Ecological Complexity 35 (2018) 13–24

Original Research Article

Rosennean Complexity and its relevance to ecology

María Luz Cárdenasa, Saida Benomara,b, Athel Cornish-Bowdena,*aAix Marseille Univ, CNRS, BIP, IMM, Marseille, FrancebDepartment of Molecular Biosciences, University of Kansas, Lawrence, KS 66045, USA

A R T I C L E I N F O

Article history:Received 21 November 2016Received in revised form 13 April 2017Accepted 25 April 2017Available online 12 June 2017

Keywords:Robert RosenComplexityEcological systemsBacterial consortiaBacterial interactionsDefinition of life

A B S T R A C T

Complexity is not the same as complicatedness: a system is complicated if it has many components, but itis complex if it cannot be modelled as a machine and has emergent properties. The theoretical biologistRobert Rosen argued that living organisms are complex in this sense, and his (M, R) systems provide adescription of a living organism in which the central point is that organisms are closed to efficientcausation, which means that all the specific catalysts needed for the organism to maintain itself must beproduced by the organism itself. This includes the catalysts needed to maintain the other catalysts. On theother hand an organism is not closed to material causation, because there must be a net overallirreversible 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 tointeractions between different organisms, allowing analysis, for example, of how two or more species canexist in symbiotic relationships with one another, able to live together, but not separately. Application ofRosennean complexity to fields other than life is possible, as we discuss. Rosen’s holistic vision oforganisms, in which all components affect all others, has implications for the concepts of hierarchy anddownward causation that are sometimes invoked in philosophical discussions, because it means thatthere is no hierarchy and no downward causation.

© 2017 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Ecological Complexity

journal homepa ge: www.elsev ier .com/locate /ecocom

1. Introduction

Robert Rosen’s book Life Itself (Rosen, 1991), a summary of morethan three decades of research on the nature of life, starting withRosen (1958), presented what he called (M, R) systems ormetabolism-repair1 systems as a way to understand life. It hasnow been cited about 550 times in the science literature—not avery large number for the major work of “biology’s Newton”(Mikulecky, 2001).2 Despite Rosen’s interest in ecology, rather fewof these citations have been in journals of ecology, just 12 in thepast 10 years (Gabora et al., 2008; Kelso, 2008; Yates, 2008;Chemero and Turvey, 2008; Chemero, 2012; Turvey and Carello,

* Corresponding author.E-mail addresses: cardenas@imm.cnrs.fr (M.L. Cárdenas), sbenomar@ku.edu

(S. Benomar), acornish@imm.cnrs.fr (A. Cornish-Bowden).1 Rosen’s repair has very little to do with ordinary uses of the word in biology. We

prefer replacement, and use this term in this article. In general it is not a good idea tochange an original author's terminology, but in Rosen’s case it can hardly beavoided.

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 consulta paper (Cornish-Bowden et al., 2007) that offers a non-mathematical explanationof Rosen’s ideas for the general biological community.

http://dx.doi.org/10.1016/j.ecocom.2017.04.0051476-945X/© 2017 Elsevier B.V. All rights reserved.

2012; Robinson, 2009; Van Orden et al., 2010; Browne et al., 2012;Cilliers et al., 2013; Keirstead, 2014). Here we shall discuss inparticular how (M, R) systems can be applied to ecologicalinteractions between organisms. However, we must first discussthe distinction that Rosen made in Essays on Life Itself betweencomplexity and complicatedness (Rosen, 2000, p. 44):

A system is complex if it has noncomputable models—thischaracterization has nothing to do with counting of parts orinteractions; such notions, being themselves predicative, arebeside the point.

In everyday language the adjectives “complex” and “compli-cated” are sometimes treated as synonymous, a tendencyencouraged by dictionaries that give each as a definition of theother. However, Rosen (2000) insisted that they are different, asnoted in the quotation above, and he regretted (Rosen, 2000, p. 43)that von Neumann had used the term “complexity” for what heregarded as “complication”. Even if one takes care to distinguishbetween the two adjectives, a problem arises with the nouns,because “complicatedness” is such a cumbersome term that thereis a temptation to use “complexity” as the noun for both. Thistemptation 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

14 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

Ecological Systems, and although there is comparatively little inthem that is particularly related to ecology, he definitely saw hisideas as being relevant to ecology, as he made clear when herecalled a year that he had spent as a Visiting Fellow at the Centerfor the Study of Democratic Institutions in Santa Barbara (Rosen,1979):

I thus almost in spite of myself found that I was fulfilling anexhortation of Rashevsky, who had told me years earlier that Iwould not be a true mathematical biologist until I hadconcerned myself (as he had) with problems of socialorganization. At the time, I had dismissed these remarks ofRashevsky with a shrug; but I later discovered (as did manyothers who tried to shrug Rashevsky off) that he had been rightall along.

As with much of what Rosen wrote, his meaning in the firstquotation does not immediately emerge at first reading: one needsto work at understanding him. The point is that a complicatedsystem is one with many components, but with properties that canbe regarded as the sum of the properties of the individual parts: inthat sense a typical chart of metabolic pathways is complicated,but, as we shall see, it is not complex. Computer simulation of theentire metabolism of an organism has been attempted only bycombining data from numerous sources (Karr et al., 2012), butsome individual pathways have been simulated using kineticparameters measured under uniform conditions, such as glycolysisin the bloodstream form of the parasite Trypanosoma brucei(Bakker et al., 1997; Eisenthal and Cornish-Bowden, 1998) andaspartate metabolism in Arabidopsis thaliana (Curien et al., 2009), abranched pathway with numerous isoenzymes, regulatory inter-actions, and multifunctional proteins, none of which can be takeninto account by a stoichiometric model that does not incorporatekinetic equations. The results support the idea that the propertiesof the whole pathway are indeed the sum of the properties of theindividual reactions (Van Eunen et al., 2012). However, simulationsof this kind assume the classical view of metabolism, in which theenzymes are “given”,3 a view not shared by Rosen, who argued thatan organism must be closed to efficient causation (Rosen, 1991),another somewhat obscure characterization, which can beunderstood to mean that all the specific catalysts (enzymes orribozymes) needed by an organism must be products of theorganism itself: organisms are therefore complex. Rosen’sdefinitions are not exactly the same as those used by otherwriters interested in the essence of living systems, but theycorrespond approximately.

The examples of kinetic metabolic models cited above weresmall models, with fewer than 15 reactions, and even for ametabolism as simple as that of the bloodstream form of T. bruceithis still falls far short of modelling the whole metabolism.Increased computer power and increased kinetic informationabout the reactions are bringing about large increases in the sizesof such models: for example, a recent kinetic model of livermetabolism (Berndt et al., 2017) is based on data for 221 reactions.Remember, however, that in the simulations of T. brucei metabo-lism the enzymes were taken as given, the question of where theycome from being ignored (it is assumed that their concentrationsdo not change during the period of simulation). This is also true ofall of the other simulations of real metabolism that we are awareof, and it restricts the period of validity to a time frame in whichprotein synthesis is negligible, 2 h for the model of aspartatemetabolism in A. thaliana (Curien et al., 2009), but possibly muchshorter in other systems. The trend to larger models will certainly

3 That is to say synthesis and degradation of catalysts are not considered in themodels.

continue, but, if we accept Rosen’s view, they will never be modelsof a whole organism, no matter how large and “complete” theybecome.

In Life Itself Rosen (1991) argued that the essence of a livingorganism could be expressed as an (M, R) system in which thereactions are possible thanks to catalysts that are produced by thesystem itself. As mentioned earlier, we have changed the termrepair by replacement, which is more exact: although DNA can berepaired to some degree, and inactivated proteins can sometimesbe repaired by chaperones or other mechanisms, damagedenzymes are usually degraded and need to be resynthesized. Thisresynthesis is what Rosen meant by “repair”. His idea that catalysts(enzymes, whether protein or RNA, and also including trans-porters) play a crucial role and that they are synthesized by theorganism is correct, as they participate, not only in classicalmetabolism, but also in DNA duplication, transcription, translation,as well as in the degradation of different types of molecules. This, inessence, means that the catalysts needed for an organism to stayalive are products of the organism itself.

Although the concept of an (M, R) system applies to modernorganisms, it acquires special significance in relation to the originof life (Cornish-Bowden and Cárdenas, 2008), because in thetransition from prebiotic to living organisms the intermediateentities must have been minimally simple.

