Athel Cornish-Bowden: Making systems biology work

1. Juan-Carlos Letelier & Jorge Soto-Andrade Facultad de Ciencias, Universidad de Chile, Santiago Dynamics and structure of biological networks marseilles - luminy, 14–17 february 2006 María Luz Cárdenas: Towards an understanding of life Athel Cornish-Bowden: Making systems biology work cnrs, marseilles

2. with Juan-Carlos Letelier & Jorge Soto-Andrade Facultad de Ciencias, Universidad de Chile, Santiago Dynamics and structure of biological networks marseilles - luminy, 14–17 february 2006 Organizational invariance and metabolic closure Letelier et al (2006) “Organizational invariance and metabolic closure: Analysis in terms of (M, R) systems” J. Theor. Biol. 238: 949-961. María Luz Cárdenas & Athel Cornish-Bowden

3. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? “Science is impelled by two main factors: technological advance and a guiding vision (overview)” Carl R Woese (2004) “A new biology for a new century” Microbiol. Mol. Biol. Rev.68, 173–186 According to Carl Woese, one of the important biologists of the 20th century, progress in science is impelled by two main factors: technological advance and guiding vision Without an adequatetechnological advancethe pathway of progress is blocked and without an adequate guiding vision there is no pathway, there is no way ahead This presentation is in the context of a search for the way ahead, looking for a guiding vision that can allow Systems Biology (very much in fashion), to achieve real success in the 21st century, and not to follow the fate of the cybernetics in the last century, which didn’t live up to its promise.

4. The question of what is life may appear too philosophical, but in reality if we want to succed in modifying the living world for medical or biotechnological purposes, we ought to understand better what is the essence of a living being. f (f ) = f Introduction What is life ? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? We think that Systems Biology as it is being developed today is too much obsessed with the accumulation of data, and that it is not leading us to a better comprehension of the essence of life. In addition, today the question about the nature of life has renewed interest, for several reasons: i) Studies of the origin of life on earth ii) The search for traces of life on another planets iii) The ambition to create artificial life iv) The wish to study living organisms as global systems Among others an essential ingredient that is missing in biology is the idea of metabolic closure, that is, the fact that metabolism produces metabolism, which produces metabolism. The notion of metabolic closure will be analysed in terms of the theory of (M,R) systems of Robert Rosen. Starting from this theory we have shown that it is possible to find objects defined by the remarkable property :

5. Proteome E Enzyme–enzyme complex 1 Enzyme–enzyme complex E 2 E E 3 2 E 3 Metabolism E 4 P S S S S 4 3 2 1 Channelling of intermediate Channelling of Metabolome S 3 What is metabolism? Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? Why is its understanding important for arriving at a definition of life? Proteins are the principal actors that allow the flux of matter and energy through the metabolic networks

6. What is really metabolism? Repair P S S S S 4 3 2 1 Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? E 1 E 2 E 3 E 4 Metabolism But… the enzymes are not a gift of heaven; they are a product of metabolism A living being can be considered as a “metabolism-repair system”, or “(M,R)-system,” that is capable of preserving its integrity of organisation in spite of the changes in its environment and in spite of the finite lifespan of all of its components. They are continuously degraded and synthesized, and for this the cell brings into play complex machineries involving numerous macromolecules (RNA, proteins) and control mechanisms.

7. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? Life as “(M,R)-systems” The theory of “(M,R)-systems” was formulated by the theoretical biologist Robert Rosen. According to him life can be considered as a Metabolism/Repair System (an “(M,R)-system”) In fact, in most cases it is not really a “repair”, but a replacementof enzymes that need to be replaced because of ordinary wear and tear, or because they are no longer needed, and the component aminoacids need to be recovered. Rosen R. (1958) “A relational theory of biological systems” Bull. Math. Biophys.20, 245-341 Rosen R. (1972) “Some relational cell models: the metabolism repair system”. In Rosen R. (Ed) Foundations of Mathematical Biology. Academic Press, NY Rosen R. (1991) “Life itself”. Columbia University Press, NY Rosen R. (2000) “Essays on Life itself” Columbia University Press, NY

