Rosennean Complexity and its Relevance to Ecology

Transcription

1 Rosennean Complexity and its Relevance to Ecology María Luz Cárdenas 1, Saida Benomar 1,2 and Athel Cornish-Bowden 1 * 1 Aix Marseille Univ, CNRS, BIP, IMM, Marseille, France, 2 Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas 66045, USA NOTE. This file is printed from the final accepted version of the paper. The PDF file typeset by the Journal will be available later. AUTHOR S CONTACTINFORMATION cardenas@imm.cnrs.fr sbenomar@ku.edu acornish@imm.cnrs.fr (corresponding author) telephone ARTICLE INFO Keywords: Robert Rosen, complexity, ecological systems, bacterial consortia, bacterial interactions, definition of life ABSTRACT Complexity is not the same as complicatedness: a system is complicated if it has many components, but it is complex if it cannot be modelled as a machine and has emergent properties. The theoretical biologist Robert Rosen argued that living organisms are complex in this sense, and his (M, R) systems provide a description of a living organism in which the central point is that organisms are closed to efficient causation, which means that all the specific catalysts needed for the organism to maintain itself must be produced by the organism 1

2 itself. This includes the catalysts needed to maintain the other catalysts. On the other hand an organism is not closed to material causation, because there must be a net overall irreversible process to provide the necessary thermodynamic driving force for metabolism. (M, R) systems are usually discussed in relation to individual organisms, but they can also be applied to interactions between different organisms, allowing analysis, for example, of how two or more species can exist in symbiotic relationships with one another, able to live together, but not separately. Application of Rosennean complexity to fields other than life is possible, as we discuss. Rosen s holistic vision of organisms, in which all components affect all others, has implications for the concepts of hierarchy and downward causation that are sometimes invoked in philosophical discussions, because it means that there is no hierarchy and no downward causation. 1. Introduction Robert Rosen s book Life Itself (Rosen, 1991), a summary of more than three decades of research on the nature of life, starting with Rosen (1958), presented what he called (M, R) systems or metabolism-repair 1 systems as a way to understand life. It has now been cited about 550 times in the science literature not a very large number for the major work of biology s Newton (Mikulecky, 2001). 2 Despite Rosen s interest in ecology, rather few of these citations have been in journals of ecology, just 12 in the past 10 years (Gabora et al., 2008; Kelso, 2008; Yates, 2008; Chemero and Turvey, 2008; Chemero, 2012; Turvey, 2008; Turvey and Carello, 2012; Robinson, 2009; Van Orden et al., 2010; Browne et al., 2012; Cilliers et al., 2013; Keirstead, 2014). Here we shall discuss in particular how (M, R) systems can be applied to ecological interactions between organisms. However, we must first discuss the distinction that Rosen made in Essays on Life Itself between complexity and complicatedness (Rosen, 2000, p. 44): A system is complex if it has noncomputable models this characterization has nothing to do with counting of parts or interactions; such notions, being themselves predicative, are beside the point. 1 Rosen s repair has very little to do with ordinary uses of the word in biology, and we prefer replacement, and we use this term in this article. In general it is not a good idea to change an original author s terminology, but in Rosen s case it can hardly be avoided. 2 This is probably due to the fact that his papers and books are difficult to read, because of the abstract mathematical language used. Readers are invited to consult a paper (Cornish-Bowden et al., 2007) that offers a non-mathematical explanation of Rosen s ideas for the general biological community. 2

3 In everyday language the adjectives complex and complicated are sometimes treated as synonymous, a tendency encouraged by dictionaries that give each as a definition of the other. However, Rosen (2000) insisted that they are different, as noted in the quotation above, and he regretted (Rosen, 2000, p. 43) that von Neumann had used the term complexity for what he regarded as complication. Even if one takes care to distinguish between the two adjectives, a problem arises with the nouns, because complicatedness is such a cumbersome term that there is a temptation to use complexity as the noun for both. This temptation should be resisted. Both Life Itself (Rosen, 1991) and Essays on Life Itself (Rosen, 2000) were published as part of a series entitled Complexity in Ecological Systems, and although there is comparatively little in them that is particularly related to ecology, he definitely saw his ideas as being relevant to ecology, as he made clear when he recalled a year that he had spent as a Visiting Fellow at the Center for the Study of Democratic Institutions in Santa Barbara (Rosen, 1979): I thus almost in spite of myself found that I was fulfilling an exhortation of Rashevsky, who had told me years earlier that I would not be a true mathematical biologist until I had concerned myself (as he had) with problems of social organization. At the time, I had dismissed these remarks of Rashevsky with a shrug; but I later discovered (as did many others who tried to shrug Rashevsky off) that he had been right all along. As with much of what Rosen wrote, his meaning in the first quotation does not immediately emerge at first reading: one needs to work at understanding him. The point is that a complicated system is one with many components, but with properties that can be regarded as the sum of the properties of the individual parts: in that sense a typical chart of metabolic pathways is complicated, but, as we shall see, it is not complex. Computer simulation of the entire metabolism of an organism has been attempted only by combining data from numerous sources (Karr et al., 2012), but some individual pathways have been simulated using kinetic parameters measured under uniform conditions, such as glycolysis in the bloodstream form of the parasite Trypanosoma brucei (Bakker et al., 1997; Eisenthal and Cornish-Bowden, 1998) and aspartate metabolism in Arabidopsis thaliana (Curien et al., 2009), a branched pathway with numerous isoenzymes, regulatory interactions, and multifunctional proteins, none of which can be taken into account by a stoichiometric model that does not incorporate kinetic equations. The results support the idea that the properties of the whole pathway are indeed the sum of the properties of the individual reactions (Van Eunen et al., 2012). However, simulations of this kind assume 3