We have analysed Rosen's view of an (M, R) system, establishedits range of validity (Letelier et al., 2006), explained it in simpleterms, defined simple examples to illustrate it (Cornish-Bowdenet 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 besingle organisms, but Rosen’s ideas also apply in more ecologicalcontexts, and that is what we shall be concerned with here,specifically in the context of consortia of different species ofbacteria. In the laboratory bacteria have usually been studied inpure culture, and supplied with the nutrients that they need. Thatis not how they exist in the wild, however: on the contrary, naturalcolonies of bacteria exist in ecological systems that contain manyspecies, and in environments that lack some of the nutrients thatsome of the species need. They are often found in a biofilm, whichhas been likened to a “city of microbes” (Watnick and Kolter, 2000).We are not yet at the stage where we can usefully study suchmixtures in Rosennean terms, but a consortium of two species,Clostridium acetobutylicum and Desulfovibrio vulgaris Hildenbor-ough (Benomar et al., 2015) provides a starting point for studyingmore natural mixtures. D. vulgaris cannot grow in pure culture onglucose or other sugars, but it can grow on a medium with glucoseas the sole carbon source if C. acetobutylicum is present in themedium. This simple example will illustrate how Rosenneancomplexity might be applied to ecological systems. We may hopethat in the future it may be possible to describe entire trophicchains in Rosennean terms, but for the present that would be tooambitious.

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 classifi-cation of the four (“aitia”), or “causes”, of which the only onethat corresponds to the modern idea of a cause (derived from DavidHume, 1748) is the efficient cause. Rosen understood this as thecatalysts needed for life (f, F and b in Fig. 1), whether protein, RNAor others. In saying that organisms are closed to efficient causation,he meant that all of the specific catalysts needed to be provided bythe organism itself, with none of them being harvested from theenvironment. That applies almost without exception to metabolic

A

f

B

Fig. 1. Rosen’s diagram showing the nature of an (M, R) system, redrawn fromFig. 10C-6 in Life Itself (Rosen, 1991). Chemical transformations are shown withopen-headed arrows, mappings (catalytic actions in normal biochemical terminol-ogy) by arrows with filled heads. The meanings of the abstract entities A, B, f and Fmay be explained as follows: the mapping f(A) ! B is the basic equation in Rosen’sscheme, and corresponds in normal biochemical terminology to the set of enzymesthat catalyse metabolism, transforming the set of food molecules A into the wholeset of metabolites B. However, the system needs to persist in time, and f is subject todegradation, 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 onf: b(f) ! F; b does not appear in Rosen’s diagram (or in this figure), but it is clearfrom his text that he regarded it as derived from B. Notice that f, b and F have dualcharacters both as mappings and as sets. In addition, notice that both types ofarrows connect B to f, the arrow with a filled head corresponding to b: this was howRosen sought to escape from what would otherwise be an infinite regress, a crucialconcept in his view of (M, R) systems.

M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24 15

reactions in life today, but highly specific catalysts did not exist atthe origin of life, and the first self-maintaining systems must haveused unspecific catalysts, such as Fe2+ or Zn2+, that were availablefrom 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, isvery difficult to understand, in part because his treatment is highlymathematical and abstract, and is expressed in terms of the theoryof categories rather than in the far more widely known set theory.4

Attempting to explain the diagram more simply we have added along legend (missing from Rosen's book). The catalyst b played anessential role in Rosen’s vision of life, and he returned to it againand again, but never explained it clearly, and he omitted it from thediagram, thereby giving the impression that the whole of B is thecatalyst, a point that has confused some authors.

We have tried to define the smallest possible (M, R) system, asshown in Fig. 2a, with identifiable chemical molecules. With twodifferences, this is the same as the example we have described andsimulated previously (Piedrafita et al., 2010). First, we haveenclosed the reactions inside a boundary. Rosen never consideredsuch a boundary, but it is present around all modern cells, and isnecessary for any ecological discussion, as one must be able todistinguish between one individual and another. At the origin oflife a boundary fabricated by the organism itself probably neitherexisted nor was required, as a natural compartment in a mineralenvironment, or a spontaneously formed lipid membrane, mighthave been enough; however, it became necessary during evolution,and most other theories of life, such as autopoiesis (Maturana andVarela, 1980) and the chemoton (Gánti, 2003), explicitly include amembrane as a product of the self-organizing system. The second(trivial) difference is that we have given explicit symbols X, Y and Zto the excreted products, as these will be needed for the ecologicalexample to be discussed. All of the metabolites are lost to theenvironment by irreversible reactions, STU ! X, ST ! Z and SU ! Y,and the overall reaction S + T + U ! X + Y + Z is assumed to besufficiently thermodynamically favoured to drive the wholeprocess. Notice also that Rosen treated the catalysts as acting onthe reactants, because he regarded them as mathematical

4 We have discussed (M, R) systems in mathematical terms elsewhere (Letelieret al., 2006; Jaramillo et al., 2010), but here we keep the mathematics to a minimum.

functions, or mappings, that transform reactants into products.Rearrangement of this scheme into the layout of Fig. 1, as shown inFig. 2b, clarifies the relationship between our very small model andRosen’s general one, which can have any size, and will typically bevery large.

For modelling purposes the same system must be drawn in away that shows the catalysed reactions as cycles of chemicalreactions, 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 ifall the steps in the mechanism are shown explicitly, as exemplifiedby the reaction catalysed by hexokinase in Fig. 4.

A more important question, however, is why the scheme needsto be even as complicated as the version in Fig. 2: why do we needto 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 thatmust be included. There must be a process representing classicalmetabolism, the reaction S + T ! STcatalysed by STU. However, STUwill have a tendency to be lost, whether by lack of stability, or bydiffusion across the enclosing boundary, or simply by dilution asthe system grows. In any case, STU needs to be a product of thesystem, so there must be a replacement reaction ST + U ! STU,catalysed by SU. However, SU is also subject to loss by the sameproperties as STU, and so it also needs to be replaced. This is wherethe 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 bereplaced by a reaction with its own catalyst, which would also needto be replaced, and so on. We are clearly on the verge of an infiniteregress, with each new reaction requiring another reaction withanother catalyst. Rosen’s way of escaping from the infinite regresswas to require the system to be closed to efficient causation: interms of Fig. 2 this means that at least one catalyst, STU in theexample, needs to catalyse more than one reaction.

In biochemistry the capacity of some proteins to fulfil morethan one function is known as moonlighting. It usually refers to verydifferent functions: for example, the glycolytic enzyme glyceral-dehyde 3-phosphate dehydrogenase has as many as ten quitedifferent functions, not only catalysing oxidation of glyceraldehyde3-phosphate by NAD, its “textbook” role in metabolism, but alsoothers, including even a structural role in the composition ofcrystallin in the vertebrate eye. Many examples are now known(Henderson and Martin, 2014; Copley, 2015), but to these must beadded many cases of less than perfect specificity of enzymes withpurely catalytic roles, and indeed, less than perfect specificity mustbe regarded as the rule rather than the exception. Perfectspecificity is sometimes simply not possible for structural reasons,even in contexts where it would be desirable, such as the chargingof tRNA molecules with the “right” amino acids, and additionalmechanisms are needed to overcome the resulting problems(Fersht and Dingwall, 1979). Numerous metabolic reactions arenow known to be sufficiently unspecific to create metabolicproblems if left uncorrected (Van Schaftingen et al., 2015). In othercases lack of perfect specificity may allow organisms to compen-sate for missing activities (Copley, 2015). However, considerationof metabolic closure suggests than less than perfect specificity ofcatalysts may be an absolute necessity for life.

Closure to efficient causation can be expressed by definingmetabolism as a function that acts on metabolism to producemetabolism (Letelier et al., 2005), or, as an algebraic equation:f(f) = f.

