels of scientific abstraction: in nuclear physics, where the collision of atoms or subatomic particles leads to the creation of new particles; in molecular chemistry, where molecules can react to form new molecules; or in social systems, where communication can lead to new communication [2]. As a result of a combinatorial explosion, it is easy to create something that is new, e.g., a molecule or a poem that is unique in the whole known universe. Nevertheless, it should be noted that novelty is relative. Whether something is considered to be new or not, depends on what is already there. Thence it follows that whether a system 1 Both authors contributed equally.

Inferring reaction systems from ordinary differential equations

“…Such a direct activation of the phosphatase acting on phosphorylated cdc2 kinase is one of the hypothetical mechanisms originally put forward for cyclin action (7,22). A further assumption is that the maximum activity ofthe kinase inactivating cdc2-the cdc2 "inactivase" (7)-remains constant throughout the cell cycle.…”

“…For instance, in [19], it is elaborated that structural information hidden in kinetic laws may affect the results obtained from structural analyses, such as elementary mode analysis [20], flux balance analysis [21], chemical organization theory [22], deficiency analysis or chemical reaction network theory [23,24].…”

Organization-Oriented Chemical Programming

“…Definition 2 (self-maintenance [9]). Given an reaction network M, R , let i denote the i-th molecular species of M and the j-th reaction rules is (A j → B j ) ∈ R. Given the stoichiometric matrix M = (m i,j ) that corresponds to M, R where m i,j denotes the number of molecules of species i produced 1 in reaction j, a set of molecular species S ⊆ M is self-maintaining, if it there exists a flux vec-…”

“…[9] states that given a differential equation describing the dynamics of a chemical reaction system and the reaction network corresponding to that system, then the set of molecular species with positive concentrations in a fixed point (i.e., stationary state), if it exists, is an organization. In other words, we can only obtain a stationary behavior with a set of molecular species that are both closed and self-maintaining.…”

“…Therefore a plethora of theoretical principles should be in our toolbox. One such tool is chemical organization theory [9]. The theory allows to relate reaction rules to the potential behavior they generate.…”