4 the classical view of metabolism, in which the enzymes are given, 3 a view not shared by Rosen, who argued that an organism must be closed to efficient causation (Rosen, 1991), another somewhat obscure characterization, which can be understood to mean that all the specific catalysts (enzymes or ribozymes) needed by an organism must be products of the organism itself: organisms are therefore complex. Rosen s definitions are not exactly the same as those used by other writers interested in the essence of living systems, but they correspond approximately. The examples of kinetic metabolic models cited above were small models, with fewer than 15 reactions, and even for a metabolism as simple as that of the bloodstream form of Trypanosoma brucei this still falls far short of modelling the whole metabolism. Increased computer power and increased kinetic information about the reactions are bringing about large increases in the sizes of such models: for example, a recent kinetic model of liver metabolism (Berndt et al., 2017) is based on data for 221 reactions. Remember, however, that in the simulations of Trypanosoma brucei metabolism the enzymes were taken as given, the question of where they come from being ignored (it is assumed that their concentrations do not change during the period of simulation). This is also true of all of the other simulations of real metabolism that we are aware of, and it restricts the period of validity to a time frame in which protein synthesis is negligible, 2h for the model of aspartate metabolism in Arabidopsis thaliana (Curien et al., 2009), but possibly much shorter in other systems. The trend to larger models will certainly continue, but, if we accept Rosen s view, they will never be models of a whole organism, no matter how large and complete they become. In Life Itself Rosen (1991) argued that the essence of a living organism could be expressed as an (M, R) system in which the reactions are possible thanks to catalysts that are produced by the system itself. As mentioned earlier, we have changed the term repair by replacement, which is more exact: although DNA can be repaired to some degree, and inactivated proteins can sometimes be repaired by chaperones or other mechanisms, damaged enzymes are usually degraded and need to be resynthesized. This resynthesis is what Rosen meant by repair. His idea that catalysts (enzymes, whether protein or RNA, and also including transporters) play a crucial role and that they are synthesized by the organism is correct, as they participate, not only in classical metabolism, but also in DNA duplication, transcription, translation, as well in the degradation of different types of molecules. This, in essence, means that the catalysts needed for an organism to stay alive are products of the organism itself. Although the concept of an (M, R) system applies to modern organisms, it acquires special significance in relation to the origin of life (Cornish-Bowden and Cárdenas, 2008), 3 That is to say synthesis and degradation of catalysts are not considered in the models. 4

5 because in the transition from prebiotic to living organisms the intermediate entities must have been minimally simple. We have analysed Rosen s view of an (M, R) system, established its range of validity (Letelier et al., 2006), explained it in simple terms, defined simple examples to illustrate it (Cornish-Bowden et al., 2007), and compared his ideas of life with those of others (Jaramillo et al., 2010; Letelier et al., 2011; Cornish-Bowden, 2015). In these we have always considered the systems at issue to be single organisms, but Rosen s ideas also apply in more ecological contexts, and that is what we shall be concerned with here, specifically in the context of consortia of different species of bacteria. In the laboratory bacteria have usually been studied in pure culture, and supplied with the nutrients that they need. That is not how they exist in the wild, however: on the contrary, natural colonies of bacteria exist in ecological systems that contain many species, and in environments that lack some of the nutrients that some of the species need. They are often found in a biofilm, which has been likened to a city of microbes (Watnick and Kolter, 2000). We are not yet at the stage where we can usefully study such mixtures in Rosennean terms, but a consortium of two species, Clostridium acetobutylicum and Desulfovibrio vulgaris Hildenborough (Benomar et al., 2015) provides a starting point for studying more natural mixtures. Desulfovibrio vulgaris cannot grow in pure culture on glucose or other sugars, but it can grow on a medium with glucose as the sole carbon source if Clostridium acetobutylicum is present in the medium. This simple example will illustrate how Rosennean complexity might be applied to ecological systems. We may hope that in the future it may be possible to describe entire trophic chains in Rosennean terms, but for the present that would be too ambitious. 2. Metabolic closure and Aristotle s four causes 2.1. An organism is closed to efficient causation For defining (M, R) systems Rosen adopted Aristotle s classification of the four a t a ( aitia ), or causes, of which the only one that corresponds to the modern idea of a cause (derived from David Hume, 1748) is the efficient cause. Rosen understood this as the catalysts needed for life ( f, F and b in Fig. 1), whether protein, RNA or others. In saying that organisms are closed to efficient causation, he meant that all of the specific catalysts needed to be provided by the organism itself, with none of them being harvested from the environment. That applies almost without exception to metabolic reactions in life today, but highly specific catalysts did not exist at the origin of life, and the first self-maintaining systems must have used unspecific catalysts, such as Fe 2+ or Zn 2+, that were available 5