2.2. Downward causation incompatible with Rosennean complexity

Papers of a philosophical nature often discuss such concepts asweak emergence and downward causation. For example, Bedau

STU ST

S

U

U T

Y

SUX Z

A

f

B ,

STU

{S, T, U} {STU, S T, SU, X, Y, Z} STU, SU

catalysis organizational

replacement

(b)(a)

metabolism

invariance

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 foodmolecules S, T and U into a product STcan maintain itself indefinitely even though the product and the catalysts STU and SU are subject to loss through degradation, or dilutiondue to growth or division. There are three catalysed reactions: S + T ! ST, metabolism (more precisely classical metabolism, as the entire system constitutes metabolism), iscatalysed 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), iscatalysed by STU. To correspond better with normal biochemical practice, continuous arrows refer to chemical processes and broken arrows to catalytic interactions. (b)Reorganization of the diagram to the arrangement of Fig.1, with labels to show what the arrows correspond to in our terminology. 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. In this minimal system the food molecules S, T and U in the set A also participate in the replacement process, and are theonly molecules used for organizational invariance, but these complications are not shown, because they were not included in Fig. 1, and they would not apply to the vastmajority of catalysts in real living organisms, which do not convert food directly into catalysts (though possibly they did at the origin of life).

16 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

(2008) opens a discussion of weak emergence with the followingwords:

Weak emergence is the view that a system’s macro propertiescan be explained by its micro properties but only in anespecially complicated way.

He goes on to argue that weak emergence is a real phenomenon,that involves “a certain kind of downward causation, and that thiskind of downward causation is irreducible in practice, due toexplanatory incompressibility”. How consistent is this withRosennean complexity? In our view it is excluded by Rosenneancomplexity, as everything in Rosen’s conception of metabolismdepends on everything else: there is no hierarchy, and hence nodownward causation in which a “higher” element in a systemdirects the behaviour of a “lower” element. Rosen did not discussthat point, but we consider that metabolic circularity excludes anypossibility of a hierarchy, even though incomplete systems ofreactions can sometimes be usefully discussed in terms ofhierarchies: for example, Westerhoff et al. (1990a,b) and Boogerdet al. (2005) examined how to analyse hierarchies in which DNAcontrols mRNA production, which controls protein production,which controls metabolic reactions. They also considered whatthey called “democratic” control, in which a metabolite may act onmRNA translation. However, they recognized that it could not

Fig. 3. Expanded view of the (M, R) system of Fig. 2. Although this appears to bemore complicated than Fig. 2a it is in fact exactly the same, but now theintermediates in the catalytic cycles are shown explicitly. For example, instead ofabbreviating the reaction catalysed by SU to a single reaction ST + U ! STU, we haveshown 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 theintermediate steps are not shown explicitly (Fig. 4b).

easily be reconciled with the ideas of metabolic control current atthat time. This type of consideration also applies to humansocieties, or indeed to all ecological systems, because even if someindividuals are more important than others, all contribute to thewhole, and have at least some effect on the whole.

Returning to the quoted sentence with which this sectionbegan, it is clear from the examples of metabolic models givenearlier that if the system considered is just a part of a larger onethen 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 metaboliccircularity rules out the possibility that that can apply to a wholeorganism. These considerations apply with even greater force toecological systems, in which every member of a communitydepends on the community as a whole.

The absence of a hierarchy has implications for the concept ofsignalling, which is often invoked in modern biochemistry. Ifeverything affects everything else, then every change in everymolecule is a signal of some kind, so the concept becomes trivial, oreven meaningless. Nonetheless, some molecules, such as AMP, aresubstrates or products of very few metabolic reactions but playimportant roles in monitoring the metabolic status of the cell, andsupply that information to different enzymes.

Fig. 4. (a) An enzyme-catalysed reaction may appear fairly simple whenrepresented as in a typical chart of metabolic pathways. (b) It appears much morecomplicated when all the intermediates are shown explicitly. However, the tworepresentations are exactly equivalent. The order of product release shown is theone most often found, but not always (Monasterio and Cárdenas, 2003).

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 mostreaders.

M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24 17

2.3. An organism is open to material cause

The need for catalytic closure must not be taken to imply that anorganism is also closed to material causation. That is quitedifferent, and would make self-organization, and thus life,impossible if it existed. The material cause of an enzyme-catalysedreaction is the set of reactants on the left-hand side of the chemicalequation (whereas the efficient cause is the enzyme). In Fig. 4,therefore, glucose and ATP correspond to the material cause andhexokinase to the efficient cause. Closure to material causationwould correspond to thermodynamic equilibrium, but a livingsystem cannot be at thermodynamic equilibrium because it needsa supply of energy in the form of irreversible reactions. In Fig. 2 thereaction S + T + U ! X + Y + Z is assumed to be irreversible, whichimplies that the reactants S, T and U are available in sufficientquantities and that the products X, Y and Z can be brought tonegligible concentrations by processes that we do not need toconsider here (though we shall consider them later in relation tocommunities of bacteria). In intermediary metabolism the drivingforce for most reactions is transfer of a phosphate group from ATP,but in all known organisms the ultimate driving forces are redoxreactions, oxidation by molecular oxygen in aerobic organisms, orother sources of oxidizing power, such as sulphate or nitrate ions,in anaerobic organisms.

2.4. The formal cause

Rosen also referred to the other two causes defined by Aristotle,the formal cause and the final cause. These are less fundamentalthan the efficient cause and the material cause for understandingthe 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 metabolitebecause it is an intermediate in a metabolic pathway, in this casethe harnessing of energy from glucose. However, once we acceptthe idea of closure to efficient causation, we see that there is no realdistinction between metabolites and enzymes, because theenzymes are themselves products of metabolism (Cornish-Bowden and Cárdenas, 2007). In Fig. 3, STU, STUS and STUST areall intermediates, and together they constitute the catalyst for theformation of ST and SU. There are many cycles of this kind inmetabolism, and as their component elements satisfy thestoichiometric conservation requirements they are clearly biolog-ical 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 regardedas an enzyme it is difficult to define enzyme in a way that wouldexclude it. Even if we define an enzyme as a catalyst whose maincomponent is a macromolecule (whether protein or RNA) there arestill anomalies. Cytochrome c, for example, is not usuallyconsidered to be an enzyme, but that is purely conventional, asit is not excluded by any reasonable definition.

2.5. The final cause

The final cause expresses the purpose of a particular process inthe whole scheme of things. It is not usually considered in modernscientific discourse, since the time of Hume (1748), because itimplies the existence of a designer, and in biology there is nodesigner, only time.

2.6. Structural closure

Structural closure does not correspond to one of Aristotle’scauses, but it is an essential characteristic of all known organismsthat allows them individuality. Although two distinct cells may

sometimes come into close enough physical contact to exchangematerial directly, as seen in Fig. 8 below, they remain distinct, andin the conditions of the culture the close contact stops whenglucose is exhausted, as C. acetobutylicum starts to sporulate. It maybe that the same phenotype exists in nature.

In all organisms that we know today structural closure is alsovital for another reason apart from maintaining individuality: allorganisms use chemical gradients across membranes to drive thesynthesis of ATP by chemiosmosis (Mitchell, 1961), which wouldbe impossible in a homogeneous medium. ATP synthase, theenzyme that catalyses this process, is found in all organisms,including Archaea, Eubacteria and Eukaryota, with sequences thatare clearly homologous (Grüber et al., 2014). It is, therefore, anancient protein. However, it is also a large protein with numeroussubunits, and it is impossible to imagine that anything so elaboratecould have existed in the first living systems. The thermodynamicdriving force needed to drive their reactions cannot have involvedATP synthase, though it must have harnessed proton gradients orother ion gradients, as suggested by Peter Mitchell several yearsbefore 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 worthmentioning that the first to define it in mechanistic terms wasMettrie (1748), who was also probably the first to recognize that anorganism is a system that makes itself, foreshadowing the idea ofmetabolic closure discussed earlier (Section 2.1). Much morerecently, Leduc (1912) saw parallels between living organisms and“osmotic forests”, the growth of inorganic crystals in solutions ofsodium silicate. His idea that the form of these growths shed lighton living organisms was treated with scepticism even in his time,and has rarely been regarded as a useful contribution to thedefinition of life. Nonetheless, in recent years Barge et al. (2011)have been repeating and extending his experiments in efforts togain a better understanding of energy management in organismsat the origin of life (Section 2.3).

The modern development begins with the publication of ErwinSchrödinger’s book What is Life? (Schrödinger, 1944). His “code-script”, an “aperiodic crystal” acting as a digital code defining thestructure of an organism, was influential in the development ofmolecular biology, alerting James Watson, for example, to theimportance of genes (Watson, 2007). However, this was just one ofthree major points that Schrödinger made. He also introduced theconcept of “negentropy” to explain how organisms needed to useirreversible processes to overcome thermodynamic constraintsthat would otherwise make metabolism impossible, in a way thatwas obvious to some, but illuminating to others. Finally, he arguedthat biology was more general than physics, and that laws ofphysics might exist that were necessary for biology, but not forphysics itself. This last point has been largely ignored, and no suchlaws have been discovered, but it had a major influence on Rosen’sthinking.