8. Sophisticated modern instruments that incorporate some capacity to detect faulty components and alert their operators to them, or even, to a very limited extent, replace them, do not provide an exception to these statements: What they can do is almost infinitely less than what living organisms can do, as they need to maintain all of their components, all of the time. No man-made machine that exists at present or that can be conceived at our current level of technology and understanding has this property. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? When parts wear out, as they inevitably do, they need to be repaired or replaced by an agency external to the machine itself. This is true no matter how we define a “machine” — whether an individual tool like an axe, an assembly of parts like an aeroplane, or an entire factory. At no level of definition does the machine make itself or maintain itself without external help.

9. Introduction What is life? (M,R) Systems Infinite Regress Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? Life as “(M,R)-systems” So, unlike man-made machines, living systems have the capacity of auto-organisation(or autoconservation) and in that sense they are autonomous systems This capacity of autoconservation of living organisms raises a major theoretical problem, because the degradation of components (or their repair), as well as their synthesis, always involves the action of a series of interdependent macromolecules, which depend in their turn on another series, as they alsoneed to be replaced, in a process involving other enzymes, also subject to wear and tear… So, there is a problem of infinite regress. How do living organisms escape from the infinite regress, maintaining their identities almost indefinitely?

10. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished Life as “(M,R)-systems” Consequently the main problem is how to explain the constancy of organisation without infinite regress. The theory of (M,R) systems proposed by Robert Rosen constitutes an effort to solve this problem. The idea is that metabolic networks must satisfy logical regularities that go beyond the thermodynamic and stoichiometric constraints, and that derive from the circular nature of biological organisation (metabolic closure). This theoretical frame is unique, because it tries to understand biological organisation in a non-reductionist way. The essential idea is to identify enzymes with mathematical functions (“mappings”) and to associate the idea of constancy of organisation with procedures for selecting functions.

11. Algebraic formulation of (M,R) Systems Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? In metabolism, each reaction is catalysed by an enzyme. For example valyl-tRNA synthetase catalyses the following transformation : E AMP + pyrophosphate + L-valyl-tRNAVal ATP + L-valine + tRNAVal For arriving at an algebraic formulation of metabolism, each enzyme can be viewed in a general way as an operator, M, that transforms a set of molecules (input materials) into another one (output materials): Mi a1 + a2 + a3 b1 + b2 + b3 The catalyst Mi acts formally as a mathematical mapping, because it transforms some variables (from the admissible set of input materials) into other variables belonging to the set of admissible output materials. Mi ((a1 ,,a2 , a3)) = (b1, b2, b3)

12. Algebraic formulation of (M,R) Systems Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? For arriving an an algebraic formulation of metabolism, each enzyme can be viewed in a general way as an operator, M, that transforms a set of molecules (input materials) into another one (output materials): Mi b1 + b2 + b3 a1 + a2 + a3 The catalyst Mi acts formally as a mathematical mapping, because it transforms some variables (from the admissible set of input materials) into some other variables belonging to the set of admissible output materials. Rosen generalized this mathematical model for a single metabolic reaction to take account of the complete network that constitute metabolism. Thus, he interpreted the overall metabolism as a type of generalized enzyme or operator (mapping), Mmet, that transforms a set of input molecules (a1, a2, a3, ……ap) of set A in a set of output molecules (b1, b2, b3, ……bq) of set B. Mmet A {a1, a2, a3, ……an} B {b1, b2, b3, ……bn}

13. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? What about the Repair or replacement System? In order to keep its organisation the system ought to “know” how it is organised: the network must contain the information. This could be possible if the knowledge of the nature of metabolites b could allow the net to deduce the identity of all the metabolites a as well as the identity of all the catalysts and to be able to replace them. We can formalise the notion of replacement by considering that what it is needed is an operator, called a selector and denoted by f, that using as input the metabolic state of the organism (the collective result of all the biochemical reactions) generatesf: F(b) = f, with the condition that b = f(a) (for some a of A) In order to have a fully organizationally invariant (M,R) system, fmust also be generated from the mathematical structure. The solution to this problem constitutes the kernel of Rosen’s work.

