Order, structure, physical organization and biological organization. Frontier Perspectives | June 22, 2005 | Grandpierre, Attila | Copyright Abstract In order to understand the nature of life, we exemplify and define the concepts of order, structure, physical organization and biological organization. Pointing to the dominant role of possible microstates over the realized ones in the concept of entropy, we obtain further quantitative insight into the relation of biological organization with the realm of possibilities. We illustrate the entropic behavior of living organisms on the S(E) diagram. Our results tell that entropy increase generates further possibilities that are favorable for biological organization. Self-organization as ordering Until now, the concepts of self-ordering and self-organization have been somewhat confused. This confusion is devastating since the way to understand life apparently leads through these two concepts. Recently, there has been a trend toward clarification of the concept of entropy to free it from misconceptions identifying entropy with disorder. (1-6) "Of all the difficult concepts of classical physics ... the most difficult is entropy." (2) Biological organization and order should be added to the list of most difficult concepts. Self-organization is a term frequently used to cover ordering processes, as well. Schrödinger thought that "life seems to be orderly and lawful behavior of matter." (7) He identified entropy with disorder (though we now know that entropy and disorder are not identical), and so obtained that order is the negative of entropy. (7) Prigogine attempted to describe self-organization as 'order through fluctuations.' 8 Following Prigogine, Jantsch, in his book The Self-Organizing Universe, attempts to describe prebiotic evolution, the functioning of bioorganisms, neurophysiology, ecology, sociobiology, and cosmic evolution, in terms of dissipative structures and the development of order from fluctuations. (9) It is widely thought that order may come "free," that order may come out of chaos. (10-11) Recently, the view that biological organization also comes for free has become popular. (10) Haken stated that a system is self-organizing if it acquires a spatial, temporal or functional structure without specific interference from the outside. (12) At the same time, he regards as typical examples of self-organization fluids heated from below, or lasers. On the basis of synergetics, he approaches biological organisms as physical systems. Knyazeva notes that synergetics is the search for laws of the formation of structures, of the emergence of order out of chaos. (13) Ordering is Different from Organization Conversely, there are people who observe that the concept of order and organization is confused because biological organization is not identical with physical ordering. Denbigh already realized the fundamental difference between order and biological organization. (14) For example, a crystal is more ordered but less organized than a living cell. Elitzur realized that an unexposed film is in a very special state that can be thought of as arranged by a refined ordering of the molecules, while its exposure to light makes it less ordered (losing its special original order) but full of information. (15) Applying Schrodinger's measure of order, the unexposed film is more highly ordered since it has less entropy than the final state that develops due to exposure. At the same time, the potential chemical energies of molecules to be liberated upon exposure are evenly distributed. After exposure, the situation reverses. Part of the potential chemical energies of the molecules will be liberated, but, at the same time, the distribution of different molecules in the end state will be highly heterogeneous. In contrast, living cells also have high chemical energies, which are liberated at decay, like the film molecules under exposure. At the same time, the cells have the capability to regenerate or reassemble themselves. In terms of Elitzur's film example, this would be like a film's ability to self-regenerate its original unexposed state, while simultaneously generating different, global patterns from time to time and from site to site, as living cells do permanently. Transforming Elitzur's film example to the case of living cells, we realize that the origin of structures seems to be only the physical half (thermodynamically downhill path) of life. The other half (thermodynamically uphill path) is the self- regenerative half. In this paper, we trace the path from order to structure, physical organization and biological organization, and point out the significance of entropy for our understanding of organization. Ordering and Structure Generation as Partial Aspects of Biological Organization The general belief is that complexity arises at a threshold somewhere between chaos and order. It seems that this notion does not exclude some ambiguities. For example, crystals show order; nevertheless, crystals arise from liquids or gases. Gases are chaotic ensembles of atoms or molecules. Now if complexity is between chaos and order, then complexity is similar to liquids. Liquids are either homogenous or amorphous. Neither of these properties are characteristic to complex systems and life. Moreover, beginning with Descartes, it has been widely thought that living organisms are nothing more than highly complex machines. Notwithstanding, Yockey pointed out that when complexity is considered as the non-compressible algebraic information content, high complexity means that a long algorithm is needed to describe the system, and therefore, highly organized systems have large entropy. (3) This means that highly organized systems and highly ordered ones occupy the opposite ends of the entropy scale; among the random sequences, the highly ordered are at the low end of the spectrum and the highly organized ones at the high end. Elitzur pointed out that randomness is related to the absence of relations between the set of elements representing the system, and one would expect that organisms, as their elements are significantly related by biological organization, are in a large distance from randomness. (16) The arising Yockey- Elitzur paradox has a crucial importance and may be resolved when realizing that organization acts between different molecules, all of which have relatively high entropies and randomness, yet simultaneously are related to each other. Certainly, the conformational states of proteins change dynamically in cells, for they are related to the government of cellular reactions occurring at a typical rate of more than [10.sup.5] reactions per second. (17) Individual proteins have a very large set of possible conformational states (~[10.sup.60]), and therefore relatively high entropies. At the same time, the conformational states of different proteins have to be coordinated; therefore their relation to each other is not random. More concretely, the conformational state represents a highly special state obtained from an extremely large set of possibilities, and so it has high entropy; thus while its selection from the set of possibilities can be regarded as random, the relation of a protein to other molecules (which also represent high entropy) is not completely random, but a very special type of relation, also highly entropic. Biological organization creates very special couplings from an extremely large set of possibilities of the interactions of proteins with other chemicals. High entropy is favorable for more possible states of molecules, as well as for more possible states of the interactions themselves. Therefore, even if the relations between molecules have an aspect of structure, if we regard these relations as exemplifying a kind of order, it would not be a type of order characterized by low entropy. Order, Structure, Physical Organization and Biological Organization 'Order' is frequently described as showing structures (A). Structures are widely regarded as arising in self-organization (B). Self-organization is widely regarded as being identical with biological organization (C). Now if A=B=C, then A=C, therefore, biological organization and ordering can be identical. We disagree, and try to call attention to the basic differences between these concepts besides the similarities. To avoid misunderstandings, we exemplify the instances of order, structure, physical organization and biological organization. Order is exemplified by crystals, magnets, etc. We define order as a constant relation between neighboring constituent elements of a system. Order usually arises by repeating the basic, simple constant relation or arrangement of neighboring elements, and therefore crystals, magnets, etc., show simple patterns, repeated basic arrangements of neighborhood elements. If we denote one unit (denoted by 1) the atoms or molecules of crystal, or the spins of a magnet, etc., the order can be characterized by the number sequence 111 ... Structures are exemplified by snowflake, molecular structure, stellar structure, or landscape, etc. We define structure as a more complex arrangement of elements. Therefore, we regard 'structure' as 'complex order.' Denoting the similar units by the same digits, a structure is described by a series of digits like 121212 ... or more complex sequences or fields of sequences. We exemplify 'physical organization' by turbulence, Benard convection, or reaction-diffusion systems like the Belousov-Zhabotinsky reaction. Such phenomena are widely regarded as showing 'dynamic