Overcoming the limits of natural computation in biological evolution toward the maximization of system efficiency

Abstract

The goal-directedness of biological evolution is realized via the anticipatory achievement of the final state of the system that corresponds to the condition of its perfection in self-maintenance and in adaptability. In the course of individual development, a biological system maximizes its power via synergistic effects and becomes able to perform external work most efficiently. In this state, defined as stasis, robust self-maintaining configurations act as attractors resistant to external and internal perturbations. This corresponds to the local energy–time constraints that most efficiently fit the integral optimization of the whole system. In evolution, major evolutionary transitions that establish new states of stasis are achieved via codepoiesis, a process in which the undecided statements of existing coding systems form the basis for the evolutionary unfolding of the system by assigning new values to them. The genetic fixation of this macroevolutionary process leads to new programmes of individual development representing the process of natural computation. The phenomenon of complexification in evolution represents a metasystem transition that results in maximization of a system’s power and in the ability to increase external work performed by the system.

INTRODUCTION: LIVING SYSTEMS ARE TELEONOMIC

Living systems continuously reproduce their own components to support their integrity, which is defined as autopoiesis (Varela et al., 1974; Heylighen, 2014). The integrity of the system represents an attractor to which it generally approximates, and this state is formed in a series of successive changes during individual development (Heylighen, 2022). Autopoiesis involves circular autocatalysis and is closed to efficient causation in Aristotelian terms (Rosen, 1991). The causal autopoietic mechanism continuously forms and supports the system’s ‘self’, which is perceived internally by the system as a set of qualia. Such systems, being circularly causal, behave as they strive to achieve some goal state (Heylighen, 2014). In fact, these systems are robust to external influences, being able to return to their state of self-maintenance, representing the property defined as conatus in philosophical systems (Damasio, 2003). Conatus can be conceived, from the perspective of autopoiesis, as ‘the twofold purposiveness of identity and sense-making’ (Thompson, 2007: 162). Haukioja (1982) emphasized the need for a process of life theory separate and apart from evolution (a theory of change). The process of evolution represents an expansion of the integral autopoietic state, which corresponds to the expansion of coding systems.

Thus, autopoiesis, being the property of self-maintained systems, is complemented by the property of codepoiesis (Barbieri, 2015), which can be described metamathematically as Gödel numbering (Igamberdiev, 2021; see also Shelah & Strüngmann, 2021) and represents an expanding phenomenon via assigning new meanings to the elements of the coding system, the process that Heraclitus defined as the Self-Growing Logos (‘logos heauton auxon’). The same process was described by Gunji et al. (2017) as an inverse Bayesian inference, and in the evolution of language it takes place via the creation of metaphors (Barbieri, 2020). All this means that biological systems expand beyond the natural computational process (Louie, 2020), and this substantiates a creative nature of biological evolution and its intrinsic property of complexification.

The selective meaning of newly generated coding systems is tested at the level of the phenotype. In the process of evolution, we observe an increase in phenotypic plasticity, and the appearance of consciousness corresponds to the maximum known phenotypic plasticity. This phenomenon was captured by Baldwin (1896) who formulated the effect of the causal role of purposeful behaviours in shaping natural selection, and on how this influenced the rise of biological complexity in evolution. The purposefulness or goal-directedness of biological systems is defined as teleonomy (Pittendrigh, 1958) and can be substantiated via the effects of an increase in phenotypic plasticity, which is manifested as a measurement of genotype by phenotype (Rosen, 1996), or as the principle of genetic assimilation formulated by Waddington (1959). The final successful ‘goal state’ can retrocausally (downward) also shape the early stages of development (Cherdantsev & Scobeyeva, 2012; Shishkin, 2018). The capacity for genome self-modification (Shapiro, 2016, 2022a, b) makes a prerequisite for the downward causation in evolution under the challenging conditions of ecological disruption, while the teleonomic process itself is developed as a complexification phenomenon that cannot be reduced to random processes, and involves the generation and interpretation of new coding systems (Igamberdiev, 2021). However, this is not simply a backward causation but rather a ‘reticulate natural causation’ that occurs between the distinct and interacting ontological hierarchies (Gontier, 2010; Sukhoverkhov & Gontier, 2021). One example of such reticulate causation is symbiogenesis (Agafonov et al., 2021; Corning, 2021), one of the essential evolutionary mechanisms of complexification.

The formulation of Alfred North Whitehead (1929) of evolution as ‘a creative advance into novelty’ assumes that those states having zero probability within the existing system can be reached in evolutionary transformations, and this is a creative evolutionary process. A similar conceptual framework was developed by David Bohm based on quantum mechanics. Bohm stated that ‘various successive living forms unfold creatively. Later members are not completely derivable from what came earlier, through a process in which effect arises out of cause … The law of this unfoldment cannot be properly understood without considering the immense multidimensional reality of which it is a projection’ (Bohm, 1980: 269–270). This concept of Bohm appears from his notion of ‘implicate order’, which contrasts with mechanistic order in physics.

Goal-directedness assumes the existence of a temporal programme to achieve the teleonomic state during individual development. This programme manifests as the operation of natural computation (Igamberdiev & Brenner, 2021). While the operation of genetic programmes does not implicitly include the temporal element of its unfolding, the programme of attaining the final state characterized by the maximization of power must include the temporal component, i.e. the encoding of temporality to achieve the integral goal-directedness in the course of individual development. Thus, the programme encompasses all ‘proximate’ (functional) biological phenomena, and it is not limited to an a priori ‘programme’ (the genome) in the sense of Mayr (1974), which was based on circular reasoning (Ayala, 1998; Krieger, 1998). It includes an ex post facto, means–ends teleonomy (Pittendrigh, 1958; Corning, 2019). I discuss here the approaches to understand how this internal programme functions in biological systems and how it expands in the course of evolution. The principle of maximum power, introduced by Lotka (1922), represents an ability to prevail against disturbance through autocatalytic feedbacks incorporated in the combined hierarchical organization, and can be realized when the system is effectively controlled through its subsystem, which is efficiently shielded from energy flows (Igamberdiev, 2007).