14. Introduction What is Life? (M,R) Systems Robert Rosen Infinite Regress Enzymes as Matematical Fonctions Metabolic closure What have we accomplished? Formally what is needed is a function bwith a property like b(f) = F. Thus b is a procedure that, given a metabolismf, produces the corresponding selector F. The operation of an organizationally invariant (M,R) system corresponds to the following three mappings acting in synergy (f, F, b) : F b f Map(A, B) A B Map (B, Map(A, B)) f (a) = b, F(b) = f, b(f) = F Metabolism is interpreted as a mapping f that transforms an instance a∈ A of the huge set A of possible molecules on the left-hand sides of equations into an instance b∈ B. Replacement (“repair” in Rosen’s terminology) is a procedure, denoted by F, that, starting with b ∈ B as input, producesf according to F(b) = f with the condition b = f(a) for some a ∈ A.

15. Introduction What is Life? (M,R) Systems Robert Rosen Infinite Regress Enzymes as Matematical Fonctions Metabolic closure What have we accomplished? F b f Map(A, B) A B Map (B, Map(A, B)) f (a) = b, F(b) = f, b(f) = F Forb to exist it is required that the equation F(b) = f, for every F must have one and only one solution, a most demanding condition ifM = Map(A, B). Rosen never clarified the nature of b, nor gave the limits within which his model is valid.

16. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? What have we accomplished? We have clarified the formulation of (M,R) systems in terms of “mappings” and “sets of mappings” We have shown in a logical way that it is possible to have a selector F that is going to choose, out of all possible metabolisms, the one that has originated the particular set b in a certain instant. … however, Rosen’s original model is too general. And, additional restrictions are required for the system to have organisational invariance. Thus we have clarified: i) the conditions in which the model of Rosen is valid, and ii) the nature ofb We have produced the first mathematical example of an (M,R) system (to be presented in next talk)

17. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? What have we accomplished and what does it mean? We have shown how to generate self-referential objects f with the remarkable property of being able to act as function, argument and result f( f ) = f Which represents exactly what metabolism is All this may constitute a small step towards explaining the circular organization of living organisms.

18. Humberto Maturana & Francisco Varela Their theory of autopoiesis has some points in common with Robert Rosen’s (M,R) systems*, but it puts less emphasis on the abstract mathematics, and more on the structural organization of living organisms and the necessity to enclose them with membranes. Both theories claim that reproduction and evolvability are not the essential defining traits of living systems *J. Letelier et al (2003) “Autopoietic and (M,R) systems” J. Theor. Biol. 222, 261–272

19. The Ouroboros f(f) = f Ouroboros

20. Groupe en train de travailler Jorge Soto-Andrade Juan-Carlos Letelier Athel Cornish-Bowden Flavio Guíñez Abarzúa

23. M. C. Escher The Ouroboros, the dragon forming a cycle, feeding on its own tail, symbolizes the eternal, cyclic nature of the universe.

24. Introduction Qu’est ce que la Vie ? Systèmes (M,R) Regression à l’infini Robert Rosen Les enzymes comme des fonctions mathématiques Clôture métabolique Qu’est ce qu’on a appris ? So, what has been achieved? Maybe a small step towards explaining the circular organization of living organisms. This allows closure of the loop of that would otherwise lead to infinite regress. f(f) = f Nonetheless, much remains to be done. Robert Rosen worked for 40 years without resolving all the problems — we cannot expect to have resolved them all either.