6 f A B Φ Fig. 1. Rosen s diagram showing the nature of an (M, R) system, redrawn from Fig. 10C-6 in Life Itself (Rosen, 1991). Chemical transformations are shown with open-headed arrows, mappings (catalytic actions in normal biochemical terminology) by arrows with filled heads. The meanings of the abstract entities A, B, f and F may be explained as follows: the mapping f (A)! B is the basic equation in Rosen s scheme, and corresponds in normal biochemical terminology to the set of enzymes that catalyse metabolism, transforming the set of food molecules A into the whole set of metabolites B. However, the system needs to persist in time, and f is subject to degradation, so it needs to be replaced from the set B by another mapping, F(B)! f. However, F also needs to be replaced, by the action of a new mapping b that acts on f : b( f )! F; b does not appear in Rosen s diagram (or in this Figure), but it is clear from his text that he regarded it as derived from B. Notice that f, b and F have dual characters as both mappings and as sets. In addition, notice that both types of arrows connect B to f, the arrow with a filled head corresponding to b: this was how Rosen sought to escape from what would otherwise be an infinite regress, a crucial concept in his view of (M, R) systems. from the environment, as well as even simpler catalysts, like H + and OH ions (Jencks, 1987). Rosen s text in his book (Rosen, 1991) to explain his diagram showing the nature of an (M, R) system, reproduced here as Fig. 1, is very difficult to understand, in part because his treatment is highly mathematical and abstract, and is expressed in terms of the theory of categories rather than in the far more widely known set theory. 4 Attempting to explain the diagram more simply we have added a long legend (missing from Rosen s book). The catalyst b played an essential role in Rosen s vision of life, and he returned to it again and again, but never explained it clearly, and he omitted it from the diagram, thereby giving the impression that the whole of B is the catalyst, a point that has confused some authors. We have tried to define the smallest possible (M, R) system, as shown in Fig. 2a, with identifiable chemical molecules. With two differences, this is the same as the example we have described and simulated previously (Piedrafita et al., 2010). First, we have enclosed the reactions inside a boundary. Rosen never considered such a boundary, but it is present around all modern cells, and is necessary for any ecological discussion, as one must be able to distinguish between one individual and another. At the origin of life a 4 We have discussed (M, R) systems in mathematical terms elsewhere (Letelier et al., 2006; Jaramillo et al., 2010), but here we keep the mathematics to a minimum. 6

7 (a) U (b) f Y STU S X STU SU U ST T Z catalysis organizational invariance replacement {S, T, U} metabolism {STU, ST, SU, X, Y, Z} STU SU A B β Φ Fig. 2. (a) A minimal (M, R) system (Cornish-Bowden et al., 2007; Cornish-Bowden and Cárdenas, 2007) capable of self-organization. A metabolic system that converts food molecules S, T and U into a product ST can maintain itself indefinitely even though the product and the catalysts STU and SU are subject to loss through degradation, or dilution due to growth or division. There are three catalysed reactions: S + T! ST, metabolism (more precisely classical metabolism, as the entire system constitutes metabolism), is catalysed by STU; ST + U! STU, replacement (repair in Rosen s terminology), is catalysed by SU; S + U! SU, organizational invariance (replication in Rosen s terminology), is catalysed by STU. To correspond better with normal biochemical practice, continuous arrows refer to chemical processes and broken arrows to catalytic interactions, and labels show what the arrows correspond to in our terminology. (b) Reorganization of the diagram to the arrangement of Fig. 1 clarifies the relationship between the two. Now b is shown explicitly as a property of B, and, as SU is a member of B, F is also a property of B. boundary fabricated by the organism itself probably neither existed nor was required, as a natural compartment in a mineral environment, or a spontaneously formed lipid membrane, might have been enough; however, it became necessary during evolution, and most other theories of life, such as autopoiesis (Maturana and Varela, 1980) and the chemoton (Gánti, 2003), explicitly include a membrane as a product of the self-organizing system. The second (trivial) difference is that we have given explicit symbols X, Y and Z to the excreted products, as these will be needed for the ecological example to be discussed. All of the metabolites are lost to the environment by irreversible reactions, STU! X, ST! Z and SU! Y, and the overall reaction S + T + U! X + Y + Z is assumed to be sufficiently thermodynamically favoured to drive the whole process. Notice also that Rosen treated the catalysts as acting on the reactants, because he regarded them as mathematical functions, or mappings, that transform reactants into products. Rearrangement of this scheme into the layout of Fig. 1, as shown in Fig. 2b, clarifies the relationship between our very small model and Rosen s general one, which can have any size, and will typically be very large. For modelling purposes the same system must be drawn in a way that shows the 7

8 U Y SUSTU SUST SU ST Z S X STU STUS STUSU STUST U T Fig. 3. Expanded view of the (M, R) system of Fig. 2. Although this appears to be more complicated than Fig. 2a it is in fact exactly the same, but now the intermediates in the catalytic cycles are shown explicitly. For example, instead of abbreviating the reaction catalysed by SU to a single reaction ST + U! STU, we have shown it as a sequence of three chemical steps, ST + SU! SUST; SUST + U! SUSTU; SUSTU! SU + STU; this last step regenerating the catalyst. As illustrated in Fig. 4, any enzyme-catalysed reaction can be shown as a simple reaction (Fig. 4a) if the intermediate steps are not shown explicitly (Fig. 4b). catalysed reactions as cycles of chemical reactions, as in Fig. 3. This may seem to be very complicated, especially for a system that purports to be a minimal example. However, any enzyme-catalysed reaction appears complicated if all the steps in the mechanism are shown explicitly, as exemplified by the reaction catalysed by hexokinase in Fig. 4. A more important question, however, is why the scheme needs to be even as complicated as the version in Fig. 2: why do we need to have as many as three cycles in a minimal model of an (M, R) system? The point is that there are (at least) three processes that must be included. There must be a process representing classical metabolism, the reaction S + T! ST catalysed by STU. However, STU will have a tendency to be lost, whether by lack of stability, or by diffusion across the enclosing boundary, or simply by dilution as the system grows. In any case, STU needs to be a product of the system, so there must be a replacement reaction ST + U! STU, catalysed by SU. However, SU is also subject to loss by the same properties as STU, and so it also needs to be replaced. This is where the idea of catalytic closure, or closure to efficient causation, becomes important. We could of course propose a new reaction, catalysed by a new catalyst, but that catalyst would also need to be replaced by a reaction with its own catalyst, which would also need to be replaced, and so on. We are clearly on the verge of an infinite regress, with each new reaction requiring another reaction with another catalyst. Rosen s way of escaping from the infinite regress was to require the system to be closed to efficient causation: in terms of Fig. 2 this means that at least one catalyst, STU in the example, needs to catalyse more 8