NATURAL COMPUTATION IN ORGANISMAL DEVELOPMENT AND EVOLUTION

The idea of natural computation arises from Leibniz (1714). Leibniz defined living systems as automata exceeding infinitely all artificial automata. The individual units of Being (agents) defined as monads in his concept perform computation by realizing their own programmes. These programmes interact via the external relational space-time, which is formed as an outward arrangement of realization of these programmes. The term ‘automata’ should be used not in the sense of mechanical clockwork (which was criticized for example by Nicholson, 2018) but more as sophisticated, problem-solving, self-referential (autonomous) robust machines (Haukioja, 1982; Kuchling et al., 2022). The process of evolution generates these ‘robust problem-solving living machines’ (Clawson & Levin, 2022). In the foundations of mathematics, Leibniz’s programme was recently implemented by Vladimir Voevodsky (1998). His concept of univalent foundations shapes an approach in which mathematics is regarded operationally as a computational activity incorporated in the dynamical processes of reality (Grayson, 2018; Rodin, 2021). In his framework, the basic mathematical structures correspond to objects called types. Voevodsky’s type theory is a deductive system with suitable rules of inference and with the goal of instrumentation of mathematical proofs, which become testable within the context of this theory via computation.

This approach provides insight into the development of real foundations of theoretical biology. In these foundations, the type of hierarchy that deals with part–whole relationships and defined as meronomy (or partonomy) is studied, in contrast to taxonomy whose categorization is based on discrete sets (Meyen, 1978; Sharov & Igamberdiev, 2014). These relationships can be associated with types in the concept of univalent foundations (Voevodsky, 1998), but with reference to their operation in the real world that includes external reality. Developmentally determined laws of possible transformations of particular characters (morphogenetic realization of meron as an object part) underlie computational transfigurations of biological structures (Vasiliev, 2009). For living systems, mathematical relationships emerge internally as an abstracting capacity in the course of development and adaptation to the external world (Matsuno, 2014).

All living systems possess internal coding structures which represent their embedded description. They are anticipatory in the sense that the embedded description generates a deterministic model of their behaviour. In other words, the anticipatory system has an internal model used to decide what action has to be taken. The discrepancies between the expected outcome and the new condition of the world (including the system itself) will trigger the acquisition of new statements (i.e. the internal model becomes updated). If the model does not provide a correct result, the system can adapt or evolve through the acquisition of new statements inside the embedded description that overcome limitations of the existing model. The newly generated statements acquire their meanings in and from the changing environment (Igamberdiev, 2015a). This matches the learning process of active inference, in which the systems minimize a free energy function of their internal states (Friston, 2010; see also Vanchurin et al., 2022a, b).

With regard to biological systems, the problems of evolution can be clarified via the paradigm of natural computation. One of the basic approaches in this direction was developed by Efim Liberman in the 1970s. He suggested the concept of the molecular computer of the cell, which operates by using the programmes written on DNA and RNA nucleotide sequences and executed by the enzymes playing the role of processing units, with nucleotide sequences interpreted as commands and addresses (Liberman, 1972, 1979). On this basis, Liberman predicted RNA splicing before its discovery and suggested the role of processing of small informational molecules (later associated with small RNAs) in tuning biological processes. Liberman defined the basic characteristic of life as a molecular and quantum computational system and introduced the idea of quantum computing in biological systems for fulfilling complex control solutions. He considered the brain as a net of molecular computers and created a model of neuron operation based on the transmission of hypersound signals via the cytoskeleton where the molecular computational system encodes the digital output. Liberman (1979) also published a hypothesis of human self-consciousness associated not with a chemical but with a physical quantum coherent system and named it as ‘extremal quantum regulator’ (Shklovskiy-Kordi & Igamberdiev, 2022).

The fundamental basis underlying the computable and non-computable aspects of biological systems was revealed by Robert Rosen (1991) who presented an alternative to a classical dualistic genetic model of the biological system. He represented a living system as an (M,R) system, where M refers to metabolism and R to repair. Letelier et al. (2006) associated R with replacement rather than with repair, i.e. the elements of the metabolic system are continuously replaced, the elements that replace them are also replaced and this can go on to the infinite regression. However, Rosen stated that the system can be ‘closed to efficient causation’ and can contain the internal principle of organizational invariance (Rosen, 1991), which results in avoiding infinite regression and closing the system in a stable non-equilibrium state in which the system, remaining open to material flows, becomes selective to them and affords being closed to efficient causes that are locked inside of it. By formulating these basic principles, Rosen introduced the general basic structure for life, which has the capacity for progressive development via internal rearrangements with the simultaneous redefinition of its organizational invariance. Rosen’s theory contains an approach to formulate a relevant formal apparatus for describing biological systems, which represents a unique attempt to structure the formal basis for describing living systems. Rosen introduced the concept which describes life as an ontologically independent, i.e. organizationally invariant, phenomenon. Its state maintains and keeps its invariant structure in the changing world (Rosen, 1991; see also Cornish-Bowden & Cárdenas, 2020).