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 todevelop their own theories. Although none of these can beregarded as extensions of Schrödinger’s ideas, all of them wereinfluenced by them. Unfortunately the various authors worked in

18 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

complete isolation from one another, with no cross-referencing,and as a result the similarities and differences between them arenot immediately obvious.6 We have discussed these theorieselsewhere, 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 aneasy comparison with (M, R) systems, autopoiesis (Maturana andVarela, 1980) and the chemoton (Gánti, 2003).

3.1. Autopoiesis

Humberto Maturana and Francisco Varela introduced autopoi-esis in the context of neurobiology (Maturana and Varela, 1980),and tried to explain a living organism as an network of processes,occurring in a compartment that continuously makes and remakesitself. They saw the membrane enclosing the system as an essentialpart of it, but they made no mention of catalysts in theirdescription. However, without catalysis it is difficult to see howtheir scheme could work. Letelier et al. (2003) argued thatautopoiesis is a subset of (M, R) systems, and that if so it is anincomplete form of (M, R) systems, a conclusion that has beencontested (McMullin, 2004; Razeto-Barry, 2012). However, auto-poiesis explicitly allows for the creation of a membrane, whereas(M, R) systems do not.

3.2. The chemoton

Tibor Gánti was a chemical engineer, and his ideas have a muchfirmer foundation in chemistry than those of most of the otherrecent authors of theories of life.7 The chemoton (Gánti, 2003)incorporates a complete metabolic cycle in which the intermedi-ates are catalytic, as they are recycled with each turn of the cycle,and the product of the cycle associates to form an enclosingmembrane. However, there are no specific catalysts for theindividual steps, and without these it is difficult to see how thesystem could operate without generating a mass of unwantedreactions. The same objection could be made about the system inFig. 2, but there is an important difference: it is one thing tosuppose that two reactants (STU and SU) just happen to have theproperties necessary for them to participate in a small number ofreactions, and no others; it is quite another to suppose the same fora 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 theway in which this actually encodes information is not very clear.

3.3. Other theories

As discussed elsewhere (Letelier et al., 2011) several othercurrent 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,

6 A newcomer in the field, Friston (2013) maintains this tradition: he refers toMaturana and Varela (1980), but to none of the others. It is particularly unfortunatethat he overlooked Kauffman (1986), who said 30 years ago that “the prebioticemergence of reflexively autocatalytic sets of protein-like polymers may have beenhighly probable”, a pre-echo of Friston’s conclusion that “biological self-organization is not as remarkable as one might think”. Their reasons are notexactly the same, but both saw self-organization as arising almost inevitably fromthe chemical properties of random ensembles of components.

7 Rosen was essentially a mathematician, though he would have disputed thisdescription, seeing himself as a theoretical biologist. Maturana and Varela wereneurobiologists.

1980; Ratner and Shamin, 1980; Feistel, 1983), were intended todevelop the hypercycle (Eigen and Schuster, 1977) to make it morerealistic.

3.4. The need for a compartment

As already noted, autopoiesis and the chemoton explicitly allowfor creation of a membrane, and the lack of this in Rosen’s originaldescription (and also in Fig. 2, as we do not specify the source of theboundary) can be regarded as a shortcoming. However, it is not soclear that a self-organizing system per se needs a membrane, aslong as suitable reactants are available to provide the necessarydriving force.

Even without a membrane fabricated by the self-organizingsystem itself, a compartment is certainly necessary, to avoidunlimited dilution of the components. Barge et al. (2011) andPisapia et al. (2017) suggest that a naturally existing inorganiccompartment could satisfy this need and provide the necessary iongradient. The view that life originated as a “prebiotic soup” in theprimitive oceans (Oparin, 1924; Haldane, 1929) is open to theobjection that the reactants would inevitably be diluted intononexistence in a compartment as large as the ocean, and wouldlose 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, andto understand his theoretical ideas it is important to keep the twoconcepts separate.8 As explained elsewhere (Cárdenas et al., 2010),in a paper that discussed Rosen’s point of view in detail, Rosen saidthat a model of an organism was impossible, whereas a simulationwas possible. He was usually more interested in models than insimulations, but in two of his less well known papers (Rosen, 1971,1973) he described how a simulation might be made. In histerminology, a model of a machine incorporates understanding ofhow the machine works; it does more than simply mimic itsbehaviour. A simulation, on the other hand, allows prediction ofhow the machine will respond to changes in its environmentwithout any knowledge of how the real machine achieves itsbehaviour. No one will deny that models of machines are possible,and Rosen certainly did not. His point was that organisms are notmachines, and that closure to efficient causation means that theycannot have computable models.9

Rosen’s claim that an organism cannot have computablemodels has been contested by several authors, including Landauerand 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 catalysisor closure, as we have discussed elsewhere (Cárdenas et al., 2010).That is not the case of Mossio et al. (2009), however, who argue onthe basis of l-algebra that models of closure to efficient causationcan indeed be computed, though the programs do not necessarilyhalt, a condition that Rosen considered indispensable. Interesting-ly, they conclude by suggesting that models of organisms mayindeed be impossible, but not because of closure to efficientcausation:

To sum up: it may well be that a full model of “life itself” is notcomputable; but if so, the reason would not be the closure to

8 Notice that Rosen’s notion of a model is different from the view of manyresearchers who apply models to various fields. He discussed his vision of themodelling 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 thatwould behave like an organism, and would halt after a finite amount ofcomputation.

Fig. 5. Competition between sulphur-reducing bacteria and methanogenicArchaea. The bacteria reduce sulphate to sulphide, whereas the Archaea reduceCO2 to methane, but they compete for acetate and hydrogen.

M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24 19

efficient causation as expressed by Rosen.

Arguments of this kind continue to be controversial, andRosen’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 suchmachines that communicate with one another one can overcomethe problems with individual computers. It remains to be seen howwidely 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 purecultures, but in mixtures containing many species, often asbiofilms, or “cities of microbes” (Watnick and Kolter, 2000). Weshall here mention some of the kinds of interactions that have beenobserved between different species of bacteria, and then discusshow Rosen’s ideas can be applied to them.

5.1.1. Syntrophic transfer of hydrogenTransfer of hydrogen between different bacterial species has

been known for about 40 years, since the discovery thatDesulfovibrio could grow in the presence of H2-utilizing methano-genic Archaea (Bryant et al., 1977). Guyot and Brauman (1986)defined this as a syntrophic relation: D. vulgaris JJ donates H2 toMethanobacterium bryantii, a hydrogenotrophic species. Theadvantage to the acceptor is obvious; the advantage to the donoris that it allows metabolic use of substances that cannot be used ifH2 accumulates, because it will disturb the favourable thermody-namics. Unlike the example of C. acetobutylicum and D. vulgaris thatwe shall consider later, this syntrophic transfer does not requiredirect physical contact between the partners, though they cannotbe too far apart, to avoid loss of H2 to the environment. Loss ofsoluble products that are consumed by another organism arebeneficial, however, as they maintain their concentrations lowenough to contribute usefully to the thermodynamic drivingforces. A gas like H2 can in principle be readily lost in solution asbubbles, and although this is certainly what happens in artificialcultures, it is less clear that it can easily occur in the densestructure of a biofilm.

More recent work has shown that such syntrophic interactionscan also involve electron transfer. For example, Geobactermetallireducens and Geobacter sulfurreducens form aggregates inwhich electrons from ethanol are transferred to fumarate throughnanowires (Summers et al., 2010).

5.1.2. Competition between microbesCompetition for the same resources is exemplified by the

competition for hydrogen and acetate between sulphur-reducingbacteria and methanogenic Archaea (Stams et al., 2005), illustratedin Fig. 5. In the presence of sufficient sulphate the competitionfavours the bacteria, and their higher affinity for acetate alsofavours them. These characteristics are industrially important forthe degradation of biomass in anoxic conditions (Muyzer andStams, 2008), because of sulphide pollution when the bacteriapredominate:

SRB10 can cause a serious problem for industries, such as theoffshore oil industry, because of the production of sulphide,which is highly reactive, corrosive and toxic.

