Self-organising systems

Equilibrium thermodynamics was developed about 150 years ago. It is concerned only with the achievement of an equilibrium state, without taking into account the time which a system requires for the transition from an initial to a final state. Thus, only the thermodynamics of irreversible processes can be used to describe processes which lead to the formation of self-organising systems. Here, the time factor, and thus also the rate at which material reactions occur, is taken into account. Evolutionary processes are irreversibly coupled with temporal sequences, so that classical thermodynamics no longer suffices to describe them (Schuster and Sigmund, 1982). 

Two further forces operate in any colloidal suspension or self-organised system. The first is due to Onsager and to Langmuir [54-56] who explained colloidal stability of clays and cylindrical particles in terms of purely repulsive... 

In our opinion these are self-organising systems that spontaneously form dissipative structures above certain characteristic volume concentrations. Such structures form in non-isolated systems far removed from thermodynamic equilibrium, where the determining variables satisfy non-linear dynamic laws. (For his pioneering work in this field the Belgian physical chemist Ilya Prigogine was awarded the Nobel prize for chemistry in 1977.) Furthermore, the conductivity of the polymers that form the structures can in our opinion be explained better by the assumption that freely mobile electrons are present within particle structures only a few nanometres in size. 

The aim of this Section is to describe the usefulness of non-equilibrium thermodynamics in understanding the relationship between structure and properties in colloidal or microemulsion systems, (I hope to convince polymer and colloid scientists to learn from progress made in self-organising systems in other fields.)... 

The threshold between order and chaos seems to be an essential requisite of complex adaptive self-organising systems (order at the edge of chaos). As these systems are dissipative, an order through fluctuations is effective in working between the above mentioned conditions. 

Fig. 8.2 A self-organising system needs a flow of energy. To continuously overcome the loss of entropy due to irreversible processes, it must be coupled to a flow delivering energy in a low entropy form and dissipate it under the form of heat or inactivated chranical derivatives...

The method has severe limitations for systems where gradients on near-atomic scale are important (as in the protein folding process or in bilayer membranes that contain only two molecules in a separated phase), but is extremely powerful for (co)polymer mixtures and solutions [147, 148, 149]. As an example Fig. 6 gives a snapshot in the process of self-organisation of a polypropylene oxide-ethylene oxide copolymer PL64 in aqueous solution on its way from a completely homogeneous initial distribution to a hexagonal structure. 

Keeley, F.W., Bellingham, C.M., and Woodhouse, K.A., Elastin as a self-organising biomaterial Use of recombinantly expressed human elastin polypeptides as a model system for investigations of structure and self-assembly of elastin, Philos. Trans. R. Soc. Lond. B Biol. Sci., 357, 185-189, 2002. 

M. Mulholland, D.B. Hibbert, P.R. Haddad and P. Parslov, A comparison of classification in artificial intelligence, induction versus a self-organising neural networks. Chemom. Intell. Lab. Systems, 30 (1995) 117-128. 

In addition, the authors suggest that all such systems must have a semi-permeable active boundary (membrane), an energy transduction apparatus and (at least) two types of functionally interdependent macromolecular components (catalysts and records). Thus, the phenomenon of life requires not only individual self-replication and self-sustaining systems, but it also requires of such individual systems the ability to develop a characteristic, evolutionary dynamic and a historical collectivist organisation. 

Hazen and Deamer looked at the chemical and physical properties of the end products of hypothetical prebiotic reactions carried out under extreme conditions of pressure and temperature, for example in CCh-rich regions of hydrothermal vents. The results of laboratory experiments indicate that prebiotic syntheses leading to a variety of products could have occurred in hydrothermal systems some of these have amphiphilic properties, and would have been capable of self-organisation processes. 