9 (a) (b) Glc Glc + ATP binding E (hexokinase) hexokinase E Glc ATP binding Glc-6P + ADP E Glc ATP chemical reaction release E Glc-6P E Glc-6P ADP release Glc-6P ADP Fig. 4. (a) An enzyme-catalysed reaction may appear fairly simple when represented as in a typical chart of metabolic pathways. (b) It appears much more complicated when all the intermediates are shown explicitly. However, the two representations are exactly equivalent. The order of product release shown is the one most often found, but not always (Monasterio and Cárdenas, 2003). than one reaction. In biochemistry the capacity of some proteins to fulfil more than one function is known as moonlighting. It usually refers to very different functions: for example, the glycolytic enzyme glyceraldehyde 3-phosphate dehydrogenase has as many as ten quite different functions, not only catalysing oxidation of glyceraldehyde 3-phosphate by NAD, its textbook role in metabolism, but also others, including even a structural role in the composition of crystallin in the vertebrate eye. Many examples are now known (Henderson and Martin, 2014; Copley, 2015), but to these must be added many cases of less than perfect specificity of enzymes with purely catalytic roles, and indeed, less than perfect specificity must be regarded as the rule rather than the exception. Perfect specificity is sometimes simply not possible for structural reasons, even in contexts where it would be desirable, such as the charging of trna molecules with the right amino acids, and additional mechanisms are needed to overcome the resulting problems (Fersht and Dingwall, 1979). Numerous metabolic reactions are now known to be sufficiently unspecific to create metabolic problems if left uncorrected (Van Schaftingen et al., 2015). In other cases lack of perfect specificity may allow organisms to compensate for missing activities (Copley, 2015). However, consideration of metabolic closure suggest that less than perfect specificity of catalysts may be an absolute necessity for life. Closure to efficient causation can be expressed by defining metabolism as a function that acts on metabolism to produce metabolism (Letelier et al., 2005), or, as an algebraic equation: f ( f )= f Downward causation incompatible with Rosennean complexity Papers of a philosophical nature often discuss such concepts as weak emergence and downward causation. For example, Bedau (2008) opens a discussion of weak emergence with the following words: 9

10 Weak emergence is the view that a system s macro properties can be explained by its micro properties but only in an especially complicated way. He goes on to argue that weak emergence is a real phenomenon, that involves a certain kind of downward causation, and that this kind of downward causation is irreducible in practice, due to explanatory incompressibility. How consistent is this with Rosennean complexity? In our view it is excluded by Rosennean complexity, as everything in Rosen s conception of metabolism depends on everything else: there is no hierarchy, and hence no downward causation in which a higher element in a system directs the behaviour of a lower element. Rosen did not discuss that point, but we consider that metabolic circularity excludes any possibility of a hierarchy, even though incomplete systems of reactions can sometimes be usefully discussed in terms of hierarchies: for example, Westerhoff et al. (1990a,b) and Boogerd et al. (2005) examined how to analyse hierarchies in which DNA controls mrna production, which controls protein production, which controls metabolic reactions. They also considered what they called democratic control, in which a metabolite may act on mrna translation. However, they recognized that it could not easily be reconciled with the ideas of metabolic control current at that time. This type of consideration also applies to human societies, or indeed to all ecological systems, because even if some individuals are more important than others, all contribute to the whole, and have at least some effect on the whole. Returning to the quoted sentence with which this section began, it is clear from the examples of metabolic models given earlier that if the system considered is just a part of a larger one then its macro properties, the properties of a metabolic pathway, for example, can indeed be calculated from its micro properties, the kinetic properties of the component reactions, but metabolic circularity rules out the possibility that that can apply to a whole organism. These considerations apply with even greater force to ecological systems, in which every member of a community depends on the community as a whole. The absence of a hierarchy has implications for the concept of signalling, which is often invoked in modern biochemistry. If everything affects everything else, then every change in every molecule is a signal of some kind, so the concept becomes trivial, or even meaningless. Nonetheless, some molecules, such as AMP, are substrates or products of very few metabolic reactions but play important roles in monitoring the metabolic status of the cell, and supply that information to different enzymes An organism is open to material cause The need for catalytic closure must not be taken to imply that an organism is also closed to material causation. That is quite different, and would make self-organization, 10