10 Sulphate-reducing bacteria.

5.2. Rosen’s theory applied to interactions between bacteria

5.2.1. Cooperative interactionsWe can now begin to discuss how (M, R) systems may be helpful

as models of interactions between different organisms. The systemin Fig. 2 depends on the availability of food molecules, S, T and Uand probably also on the disappearance of at least some out of X, Yand Z. If S, T and U are not all available, or if X, Yand Z are not kept atsufficiently low concentrations, the system cannot thrive.

However, suppose now that system I exists in co-culture withanother, system II, that uses the Z excreted by system I, and itselfexcretes S that the other can consume (Fig. 6). Then both cansurvive in a mixed culture in conditions that would not allow eitherto grow in pure culture. Notice also that each partner consumessome of the output from the other, thereby keeping theconcentrations of S and Z low, and thus improving thethermodynamic state. If the two systems are in close physicalcontact (by reason, for example, of their presence in a biofilm),then dilution into the bulk solution is avoided, and although thediagram now looks more complicated (Fig. 7) the qualitativeproperties should be similar.

Real bacteria in the wild do not exist in mixtures between justtwo partners; many different species share the same environment,some providing nutrients that others need, some consumingnutrients that are toxic for others, for example by perturbing thepH, and others competing for the same nutrients. However, thesame principles apply.

5.2.2. Competition between bacteriaFig. 6 can also serve to illustrate competition between bacteria

in the same medium. As both of the systems illustrated require Tand U as nutrients, then, even if all the other nutrients, S and Z, areavailable in sufficient amounts the competition for T and U maycause one to outgrow the other to the point that it cannot maintainitself.

In a real ecological system with many components all theseeffects may occur simultaneously: diffusion through the medium,transfer by direct contact, and competition for the same food. Evenif the composition of the medium is artificially maintainedconstant, as in laboratory conditions, there is no certainty thatany steady state will be established or, if it is established, that it willbe maintained. Instead, in the general case we may expect chaoticbehaviour, that is to say it switches between states in sequencesthat appear random, though they would be fully determined by theinitial conditions if these could be defined precisely enough.

5.2.3. C. acetobutylicum and D. vulgaris in co-cultureHere 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. D. vulgarisis a Gram-negative sulphur-reducing species, whereas C. acetobu-tylicum is a strictly anaerobic Gram-positive species that grows onsugars such as glucose. D. vulgaris does not normally metabolizeglucose, because it lacks the permeases that would allow glucose toenter its cells. Not surprisingly, therefore, it does not grow as a pure

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 onthe 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 Zis 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 itresembles the syntrophic transfer of H2 between Desulfovibrio and methanogens.

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 themwithout 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 withconsumption of Z by system II. This possibility can exist in nature, as we shall discuss for the bacteria Clostridium acetobutylicum and Desulfovibrio vulgaris.

20 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

culture in a medium containing glucose and yeast extract, but noother energy source. In co-culture there is no growth of D. vulgarisif it is separated from C. acetobutylicum by a dialysis membranepermeable to ions like acetate: they have to be present in the sameenvironment, presumably because if D. vulgaris had to rely onacetate and so on excreted into the bulk phase the concentrationswould be too small. In co-culture the two bacteria show closephysical contact, as seen in the electron micrograph in Fig. 8(Benomar, 2012), suggesting that nutrients pass directly from onecell to another without passing through the medium, as indicatedschematically in Fig. 7, and that the type of interaction illustrated inFig. 6 does not apply. Fluorescent labelling experiments showedthat this is the case, and that molecules as large as proteins can beexchanged in both directions in this way (Benomar et al., 2015).The co-culture of the two bacteria has the emergent property thatthe total production of H2 is greater than the sum of what they canproduce alone. So in this case the two bacteria together constitutean (M, R) system, and if the association is long-lasting one couldargue that they constitute a super-organism.

For fuller discussion of this system, with additional micro-graphs, see Benomar et al. (2015).

5.3. Metabolic regulation and control in the context of ecology

Metabolic control analysis (Kacser et al., 1995) is weakly relatedto (M, R) systems, though without the complexity. It was developedas a way of relating the flux through a metabolic pathway, and theconcentrations of intermediates, to the kinetic properties of the

enzyme-catalysed reactions in the pathway. It has become thepreferred approach to such questions, but it has also been appliedmore widely, for example to the contributions of different organs inthe whole mammalian body to plasma concentrations and organfluxes (Brown, 1994), and, more relevant to the present context, toecosystems, either directly (Giersch, 1991) or by extending thebasic theory (Westerhoff et al., 2002). For example, Westerhoffet al. (2002) wrote as follows:

Deductive laws such as those of MCA11 have the potential ofbeing equally applicable to systems that differ in details but aresimilar in their general principles. A trophic chain or aconsortium of organisms at steady state would seem to havesome properties in common with biochemical networks.Mapping the “assimilation of the prey into the biomass ofthe predator” onto “enzyme-catalysed process” and “organism”

onto “metabolic intermediate” for instance, would seem tomake the two systems isomorphic.

This approach is to some degree an oversimplification, but ithelps to explain how control of a specific output, such as“assimilation of the prey into the biomass of the predator”, isnot the consequence of one particular enzyme or process, but isshared by the different processes. Similar considerations apply to(M, R) systems, and the quotation suggests that (M, R) systems haverelevance to ecology.

11 Metabolic control analysis.

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 cangrow 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 closeinteraction is necessary for Desulfovibrio vulgaris to be able to grow on the metabolic products of Clostridium acetobutylicum.

M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24 21

5.4. Beyond the molecular domain

To date there have been few attempts to extend Rosen’s analysisbeyond the molecular domain, but there have been some from thepast decade:

� Lindo and Gonzalez (2010) discussed Rosen’s modelling relationin the context of understanding the bryosphere;12

� Seck and Honig (2012) applied it to socio-political conflict;� Cilliers et al. (2013) discussed Rosennean complexity in relationto resource management, especially in South Africa;

� Poli (2016) applied Rosen’s modelling relation in the context ofbelief systems and social conflict.

All of the cited authors showed understanding of Rosen’s ideas,but none of them applied them in any detail.

Both (M, R) systems and autopoiesis were developed forunderstanding living organisms, so it is worth asking whetherRosennean complexity can be usefully applied to topics other thanlife and ecology, especially as concepts from autopoiesis are nowbeing invoked in an astonishingly wide variety of fields, includinguniversity organization (Lenartowicz, 2015), architecture (Dollens,2015), literary criticism (Berk, 2015), accountancy (Khan and Gray,2016), psychology (Bickhard, 2016), management (Vásquez andDittus Benavente, 2016), and many others. Whether these conceptsshed any useful light on such fields is arguable, however, and someof the applications are superficial at best. For example, we are notconvinced that it is useful to ask whether buildings can think(Dollens, 2015). On the other hand, Lenartowicz (2015), in her

12 “The bryosphere is defined as the combined complex of living and dead mosstissue and associated organisms, representing a tightly coupled system of bothabove and below ground processes. It covers a large proportion of the terrestrialEarth’s surface and exists at the interface of the lithosphere, pedosphere,atmosphere, and hydrosphere” (Lindo and Gonzalez, 2010).

study of the nature of the university, makes some valuable points,noting that universities maintain their identities while respondingto changing political and societal conditions: for example, a largemajority of the surviving European institutions founded before1520 are universities. Most attempts to extend autopoiesis toecology, such as that of Naruse and Iba (2008), take as their startingpoint the application by Luhmann (1988) to social and economicsystems. He said, for example,

Society is an autopoietic system based on meaningfulcommunication. It consists of communications, it consists onlyof communications, it consists of all communications. Itreproduces communication through communication . . . . Soci-ety is therefore a closed and an open system at the same time,and communication is the form of the elementary operationthat constantly makes this combination and reproduces it.13

The last sentence evokes the ideas of closure and openness in(M, R) systems, though it is probably clearer to say that society isclosed to efficient causation and open to material causation.

There are no mathematical equations or computer simulationsin Luhmann’s book. Not everyone will miss these, but those who domay feel that his qualitative remarks about autopoiesis need to betranslated into a formal theory. The same is true of the paper ofNaruse and Iba (2008), and appears to be true in general ofapplications of autopoiesis outside its original domain. Forexample, Naruse and Iba (2008) represent their view of anecosystem with a figure similar to Fig. 9. The main point is, likeLuhmann’s, that ecosystems are systems of communication, but itdoes not go beyond that.

