Computational power and generative capacity of genetic systems

Generation of genetic codes with 2-adic codon algebra and adaptive dynamics

This is a brief review on modeling genetic codes with the aid of 2-adic dynamical systems. In this model amino acids are encoded by the attractors of such dynamical systems. Each genetic code is coupled to the special class of 2-adic dynamics. We consider the discrete dynamical systems, These are the iterations of a function F:Z2→Z2, where Z2 is the ring of 2-adic numbers (2-adic tree). A genetic code is characterized by the set of attractors of a function belonging to the code generating functional class. The main mathematical problem is to reduce degeneration of dynamic representation and select the optimal generating function. Here optimality can be treated in many ways. One possibility is to consider the Lipschitz functions playing the crucial role in general theory of iterations. Then we minimize the Lip-constant. The main issue is to find the proper biological interpretation of code-functions. One can speculate that the evolution of the genetic codes can be described in information space of the nucleotide-strings endowed with ultrametric (treelike) geometry. A code-function is a fitness function; the solutions of the genetic code optimization problem are attractors of the code-function. We illustrate this approach by generation of the standard nuclear and (vertebrate) mitochondrial genetics codes.

Toward understanding the emergence of life: A dual function of the system of nucleotides in the metabolically closed autopoietic organization

General structure of metabolism includes the reproduction of catalysts that govern metabolism. In this structure, the system becomes autopoietic in the sense of Maturana and Varela, and it is closed to efficient causation as defined by Robert Rosen. The autopoietic maintenance and operation of the catalysts takes place via the set of free nucleotides while the synthesis of catalysts occurs via the information encoded by the set of nucleotides arranged in polymers of RNA and DNA. Both energy charge and genetic information use the components of the same pool of nucleoside triphosphates, which is equilibrated by thermodynamic buffering enzymes such as nucleoside diphosphate kinase and adenylate kinase. This occurs in a way that the system becomes internally stable and metabolically closed, which initially could be realized at the level of ribozymes catalyzing basic metabolic reactions as well as own reproduction. The function of ATP, GTP, UTP, and CTP is dual, as these species participate both in the general metabolism as free nucleotides and in the transfer of genetic information via covalent polymerization to nucleic acids. The changes in their pools directly impact both bioenergetic pathways and nucleic acid turnover. Here we outline the concept of metabolic closure of biosystems grounded in the dual function of nucleotide coenzymes that serve both as energetic and informational molecules and through this duality generate the autopoietic performance and the ability for codepoietic evolutionary transformations of living systems starting from the emergence of prebiotic systems.

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

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.

Binary oppositions, algebraic holography and stochastic rules in genetic informatics

The article is devoted to the author's results of the algebraic analysis of molecular genetic systems, including a set of structured DNA alphabets and long nucleotide sequences in single-stranded DNA of eukaryotic and prokaryotic genomes. A connection of the system of DNA n-plets alphabets with principles of algebraic holography is shown, which concerns a popular theme of holography principles in genetically inherited physiology. In addition, a relation between DNA n-plets alphabets and the Poincaré disk model of Lobachevski hyperbolic geometry is revealed. This relation can explain known facts of the relationship of physiological phenomena with hyperbolic geometry. Considering long DNA sequences as a bunch of many parallel texts written in different n-plets alphabets led to the discovery of some universal rules of the stochastic organization of genomic DNAs. These rules are discussed concerning the general problem of the biological dualism "probability-vs-determinism". In general, the presented results give pieces of evidence in favor of the efficiency of a model approach to living organisms as quantum-informational algebraic-harmonic essences.

Complexification of eukaryote phenotype: Adaptive immuno-cognitive systems as unique Gödelian block chain distributed ledger

The digitization of inheritable information in the genome has been called the 'algorithmic take-over of biology'. The McClintock discovery that viral software based transposable elements that conduct cut-paste (transposon) and copy-paste (retrotransposon) operations are needed for genomic evolvability underscores the truism that only software can change software and also that viral hacking by internal and external bio-malware is the Achilles heel of genomic digital systems. There was a paradigm shift in genomic information processing with the Adaptive Immune System (AIS) 500 mya followed by the Mirror Neuron System (MNS), latterly mostly in primate brains, which reaches its apogee in human social cognition. The AIS and MNS involve distinctive Gödelian features of self-reference (Self-Ref) and offline virtual self-representation (Self-Rep) for complex self-other interaction with prodigious open-ended capacity for anticipative malware detection and novelty production within a unique blockchain distributed ledger (BCDL). The role of self-referential information processing, often considered to be central to the sentient self with origins in the immune system 'Thymic self', is shown to be part of the Gödel logic behind a generator-selector framework at a molecular level, which exerts stringent selection criteria to maintain genomic BCDL. The latter manifests digital and decentralized record keeping where no internal or external bio-malware can compromise the immutability of the life's building blocks and no novel blocks can be added that is not consistent with extant blocks. This is demonstrated with regard to somatic hypermutation with novel anti-body production in the face of external non-self antigen attacks.