The authors chose pyruvic acid as their model compound this C3 molecule plays a central role in the metabolism of living cells. It was recently synthesized for the first time under hydrothermal conditions (Cody et al., 2000). Hazen and Deamer carried out their experiments at pressures and temperatures similar to those in hydrothermal systems (but not chosen to simulate such systems). The non-enzymatic reactions, which took place in relatively concentrated aqueous solutions, were intended to identify the subsequent self-selection and self-organisation potential of prebiotic molecular species. A considerable series of complex organic molecules was tentatively identified, such as methoxy- or methyl-substituted methyl benzoates or 2, 3, 4-trimethyl-2-cyclopenten-l-one, to name only a few. In particular, polymerisation products of pyruvic acid, and products of consecutive reactions such as decarboxylation and cycloaddition, were observed the expected tar fraction was not found, but water-soluble components were found as well as a chloroform-soluble fraction. The latter showed similarities to chloroform-soluble compounds from the Murchison carbonaceous chondrite (Hazen and Deamer, 2007). 

Eigen s theory describes the self-organisation of biological macromolecules on the basis of kinetic considerations and mathematical formulations, which are in turn based on the thermodynamics of irreversible systems. Evolutionary processes are irreversibly linked to the flow of time. Classical thermodynamics alone cannot describe them but must be extended to include irreversible processes, which take account of the arrow of time (see Sect. 9.2). Eigen s theory is based on two vital concepts ... 

Hans Kuhn, who described his own models in an article on the Self-organisation of Molecular Systems and the Evolution of the Genetic Apparatus (Kuhn, 1972), also worked in the Max Planck Institute for Biophysical Chemistry in Gottingen. Eigen... 

Cycle 3 this is the membrane growth cycle. The starting material for the outer envelope of the system comes from cycle 1 and is capable of self-organisation processes which lead to the membrane (T. Ganti, 1997). 

Self-organisation is a property of complex systems these are an important area of physics and have been studied intensively in the last few years. Since 1993, the Max Planck Society has had an institute for Physics of Complex Systems in Dresden. This is an interdisciplinary research area, dealing with problems which span the range from the cosmos to the living cell. 

Genuine self-organisation, i.e., self-organisation as a property of the system. Here, a system with a high degree of complexity organises itself under certain conditions. A typical example is Eigen s hypercycle model (see Sect. 8.3). 

Dissipative self-organisation, for example in evolving systems. 

Systems with dissipative self-organisation are important for processes which lead to biogenesis. These are open systems, the internal state of which is dominated by a disequilibrium far away from the equilibrium state. 

According to Stuart Kauffman, self-organisation processes initiate a trend which leads to more complex states of the system. In living systems, there are two forces which determine order (Kauffman, 1995) ... 

Attempts have recently been made to link the RNA world with the lipid world. Two groups involved in RNA and ribozyme research joined up with an expert on membrane biophysics (Szostak et al., 2001). They developed a model for the formation of the first protocells which takes into account both the most recent experimental results on replication systems and the self-organisation processes of amphiphilic substances to give supramolecular structures. 

D. W. Deamer and J. P. Dworkin have reported in detail on the contribution of chemistry and physics to the formation of the first primitive membranes during the emergence of precursors to life the authors discussion ranges from sources of amphiphilic compounds, growth processes in protocells, self-organisation mechanisms in mixtures of prebiotic organic compounds (e.g., from extracts of the Murchison meteorite) all the way to model systems for primitive cells (Deamer and Dworkin, 2005). 

Self-organisation of surfactant molecules in a water-surfactant system... 

The point is that this approach ignores the distinctive feature of the bi-molecular process - its non-equilibrium character. The fundamental result known in the theory of non-equilibrium systems [2, 3] is that they tend to become self-organised to a degree which could be characterised by the joint correlation functions, Xv(r, t) and Y(r, t). The idea to use n t)r as a small parameter were right, unless there are no other distinctive parameters of the same dimension as tq. 

Of special interest is the so-called Belousov-Zhabotinsky class of similar reactions [4, 6-12], This system can serve as an extremely successful example of self-organisation proper mixing of several liquids in a given proportion and at certain temperature demonstrates practically all kinds of the autowave processes just mentioned. 

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