11 and thus life, impossible if it existed. The material cause of an enzyme-catalysed reaction is the set of reactants on the left-hand side of the chemical equation (whereas the efficient cause is the enzyme). In Fig. 4, therefore, glucose and ATP correspond to the material cause and hexokinase to the efficient cause. Closure to material causation would correspond to thermodynamic equilibrium, but a living system cannot be at thermodynamic equilibrium because it needs a supply of energy in the form of irreversible reactions. In Fig. 2 the reaction S + T + U! X + Y + Z is assumed to be irreversible, which implies that the reactants S, T and U are available in sufficient quantities and that the products X, Y and Z can be brought to negligible concentrations by processes that we do not need to consider here (though we shall consider them later in relation to communities of bacteria). In intermediary metabolism the driving force for most reactions is transfer of a phosphate group from ATP, but in all known organisms the ultimate driving forces are redox reactions, oxidation by molecular oxygen in aerobic organisms, or other sources of oxidizing power, such as sulphate or nitrate ions, in anaerobic organisms The formal cause Rosen also referred to the other two causes defined by Aristotle, the formal cause and the final cause. These are less fundamental than the efficient cause and the material cause for understanding the nature of metabolic closure, but they ought to be mentioned. The formal cause of an element is a definition of its role in a system: in a metabolic context, we call glucose 6-phosphate a metabolite because it is an intermediate in a metabolic pathway, in this case the harnessing of energy from glucose. However, once we accept the idea of closure to efficient causation, we see that there is no real distinction between metabolites and enzymes, because the enzymes are themselves products of metabolism (Cornish-Bowden and Cárdenas, 2007). In Fig. 3, STU, STUS and STUST are all intermediates, and together they constitute the catalyst for the formation of ST and SU. There are many cycles of this kind in metabolism, and as their component elements satisfy the stoichiometric conservation requirements they are clearly biological catalysts and they fit the usual definition of an enzyme: ornithine, for example, is used and regenerated by the urea cycle, and thus has a catalytic role, so although it is not usually regarded as an enzyme it is difficult to define enzyme in a way that would exclude it. Even if we define an enzyme as a catalyst whose main component is a macromolecule (whether protein or RNA) there are still anomalies. Cytochrome c, for example, is not usually considered to be an enzyme, but that is purely conventional, as it is not excluded by any reasonable definition. 11

12 2.5. The final cause The final cause expresses the purpose of a particular process in the whole scheme of things. It is not usually considered in modern scientific discourse, since the time of Hume (1748), because it implies the existence of a designer, and in biology there is no designer, only time Structural closure Structural closure does not correspond to one of Aristotle s causes, but it is an essential characteristic of all known organisms that allows them individuality. Although two distinct cells may sometimes come into close enough physical contact to exchange material directly, as seen in Fig. 8 below, they remain distinct, and in the conditions of the culture the close contact stops when glucose is exhausted, as Clostridium acetobutylicum starts to sporulate. It may be that the same phenotype exists in nature. In all organisms that we know today structural closure is also vital for another reason apart from maintaining individuality: all organisms use chemical gradients across membranes to drive the synthesis of ATP by chemiosmosis (Mitchell, 1961), which would be impossible in a homogeneous medium. ATP synthase, the enzyme that catalyses this process, is found in all organisms, including Archaea, Eubacteria and Eukaryota, with sequences that are clearly homologous (Grüber et al., 2014). It is, therefore, an ancient protein. However, it is also a large protein with numerous subunits, and it is impossible to imagine that anything so elaborate could have existed in the first living systems. The thermodynamic driving force needed to drive their reactions cannot have involved ATP synthase, though it must have harnessed proton gradients or other ion gradients, as suggested by Peter Mitchell several years before he proposed the chemiosmotic hypothesis (Mitchell, 1957). 3. Theories of life There have been efforts to define life since the earliest times. We shall not try here to review the whole history, but it is worth mentioning that the first to define it in mechanistic terms was Mettrie (1748), who was also probably the first to recognize that an organism is a system that makes itself, foreshadowing the idea of metabolic closure discussed earlier (Section 2.1). Much more recently, Leduc (1912) saw parallels between living organisms and osmotic forests, the growth of inorganic crystals in solutions of sodium silicate. His idea that the form of these growths shed light on living organisms was treated with scepticism even in his time, and has rarely been regarded as a useful contribution to the 12

