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Coherence As a Basis of Computational Properties in Metabolic Networks

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Coherence As a Basis of Computational Properties in Metabolic Networks BioSystems 50 (1999) 1–16 Foundations of metabolic organization: coherence as a basis of computational properties in metabolic networks Abir U. Igamberdiev * Department of Plant Physiology and Biochemistry, Voronezh State Uni6ersity, Voronezh 394693, Russia Received 4 March 1998; received in revised form 3 August 1998; accepted 31 August 1998 Abstract Biological organization is based on the coherent energy transfer allowing for macromolecules to operate with high efficiency and realize computation. Computation is executed with virtually 100% efficiency via the coherent operation of molecular machines in which low-energy recognitions trigger energy-driven non-equilibrium dynamic processes. The recognition process is of quantum mechanical nature being a non-demolition measurement. It underlies the enzymatic conversion of a substrate into the product (an elementary metabolic phenomenon); the switching via separation of the direct and reverse routes in futile cycles provides the generation and complication of metabolic networks (coherence within cycles is maintained by the supramolecular organization of enzymes); the genetic level corresponding to the appearance of digital information is based on reflective arrows (catalysts realize their own self-reproduction) and operation of hypercycles. Every metabolic cycle via reciprocal regulation of both its halves can generate rhythms and spatial structures (resulting from the temporally organized depositions from the cycles). Via coherent events which percolate from the elementary submolecular level to organismic entities, self-assembly based on the molecular complementarity is realized and the dynamic informational field operating within the metabolic network is generated. © 1999 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Coherence; Computation; Futile cycle; Information transfer; Metabolic network; Morphogenesis; Non- locality; Switching 1. Introduction The temporal and the spatial organization of biosystems is essentially determined by their dy- namic structure which in turn is based on * Department of Plant Physiology, University of Umea˚, S-901 87 Umea˚, Sweden. Tel.: +46-90-786-5422; Fax: +46- metabolic organization. The limited energy auton- 90-786-6676; e-mail: [email protected]. omy of living systems from local, high-energy 0303-2647/99/$ - see front matter © 1999 Elsevier Science Ireland Ltd. All rights reserved. PII: S0303-2647(98)00084-7 2 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 potentials is achieved via their internal metabolic digital information is realized within hypercycles structure by the sensitivity to non-local low-en- and corresponds to the operation of the genetic ergy fluxes. A certain subsystem (the ‘epistemon’) code. is capable of interactions with these low-energy In terms of quantum mechanics, Planck’s con- constraints (Barham, 1990, 1996). This explains stant determines the condition of the smallest the adaptive behavior of biological systems and possible time interval that is necessary to transfer their internal dynamical organization. The inter- the energy of a wave to the ideal detector system action between the high-energy (based on the (Popp, 1995), and real times of measurement form dynamic coherent non-equilibrium energy-driven concrete patterns of interactions leading to the processes) and the low-energy constraints (based realization of coherent events and formation of on quantum coherent phenomena) underlies bio- spatial structures. Dicke (1959) showed that the logical organization (Igamberdiev, 1992, 1993). ordinary imaging of spontaneous reemission of Low-energy recognitions, possibly based on the light from optically dense media (i.e. interference bosonic fields, trigger energy-driven non-equi- pattern) becomes completely changed as soon as librium dynamic process. mutual distances of absorbing molecular antennae The concept of coherence as an organizing prin- get much smaller than the wavelength of light. ciple of biological structures was introduced by These events based on multiple propagation and Gurwitsch (1923) who formulated the idea of a diffraction can significantly improve the degree of low-energetic field determining the biosystem’s or- coherence of light. Sequential quantum measure- ganization as a total entity. In his views, this field ments generate a time irreversible process orga- determines the continuous operation of a biosys- nized as a set of multiple coherent events (Dicke, tem, whereas the discrete representation of biosys- 1989). On macroscales coherence involving en- tems is illustrated by the Mendelian, genetic ergy-driven ordering of processes represents an- approach. On a quantum level, a coherence