13 Die Gesellschaft ist ein autopoietisches System auf der Basis von sinnhafterKommunikation. Sie besteht aus Kommunikationen, sie besteht nur aus Kommu-nikationen, sie besteht aus allen Kommunikationen. Sie reproduziert Kommunika-tion durch Kommunikation . . . . Gesellschaft ist also ein geschlossenes und einoffenes System zugleich, und Kommunikation ist die Form der elementarenOperation, die diese Kombination laufend leistet und reproduziert.

Fig. 9. A representation of an ecosystem as a set of communications, redrawn fromthe part entitled “Our Understanding that elements of an ecology are commu-nications” of Fig. 6 of Naruse and Iba (2008).

22 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

These extensions go beyond the concept of autopoiesis asMaturana and Varela (1980) defined it originally. For example,Maturana (2002) wrote

We living systems are molecular systems that exist in themolecular domain spontaneously without external processesdriving them. As I say this I also claim that autopoiesis occursonly in the molecular domain.

This was also, to some degree, Varela’s view, but he recognizedthe possibility of self-constituted autonomy in other domains(Froese, 2011).

Rosen would probably have had similar objections if theconcept of (M, R) systems had been extended to the organization ofuniversities and so on during his lifetime. Nonetheless, theoriginators of a theory are not its owners, and cannot dictatehow it might be extended to domains different from those thatthey originally had in mind. It is for researchers in the differentfields to decide whether theories such as (M, R) systems orautopoiesis shed any useful light on their work.

6. Discussion

Rosen was interested in relational biology, a term introduced byRashevsky (1954) to refer to relations between molecules andrelations between organisms: that is why we think that (M, R)systems can shed light on ecological systems. In this context it isworth recalling that both Life Itself (Rosen, 1991) and Essays on LifeItself (Rosen, 2000), his best known books, appeared in a series onecological complexity.

As we have seen, interaction between two bacterial speciesallows D. vulgaris to grow on glucose if C. acetobutylicum is presentin the same medium and is in close contact. This is just one of manyexamples of interactions between different species that are nowknown to exist in nature, including host–parasite interactions,host–symbiont interactions, and symbiont–symbiont interactions(Schulze et al., 2016), in which the system is more than the sum ofits parts. An example of host–symbiont interactions is found in thecockroach Blattella germanica, which obtains nitrogen from theuric acid stores of an obligate bacterial symbiont (Patiño Navarreteet al., 2014). An example of symbiont–symbiont interactions isfound between two spirochaete species resident in the gut oftermites: this interaction allows one that requires H2 to consumethe H2 excreted by the other (Rosenthal et al., 2011).

The cockroach example is now the subject of a genome-scalemetabolic model (Ponce-de-León et al., 2013). Large-scale modelsof this kind are increasingly being developed, but in no case are thekinetic parameters needed for a real kinetic model available:instead they are stoichiometric models, ones that are restricted toinformation about what reactions are present, with no informationabout their kinetic properties. Such models provide valuableinformation as a first step (Cornish-Bowden and Cárdenas, 2002),explaining, for example, why Escherichia coli can grow anaerobi-cally on glucose, but not on glycerol, succinate or acetate (Stelling

et al., 2002), but they are not a substitute for kinetic models whenkinetic data are available.

It will be a long time before full or even partial kineticparameters are known on a genome-wide scale that would allowmodels of the sort used for small metabolic systems, such asaspartate metabolism in A. thaliana (Curien et al., 2009).Nonetheless, this example illustrates why real kinetic modelsare indispensible for a full understanding of what is happening.Stoichiometric models reveal nothing about feedback inhibition orother regulatory interactions, or about the roles of differentisoenzymes that catalyse the same reactions, though this isessential information for understanding aspartate metabolism inA. thaliana. In principle the relevant part of the metabolic pathwaysfor the two bacteria considered earlier is small enough to bemodelled kinetically, but almost none of the relevant kineticparameters are known, so it cannot be done at present.

There appears to be no reason why the sort of application of (M,R) systems to symbiotic interactions between C. acetobutylicumand D. vulgaris should not be extended in a natural way to otherorganisms, whether symbiotic or competitive. By comparison, theextensions of autopoiesis outside the realm of single organismsseem to be purely qualitative.

Application of (M, R) systems to the molecular domain hasshown why hierarchies and downward causation are not usefulconcepts in these systems, and the same is certainly true forecological systems.

Acknowledgements

This work was supported by the CNRS. We thank Dr. WolfgangNitschke for checking our translation of the quotation fromLuhmann’s book, and Dr. Tom Froese for shedding some light onFrancisco Varela’s attitude to extensions of the concept ofautopoiesis.

References

Bakker, B.M., Michels, P.A.M., Opperdoes, F.R., Westerhoff, H.V., 1997. Glycolysis inbloodstream form Trypanosoma brucei can be understood in terms of thekinetics of the glycolytic enzymes. J. Biol. Chem. 272, 3207–3215.

Barge, L.M., Doloboff, I.J., White, L.M., Stucky, G.D., Russell, M.J., Kanik, I., 2011.Characterization of iron-phosphate-silicate chemical garden structures.Langmuir 28, 3714–3721.

Bedau, M.A., 2008. Is weak emergence just in the mind? Minds Mach. 18, 443–459.Benomar, S., 2012. Étude d’un écosystème bactérien synthétique anaérobie

producteur d’hydrogène: impacte des interactions bactérie-bactérie sur lemétabolisme. (Doctoral thesis). Aix-Marseille Université.

Benomar, S., Ranava, D., Cárdenas, M.L., Trably, E., Rafrafi, Y., Ducret, A., Hamelin, J.,Lojou, E., Steyer, J.P., Giudici-Orticoni, M.T., 2015. Nutritional stress inducesexchange of cell material and energetic coupling between bacterial species. Nat.Commun. 6, 6283.

Berk, S., 2015. Verschollen unter Amazonen: transformations of the feminine anddeconstructive autopoiesis in Kafka's Der Verschollene. Ger. Q. 88, 60–81.

Berndt, N., Bulik, S., Wallach, I., König, M., Holzhütter, H.G., 2017. Computationalassessment of liver metabolism. Mol. Syst. Biol. (in press).

Bickhard, M.H., 2016. Inter- and en- activism: some thoughts and comparisons. NewIdeas Psychol. 41, 23–32.

Boogerd, F.C., Bruggeman, F.J., Richardson, R.C., Stephan, A., Westerhoff, H.V., 2005.Emergence and its place in nature: a case study of biochemical networks.Synthese 145, 131–164.

Brown, G.C., 1994. Control analysis applied to the whole-body – control by bodyorgans over plasma-concentrations and organ fluxes of substances in the blood.Biochem. J. 297, 115–122.

Browne, D., O’Regan, B., Moles, R., 2012. Comparison of energy flow accounting,energy flow metabolism ratio analysis and ecological footprinting as tools formeasuring urban sustainability: a case-study of an Irish city-region. Ecol. Econ.83, 97–107.

Bryant, M.P., Campbell, L.L., Reddy, C.A., Crabill, M.R.,1977. Growth of Desulfovibrio inlactate or ethanol media low in sulfate in association with H2-utilizingmethanogenic bacteria. Appl. Environ. Microbiol. 33, 1162–1169.

Cárdenas, M.L., Letelier, J.C., Gutierrez, C., Cornish-Bowden, A., Soto-Andrade, J.,2010. Closure to efficient causation, computability and artificial life. J. Theor.Biol. 263, 79–92.

Chemero, A., 2012. Modeling self-organization with nonwellfounded set theory.Ecol. Psychol. 24, 46–59.

M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24 23

Chemero, A., Turvey, M.T., 2006. Complexity and “closure to efficient cause”. In:Kepa, Ruiz-Mirazo, Barandarian, R. (Eds.), ALIFE X: Workshop on ArtificialAutonomy. MIT Press, Cambridge, MA, pp. 13–18.

Chemero, A., Turvey, M.T., 2007. Complexity, hypersets, and the ecologicalperceptive on perception-action. Biol. Theory 2, 23–36.