13 definition of life. Nonetheless, in recent years Barge et al. (2011) have been repeating and extending his experiments in efforts to gain a better understanding of energy management in organisms at the origin of life (Section 2.3). The modern development begins with the publication of Erwin Schrödinger s book What is Life? (Schrödinger, 1944). His codescript, an aperiodic crystal acting as a digital code defining the structure of an organism, was influential in the development of molecular biology, alerting James Watson, for example, to the importance of genes (Watson, 2007). However, this was just one of three major points that Schrödinger made. He also introduced the concept of negentropy to explain how organisms needed to use irreversible processes to overcome thermodynamic constraints that would otherwise make metabolism impossible, in a way that was obvious to some, but illuminating to others. Finally, he argued that biology was more general than physics, and that laws of physics might exist that were necessary for biology, but not for physics itself. This last point has been largely ignored, and no such laws have been discovered, but it had a major influence on Rosen s thinking. What is Life? stimulated several later authors (Rosen, 1971; Eigen and Schuster, 1977; Maturana and Varela, 1980; Gánti, 2003; Kauffman, 1986) 5 to think deeply about the nature of life, and to develop their own theories. Although none of these can be regarded as extensions of Schrödinger s ideas, all of them were influenced by them. Unfortunately the various authors worked in complete isolation from one another, with no cross-referencing, and as a result the similarities and differences between them are not immediately obvious. 6 We have discussed these theories elsewhere, comparing them with one another and with Rosen s (M, R) systems (Jaramillo et al., 2010; Letelier et al., 2011; Cornish-Bowden, 2015), and will concentrate here on the two that allow an easy comparison with (M, R) systems, autopoiesis (Maturana and Varela, 1980) and the chemoton (Gánti, 2003) Autopoiesis Humberto Maturana and Francisco Varela introduced autopoiesis in the context of neurobiology (Maturana and Varela, 1980), and tried to explain a living organism as an 5 We refer to Gánti (2003) as the first full account of his ideas in English. However, before that time he published extensively in Hungarian, from Gánti (1971) onwards; these earlier publications are unfortunately unlikely to be readily accessible to most readers. 6 A newcomer in the field, Friston (2013) maintains this tradition: he refers to Maturana and Varela (1980), but to none of the others. It is particularly unfortunate that he overlooked Kauffman (1986), who said 30 years ago that the prebiotic emergence of reflexively autocatalytic sets of protein-like polymers may have been highly probable, a pre-echo of Friston s conclusion that biological self-organization is not as remarkable as one might think. Their reasons are not exactly the same, but both saw self-organization as arising almost inevitably from the chemical properties of random ensembles of components. 13

14 network of processes, occurring in a compartment that continuously makes and remakes itself. They saw the membrane enclosing the system as an essential part of it, but they made no mention of catalysts in their description. However, without catalysis it is difficult to see how their scheme could work. Letelier et al. (2003) argued that autopoiesis is a subset of (M, R) systems, and that if so it is an incomplete form of (M, R) systems, a conclusion that has been contested (McMullin, 2004; Razeto-Barry, 2012). However, autopoiesis explicitly allows for the creation of a membrane, whereas (M, R) systems do not The chemoton Tibor Gánti was a chemical engineer, and his ideas have a much firmer foundation in chemistry than those of most of the other recent authors of theories of life 7. The chemoton (Gánti, 2003) incorporates a complete metabolic cycle in which the intermediates are catalytic, as they are recycled with each turn of the cycle, and the product of the cycle associates to form an enclosing membrane. However, there are no specific catalysts for the individual steps, and without these it is difficult to see how the system could operate without generating a mass of unwanted reactions. The same objection could be made about the system in Fig. 2, but there is an important difference: it is one thing to suppose that two reactants (STU and SU) just happen to have the properties necessary for them to participate in a small number of reactions, and no others; it is quite another to suppose the same for a system with many reactions. A comparison between (M, R) systems and the chemoton may be found elsewhere (Cornish-Bowden, 2015). Gánti s scheme also includes a rudimentary information cycle, an element missing from (M, R) systems and autopoiesis, but the way in which this actually encodes information is not very clear Other theories As discussed elsewhere (Letelier et al., 2011) several other current theories are in existence: RAF sets (Hordijk and Steel, 2004) extend and formalize Kauffman s autocatalytic sets (Kauffman, 1986). Sysers, proposed independently in several papers (White, 1980; Ratner and Shamin, 1980; Feistel, 1983), were intended to develop the hypercycle (Eigen and Schuster, 1977) to make it more realistic. 7 Rosen was essentially a mathematician, though he would have disputed this description, seeing himself as a theoretical biologist. Maturana and Varela were neurobiologists. 14

15 3.4. The need for a compartment As already noted, autopoiesis and the chemoton explicitly allow for creation of a membrane, and the lack of this in Rosen s original description (and also in Fig. 2, as we do not specify the source of the boundary) can be regarded as a shortcoming. However, it is not so clear that a self-organizing system per se needs a membrane, as long as suitable reactants are available to provide the necessary driving force. Even without a membrane fabricated by the self-organizing system itself, a compartment is certainly necessary, to avoid unlimited dilution of the components. Barge et al. (2011) and Pisapia et al. (2017) suggest that a naturally existing inorganic compartment could satisfy this need and provide the necessary ion gradient. The view that life originated as a prebiotic soup in the primitive oceans (Oparin, 1924; Haldane, 1929) is open to the objection that the reactants would inevitably be diluted into nonexistence in a compartment as large as the ocean, and would lose the possibility of generating ion gradients. 4. Rosen s view of simulating and modelling an organism Rosen did not regard simulation as the same as modelling, and to understand his theoretical ideas it is important to keep the two concepts separate. 8 As explained elsewhere (Cárdenas et al., 2010), in a paper that discussed Rosen s point of view in detail, Rosen said that a model of an organism was impossible, whereas a simulation was possible. He was usually more interested in models than in simulations, but in two of his less well known papers (Rosen, 1971, 1973) he described how a simulation might be made. In his terminology, a model of a machine incorporates understanding of how the machine works; it does more than simply mimic its behaviour. A simulation, on the other hand, allows prediction of how the machine will respond to changes in its environment without any knowledge of how the real machine achieves its behaviour. No one will deny that models of machines are possible, and Rosen certainly did not. His point was that organisms are not machines, and that closure to efficient causation means that they cannot have computable models. 9 Rosen s claim that an organism cannot have computable models has been contested by several authors, including Landauer and Bellman (2002); Wells (2006); Chemero and Turvey (2006, 2007, 2008); Chu and Ho (2006, 2007a,b) and Mossio et al. (2009). Some of these arguments derive from misunderstanding catalysis or closure, as we have discussed 8 Notice that Rosen s notion of a model is different from the view of many researchers who apply models to various fields. He discussed his vision of the modelling relation in great detail in an earlier book, Anticipatory Systems (Rosen, 1985). 9 By computable he meant that a model could be set up in a Turing machine that would behave like an organism, and would halt after a finite amount of computation. 15