Organizational invariance is a prerequisite of computability within the system, while living systems nevertheless operate beyond computability and cannot be reduced to their formal models. The (M,R) representation of living system inexactly parallels the division of operative information (OI) for ‘regulating a self-maintaining and potentially replicating automaton’ into maintenance information (MI) and reproductive information (RI) suggested by Haukioja (1982). MI regulates those structures and functions serving to maintain the automaton. RI determines the formation of new automata. Haukioja (1982) further subdivides MI into at least four functions – for resource supply, environmental stimuli, internal processes (which could be equivalent to metabolism + DNA repair) and allocation of resources.

The idea of evolution based on expansion of the process of natural computation was incorporated by James Shapiro (2016, 2022a, b) in his concept of natural genetic engineering (NGE). According to Shapiro (2013, 2017), evolutionary variations generating phenotypic adaptations and novel taxa result from complex cellular activities altering genome content and expression: (1) symbiogenetic cell mergers produced the mitochondrion-bearing ancestor of eukaryotes and chloroplast-bearing ancestors of photosynthetic eukaryotes; (2) interspecific hybridizations and genome doublings generated new species and adaptive radiations of higher plants and animals; and (3) interspecific horizontal DNA transfer encoded virtually all of the cellular functions between organisms and their viruses in all domains of life.

Donald Williamson (2003) proposed that symbiogenesis has occurred across phyla. Consequently, assuming that evolutionary processes occur in isolated genomes of individual species has become an unrealistic abstraction. Adaptive variations also involved natural genetic engineering of mobile DNA elements to rewire regulatory networks (Shapiro, 2016, 2017). In the most highly evolved organisms, biological complexity scales with ‘non-coding’ DNA content more closely than with protein-coding capacity, which is reflected as the C-value paradox (Zuckerkandl, 1976). Coincidentally, we have learned how so-called ‘non-coding’ RNAs that are rich in repetitive mobile DNA sequences are key regulators of complex phenotypes (Gurtan & Sharp, 2013). Both biotic and abiotic ecological challenges serve as triggers for episodes of elevated genome change. The intersections of cell activities, biosphere interactions, horizontal DNA transfers and non-random read–write genome modifications by natural genetic engineering provide a rich molecular and biological foundation for understanding how ecological disruptions can stimulate productive, often abrupt, evolutionary transformations, often through the formation of hopeful monsters (Dietrich 2003; Chouard, 2010) – the idea proposed by Geoffroy Saint-Hilaire (Iurato & Igamberdiev, 2021).

The relationship between natural computation and unfolding biological structures in the processes of development and evolution was analysed from the thermodynamic perspective by Vanchurin et al. (2022a, b). This theory aims to merge learning and thermodynamics into a single, coherent framework for modelling biological evolution. It associates the origin of life with a phase transition that gave rise to a distinct, highly efficient form of a learning algorithm, which can be realized via natural selection. In this context, major evolutionary transitions are considered as phase transitions, where two distinct grand potentials, characterizing units at different levels (e.g. molecules vs. cells), become equal or dual, and, as a result, the lower-level units display collective behaviour within the whole system forming a meronomical (part–whole) relationship (Meyen, 1978). The evolving biological systems, being open to the fluxes of matter and energy, are closed (to efficient causation, in Rosen’s terms) in reaching the final state of equilibrium, which is actually a long-living state of stable non-equilibrium. This is related to the notion of ‘dynamic tension’ emerging ‘at the edge of chaos’, according to Norman Packard’s concept as interpreted by Brian Goodwin (1994). In other words, in biological systems, stability is often dependent on a highly energetic dynamic involving feedback, which has certain parallels with the concept of tensegrity of Buckminster Fuller, which is applicable in embryology (Gordon & Gordon, 2016a, b).

Figure 1 presents the incorporation of the arrows of the central dogma of molecular biology into the structure of the (M,R) system of Rosen (1991), redesigned from its modification presented in Igamberdiev & Shklovskiy-Kordi (2016). The scheme reflects evolutionary transformations, in which M corresponds to the maintenance and R to the evolutionary reconstruction of a biological system. The pool of nucleic acids is organized into stably fixed and combinatorial pools, the latter formed through the generative dynamics of evolutionary language game in the sense of Ludwig Wittgenstein (1953). The scheme introduces an interpretation of elements of the combinatorial nucleic acid pool via the phenotypic actualization in protein sets for testing their functionality, and a subsequent memorization of useful combinations representing the fixed points of the states of stable non-equilibrium and corresponding to the system’s goals. The central dogma in its original representation is considered by Denis Noble (2021) to be an illusion, and the current representation shows it as a part of the more extended structure where replication, transcription and translation are only parts of the relational organization of the biological system.

EVOLUTIONARY LANGUAGE GAMES

An active combinatorial process of modification of information, which represents an internalized language game and corresponds to the process of natural computation, allows a system to expand and create new codes, i.e. it corresponds to codepoiesis (Barbieri, 2015). Natural computation has its limits, but it also has a property of overcoming these limits, and this corresponds to evolution. Any sufficiently powerful consistent logical system is incomplete. According to Gödel’s incompleteness theorem, it has true statements expressed by the language inherent to this system which cannot be proven within its framework. This assumes that the foundation of these statements exists outside the formal language of the system being imposed, through the creative process of evolutionary transformation. The proof of Gödel’s incompleteness theorem is based on the attribution of metamathematical statements about the formal system into the system itself. Through this essentially non-deterministic process, certain elements of the formal system attain the properties reflecting a whole system via the encoding of these metamathematical statements about the whole system. This procedure, of generating reflective arrows defined as Gödel numbering, generates the condition in which previously non-formalized basic relationships and operations within the system are converted into relationships and operations having a simple algorithmic nature. As a result, a programme appears which can be used for construction of a model of the system as an interpretation in the formalized language. In biological systems, encoding represents an internal property of a whole system: the code is a consequence of a reflection of the entity (living system) into the finite set of its molecular structures (Igamberdiev, 1998).

