Relational Biology was conceived by Nicolas Rashevsky (1899-1972) and developed into a coherent (if mathematically rather impenetrable) theory of life's ontological causal structure by Robert Rosen (1934-1998). Aloisius Louie (see https://ahlouie.com) has led the continued development of what he calls the Rashevsky-Rosen school in Relational Biology, but up to now their classic representation of the causal structure of an organism (Rosen’s (M,R)-system) has been highly resistant to practical interpretation (i.e. as an embodied biochemical realisation).
Few people understood that Rosen’s (M,R)-system was only one of several valid representations of the same basic causal structure, e.g. of a living cell, and only one person (as far as I can tell) has investigated any of the alternatives. That person is Prof. Jannie Hofmeyr of Stellenbosch University, South Africa - systems biochemist with interests in code biology, systems theory and sustainable development (among many other things!).
Prof Jan-Hendrik (Jannie) Hofmeyr (image from https://scibraai.co.za/jan-hendrik-hofmeyr-biochemist-believes-perceptions-can-shifted/)
In a recent work, Prof. Hofmeyr used what turns out to be a far more appropriate alternative to establish the first biochemically informed realisation of a category-theory based representation of the living cell, consisting of linked networks having closure to efficient causation (Fig. 1). In so doing, he emphasised the separate parts of i) fabrication and ii) (self) assembly, which combine as manufacture. Fabrication is the making of biological molecules, not simply through spontaneous (thermodynamically driven) composition, but by programmed construction (especially the production of useful peptide chains). Assembly is the correct folding of these into functional forms and the arrangement of them into functional relationships. ‘Manufacture’ he says is a composite process involving “making from raw materials the parts of the artefact, which are then assembled into the artefact itself”. All cells do both in the process of autopoiesis: the difference between a factory which fabricates parts and then assembles them into, e.g. washing machines, is that all living cells continually manufacture their own material selves (other than possible dormant periods of course). To achieve that, the manufacturing process is definitively closed to efficient causation - a clef system (closed to efficient causation), meaning it is the efficient cause of itself.
Fig.1
The paper is full of innovative insight, building on his previous works in 2007 and 2017 (see brief explanation on the Molecular Biology pages), rising to a crescendo with the first ever relational model of life that is ‘fleshed out’ with biochemistry. This he calls the (F,A) cell model, with a nod to (M,R), but F is for fabrication and A for assembly, better describing autopoieses than the very confusing terms used by Rosen. The (F,A) cell model is shown in Fig. 2 below.
Fig.2
Obviously it takes some explaining before this can be properly appreciated. First note that we have the solid arrows for material causation and dashed for efficient causation. A fine dotted arrow represents either an injection into a disjoint union of sets such as U+A+L or a projection from a Cartesian product of sets such as mRNA x r. The latter is an instance of a catalyst, here the ribosome (r), that acts as a multifunctional efficient cause, each function determined by additional information supplied by a formal cause, here an mRNA, that can be said to inform the efficient cause. A combination of an mRNA and a ribosome jointly act on a set of aminoacyl-tRNAs to form a particular polypeptide (P) from the amino acids they carry. This is a specific example of the situation where an efficient cause f needs to be informed by a freestanding formal cause i in order to jointly form the processor for a transformation A --> B. The fine dotted projection arrows resolve the Cartesian product f x i into the efficient cause f and the formal cause i, so allowing them to appear in the diagram as distinct entities. On the other hand, eM (enzymes of intermediary metabolism) are seen as efficient causes (as catalysts) for transforming nutrients (N) into nucleotides (U), amino acids (A) and membrane lipids (L), and eM is shown explicitly resolved as one of the list of functional (folded) proteins (top right). These were made in two steps: first their fabrication as an unfolded polypeptide chain (by mRNA x r acting on the set of aa-tRNAs) and then (another of Hofmeyr’s insights) by the action of the intracellular milieu (m) (biochemical environment) and chaperone proteins as efficient cause of their correct folding. The milieu is (mainly) composed of electrolytes (material cause) that are ‘managed’ (efficient cause) by the transmembrane electrolyte transporters (tE) (these being explicitly resolved as members of the list of proteins along with eM and pR and others.