Chemero, A., Turvey, M.T., 2008. Autonomy and hypersets. BioSystems 91, 320–330.Chu, D., Ho, W., 2006. A category theoretical argument against the possibility of

artificial life: Robert Rosen’s central proof revisited. Artif. Life 12, 117–134.Chu, D., Ho, W.K., 2007a. Computational realizations of living systems. Artif. Life 13,

369–381.Chu, D., Ho, W.K., 2007b. The localization hypothesis and machines. Artif. Life 13,

299–302.Cilliers, P., Biggs, H.C., Blignaut, S., Choles, A.G., Hofmeyr, J.H.S., Jewitt, G.P.W., Roux,

D.J., 2013. Complexity, modeling, and natural resource management. Ecol. Soc.18.

Copley, S.D., 2015. An evolutionary biochemist’s perspective on promiscuity. TrendsBiochem. Sci. 40, 72–78.

Cornish-Bowden, A., 2015. Tibor Gánti and Robert Rosen: contrasting approaches tothe same problem. J. Theor. Biol. 381, 6–10.

Cornish-Bowden, A., Cárdenas, M.L., 2002. Systems biology: metabolic balancesheets. Nature 420, 129–130.

Cornish-Bowden, A., Cárdenas, M.L., 2007. Organizational invariance in (M, R)-systerns. Chem. Biodivers. 4, 2396–2406.

Cornish-Bowden, A., Cárdenas, M.L., 2008. Self-organization at the origin of life. J.Theor. Biol. 252, 411–418.

Cornish-Bowden, A., Cárdenas, M.L., Letelier, J.C., Soto-Andrade, J., 2007. Beyondreductionism: metabolic circularity as a guiding vision for a real biology ofsystems. Proteomics 7, 839–845.

Curien, G., Bastien, O., Robert-Genthon, M., Cornish-Bowden, A., Cárdenas, M.L.,Dumas, R., 2009. Understanding the regulation of aspartate metabolism using amodel based on measured kinetic parameters. Mol. Syst. Biol. 5, 271.

Dollens, D., 2015. Autopoiesis + extended cognition + nature = can buildings think?Commun. Integ. Biol. 8, e994373.

Eigen, M., Schuster, P., 1977. The hypercycle: a principle of natural self-organization.Part A: Emergence of the hypercycle. Naturwissenschaften 11, 541–565.

Eisenthal, R., Cornish-Bowden, A.,1998. Prospects for antiparasitic drugs: the case ofTrypanosoma brucei, the causative agent of African sleeping sickness. J. Biol.Chem. 273, 5500–5505.

Feistel, R., 1983. On the evolution of biological macromolecules. III. Precellularorganization. Stud. Biophys. 93, 113–120.

Fersht, A.R., Dingwall, C., 1979. Evidence for the double-sieve editing mechanism inprotein-synthesis – steric exclusion of isoleucine by valyl-transfer RNA-synthetases. Biochemistry 18, 2627–2631.

Friston, K., 2013. Life as we know it. J. R. Soc. Interface 10, 20130475.Froese, T., 2011. From second-order cybernetics to enactive cognitive science: Varela

’s turn from epistemology to phenomenology. Syst. Res. Behav. Sci. 28, 631–645.Gabora, L., Rosch, E., Aerts, D., 2008. Toward an ecological theory of concepts. Ecol.

Psychol. 20, 84–116.Gánti, T., 1971. Az élet principiuma. Gondolat Budapest.Gánti, T., 2003. The Principles of Life. Oxford University Press, Oxford.Giersch, C., 1991. Sensitivity analysis of ecosystems – an analytical treatment. Ecol.

Model. 53, 131–146.Grüber, G., Manimekalai, M.S.S., Mayer, F., Müller, V., 2014. ATP synthases from

archaea: the beauty of a molecular motor. Biochim. Biophys. Acta, Bioenerg.1837, 940–952.

Guyot, J.P., Brauman, A., 1986. Methane production from formate by syntrophicassociation of Methanobacterium bryantii and Desulfovibrio vulgaris JJ. Appl.Environ. Microbiol. 52, 1436–1437.

Haldane, J.B.S., 1929. The origin of life. Rationalist Ann. 148, 3–10 Complete textavailable at www.uv.es/orilife/textos/Haldane.pdf.

Henderson, B., Martin, A.C.R., 2014. Protein moonlighting: a new factor in biologyand medicine. Biochem. Soc. Trans. 42, 1671–1678.

Hordijk, W., Steel, M., 2004. Detecting autocatalytic, self-sustaining sets in chemicalreaction systems. J. Theor. Biol. 227, 451–461.

Hume, D., 1748. An Enquiry Concerning Human Understanding, Oxford World’sClassics, reprinted 2008 Oxford.

Jaramillo, S., Honorato-Zimmer, R., Pereira, U., Contreras, D., Reynaert, B.,Hernández, V., Soto-Andrade, J., Cárdenas, M.L., Cornish-Bowden, A., Letelier, J.C., et al., 2010. M, R) systems and RAF sets: common ideas, tools and projections.In: Fellermann, H. (Ed.), Proceedings of the Alife XII Conference, Odense,Denmark. MIT Press, Cambridge, MA, pp. 94–124.

Jencks, W.P., 1987. Catalysis in Chemistry and Enzymology. Dover Publications, NewYork Original edition (1969) published by McGraw-Hill, New York.

Kacser, H., Burns, J.A., Fell, D.A., 1995. The control of flux. Biochem. Soc. Trans. 23,341–366.

Karr, J.R., Sanghvi, J.C., Macklin, D.N., Gutschow, M.V., Jacobs, J.M., Bolival Jr., B.,Assad-Garcia, N., Glass, J.I., Cover, M.W., 2012. A whole-cell computationalmodel predicts phenotype from genotype. Cell 150, 389–401.

Kauffman, S.A., 1986. Autocatalytic sets of proteins. J. Theor. Biol. 119, 1–24.Keirstead, J., 2014. Fit for purpose? Rethinking modeling in industrial ecology. J. Ind.

Ecol. 18, 161–163.Kelso, J.A.S., 2008. An essay on understanding the mind. Ecol. Psychol. 20, 180–208.Khan, T., Gray, R., 2016. Accounting, identity, autopoiesis. Meditari Acc. Res. 24, 36–

55.Landauer, C., Bellman, K., 2002. Theoretical biology: organisms and mechanisms..

In: Dubois, M. (Ed.), Computing Anticipatory Systems: CASYS 2001 – Fifth

International Conference, American Institute of Physics, College Park, MD, pp.59–70.

Leduc, S., 1912. La Biologie Synthétique (Synthetic Biology). Poinat, Paris.Lenartowicz, M., 2015. The nature of the university. High. Educ. 69, 947–961.Letelier, J.C., Cárdenas, M.L., Cornish-Bowden, A., 2011. From L’Homme Machine to

metabolic closure: steps towards understanding life. J. Theor. Biol. 286,100–113.Letelier, J.C., Kuboyama, T., Yasuda, H., Cárdenas, M.L., Cornish-Bowden, A., 2005. A

self-referential equation, f(f) = f, obtained by using the theory of (M, R) systems:overview and applications. In: Anai, H., Horimoto, K. (Eds.), Algebraic Biology2005. Universal Academy Press, pp. 115–126.

Letelier, J.C., Marin, G., Mpodozis, J., 2003. Autopoietic and (M, R) systems. J. Theor.Biol. 222, 261–272.

Letelier, J.C., Soto-Andrade, J., Abarzúa, F.G., Cornish-Bowden, A., Cárdenas, M.L.,2006. Organizational invariance and metabolic closure: analysis in terms of (M,R) systems. J. Theor. Biol. 238, 949–961.

Lindo, Z., Gonzalez, A., 2010. The bryosphere: an integral and influential componentof the Earth’s biosphere. Ecosystems 13, 612–627.

Louie, A.H., 2009. More Than Life Itself: A Synthetic Continuation in RelationalBiology. Ontos Verlag, Heusenstamm, Germany.

Luhmann, N., 1988. Die Wirtschaft der Gesellschaft. Suhrkamp Verlag, Frankfurt.Maturana, H., Varela, F., 1980. Autopoiesis and Cognition: The Realisation of the

Living. Reidel Publishing Company, Dordrecht.Maturana, H.R., 2002. Autopoiesis, structural coupling and cognition: a history of

these and other notions in the biology of cognition. Cybern. Hum. Knowing 9, 5–34.

McMullin, B., 2004. Thirty years of computational autopoiesis: a review. Artif. Life10, 277–295.