The appearance of new encoding systems corresponds to construction of new formulae (new Gödel numbers), and for this it is necessary to overcome the limits of the existing formal system, i.e. to realize ‘a metatheoretic jump’ for encoding a new possible organization. This jump cannot be deterministically inferred from the existing formal system. This increase in ‘informational content’ is non-algorithmic, as the interaction between individual computational systems non-computably generates emergent phenomena (Kampis, 1996). This means that the truth of a new formula cannot be proven by finite means. In real functional languages as a means of communication the ambiguity is internally embodied, which incorporates this non-deterministic aspect in their structure (Solé & Seoane, 2015). Newly generated structures acquire their meanings not in relation to the previously existing reality, but to the changed reality non-recursively modified after the inclusion of this structure within it. This is the basic principle of the Red Queen concept that organisms adapt evolutionarily to the landscape in which competing organisms also are evolving (Van Valen, 1973). The evolved system is positioned in relation to a non-predefined evolutionary landscape.

Expansion beyond the existing computational process occurs via the vast generation of combinatorial rearrangements in search of the true Gödel number (Markose, 2022). The purposefulness of this combinatorial activity consists in the goal-directedness of finding the fixed point where f(x) = x, which corresponds to the condition of stasis (Gould & Eldredge, 1993), or stable non-equilibrium state (Bauer, 1920, 1935). Such activity cannot be reduced only to the mutational process and includes active combinatorial transformations intensified under stress conditions in the course of adaptation to novel environmental changes. The capacity for active rearrangements according to molecular addresses was postulated by Liberman (1972, see also Shklovskiy-Kordi & Igamberdiev, 2022). Olovnikov (2022) has suggested that major combinatorial events in the evolution of eukaryotes are associated with the meiotic eco-crossover that uses stress-dependent versions of circular RNAs synthesized as variants of alternative splicing. These circular RNAs, binding to homologous epimutations on the homologous parent chromosomes of the meiocyte, produce topologically specific recombinations that create random mutations in non-random genomic sites.

The irreversibility of transformations follow from their metatheoretical logical foundations, according to which a newly appearing coding structure is non-deducible from the existing structure and cannot be obtained by reversible logical operations. The transformation in evolution appears to be analogous to the creation of new formulas (Gödel numbers), which were absent in the initial formalized calculus. The active combinatorial process of self-modification of information via molecular addresses, being an internalized language game, has a prerequisite to generate wide possibilities for creating Gödel numbers. The new solution appearing during evolution cannot be obtained in a recursive combinatorial way. Therefore, evolution cannot be predicted with certainty; it can be only prognosticated with more or less exactness (Matsuno, 1992).

The evolutionary language game without strictly fixed rules can be internalized within a system into a concrete dynamics of transformation of genetic material during individual development. From this perspective, it will represent a history of evolutionary innovation, which is reflected as a recapitulation. Finite time of observation propagation (Gunji, 1994), i.e. the realization of information, is an important part of competition between programmes: they may differ in their intrinsic times of realization, and this leads to specific development of a dynamic process and to the possibility of its evolutionary rescaling (Igamberdiev, 2014). The previous elements of a coding system can attain new values, establishing a new level of the system’s organization. The logical basis of evolution is incompleteness of the coding system, which allows it to ascribe arbitrary values to the statements which cannot be proven in the frameworks of this system. During complexifying macroevolution, the values are assigned to the previously undefined variables via their encoding by using new codes or rearranging the old ones (Igamberdiev, 2021).

In the continuous natural process of proving Gödel’s theorem, every new proof corresponds to a new equilibrium state, matching to a discrete state of evolutionary stasis. In fact, what is termed ‘equilibrium’ by Gould & Eldredge (1993) in reality represents a discrete stable non-equilibrium state that is generally distinguished from other states by the absence of smooth transitions, i.e. corresponding to punctuated equilibrium. The new stasis corresponds to a new archetype, and, correspondingly, to a new relationship of parts to the whole, which can be analysed within the framework of meronomy approaches. The epimorphism principle introduced in biology by Nicolas Rashevsky (1967), and represented by Rosen (1991) as the principle of organizational invariance, is an important foundation of the whole-part relationship in meronomy. It claims that different organisms can be mapped onto each other such that the basic relationships characterizing the organism as a whole are preserved, i.e. all organisms are topologically invariant with respect to qualitative relationships within them.

The evolutionary process of achieving the final state of stasis through the parallel interrelated sequence of events representing the unfolding of natural computation and of the natural dynamic processes is presented in Figure 2. In this evolutionary process, the underlying physical quantum uncertainty, appearing as incomplete identification in the interaction between organism and environment, matches the logical undecidability, which is resolved through the formation of a new statement about the system with its following memorization in the coding structures. This corresponds to the intrinsic growth of complexity appearing as the development of hierarchy between levels of the system.

