The following basic question is studied here: In the relatively stable molecular environment of a vertebrate body, can a dynamic idiotypic immune network develop a natural tolerance to endogenous components? The approach is based on stability analyses and computer simulation using a model that takes into account the dynamics of two agents of the immune system, namely B-lymphocytes and antibodies. The study investigates the behavior of simple immune networks in interaction with an antigen whose concentration is held constant as a function of the symmetry properties of the connectivity matrix of the network. Current idiotypic network models typically become unstable in the presence of this type of antigen. It is shown that idiotypic networks of a particular connectivity show tolerance towards auto-antigen without the need for ad hoc mechanisms that prevent an immune response. These tolerant network structures are characterized by aperiodic behavior in the absence of auto-antigen. When coupled to an auto-antigen, the chaotic attractor degenerates into one of several periodic ones, and at least one of them is stable. The connectivity structure needed for this behavior allows the system to adopt particular dynamic concentration patterns which do not lead to an unbounded immune response. Possible implications for the understanding of autoimmune disease and its treatment are discussed.

The major insight in Robert Rosen’s view of a living organism as an (M, R)-system was the realization that an organism must be “closed to efficient causation”, which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.

Key words: (M, R) systems, Metabolic circularity, Robert Rosen, Definitions of life, Autopoiesis, Autocatalytic sets, Chemoton, Impredicativity

Questions concerning the nature and origin of living systems and the hierarchy of their evolutionary processes are considered, and several problems which arise in connection with formerly developed theories – the autopoiesis of Maturana & Varela, the POL theory of Haukioja and the earlier developed evolutionary theory of Csányi – are discussed. The organization of living systems, the use of informational terms and the question how reproduction can enter into their characterization, problems of autonomy and identity are included in the list. It is suggested that replication – a copying process achieved by a special network of interrelatedness of components and component-producing processes that produces the same network as that which produced them – characterizes the living organization. The information “used” in this copying process, whether it is stored by special means or distributed in the whole system, is called replicative information. A theoretical model is introduced for the spontaneous emergence of replicative organization, called autogenesis. Autogenesis commences in a system by an organized “small” subsystem, referred to as AutoGenetic System Precursor (AGSP), which conveys replicative information to the system. During autogenesis, replicative information increases in system and compartment(s) form. A compartment is the co-replicating totality of components. The end state of autogenesis is an invariantly self-replicating organization which is unable to undergo further intrinsic organizational changes. It is suggested that replicative unities – such as living organisms – evolve via autogenesis. Levels of evolution emerge as a consequence of the relative autonomy of the autogenetic unities. On the next level they can be considered as components endowed with functions and a new autogenetic process can commence. Thus evolution proceeds towards its end state through the parallel autogenesis of the various levels. In terms of applications, ontogenesis is dealt with in detail as an autogenetic process as is the autogenesis of the biosphere and the global system.

Based upon the shape-space formalism, a model of an idiotypic network including both bound and free immunoglobulins is simulated. Our point of interest is the network development in the context of self antigens. The investigations are organized around simulations initiated by various spatial configurations of antigens; the behavior of the system with respect to antigens is analyzed in terms of morphogenetic processes occurring in the shape space. For certain values of the parameters, the network expands by traveling waves. The resulting spatial pattern is a partition of the shape space into zones where introduction of an antigen entails an infinite growth of the clones binding to it, and into zones where, on the contrary, the anti-antigen idiotypes decrease. Among the parameter combinations tested, some produce a partition that remains static whereas others produce a partition that changes in time. For other values of the parameters, the patterns generated do not partition shape space into zones; in these cases, it is observed that the system systematically explodes when an antigen is present.

At first sight, life and cognition only seem to deal with each other in an indirect way, the former as is perhaps necessary as a precondition for the mere possibility of the latter. However, looking at the question more closely and especially when we include the central problem of the emergence of life from inanimate pre-stages, we arrive at a reasonable conclusion of complete identity between life process and cognitive act: through the spontaneous formation of living systems, i.e. of exceptionally stable processual structures far from the thermodynamic equilibrium, external influence – which only now can be opposed to internal correlations – is transformed into an adaptive integration or, in cognitive terms, into a meaningful interpretation by a (within limited conditions of stability surviving) living system. Thereby the purely quantitative notion of “information” has to be subjected to a decisive relativization, since it is not before the system formation itself that it makes sense to speak of information. Far-reaching conceptual consequences follow from the possibility of conclusively demonstrating the fundamental equation of life and cognition.