Mettrie, J.J.O., 1748. L’Homme Machine, (Man a Machine). Elie Luzac, Leyden URLhttp://www.pianotype.net/eBook/l'homme-machine.pdf.

Mikulecky, D.C., 2001. Robert Rosen (1934–1998): a snapshot of biology’s Newton.Comput. Chem. 25, 317–327.

Mitchell, P., et al., 1957. The origin of life and the formation and organising functionsof natural membranes. In: Oparin, A.I. (Ed.), Proceedings of the FirstInternational Symposium on the Origin of Life on the Earth. Academy ofSciences, Moscow, pp. 229–234.

Mitchell, P., 1961. Coupling of phosphorylation to electron and hydrogen transfer bya chemi-osmotic type of mechanism. Nature 191, 144–148.

Monasterio, O., Cárdenas, M.L., 2003. Kinetic studies of rat liver hexokinase D(“glucokinase”) in non-co-operative conditions show an ordered mechanismwith MgADP as the last product to be released. Biochem. J. 371, 29–38.

Mossio, M., Longo, G., Stewart, J., 2009. A computable expression of closure toefficient causation. J. Theor. Biol. 257, 489–498.

Muyzer, G., Stams, A.J.M., 2008. The ecology and biotechnology of sulphate-reducing bacteria. Nat. Rev. Microbiol. 6, 441–454.

Naruse, M., Iba, T., 2008. Ecosystem as an autopoietic system: consideringrelationship between ecology and society based on Luhmann’s theory. URLhttp://web.sfc.keio.ac.jp/iba/papers/2008JJNAMS08-ecosystem.pdf.

Oparin, A.I., 1924. The Origin of Life. Moscow Worker, Moscow (in Russian). Englishtranslation (1968) as “The Origin and Development of Life”, NASA TTF-488,Washington: D.C.

Palmer, M.L., Williams, R.A., Gatherer, D., 2016. Rosen’s (M, R) system as an X-machine. J. Theor. Biol. 408, 97–104.

Patiño Navarrete, R., Piulachs, M.D., Belles, X., Moya, A., Latorre, A., Peretó, J., 2014.The cockroach Blattella germanica obtains nitrogen from uric acid through ametabolic pathway shared with its bacterial endosymbiont. Biol. Lett. 10,20140407.

Piedrafita, G., Montero, F., Morán, F., Cárdenas, M.L., Cornish-Bowden, A., 2010. Asimple self-maintaining metabolic system: robustness, autocatalysis,bistability. PLoS Comput. Biol. 6, e1000872.

Pisapia, C., Gérard, E., Gérard, M., Lecourt, L., Lang, S.Q., Pelletier, B., Payri, C.E.,Monnin, C., Guentas, L., Postec, A., Quéméneur, M., Erauso, G., Ménez, B., 2017.Mineralizing filamentous bacteria from the Prony Bay hydrothermal field givenew insights into the functioning of serpentinization-based subseafloorecosystems. Front. Microbiol. 8, 57.

Poli, R., 2016. Belief systems and the modeling relation. Found. Sci. 21, 195–206.Ponce-de-León, M., Montero, F., Peretó, J., 2013. Solving gap metabolites and blocked

reactions in genome-scale models: application to the metabolic network ofBlattabacterium cuenoti. BMC Syst. Biol 7, 114.

Rashevsky, N., 1954. Topology and life: in search of general mathematical principlesin biology and sociology. Bull. Math. Biol. 16, 317–348.

Ratner, V., Shamin, V., 1980. Mathematical Models of Evolutionary Genetics. ICG,Novosibirsk.

Razeto-Barry, P., 2012. Autopoiesis 40 years later. A review and a reformulation.Origins Life Evol. Biosphere 42, 543–567.

Robinson, L.W., 2009. A complex-systems approach to pastoral commons. Hum.Ecol. 37, 441–451.

Rosen, R., 1958. A relational theory of biological systems. Bull. Math. Biophys. 20,234–245.

Rosen, R., 1971. Some realizations of (M, R)-systems and their interpretation. Bull.Math. Biophys. 33, 303–319.

Rosen, R., 1973. On the dynamical realization of (M, R)-systems. Bull. Math. Biol. 35,1–9.

Rosen, R., 1979. Anticipatory systems in retrospect and prospect. Gen. Syst. 24, 11–23.

Rosen, R., 1985. Anticipatory Systems. Pergamon Press, Oxford.Rosen, R., 1991. Life Itself. Columbia University Press, New York.

24 M.L. Cárdenas et al. / Ecological Complexity 35 (2018) 13–24

Rosen, R., 2000. Essays on Life Itself. Columbia University Press, New York.Rosenthal, A.Z., Matson, E.G., Eldar, A., Leadbetter, J.R., 2011. RNA-seq reveals

cooperative metabolic interactions between two termite-gut spirochete speciesin co-culture. ISME J. 5, 1133–1142.

Schrödinger, E., 1944. What is Life? Cambridge University Press, Cambridge.Schulze, S., Schleicher, J., Guthke, R., Linde, J., 2016. How to predict molecular

interactions between species? Front. Microbiol. 7, 442.Seck, M.D., Honig, H.J., 2012. Multi-perspective modelling of complex phenomena.

Comput. Math. Organ. Theory 18, 128–144.Stams, A.J.M., Plugge, C.M., de Bok, F.A.M., van Houten, B.H.G.W., Lens, P., Dijkman,

H., Weijma, J., 2005. Metabolic interactions in methanogenic and sulfate-reducing bioreactors. Water Sci. Technol. 52, 13–20.

Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., Gilles, E.D., 2002. Metabolicnetwork structure determines key aspects of functionality and regulation.Nature 420, 190–193.

Summers, Z.M., Fogarty, H.E., Leang, C., Franks, A.E., Malvankar, N.S., Lovley, D.R.,2010. Direct exchange of electrons within aggregates of an evolved syntrophiccoculture of anaerobic bacteria. Science 330, 1413–1415.

Turvey, M.T., 2008. Philosophical issues in self-organization as a framework forecological psychology – introduction. Ecol. Psychol. 20, 240–243.

Turvey, M.T., Carello, C., 2012. On intelligence from first principles: guidelines forinquiry into the hypothesis of physical intelligence (PI). Ecol. Psychol 24, 3–32.

Van Eunen, K., Kiewiet, J.A.L., Westerhoff, H.V., Bakker, B.M., 2012. Testingbiochemistry revisited: how in vivo metabolism can be understood from in vitroenzyme kinetics. PLoS Comput. Biol. 8, e1002483.

Van Orden, G.C., Kello, C.T., Holden, J.G., 2010. Situated behavior and the place ofmeasurement in psychological theory. Ecol. Psychol. 22, 24–43.

Van Schaftingen, E., Veiga-da-Cunha, M., Linster, C.L., 2015. Enzyme complexity inintermediary metabolism. J. Inherit. Metab. Dis. 38, 721–727.

Vásquez, C., Dittus Benavente, R., 2016. Revisiting autopoiesis: studying theconstitutive dynamics of organization as a system of narratives. Manag.Commun. Q. 30, 269–274.

Watnick, P., Kolter, R., 2000. Biofilm, city of microbes. J. Bact. 182, 2675–2679.Watson, J.D., 2007. Avoid Boring People: Lessons from a Life in Science. Knopf, New

York.Wells, A.J., 2006. In defense of mechanism. Ecol. Psychol. 18, 39–65.Westerhoff, H.V., Aon, M.A., van Dam, K., Cortassa, S., Kahn, D., van Workum, M.,

1990a. Dynamic and hierarchical coupling. Biochim. Biophys. Acta 1018, 142–146.

Westerhoff, H.V., Koster, J.J., van Workum, M., Rudd, K.E., 1990b. On the control ofgene expression. In: Cornish-Bowden, A., Cárdenas, M.L. (Eds.), Control ofMetabolic Processes. Plenum Press, New York and London, pp. 399–412.

Westerhoff, H.V., Getz, W.M., Bruggeman, F., Hofmeyr, J.H.S., Rohwer, J.M., Snoep, J.L., 2002. ECA: control in ecosystems. Mol. Biol. Rep. 29, 113–117.

White, D., 1980. A theory for the origin of a self-replicating chemical system. I:Natural selection of the autogen from short, random oligomers. J. Mol. Evol. 16,121–147.

Yates, F.E., 2008. Homeokinetics/homeodynamics: a physical heuristic for life andcomplexity. Ecol. Psychol. 20, 148–179.