THE HYPOTHESIS OF TEMPORAL CODE IN INDIVIDUAL DEVELOPMENT

It is difficult to explain individual development of multicellular organisms consisting of spatiotemporal patterns of switching different genes through the known rules of operation of the genetic coding system. The temporal organization of complex organisms requires the temporal programming of concrete developmental processes that result in the final fully developed state characterized by maximization of the system’s power. The temporal organization of biological systems is modified in evolution via time rescaling (Igamberdiev, 2014), which includes acceleration of certain stages, anticipation of new structures that become fully established at future stages of evolution (Gould, 1977) and merging of different structures through symbiogenesis. In these processes, the evolutionary history of attaining new structures is reflected in the process of individual development, which is accentuated in the concept of recapitulation (Mayr, 1994). The latter reflects the property of heredity as a memory, i.e. of the evolutionary learning process, which itself represents an indirect indication of the temporal code. The necessity of a temporal coding mechanism was stated by Korochkin (1981, 2002), who associated it with repeated sequences in the genome acting as biological clocks.

The process of unfolding of structures during morphogenesis includes the phenomenon of hyper-restoration, which can be considered as an expansion of the stable non-equilibrium state in its attribution to the developing complex organisms (Beloussov, 2015). It is realized, in particular, when the interactions of cytoskeletal fibrils form the type of positional energy that is fed by external non-equilibrium fluxes but produces internal outputs resulting in complexification of the structure of a developing organism. Morphogenesis can be analysed in terms of the continuous hyper-restoration events that finally lead to the formation of a stable non-equilibrium state characterized by the maximization of power via the optimization of energy–time constraints. The problem of internal programming of hyper-restoration and hence of morphogenetic unfolding is the central one in developmental biology (Igamberdiev, 2018). It is not yet fully resolved but it is possible to outline the basic principles of encoding of temporal development. The most well-known and fully established temporal programme determines the process of ageing; this is the telomerase mechanism predicted by Olovnikov (1973) and empirically established later (Blackburn et al., 1989).

Hyper-restoration phenomena are closely associated with the emission of coherent quanta that can transmit information and coordinate morphogenetic events in multicellular structures (Igamberdiev, 2015a). Alexander Gurwitsch (1922, 1923), who introduced this idea, considered coherent photons as mitogenetic rays emitted in the course of cell division and transferring morphogenetic information to adjacent cells (see also Gurwitsch & Gurwitsch, 1959). This process, which was indirectly confirmed in several more recent studies (Cifra et al., 2010; Cifra, 2012), has certain similarities with the ideas of Liberman (1979) on the transmission of signals via the cytoskeleton through which the molecular computational system encodes the digital output. This type of mechanism may represent an alternative mode of communication to the coding processes that operate in the establishment of the pattern of differentiation. The postulated differentiation code and the transmission of coherent quanta can work together in establishing the structural pattern of the multicellular organism in its final goal-directed state.

‘The novelty of continuing differentiation’ (Gordon, 1999), which results in multitype multicellularity, awaits explanation from the viewpoint of natural computation. Richard and Natalie Gordon made an important attempt to explain embryogenesis by postulating the temporal code of differentiation (Gordon & Gordon, 2016a, b, 2019). They suggested that the differentiation code is associated with the structure resembling the mitotic spindle for the individual eukaryotic cell but expanded to a multicellular level. They discovered and described a structure, which they termed the ‘cell state splitter’, in axolotl embryos. The cell state splitter in axolotl ectoderm contains a microfilament ring, a mat of microtubules at the apical surface and an intermediate filament ring (Martin & Gordon, 1997). The microtubules and microfilament ring are in mechanical opposition within a tensegrity assembly. This structure, which is a membraneless organelle, produces two types of propagating waves (contraction or expansion) and generates the parametrical differentiation tree in which each tissue is designated by a binary differentiation code based on the sequence of contraction/expansion waves its cells have experienced (Gordon & Gordon, 2016a, b, 2019). The cell splitter operates in a bistable mode, in which perturbations cause it to contract or expand radially while the intermediate filament ring provides metastability against small perturbations. Like the mitotic spindle in cell division, this structure works at the level of the multicellular organism and triggers cell differentiation (Gordon, 2021; Gordon & Stone, 2021).

Further work is needed to establish the mechanisms that result in attaining the final fully developed state that is characterized by thermodynamic characteristics first outlined by Lotka (1922), possessing an ability to prevail against disturbance through the autocatalytic feedbacks incorporated in its combined organization, the property defined as ascendency (Ulanowicz, 1997). The morphogenetic development of biological systems results ultimately in alteration of their organization and energy flow structure such that the useful energy transformation becomes maximized via the constrained release of energy that delays the production of entropy (Kauffman, 2020). This means that the energy flows in biological evolution can be evaluated via economic criteria such as productivity, efficiency, and the costs and benefits (‘profitability’) of various mechanisms for capturing and utilizing energy to build biomass and do work (Corning, 2020, 2022). This essential property underlines the goal-directedness of biological development (Gordon & Stone, 2016) corresponding to the criteria outlined in the principle of Lotka (1922) and its more modern interpretations (Odum, 1995).

CHARACTERISTICS OF STASIS IN EVOLUTION

Although the common view considers the achieved stable states in evolution as states of equilibrium (Gould & Eldredge, 1993; Shishkin, 2018), in fact they represent the stable non-equilibrium states in the sense of Bauer (1935). The basic properties of these states can be analysed from the physical point, which includes thermodynamic approaches and Rosen’s relational analysis. In fact, the stable 
non-equilibrium states are based on the balance between equilibrium and non-equilibrium reactions. The equilibrium (buffering) reactions appear as a source of useful energy for biochemical systems (Shnoll, 1979; Igamberdiev & Kleczkowski, 2009, 2019), and this energy can be used to drive the processes requiring energy consumption such as ATP synthesis, CO₂ fixation, transfer of genetic information, etc. The shifts in the equilibria determine development of the system and the limits of its adaptability.