The problem of representing information in automaton models of self-replication is considered. It is shown that, unlike in the natural reproduction process, in a computable model the reproduced entities do not contain all the information necessary for guiding the process. Current theoretical understanding of life and its replication, based on such models, is argued to be essentially inadequate. The solution to this problem is claimed to require recognition of the theoretical fact that information in living systems is different from that subsumed under the category of “knowledge”, which is representable as computer programs or triggers of state transitions. A discussion of fundamentals of a new theory of information and its relationship to replication models is given and a new direction of further developments of biological theories is envisioned.

From the many attempts to produce a conceptual framework for the organization of living systems, the notions of (M, R) systems and Autopoiesis stand out for their rigor, their presupposition of the circularity of metabolism, and the new epistemologies that they imply. From their inceptions, these two notions have been essentially disconnected because each has defined its own language and tools. Here we demonstrate the existence of a deep conceptual link between (M, R) systems and Autopoietic systems. This relationship permits us to posit that Autopoietic systems, which have been advanced as capturing the central aspects of living systems, are a subset of (M, R) systems. This result, in conjunction with previous theorems proved by Rosen, can be used to outline a demonstration that the operation of Autopoietic systems cannot be simulated by Turing machines. This powerful result shows the potential of linking these two models. Finally, we suggest that the formalism of (M, R) systems could be used to model the circularity of metabolism.

Key words: Autopoiesis, (M, R) systems, Circularity, Metabolism, Closure, Turing–Church hypothesis

The nature of life has been a topic of interest from the earliest of times, and efforts to explain it in mechanistic terms date at least from the 18th century. However, the impressive development of molecular biology since the 1950s has tended to have the question put on one side while biologists explore mechanisms in greater and greater detail, with the result that studies of life as such have been confined to a rather small group of researchers who have ignored one another’s work almost completely, often using quite different terminology to present very similar ideas. Central among these ideas is that of closure, which implies that all of the catalysts needed for an organism to stay alive must be produced by the organism itself, relying on nothing apart from food (and hence chemical energy) from outside. The theories that embody this idea to a greater or less degree are known by a variety of names, including (M, R) systems, autopoiesis, the chemoton, the hypercycle, symbiosis, autocatalytic sets, sysers and RAF sets. These are not all the same, but they are not completely different either, and in this review we examine their similarities and differences, with the aim of working towards the formulation of a unified theory of life. – Highlights: There have been many isolated attempts to define the essentials of life, A major unifying feature is metabolic closure, Metabolic closure requires some molecules to fulfill more than one function, There can be no hierarchy in the overall organization of a living system.

Key words: Origin of life, (M, R) systems, Autopoiesis, Chemoton, Self-organization

This article analyses the work of Robert Rosen on an interpretation of metabolic networks that he called (M, R) systems. His main contribution was an attempt to prove that metabolic closure (or metabolic circularity) could be explained in purely formal terms, but his work remains very obscure and we try to clarify his line of thought. In particular, we clarify the algebraic formulation of (M, R) systems in terms of mappings and sets of mappings, which is grounded in the metaphor of metabolism as a mathematical mapping. We define Rosen’s central result as the mathematical expression in which metabolism appears as a mapping f that is the solution to a fixed-point functional equation. Crucially, our analysis reveals the nature of the mapping, and shows that to have a solution the set of admissible functions representing a metabolism must be drastically smaller than Rosen’s own analysis suggested that it needed to be. For the first time, we provide a mathematical example of an (M, R) system with organizational invariance, and we analyse a minimal (three-step) autocatalytic set in the context of (M, R) systems. In addition, by extending Rosen’s construction, we show how one might generate self-referential objects f with the remarkable property f(f)=f, where f acts in turn as function, argument and result. We conclude that Rosen’s insight, although not yet in an easily workable form, represents a valuable tool for understanding metabolic networks.

Key words: (M, R) systems, Metabolic network, Metabolic closure, Infinite regress, Systems biology

Does natural selection favor veridical perceptions, those that more accurately depict the objective environment? Students of perception often claim that it does. But this claim, though influential, has not been adequately tested. Here we formalize the claim and a few alternatives. To test them, we introduce “interface games,” a class of evolutionary games in which perceptual strategies compete. We explore, in closed-form solutions and Monte Carlo simulations, some simpler games that assume frequency-dependent selection and complete mixing in infinite populations. We find that veridical perceptions can be driven to extinction by non-veridical strategies that are tuned to utility rather than objective reality. This suggests that natural selection need not favor veridical perceptions, and that the effects of selection on sensory perception deserve further study.

Key words: evolution, replicator dynamics, interface games, sensation, game theory.