Neuron quantum computers and a way to unification of science: A compendium of Efim Liberman's scientific work.

In 1972, Efim Liberman, a Soviet biophysicist, pioneered a brand-new approach to studying the operation of the brain, the live cell and the human mind by publishing a paper titled "Cell as a molecular computer" (1972). In this paper, Liberman posited that a consecutive/parallel stochastic molecular computer (MCC) controls a living cell. An MCC operates with molecule-words (DNA, RNA, proteins) according to the program recorded in DNA and RNA. Computational operations are implemented by molecular operators acting as enzymes. An MCC is present in each live cell. A neuron cell MCC can be involved in solving tasks for the entire organism. Neuron MCC investigation was started with studying an impact of an intracellular injection of cyclic AMP on electric activity of a neuron. Cyclic nucleotides were considered as input words for an MCC, which are generated inside a neuron as a result of synaptic activity. This led Efim Liberman to the idea that, in order to solve complex physical problems, which are encountered by a neuron and require rapid solutions, the molecular computer adjusts the operation of the quantum molecular regulator, which uses the "computational environment" of the cytoskeleton and quantum properties of the elementary hypersound quasiparticles for completing mathematical operations for the minimum price of action. Efim Liberman suggested that the human self-consciousness is a quantum computer of even a higher level and designated it as an extreme quantum regulator. In order to describe such systems, he suggested to join biology, physics and mathematics into a unified science, and formulated its four fundamental principles. Results of Efim Liberman's theoretical and experimental studies on the topic of biological computation are summarized in this review.

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.

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.

Computational power and generative capacity of genetic systems.

Semiotic characteristics of genetic sequences are based on the general principles of linguistics formulated by Ferdinand de Saussure, such as the arbitrariness of sign and the linear nature of the signifier. Besides these semiotic features that are attributable to the basic structure of the genetic code, the principle of generativity of genetic language is important for understanding biological transformations. The problem of generativity in genetic systems arises to a possibility of different interpretations of genetic texts, and corresponds to what Alexander von Humboldt called "the infinite use of finite means". These interpretations appear in the individual development as the spatiotemporal sequences of realizations of different textual meanings, as well as the emergence of hyper-textual statements about the text itself, which underlies the process of biological evolution. These interpretations are accomplished at the level of the readout of genetic texts by the structures defined by Efim Liberman as "the molecular computer of cell", which includes DNA, RNA and the corresponding enzymes operating with molecular addresses. The molecular computer performs physically manifested mathematical operations and possesses both reading and writing capacities. Generativity paradoxically resides in the biological computational system as a possibility to incorporate meta-statements about the system, and thus establishes the internal capacity for its evolution.