Filling buffer reservoirs corresponds to the accumulation of useful energy. One of the most common examples is bicarbonate buffering via carbonic anhydrase, which plays an essential role in vital physiological processes such as carbon fixation in photosynthesis (Igamberdiev, 2015b). This buffer, as well as the phosphate buffer, operates effectively at a pH close to neutral. The use of nucleoside triphosphates and in some organisms of pyrophosphate (Igamberdiev & Kleczkowski, 2021) as the source of energy (‘energy currency’) is based on the utilization of the stored energy of the phosphate buffer (Igamberdiev & Kleczkowski, 2009). The breakage of a phosphate bond results in local acidification, and protons stored in phosphate buffer are released for catalysis (via enzymes) or for mechanical movement (via actin). This reaction can then be coupled with thermodynamically unfavourable reactions, driving biosynthetic processes. By using ATP in enzymatic reactions or cytoskeleton movement, the release of energy from the phosphate buffer becomes vectorized, and such vectorization is achieved during enzymatic reactions through the link between ATP hydrolysis (accompanied by the release of a proton) and an endergonic metabolic process. This drives the conformational changes in protein molecules and supports mechanic macromolecular processes (Igamberdiev & Kleczkowski, 2009). For the endergonic reaction of ATP synthesis, it has experimentally been shown that it can operate at optimal efficiency only if conductance of the load, i.e. the ATP-utilizing reactions in a living cell, is exactly matched by the output conductance of oxidative phosphorylation (Stucki, 1980). This is achieved via buffering as a result of the adenylate kinase equilibrium (Igamberdiev & Kleczkowski, 2003).

The autopoietic state assumes a joint operation of not only the equilibrium and the non-equilibrium reactions, where the equilibrium reactions serve as a source of energy for the operation of non-equilibrium reactions, but also of the energetic and the information fluxes within the whole system. This can be analysed via the adaptation of Rosen’s theory of (M,R) systems (Rosen, 1985). In the condition of metabolic closure, which is central to this theory, some elements fulfil the role of ‘double duty’, serving both as energetic and as informational components. The factor of organizational invariance functions as a parameter that redistributes and links energetic and informational components such that they are tightly equilibrated through the balance of energy and information fluxes. This factor goes beyond reductionistic molecular approaches and represents an integral whole parameter that drives biological development as a goal-directed process (see Wolpert, 1994; Laubichler & Wagner, 2001).

In complex systems, the function is ‘spread’ over the parts of the system in a manner which does not map one to one onto those parts. The main idea of relational biology (Rosen, 1991) is that functional components have the same reality as the parts, if not more so, a very profound notion. What is replicated is a functional component, not a material part as such. From this point of view, the distinction between genotype and phenotype is dynamic and flexible, so it is not possible to define what is primary and what is secondary. Evolution is based on the re-establishment of the parameter of organizational invariance rather than on independent and casual changes in the genotype.

The arrangement of the equilibrium and non-equilibrium reactions determines the stability of the hypercyclic organization of biological systems (Igamberdiev, 1999), which corresponds to its autopoietic state. Note here that the autopoietic state corresponds to the dynamic condition of the stasis, while the evolutionary transitions that connect these states in the landscape of punctuated equilibrium correspond to the process of codepoiesis (Barbieri, 2015), which cannot be fully predicted and is modelled metamathematically as a generation of new coding statements (Igamberdiev, 2021).

In the evolutionarily achieved condition of autopoietic stasis, the biological organism efficiently maximizes its power via synergistic effects. Alfred Lotka (1922), who formulated this principle, even considered it as the fourth principle of energetics in open-system thermodynamics. He viewed the state of maximization of power as a general attractor in the evolutionary dynamics of open systems. Bauer (1935) also came to the conclusion that the most essential characteristic feature of the evolutionary process is a capacity of evolving biological systems to increase in their external work. According to Odum & Pinkerton (1955), during self-organization biological systems, as examples of open systems, maximize the intake of power and the transformation of energy to reinforce their functional efficiency and reproduction (Odum, 1995). This represents the case of goal-directedness, as it results in an ability to prevail against disturbance through the autocatalytic feedbacks incorporated in the system’s autopoietic organization. The most optimal integration of parts into the organized whole corresponds to the local energy–time constraints that most efficiently fit to the integral optimization of the whole system. The energy–time uncertainty ratio is the basis of non-demolition measurements that underlie the optimized operation of biological macromolecules (Igamberdiev, 1993, 2004). The integration of local non-demolitions into the organized whole system in its ascendant perspective represents the state in which its efficiency as an integral unit is optimized by gaining the whole spectrum of ability to discover and utilize resources (Freeman, 2020).

Evolutionary concepts claiming the existence of the general intrinsic laws of form transformation (Berg, 1922, Meyen, 1973; Van Valen, 1982; Lima de Faria, 1997) suggest that the laws of evolution are based on objective rules of transformations of forms independent of adaptability and natural selection. In reality, a new feature appears in evolution initially as an exaptation, which is an anticipation of the future adaptation, representing a feature available for advantageous cooptation by descendants (Gould & Vrba, 1982). This enhances fitness without having a current role being empowered by the functional value in the course of evolution. Berg (1922), in his concept of nomogenesis, called them ‘anticipations of phylogenesis by ontogenesis’ and suggested that they play a role in ‘phylogenetic acceleration’, i.e. in time rescaling (Igamberdiev, 2014). In fact, the ‘laws of evolution’, which are not explicitly formulated in the concept of nomogenesis, represent the directed trajectories toward the teleonomic final state characterized by the maximization of power. These trajectories initially appear as duplications of parts of differentiation trees and represent the basis for macroevolution (Gordon, 1999). In this context, nomogenetic evolution acquires a rational explanation. Microevolution represents a change of the differentiation tree that preserves the topology of the tree, while macroevolution denotes any change that alters the topology of the differentiation tree.