The full cast of actors is given in the legend for Hofmeyr’s Fig. 11 (see reference):
"The (F,A) cell model: a graph-theoretic relational model of the self-manufacturing cell that is realised by the cell biochemistry in Fig. 10. N: nutrients, U: nucleotides, A: amino acids, L: membrane lipids, DNA: deoxyribonucleic acid, RNA: ribonucleic acid, mRNA: messenger RNA, tRNA: transfer RNA, aa-tRNA: aminoacyl-tRNA, rRNA: ribosomal RNA, P=PN + PM + PS + PT + PR + PC + PE : non-functional, unfolded polypeptides, r: ribosomes, tN: nutrient transporters, eM: catabolic/anabolic enzymes of intermediary metabolism, eS: aminoacyl-tRNA synthetases, eT: transcription enzymes, pR: ribosomal proteins, m: intracellular milieu, eC: chaperones, eE: electrolyte transporters."
PN will become tN, PM -> eM, etc. once they are folded in the context of the milieu with its chaperones etc.
The colour coding of the relations delineates processes as:
blue - nutrient transport / intermediary metabolism;
green - polypeptide synthesis;
red - sequence information transfer;
violet - genetic code instantiation in aa-tRNAs;
orange - folding/self-assembly of polypeptides;
cyan - electrolyte transport.
The complete diagram describes the causal relations, in graph theoretic terms, of the more familiar biochemical pathway diagram referred to in the caption as Fig. 10 (which is where Hofmeyr had left things in his 2017 paper) (reproduced here as Fig 3.).
Fig.3
It is not easy to see (because of the complexity) how Fig. 2 is a realisation of Fig 1., but in Hofmeyr’s paper, that is shown very nicely with a series of diagrams that lead you from one to the other and also show that the full system in Fig. 2 is in fact composed of three interacting classes of efficient causation: a) the fabrication processes involving metabolic enzymes, aa-tRNAs transcription enzymes and ribosomes (all specialised sorts of enzymes); b) the assembly process in which the intracellular milieu with accompanying chaperones guide folding and self-assembly into functional proteins and their complexes and c) the homeostatic maintenance of the intracellular milieu, requiring electrolyte transporters and the lipid membrane.
After having unveiled the (F,A) model of the cell, Prof. Hofmeyr then uses it to interpret Rosen’s (M,R)-system, Gánti’s chemoton, Barbieri’s “genotype-phenotype-ribotype ontology” and even Pattee’s symbol-function “epistemic cut” in a new biochemically relevant way (noting that Gánti’s chemoton is all uncatalysed biochemistry). In his discussion, he notes how several aspects of the (M,R)-system have led to much discourse with little progress; how formal cause is critical to understanding cellular self-manufacture (and therefore how bad its misunderstanding has been for progress) and how crucial is the (typically neglected) role of context in the form of the intracellular milieu, which should be regarded as an active (causal) component of the living cell. He ends with a lesson we can all appreciate: “For us the cell’s lesson is to realise that our functionalising contexts have agency, and should therefore be continuously monitored, cherished and actively maintained from within by the members of our organisations and societies.”
For my own part, at the end of my review for the journal, I wrote that the most obvious innovation (though there are many) in this model is the incorporation (literally) of information (via formal cause), which for the first time gives informational oligomers an integrated role in the clef system of the cell and exposes the need for translation between the symbolic domain and the physical domain, identifying each with an observed biochemical subsystem. Although the ideas were inspired by (among other things) Rosen’s work that led to the replicative (M,R)-system, now that we have this model from Prof. Hofmeyr, I think it is time for us to move beyond Rosen’s replicative (M,R)-system - I certainly will.
REFERENCE
Hofmeyr, J-H. S. A biochemically-realisable relational model of the self manufacturing cell. Biosystems. 207: 104463. doi.org/10.1016/j.biosystems.2021.104463
Preprint available at biorxiv.