Natural computation and its limits: Efim Liberman at the dawn of a new science

Efim A. Liberman (1925-2011) can be considered as a founder of the new field of science that explores natural computation and its limits. He named it Chaimatics and suggested its generalization to the ultimate all-encompassing theory that unites biology, physics and mathematics. He made a number of experimental discoveries, including color coding in the retina, the participation mechanisms of Ca²⁺ ions in synaptic transmission, and the measurement of potential in the coupling membranes of mitochondria and chloroplasts. He also made a decisive contribution to the proof of the chemiosmotic hypothesis of oxidative phosphorylation. In a series of works started in 1972, Liberman developed the concept of the molecular computer of the cell, which includes the programs written on DNA and RNA nucleotide sequences and executed by enzymes playing the role of processing units whereas nucleotide sequences are interpreted as commands and addresses. In this framework, Liberman predicted RNA splicing before its discovery and suggested the role of processing of small informational molecules (later defined as small RNAs) in controlling biological processes. Efim Liberman defined the fundamental property of life as a molecular and quantum computational system and introduced the idea of quantum computing inside a cell for making decisions on complex control tasks described by equations of mathematical physics. He approached the brain as a net of molecular computers and created a model of neuron operation based on the transmission of hypersound signals via cytoskeleton where the molecular computational system encodes the digital output. In 1979 Liberman published a hypothesis of human self-consciousness associated with not a chemical, but with a physical quantum coherent system and named it "extremal quantum regulator". We review here the contributions of Liberman in understanding the mechanisms of intracellular processing of information and his efforts to create an integrative theory of natural computation that aims to unite biology, physics and mathematics.

Mathematics in biological reality: The emergence of natural computation in living systems

Mathematics is a powerful tool to express the computable part of the reality of the physical world. For living systems, mathematical relations emerge internally as an abstracting capacity in the course of development and adaptation to the external world. All living systems possess internal coding structures which represent their embedded description. They are anticipatory in the sense that the embedded description generates deterministic model of their behavior. If the model does not provide a correct result, they can evolve through the acquisition of new statements inside the embedded description that overcome limitations of the existing model. The newly generated statements acquire meaning in and from the changing environment. The growth of complexity, being a consequence of the internal active adaptation to externality performed by the systems, increases the amount of external work and generates the observed patterns of spatiotemporal structures of evolving systems. In living systems, the symbolic memory constraints are dynamic processes in themselves, co-evolving with the other components of biological systems. Separation of the symbolic memory and the dynamic laws (defined as the epistemic cut), required for self-replication of biological systems, forms the basis for their onto-epistemic relation to reality. In this regard, living systems possess their own internal abstracting capacity and invent mathematics. The digital structure of the genetic code is a manifestation of this mathematics.

A quantum mechanical approach towards the calculation of transition probabilities between DNA codons

The role of quantum tunneling in altering the structure of nucleotides to each other and causing a mutational event in DNA has been a topic of debate for years. Here, we introduce a new quantum mechanical approach for analyzing a typical point-mutation in DNA strands. Assuming each codon as a base state, a superposition of codon states could provide a physical description for a set of codons encoding the same amino acid and there are transition amplitudes between them. We choose the amino acids Phe and Ile as our understudy bio-systems which are encoded by two and three codons, respectively. We treat them as large quantum systems and use double- and triple-well potential models to study the fundamental behaviors of them in interaction with a harmonic environment. We use the perturbation theory to calculate the transition probabilities between the codons which encoding the same amino acid and determine the transition rates of some point mutations. Moreover, we evaluate the quantum biological channel capacity for these transitions to show that the channel capacity depends on the system-environment interaction via the dissipation factor Γ. The obtained results demonstrate that the tunneling rate is under the control of capacity of the corresponding biological channel. In other words, the reduction in quantum channel capacity prevents the quantum tunneling rate to be increased.