The most efficient maximization of power of the system assumes its effective control by its subsystem, which is efficiently shielded from energy flows and approaches zero entropy. This can be reached in highly ordered coherent states that can exist, in particular, inside the macromolecular complexes (Matsuno & Paton, 2000; Igamberdiev, 2004, 2007). The appearance of DNA that stores the information, which is more flexibly exchanged at the level of RNA, became the efficient controlling event that enabled the reproduction and shaping of living systems as organizationally invariant entities. The very high accuracy of DNA replication appears not as a property of the DNA itself, but is instead a function of the whole living cell, which is a vast and complex array of DNA repair systems (Noble, 2018, 2021). The stable non-equilibrium system of living organism maintains and supports the internal quantum state (IQS), which is a decoherence-free subspace shielded from thermal fluctuations (Igamberdiev, 2004, 2007), with its most coherent part corresponding to perception and conscious activity. It governs the rest of the body of a complex living system by sending the commands to it and ensuring that the heat machine of the organism operates with maximum power and efficiency. Generally speaking, IQS is the most advanced form of quantum known in the Universe. IQS holds the superposition of the potential contradictory states and it is mapped to a macroscopic measuring device (‘body’), sending commands to it (Igamberdiev, 2007).

INTERNAL CONTROL IN BIOSYSTEMS

The view of living systems subdivided into low- and high-energy parts constitutes the basis of theoretical biology as it was formulated by Jakob von Uexküll (1909). This idea was further developed in the foundations of molecular biology. According to Pattee (2001), the evolutionary process is possible upon the separation of energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control, which Pattee defined as the epistemic cut. Such control is achieved via the process of measurement in which the dynamic state is coded into molecular symbols. These symbols represent the system of codes that are interpreted in the context of the whole biological organization (Barbieri, 2015). The process of internal measurement (Matsuno, 1995) includes the measurement of genotype by phenotype (Rosen, 1991, 1996), in which the dynamic coding structures are interpreted, rearranged and reassembled, which involves the dynamic part of the coding system represented by RNA (Witzany, 2016). The dynamic cycles create internal closure events, and thus provide an engine for creating novelty when the boundary conditions of the system foster the constraints that fundamentally change the phase space (Lehman & Kauffman, 2021; Roli & Kauffman, 2020). The principle of an epistemic cut is viewed by Pattee (2001) as the basic foundation of life. In the dynamic cycle of information perception and processing described by von Uexküll (1909) and reformulated by Barham (1996), low- and high-energy processes are united in the single dynamic system adapting to the environment. This becomes the basis of generating the boundary between the object and the subject (Rosen, 1993). A biological system thus can anticipate its response to external stimuli, and, as Matsuno (2022) mentioned, any biological organism as the internal observer is retrocausal in identifying and feeding upon the necessary resources.

The Funktionkreis introduced by von Uexküll (1909) depicts the interconnection between the low-energy recognition of external signals and the high-energy activity of the operation of a biological system. This concept describes how the self-supporting energy autonomy of living systems from local high-energy potentials is achieved via their internal metabolic structure based on the sensitivity to non-local low-energy fluxes. The Funktionskreis encompasses the coherence, adaptation and interaction between the system (acting as a subject) and its environment (the Umwelt appearing as an objective external reality) as a purposeful whole (‘planmäßiges Ganzes’). Funktionskreis is related to Corning’s definition of control information (CI) and to Haukioja’s MI, which include resource acquisition and allocation (Haukioja, 1982). Corning (2001) defined CI as ‘the capacity (know how) to control the acquisition, disposition and utilization of matter/energy in purposive (cybernetic) processes.’

Thus, biological dynamics includes both low- and high-energy processes separated through the epistemic cut. To function successfully, a biological organism should efficiently maximize its power via synergistic effects, a principle formulated by Lotka (1922), as discussed above. A biological cell represents an example of an open system (Odum & Pinkerton, 1955), which during self-organization maximizes power intake and energy transformation in order to reinforce production and efficiency (Odum, 1995). The maximum power principle was confirmed empirically (Cai et al., 2006). Individual development of the system continuously transforms the organization and energy flow structure of the system such that the useful energy transformation becomes maximized. This results in its ability to prevail against disturbance through the autocatalytic feedbacks incorporated in its combined organization, the property defined as ascendency (Ulanowicz, 1997). According to Bauer (1935), a capacity for an increase in external work is the main characteristic feature of the evolutionary process.

Schrödinger’s statement that the aperiodic crystal forming the hereditary substance is largely withdrawn from the disorder of heat motion means that the physical principle, which is similar to Nernst’s law, is realized in biological systems (Schrödinger, 1944). Although the relationship of stability and accuracy to certain structures in biological systems is essentially incorrect, representing a function of the whole living entity (Noble, 2018, 2021), Schrödinger’s concept grasps the fact that a living system contains an entangled state controlling its dynamics and shielded from heat motion.

These entangled states, at least at higher levels of organization, are experienced as qualia that allow the dynamic actions in which the initial states are used to accomplish the resulting outputs to be perceived. A prerequisite for this entangled shielded part of a living system is the principle of a steady non-equilibrium state formulated by Ervin Bauer (1920, 1935). This means that Nernst’s Third Law of Thermodynamics is as essential as the Second Law for biological processes. However, it should be properly understood and adequately formulated to explain its importance for living systems. A special approximation to very low dissipation of energy via the maintenance of quantum coherence within a heat engine can be achieved in living systems, which can be seen as equivalent to the approximation to zero temperature (Igamberdiev, 1993, 2004).