16 SO 4 2 Acetate H 2 CO 2 Sulphatereducingenic 4 Methano- H 2 S CH bacteria Archaea Fig. 5. Competition between sulphur-reducing bacteria and methanogenic Archaea. The bacteria reduce sulphate to sulphide, whereas the Archaea reduce CO 2 to methane, but they compete for acetate and hydrogen. elsewhere (Cárdenas et al., 2010). That is not the case of Mossio et al. (2009), however, who argue on the basis of l-algebra that models of closure to efficient causation can indeed be computed, though the programs do not necessarily halt, a condition that Rosen considered indispensable. Interestingly, they conclude by suggesting that models of organisms may indeed be impossible, but not because of closure to efficient causation: To sum up: it may well be that a full model of life itself is not computable; but if so, the reason would not be the closure to efficient causation as expressed by Rosen. Arguments of this kind continue to be controversial, and Rosen s point of view has been strongly defended by Louie (2009). A possible resolution may be found in an argument (Palmer et al., 2016) that by expanding a finite-state machine into a set of such machines that communicate with one another one can overcome the problems with individual computers. It remains to be seen how widely the conclusions will be accepted. 5. Applications of Rosennean complexity to ecology 5.1. Interactions between bacteria in the wild As already noted, bacteria do not exist in the wild as pure cultures, but in mixtures containing many species, often as biofilms, or cities of microbes (Watnick and Kolter, 2000). We shall here mention some of the kinds of interactions that have been observed between different species of bacteria, and then discuss how Rosen s ideas can be applied to them Syntrophic transfer of hydrogen Transfer of hydrogen between different bacterial species has been known for about 40 years, since the discovery that Desulfovibrio could grow in the presence of H 2 -utilizing methanogenic Archaea (Bryant et al., 1977). Guyot and Brauman (1986) defined this as a syntrophic relation: Desulfovibrio vulgaris JJ donates H 2 to Methanobacterium bryantii, a hydrogenotrophic species. The advantage to the acceptor is obvious; the advantage to the donor is that it allows metabolic use of substances that cannot be used if H 2 accumulates, 16

17 because it will disturb the favorable thermodynamics. Unlike the example of Clostridium acetobutylicum and Desulfovibrio vulgaris that we shall consider later, this syntrophic transfer does not require direct physical contact between the partners, though they cannot be too far apart, to avoid loss of H 2 to the environment. Loss of soluble products that are consumed by another organism are beneficial, however, as they maintain their concentrations low enough to contribute usefully to the thermodynamic driving forces. A gas like H 2 can in principle be readily lost in solution as bubbles, and although this is certainly what happens in artificial cultures, it is less clear that it can easily occur in the dense structure of a biofilm. More recent work has shown that such syntrophic interactions can also involve electron transfer. For example, Geobacter metallireducens and Geobacter sulfurreducens form aggregates in which electrons from ethanol are transferred to fumarate through nanowires (Summers et al., 2010) Competition between microbes Competition for the same resources is exemplified by the competition for hydrogen and acetate between sulphur-reducing bacteria and methanogenic Archaea (Stams et al., 2005), illustrated in Fig. 5. In the presence of sufficient sulphate the competition favours the bacteria, and their higher affinity for acetate also favours them. These characteristics are industrially important for the degradation of biomass in anoxic conditions (Muyzer and Stams, 2008), because of sulphide pollution when the bacteria predominate: SRB 10 can cause a serious problem for industries, such as the offshore oil industry, because of the production of sulphide, which is highly reactive, corrosive and toxic Rosen s theory applied to interactions between bacteria Cooperative interactions We can now begin to discuss how (M, R) systems may be helpful as models of interactions between different organisms. The system in Fig. 2 depends on the availability of food molecules, S, T and U and probably also on the disappearance of at least some out of X, Y and Z. If S, T and U are not all available, or if X, Y and Z are not kept at sufficiently low concentrations, the system cannot thrive. 10 Sulphate-reducing bacteria 17

18 U U I Y V II X STU SU ST Z Z W ZT ZU ZTU S S S Z U T T U Fig. 6. Two cooperating (M, R) systems. The system on the left (I) is the same as that in Fig. 2, and depends on the availability of S, T and U from the environment. The system on the right (II) is similar in structure, but it depends on T, U and Z as input, and excretes S, V and W. System I cannot continue if S is not available, and system II cannot continue if Z is not available. However, if both are present together each can consume the products of the other. As there is no direct transfer of S and Z between partners in this example it resembles the syntrophic transfer of H 2 between Desulfovibrio and methanogens. However, suppose now that system I exists in co-culture with another, system II, that uses the Z excreted by system I, and itself excretes S that the other can consume (Fig. 6). Then both can survive in a mixed culture in conditions that would not allow either to grow in pure culture. Notice also that each partner consumes some of the output from the other, thereby keeping the concentrations of S and Z low, and thus improving the thermodynamic state. If the two systems are in close physical contact (by reason, for example, of their presence in a biofilm), then dilution into the bulk solution is avoided, and although the diagram now looks more complicated (Fig. 7) the qualitative properties should be similar. Real bacteria in the wild do not exist in mixtures between just two partners; many different species share the same environment, some providing nutrients that others need, some consuming nutrients that are toxic for others, for example by perturbing the ph, and others competing for the same nutrients. However, the same principles apply Competition between bacteria Fig. 6 can also serve to illustrate competition between bacteria in the same medium. As both of the systems illustrated require T and U as nutrients, then, even if all the other nutrients, S and Z, are available in sufficient amounts the competition for T and U may cause one to outgrow the other to the point that it cannot maintain itself. In a real ecological system with many components all these effects may occur simul- 18