via other scale of coherent phenomena. Coherence is synchronization of phases of the wave functions a physical representation of the integrative princi- between different components possessing non-lo- ple coordinating individual events in the orga- cal character is realized. Quantum coherence nized state. means that the de Broglie wavelengths of the The goal of this paper is to trace coherent particles are overlapping, and their trajectories events from the macromolecular to the morpho- emerge through a dynamical form-generating pro- genetic level, and to define possible ways for cess. It determines properties at a certain space- theoretical description of metabolism which func- time point when they are known at another. tions as an interconnecting network for different Coherent states involving Bose–Einstein conden- levels of organization of biosystems. I will discuss sation (the most ordered form of condensed phase how the computable events are formed and main- possible when a macroscopic number of particles tained by the coherent phenomena. A variety of occupies the same single-particle state) actually models have been proposed which may fit to- bridge the gap between micro and macroscales, gether in the framework of coherence. Some of realizing the ‘prehension’ (Whitehead, 1929) of ideas presented here are difficult to examine ex- single points into total entities. perimentally at present, however, it is important The dynamics of enzymes and high-order struc- to introduce them as a basis for further discussion tures is explained by coherent phenomena of biological organization. (Fro¨hlich, 1983). The quantum coherent state is limited by the minimum uncertainty condition (Li, 1995), allowing for the provision of computa- 2. Enzyme operation as a cyclic process with tion and information transfer with almost 100% coherent energy transfer efficiency. The information based on specific recognitions triggering dynamical energy-driven The enzyme molecule is a basic unit of biologi- processes appears as non-digital; the transfer of cal organization. Recognition of substrates by A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 3 enzymes is connected with the correspondence of There is an essential provision and enhance- the active site of the enzyme to certain molecular ment of computation via coherence. It is possible coordinates of a substrate (key-lock paradigm). It that this may be based on the emergence of the is an example of molecular complementarity entangled particles within the enzyme molecules (Root-Bernstein and Dillon, 1997) percolating to which are involved in the transformation of the different levels of biological organization. In gen- initial state (corresponding to interaction with eral, the recognition process is quantum–mechan- substrate molecule) to the final state (of the re- ical in nature, being a non-demolition leasing of a product molecule) as was shown measurement characterized by low energy dissipa- for the quantum teleportation phenomenon tion and hence by high precision (Igamberdiev, (Bouwmeester et al., 1997). The computation 1993, 1998). During this process, the bosonic should be executed with virtually 100% efficiency fields mediate momentum exchange between the which is realized via the non-demolition coherent enzyme and the substrate leading to the formation operation of molecular machines. Coherent dipole of joint coordinate scale and then to the redistri- oscillations were for the first time postulated by bution of atoms within new coordinates (the con- Fro¨hlich (1983) for explanation of enzyme opera- version of a substrate into product). The joint tion which should be based on the resonant elec- wave function may collapse whenever the two tromagnetic energy transfer on a frequency bosonic fields (of the enzyme and the substrate) specific for each observed interaction. Proteins overlap and share an identity (or when they cease and their targets may have the same characteristic to do so) (Zohar, 1990). frequencies. A soliton-like mechanism was pro- Such a mechanism for enzyme–substrate inter- posed to be involved in the resonance recognition action is speculative, however, it is indirectly sup- process (Ciblis and Cosic, 1997), and excitations ported by the experiments of Comorosan (1975) produce oscillations of particular frequencies. who observed the enhancement of enzymic activi- The energy released when a substrate is recog- ties which appear only at sharply defined sub- nized by the enzyme molecule (which corresponds strate irradiation times at certain wavelengths. to a new coordinate scale emerged) turns the The following parameters were introduced: (a) a latter into the different alternate conformation minimum substrate irradiation time inducing the which results in the realization of the actual work first effect (tm) and (b) a fixed time period that delimits two successive effects
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