It is claimed that super-cold states composed of the identical wave function (Bose–Einstein condensates) are impossible in living systems, but the shielded states in heat engines of living bodies possess similar physical properties (Khrennikov, 2022). Iosif Rapoport (1965) in his book Microgenetics, in an attempt to explain why the transmission of information in biological systems occurs with a very high degree of precision, suggested that only in living systems can the orderly state be reached at temperatures of ~300 K, and considered this property inherent to living systems as the new law of thermodynamics operating in biology. In fact, such orderly states can be described as having ‘effective’ temperatures close to 0 K, and reached in highly ordered coherent states existing inside macromolecular complexes (Matsuno & Paton, 2000). In a recent paper, Khrennikov (2022) distinguishes between the orderly coherent states described by Fröhlich (1983) and realized at high temperatures, and the Bose–Einstein condensates appearing at ultralow temperatures. While, according to the Third Law of Thermodynamics of Nernst, the zero entropy state can be reached only in the conditions of zero temperature (0 K), in fact, low-energy dissipation in orderly coherent states also refers to their ultralow ‘effective’ temperatures (in the range of nano- and microkelvin) may indicate the similar nature of orderly coherent Fröhlich states and Bose–Einstein condensates. The rescaling of energy–time constraints at the molecular level provides the flexibility of the integral organization of a biological system and its adaptability to changing external conditions.

The quantum coherent state is limited by the minimum uncertainty condition allowing for the provision of computation and information transfer with almost 100% efficiency, which is described by the model of quantum non-demolition measurement (Igamberdiev, 1993). The information based on specific recognitions triggering dynamical energy-driven processes is non-digital, while the transfer of digital information is realized within functional hypercycles and corresponds to the operation of the genetic code. Almost 100% efficiency of information transfer in biological systems, not only at the level of genetic information but also in the enzymatic catalysis, which provides the turnover of nucleic acids, lipids, carbohydrates and other compounds, can be described as a close-to-zero entropy state of macromolecular biological systems, as was originally suggested by Rapoport (1965).

Thus, the physical structure of a biological system incorporates the two states, one being a low-energy coherent state and corresponding to the internal knowledge of itself, and the other being a high-energy dynamic state corresponding to the dynamic action of the system. Their opposition constitutes the principle of the epistemic cut and represents the basic foundation of living organization. The highly ordered coherent state constrains the release of energy to a few degrees of freedom in non-equilibrium processes (Kauffman, 1995, 2020). Achieving maximum power appears as a teleonomic attractor in the development of an individual biological system in the sense of a robust condition characterized by the property of the introduction of the system’s integrity. It is possible upon the precise control achieved through low-dissipation mechanisms that provide precise reactions of the system toward certain stimuli. We can conclude that the functional autocatalytic cycle of a living process is based on the two inseparable thermodynamic principles, one being the principle of minimum dissipation achieved in the steady states of open systems, which could be realized not only near equilibrium (Prigogine, 1980) but also in the stable non-equilibrium state inherent to living matter (Bauer, 1920), and the other representing the maximum power principle of the system’s actual realization (Lotka, 1922). Both represent the dual principle of biological organization and substantiate the teleonomic nature of biological systems.

In fact, the states with low energy dissipation correspond to the states of high order (low entropy) described by the third law of thermodynamics, and their link to the high-energy states represents the controlling information in the organization of living matter (Corning, 2001). The principle of maximization of power introduced by Lotka as the fourth thermodynamic law realized in living systems directly relates to the subdivision of the system into the controlling (low-energy) and controlled (high-energy) parts. The maximization of power can take place only when it is controlled by the highly ordered coherent state of the system determining its organizational invariance.

CONCLUSIONS

The process of evolutionary transformations generally corresponds to the model of punctuated equilibrium, according to which the appearance of a species results in a long-lasting stable state defined as stasis, characterized by little evolutionary change for most of its geological history (Gould & Eldredge, 1993). Rare geologically rapid events of branching speciation (cladogenesis) correspond to splitting species into two or more, rather than to a gradual transformation. Living systems evolve via a search for a new stasis upon the loss, under critical conditions, of effective regulation of normal development (Shishkin, 2018). The concept of goal-directedness assumes that the primary evolutionary object is not just DNA but rather a whole living cellular system in the stable non-equilibrium state, which is realized, in particular, at the later stages of development. Its disturbance under new conditions drives evolution toward the transition to a new stable non-equilibrium (evolutionary stasis) through the duplication of parts of the differentiation tree. Retrocausally, disturbance of the fully developed stage leads to remodelling of the developmental system in its earlier stages. This process explains the teleonomic feature of the evolutionary process, in which phenomena such as recapitulation, anticipation of new evolutionary changes and metasystem transition obtain the concrete logical justification that naturally describes the goal-directedness of the evolutionary process.

ACKNOWLEDGEMENTS

This article is a contribution to a special issue on Teleonomy in Living Systems, guest edited by Richard I. Vane-Wright and Peter A. Corning, based on a Linnean Society meeting held on 28/29 June 2021. The author thanks the guest editors, and also Richard Gordon and Marcello Barbieri, for their inspiration and involvement in discussing the ideas presented in this paper. Special thanks also for the anonymous reviewers who provided detailed suggestions and comments that helped to improve the manuscript. This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors. The author has no conflicts of interest to declare.

DATA AVAILABILITY

There are no data underlying this work.

REFERENCES