26. R. Rosen (1991) Life Itself, Columbia University Press, New York R. Rosen (2000) Essays on Life Itself, Columbia University Press, New York R. Rosen (1972) “Some relational cell models: the metabolism-repair system” in Foundations of Mathematical Biology (ed. R. Rosen) Academic Press, New York

27. f(f) = f ’ ’ ´ ο ουροβορος

28. Notice that “repair” is essentially the resynthesis of enzymes that need to be replaced because of ordin-ary wear and tear. This resynthesis is itself catalysed by other enzymes that are themselves subject to wear and tear, and thus need to be replaced also, in a process involving other enzymes, also subject to wear and tear… Repair Decay This is the essential question that Rosen sets out to solve, and the one that we seek to explain, illustrate and extend. …The possibility of infinite regress is obvious. Yet living organisms are not infinitely large; nor are they infinitely complex. P S S S S 4 3 2 1 How do they escape from the infinite regress, main-taining their identities almost indefinitely? What is metabolism, and why is it important for arriving at a definition of life? E 1 E 2 E 3 E 4 Metabolism Rosen sees life as a metabolism-repair system, or “(M,R)-system,” capable of maintaining its organizational integrity in spite of changes in its environment and in spite of the finite lifetimes of its component enzymes.

29. Introduction What is life? (M,R) Systems Infinite Regression Robert Rosen Enzymes as mathematical functions Metabolic closure What have we accomplished? So, in simple words, Rosen saw metabolism as a mathematical operation that transforms metabolic components of a set a in components of a set b. In order to keep its organisation the system ought to "know" how it is organised: the network must contain the information. This could be possible if the knowledge of the nature of metabolites b could allow the net to deduce the identity of all the métabolites a as well as the identity of all the catalysts and to be able to replace them. We can formalise the notion of replacement by considering that what it is needed is an operator, called a selector and denoted by f, that using as input the metabolic state of the organism (the collective result of all the biochemical reactions) generates f : F(b) = f, with the condition that b = f(a) (for some a of A) In order to have a fully organizationally invariant (M,R) system, f must also be generated from the mathematical structure. The solution to this problem constitutes the kernel of Rosen's work.

30. Before trying to discuss a biological example of this we need to ask whether what Rosen is demanding is possible even at an abstract level, as Christopher Landauer and Kirstie Bellman* have denied that it is, claiming that some of his ideas are “simply false.” We have developed a purely formal and mathe-matical example to show that Landauer and Bellman are mistaken, but I shall not describe this here. *C. Landauer & K. Bellman (2002) in Theoretical Biology: Organisms and Mechanisms, AIP Conference Proceedings Vol. 627, pp. 59–70. Rosen sees a “metabolism” as a mathemati-cal operation that transforms all of the left-hand sides of all of the component processes into all of the right-hand sides. In order to maintain its organization the system needs to “know” how it is organized: the network itself must contain the informa-tion needed to replace any part of itself that needs to be replaced. This would be possible if knowledge of all the right-hand sides allowed all of the left-hand sides to be deduced, together with the identities of all the catalysts.

32. Introduction What is Life? Artificial life (M,R) Systems Infinite Regress Robert Rosen Metabolic closure Metabolic exemple Achievements …then we find Rosen praised in the most extravagant terms: 99% of biologists have never heard of Robert Rosen, but if we ignore these and just consider the exceptions… “Biology’s Newton” (Don Mikulecky, 2001) “The work of Rosen will keep scholars busy for decades” (John Casti, 2002)

33. 1. He presented it in resolutely mathematical terms, making no concessions to any difficulties that readers might encounter. 2. He provided no examples to illustrate the central points (not even mathematical ones, and certainly not biological ones). 3. He did not define the limits within which his conclusions were valid. Essential problems with Robert Rosen’s work Bringing Rosen’s ideas to a broader audience will involve describing them intelligibly, illustrating them with intelligible examples, and defining their range of validity.