19 U U Y I II V X STU SU ST Z S W ZT ZU ZTU U T T U Fig. 7. Closely associated (M, R) systems. This is based on the example in Fig. 6, but now the two systems are in close physical contact, so that material can pass between them without being released into the bulk phase. Consumption of S by system I favours growth of system II by displacing the equilibrium (removing its product), and similarly with consumption of Z by system II. This possibility can exist in nature, as we shall discuss for the bacteria Clostridium acetobutylicum and Desulfovibrio vulgaris. taneously: diffusion through the medium, transfer by direct contact, and competition for the same food. Even if the composition of the medium is artificially maintained constant, as in laboratory conditions, there is no certainty that any steady state will be established or, if it is established, that it will be maintained. Instead, in the general case we may expect chaotic behaviour, that is to say it switches between states in sequences that appear random, though they would be fully determined by the initial conditions if these could be defined precisely enough Clostridium acetobutylicum and Desulfovibrio vulgaris in co-culture Here we shall briefly indicate the characteristics of two species of bacteria, which are found together in nature (Muyzer and Stams, 2008), and their capacity to grow in different conditions. Desulfovibrio vulgaris is a Gram-negative sulphur-reducing species, whereas Clostridium acetobutylicum is a strictly anaerobic Gram-positive species that grows on sugars such as glucose. Desulfovibrio vulgaris does not normally metabolize glucose, because it lacks the permeases that would allow glucose to enter its cells. Not surprisingly, therefore, it does not grow as a pure culture in a medium containing glucose and yeast extract, but no other energy source. In co-culture there is no growth of Desulfovibrio vulgaris if it is separated from Clostridium acetobutylicum by a dialysis membrane permeable to ions like acetate: they have to be present in the same environment, presumably because if Desulfovibrio vulgaris had to rely on acetate and so on excreted into the bulk phase the concen- 19

20 a. D. vulgaris C. acetobutylicum 1 µm b. c. C. acetobutylicum 1 µm D. vulgaris Fig. 8. Interaction of two species of bacteria in co-culture, suggesting Fig. 7 as a model. Desulfovibrio vulgaris cannot grow in pure culture on glucose or other sugars, but it can grow on a medium with glucose as the sole carbon source if Clostridium acetobutylicum is present in the medium. (a) The micrograph shows a culture containing both bacteria. (b) Another view at larger magnification, showing that the two bacteria communicate in close physical contact. (c) An enlargement of part of the same view. The close interaction is necessary for Desulfovibrio vulgaris to be able to grow on the metabolic products of Clostridium acetobutylicum. 20

21 trations would be too small. In co-culture the two bacteria show close physical contact, as seen in the electron micrograph in Fig. 8 (Benomar, 2012), suggesting that nutrients pass directly from one cell to another without passing through the medium, as indicated schematically in Fig. 7, and that the type of interaction illustrated in Fig. 6 does not apply. Fluorescent labelling experiments showed that this is the case, and that molecules as large as proteins can be exchanged in both directions in this way (Benomar et al., 2015). The co-culture of the two bacteria has the emergent property that the total production of H 2 is greater than the sum of what they can produce alone. So in this case the two bacteria together constitute an (M, R) system, and if the association is long-lasting one could argue that they constitute a super-organism. For fuller discussion of this system, with additional micrographs, see Benomar et al. (2015) Metabolic regulation and control in the context of ecology Metabolic control analysis (Kacser et al., 1995) is weakly related to (M, R) systems, though without the complexity. It was developed as a way of relating the flux through a metabolic pathway, and the concentrations of intermediates, to the kinetic properties of the enzyme-catalysed reactions in the pathway. It has become the preferred approach to such questions, but it has also been applied more widely, for example to the contributions of different organs in the whole mammalian body to plasma concentrations and organ fluxes (Brown, 1994), and, more relevant to the present context, to ecosystems, either directly (Giersch, 1991) or by extending the basic theory (Westerhoff et al., 2002). For example, Westerhoff et al. (2002) wrote as follows: Deductive laws such as those of MCA 11 have the potential of being equally applicable to systems that differ in details but are similar in their general principles. A trophic chain or a consortium of organisms at steady state would seem to have some properties in common with biochemical networks. Mapping the assimilation of the prey into the biomass of the predator onto enzyme-catalysed process and organism onto metabolic intermediate for instance, would seem to make the two systems isomorphic. This approach is to some degree an oversimplification, but it helps to explain how control of a specific output, such as assimilation of the prey into the biomass of the predator, is not the consequence of one particular enzyme or process, but is shared by the different processes. Similar considerations apply to (M, R) systems, and the quotation suggests that (M, R) systems have relevance to ecology. 11 Metabolic control analysis. 21