Philosophy in Reality: Scientific Discovery and Logical Recovery

Three disciplines address the codified forms and rules of human thought and reasoning: logic, available since antiquity; dialectics as a process of logical reasoning; and semiotics which focuses on the epistemological properties of the extant domain. However, both the paradigmatic-historical model of knowledge and the logical-semiotic model of thought tend to incorrectly emphasize the separation and differences between the respective domains vs. their overlap and interactions. We propose a sublation of linguistic logics of objects and static forms by a dynamic logic of real physical-mental processes designated as the Logic in Reality (LIR). In our generalized logical theory, dialectics and semiotics are recovered from reductionist interpretations and reunited in a new synthetic paradigm centered on meaning and its communication. Our theory constitutes a meta-thesis composed of elements from science, logic and philosophy. We apply the theory to gain new insights into the structure and role of semiosis, information and communication and propose the concept of ‘ontolon’ to define the element of reasoning as a real dynamic process. It is part of a project within natural philosophy, which will address broader aspects of the dynamics of the growth of civilizations and their potential implications for the information society.

Thermodynamic buffering, stable non-equilibrium and establishment of the computable structure of plant metabolism

The equilibria of coenzyme nucleotides and substrates established in plant cells generate simple rules that govern the plant metabolome and provide optimal conditions for the non-equilibrium fluxes of major metabolic processes such as ATP synthesis, CO₂ fixation, and mitochondrial respiration. Fast and abundant enzymes, such as adenylate kinase, carbonic anhydrase or malate dehydrogenase, provide constant substrate flux for these processes. These "buffering" enzymes follow the Michaelis-Menten (MM) kinetics and operate near equilibrium. The non-equilibrium "engine" enzymes, such as ATP synthase, Rubisco or the respiratory complexes, follow the modified version of MM kinetics due to their high concentration and low concentration of their substrates. The equilibrium reactions serve as control gates for the non-equilibrium flux through the engine enzymes establishing the balance of the fluxes of load and consumption of metabolic components. Under the coordinated operation of buffering and engine enzymes, the concentrations of free and Mg-bound adenylates and of free Mg²⁺ are set, serving as feedback signals from the adenylate metabolome. Those are linked to various cell energetics parameters, including membrane potentials. Also, internal levels of reduced and oxidized pyridine nucleotides are established in the coordinated operation of malate dehydrogenase and respiratory components, with proton concentration as a feedback from pyridine nucleotide pools. Non-coupled pathways of respiration serve to equilibrate the levels of pyridine nucleotides, adenylates, and as a pH stat. This stable non-equilibrium organizes the fluxes of energy spatially and temporally, controlling the rates of major metabolic fluxes that follow thermodynamically and kinetically defined computational principles.

I-Ching, dyadic groups of binary numbers and the geno-logic coding in living bodies

The ancient Chinese book I-Ching was written a few thousand years ago. It introduces the system of symbols Yin and Yang (equivalents of 0 and 1). It had a powerful impact on culture, medicine and science of ancient China and several other countries. From the modern standpoint, I-Ching declares the importance of dyadic groups of binary numbers for the Nature. The system of I-Ching is represented by the tables with dyadic groups of 4 bigrams, 8 trigrams and 64 hexagrams, which were declared as fundamental archetypes of the Nature. The ancient Chinese did not know about the genetic code of protein sequences of amino acids but this code is organized in accordance with the I-Ching: in particularly, the genetic code is constructed on DNA molecules using 4 nitrogenous bases, 16 doublets, and 64 triplets. The article also describes the usage of dyadic groups as a foundation of the bio-mathematical doctrine of the geno-logic code, which exists in parallel with the known genetic code of amino acids but serves for a different goal: to code the inherited algorithmic processes using the logical holography and the spectral logic of systems of genetic Boolean functions. Some relations of this doctrine with the I-Ching are discussed. In addition, the ratios of musical harmony that can be revealed in the parameters of DNA structure are also represented in the I-Ching book.

The quantum basis of spatiotemporality in perception and consciousness

Living systems inhabit the area of the world which is shaped by the predictable space-time of physical objects and forces that can be incorporated into their perception pattern. The process of selecting a "habitable" space-time is the internal quantum measurement in which living systems become embedded into the environment that supports their living state. This means that living organisms choose a coordinate system in which the influence of measurement is minimal. We discuss specific roles of biological macromolecules, in particular of the cytoskeleton, in shaping perception patterns formed in the internal measurement process. Operation of neuron is based on the transmission of signals via cytoskeleton where the digital output is generated that can be decoded through a reflective action of the perceiving agent. It is concluded that the principle of optimality in biology as formulated by Liberman et al. (BioSystems 22, 135-154, 1989) is related to the establishment of spatiotemporal patterns that are maximally predictable and can hold the living state for a prolonged time. This is achieved by the selection of a habitable space approximated to the conditions described by classical physics.

Inverse Bayesian inference as a key of consciousness featuring a macroscopic quantum logical structure

To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions.