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 denoted by the ~ of substrate conversion into the product (Blumen- parameter (Comorosan et al., 1972). Different feld, 1983). This conformational movement passes enzymes and isozymes reveal higher activities at slowly, providing for the transition to a macro- different irradiation times. scopic time scale. This fact can explain high spe- Computational power of enzymes cannot be cificity of enzyme operation in accordance to the deduced from their elementary structure: it is quantum non-demolition measurement theory of essentially unprogrammable (Conrad, 1992). Elec- Braginsky et al. (1980) (Igamberdiev, 1992, 1993). tronic-conformational interactions during an Enzyme operation corresponds to the realization enzyme’s operation constitute a non-classical- of a ‘squeezed’ state in quantum measurement, classical interface through which percolation to which is considered as a basic event in informa- the macro level is realized (Conrad, 1984, 1994). tion transfer and computation (Braginsky and Wave function reduction (collapse of superposi- Khalili, 1992). Slow conformation changes in tions) must continually occur due to the continual biomolecules allow for a long-lived transition redefinition of forces between particles. Such me- state within which many of energy quanta corre- diation of forces takes place during enzyme opera- late coherently (Matsuno, 1995). tion (in electronic-conformational interactions). In the presence of a substrate, the process of Therefore we can view the visible structures of conformational movement is connected with the biological systems as exploiting the unmanifest realization of highly effective and specific actual structures of the vacuum in order to perpetuate work. The reverse transition in the enzyme–sub- themselves (Conrad, 1996). strate cycle is identical to the transition in the 4 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 absence of substrate molecule. During this transi- The energy release after substrate sorbtion in tion the energy which is not transformed into the the active site leads to the division of charges actual work is released, and this corresponds to its inside the enzyme–substrate complex resulting in dissipation. The direct (with substrate) and the their deposition in different parts of the protein reverse (after releasing a product) conformational molecule (Green and Vande Zande, 1981). A sim- movements of an enzyme molecule are realized by ilar deposition of charges takes place on the oppo- different routes, and there is an elementary cyclic site sides of biomembranes during the structure representing the catalytic process. This chemiosmotic process. Here the basic quantum cycle is characterized by different pathways for coherence participating in the initial recognition the enzyme–substrate complex formation and de- process triggers dynamic energy-driven coherence. composition. According to Conrad (1979), an en- Long-range mobile protonic states are the most zyme can be considered as a macromolecule essential coherent events in organized cellular pro- which makes possible a cyclic reaction involving cesses via which interactions of the electronic and an energy loan which is used for barrier removal the nuclear degrees of freedom are realized. The and which arises from transient pairing. energy of the divided but non-locally connected The enzyme–substrate cycles are characterized charges is used for substrate conversion via break- by a clear distinction between the catalyst and the age and formation of chemical bonds. Therefore substrate and therefore by hierarchical (two-level) the effect of deposition (in this case of charge structure. In oscillatory chemical reactions, an deposition) is essential during enzyme–substrate interactions. Enzymes serve as intermediary intermediate serves at a certain stage as a catalyst, agents in coupling mobile protons to chemical whereas in the enzyme–substrate cycle the cata- reaction coordinates (Welch and Berry, 1983). lyst is strongly distinguished from the substrate After the formation of a cycle, the non-equi- and acts as a molecular machine. The direct and librium state is consistently reproduced according the reverse vectors forming the cycle are found to to the principle of steady non-equilibrium state be quite different: in the presence of a substrate formulated by Bauer (1935). Thus, the cycle is the initially linear structure of the reaction is represented as an elementary non-equilibrium transformed into the cyclic structure and switch- structure which determines the temporal (rhyth- ing (logical gate) is realized. The absence of dis- mic) and the spatial (morphological) parameters tinction between the catalyst and the substrate in of the biosystem. The first parameters are deter- biosystems is evident only during the processing mined by the periods of cycle turnover, whereas of biological macromolecules, e.g. in autocatalytic the second are determined by the depositions splicing of RNA-precursors and also during from the cycles. protein folding which is regarded as an autocata- Coherence within cycles is maintained by the lytic process based on intramolecular specific supramolecular organization of enzymes forming recognitions (Conrad, 1979; Veeraraghavan et al., cycles which are assembled in multienzyme com- 1996). We can hypothesize that enzymatic cataly- plexes (metabolons). Assembly in metabolons is sis was built over these autocatalytic processes possible because of the specific recognition of which themselves were ‘improved’ via participa- molecules of different enzymes, and of specific tion of chaperonins filtering out of intramolecular relation of consequent enzyme to preceding en- interference so that incorrect associations are zyme-product complex (Welch and Berry, 1985). avoided. Enzymatic catalysis may have been pre- The enzymes constituting metabolons are orga- ceded by the less specific and slower primarily nized in such a way that the enzymes of the direct catalytic process realized by molecules now serv- and reverse routes are regulated reciprocally in a ing as coenzymes (Maden, 1995). Emergence of metabolon structure, e.g. dehydrogenases of the autocatalysis from the simple chemical reactions Krebs cycle forming NADH are connected with of lower amino acids was proposed by Gurwitsch NADH dehydrogenase of electron transport chain and Gurwitsch (1942). (Srere, 1987) and that organization facilitates A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 5 metabolic channeling and maintenance of the therefore with the reaction of ATP generation, NADH/NAD ratio in a homeostatic manner par- whereas in the reverse reaction only phosphate ticularly in response to external influences. It has release takes place. The significant change in free been proposed that the metabolic channeling of energy makes possible the realization of the direct NAD(P)H occurs between dehydrogenases differ- route only in connection with ATP breakdown ing in stereospecificity (to A- and B-hydrogen whereas the reverse reaction can occur without atoms of nicotinamide ring) (Srivastava and Bern- linkage to pools of adenine nucleotides. The direct hardt, 1987). and the reverse reactions in this case are catalyzed The macromolecular complexes have configura- by two different enzymes, and the initially linear tions which allow coherent energy transduction path is transformed into the cyclic one. Its opera- and machine-like computational properties tion leads to energy waste, therefore the cycle is (Schneider, 1991). They are often associated with considered as an indirect ATPase or as a futile the non-equilibrium energy sources (e.g. proton cycle. gradients) and realize a conformational cycle co- The initial uncoupled structure of futile cycle ordinated with a corresponding metabolic cycle or seems to be very disadvantageous, but transition process. The direct and the reverse paths are to a hierarchical organization with strongly cou- therefore non-locally connected by the proton pled reaction networks converts it into a powerful fluxes (Welch and Berry, 1983). These systems can mechanism of reciprocal regulation of the direct effectively channel metabolites and are examples and reverse metabolic pathways, i.e. it serves as a of kinetic perfection (Ova´di, 1991). metabolic switcher. Allosteric kinetics is effective for the reciprocal regulation of the two enzymes forming the futile cycle. It results in the effective 3. Switching in futile cycles regulation of the direct and reverse routes in such a way that these reactions become separated in The enzyme–substrate interaction can be repre- time and the energy loss is minimized (Koshland, sented as a cyclic structure (enzyme molecule un- 1984). The separation between the direct and re- dergoes cyclic conformational transition), whereas verse reactions seems to be the initial precondition substrate conversion into a product is a linear for the appearance of networks of increasing life- process. The enzyme does not displace chemical time and stability. equilibrium in triggering the linear route of reac- Regulation of activity of enzymes also can be tion. In general, this route is reversible, and only achieved via their covalent modifications, which is transformation of this linear route into the cyclic regulation of the directions of metabolic processes one can be considered as a precondition to the via futile cycles. The enzymes which regulate ac- formation of a branched metabolic network. tivity of other enzymes were selected during evo- The separation between the direct and reverse lution in the direction of their slower operation routes of biochemical reaction, one being linked which avoids energy loss (Koshland, 1984). The (coupled), whereas the other non-coupled with the covalent and allosteric regulation generated dur- pool of certain (often energy-rich) compounds, ing the transformation of a futile cycle into the results in symmetry-breaking and in ‘‘inequality’’ reciprocal regulatory mechanism leads to a new between the direct and reverse pathways. Conse- hierarchical level in which the enzyme serves as quently, separation between the direct and reverse both catalyst and regulated molecule. Contrary to reactions leads to the generation of an elementary trivial competitive or non-competitive inhibition, metabolic substrate cycle (Igamberdiev, 1994). allosteric regulation often needs the complication Reactions connected with the essential change of enzyme structure via the inclusion of regulatory of free energy, e.g. linked with phosphate transfer domain into a molecule. As a result, feedbacks or oxidation–reduction, are preferable for the and feedforwards are generated in metabolic generation of such elementary cycles. The direct structures and the distant points in metabolic reaction can be coupled with ATP utilization and pathways become ‘stuck together’ via the regula- 6 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 tory interactions. This can lead to the generation they can play different roles, all connected with of oscillations and to relaxation periods of up to a the specific recognition. They can serve as special- minute or more in the system. The integration of ized substrates (coenzymes), as switchers between many individual reactions into systemic units can the direct and reverse (e.g. catabolic and anabolic) be achieved by the mechanisms of allosteric mod- routes of metabolism, and (via polymerization) as ulations, transport mechanisms, etc. (Marijua´n matrices for the reproduction of catalysts them- and Westley, 1992). selves. In the last case we see transition from the Reciprocal regulation in futile cycles maintains switching network to information transfer in hy- energy charge and reducing potential of the cell in percycles (via encoding). A low-energy recogni- a homeostatic manner. ATP/ADP/AMP and tion process turns on high energy processes NAD(P)H/NAD(P) ratios themselves behave as connected with charge separation and proton universal switchers for many enzyme systems, act- transfer, and dynamic energy homeostasis is ing as their allosteric regulators, and the rate and achieved within the system. direction of metabolic flow are determined by the ratios of nucleotides. Connection between high and low energy con- 4. Generation of bifurcations and formation of straints is realized via recognition of weak forces metabolic cycles by ‘epistemons’, and this results in the phe- nomenon of ultrasensitivity (Koshland, 1987). The transformation of a reversible enzymatic The amplified output which corresponds to ultra- reaction into two practically irreversible reactions sensitivity is possible because of switching, or creating a cycle leads to the possibility of genera- threshold phenomena. It is achieved either by the tion of bifurcations and to the formation of functioning of enzymes as switchers and includes metabolic cycles (a possible scenario outlined be- allosteric phenomena generating cooperativity, low). It is common that enzymes catalyzing corre- zero-order ultrasensitivity by reversible covalent spondingly the direct and reverse reactions are modifications of enzymes following Michaelis– distinguished by their specificity. Demolition in Menten kinetics, or by the combination of these enzyme–substrate interactions in one branching two factors. The switching phenomenon is multi- of a futile cycle leads to the formation of new plied in metabolic sequences by means of multi- mappings and the generation of order (complica- step ultrasensitivities (an allosteric effector tion of a metabolic informational field). A non- activates or inhibits more than one enzyme in a coherent event (bifurcation) after internalization pathway as in glycogen synthesis and degrada- within a metabolic network becomes a coherent tion), by branchpoint ultrasensitivity (as in event (in the dynamic process). This internaliza- branchpoint combination of the slower rate of tion takes place via a new molecular complemen- formation of a compound and the faster rate of tarity provided by the establishment of a new its depletion can cause the step to decrease by a coherent structure. This may take place in the factor of hundreds), or by amplification of sensi- quantum potential field and generate a new ap- tivity by a combination of different types of am- propriate realization from the changed field of plified outputs. By this the transition from possibilities. It cannot be deduced deterministi- low-energy non-local input to high-energy re- cally from the previous structure. The new state sponse of the system is realized and an exchange vector reduction describes how a previously stable of signals loaded by meaning is possible. state of the system (corresponding to one of the The cost of regulation can be very high, e.g. the preferred states) becomes unstable (or metastable) cost of covalent regulation reaches 20% of energy upon a change in environment and has to be available in the biosystem, but maintaining of resolved to a new stable state. This corresponds to homeostasis is the price of this cost (Koshland, the phenomenon of the establishment of the co- 1987). Nucleotides are molecules which can be herent states via decoherence (Zurek et al., 1993). specifically acknowledged by enzymes, therefore The system of mappings constructs the classical A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 7 dynamical coherence as order generation from growth, filling in such voids is an emergent self- chaos. generating process. We can consider the forma- Oxidase is usually less specific than reductase tion of metabolic networks as spontaneous in and operates with a higher turnover number. A complex systems (Kauffman, 1993), but this splitting is therefore possible in an oxidative reac- process is essentially a non-local and non- tion with increasing metabolic flow. During evolu- computable phenomenon of molecular comple- tion, the generation of bifurcations was mentarity based on coherence between its differ- significantly promoted by the effects of oxygen ent constituents. Proton circuits connecting diff- (Gottlieb, 1989). erent metabolic paths may maintain non-locality. In general, a change in relaxation time leads to Thus, formation of a biochemical cycle is the alteration in specificity of biomacromolecules to result of evolutionary transformation of a certain certain interactions, and this can result in branch- reaction into different direct and reverse reactions ing behavior. Irreversible symmetry-breaking and subsequent ‘unfolding’ of the initial futile emerges from indefinite states provided by quan- cycle. This corresponds to transition from simple tum measurements. Classical macroscopic bifurca- uncoupled processes to the integrated strongly tions seem to be a consequence of quantum coupled reaction networks. The splitting of oxida- properties of biosystems, and generation of a tive–reductive reactions leads to the generation of metabolic network emerges from quantum phe- bifurcation in one branch and consequently to the nomena. Quantum uncertainty in molecular inter- appearance of alternative mapping (alternative actions is a powerful engine in the formation of pathway of metabolic conversion). The latter, af- complex metabolic structure within biosystems ter several stages, can result in the formation of a (Matsuno, 1992), and is realized on a quantum- compound identical to the initial substrate. There- classical interface. fore the futile cycle subsequently unfolds into the Bifurcations can be generated in the oxidative– complete metabolic cycle. reductive futile cycle because of the lower specific- The unfolding of a futile cycle into a metabolic ity of the enzyme in its oxidative branch. Heat cycle often needs more additional reactions. The production in dissipative oxidative reactions can initial oxidative reaction of a futile cycle in the also promote generation of bifurcations. The in- formed metabolic cycle becomes only a regulatory crease of flow via the oxidative path, influenced reaction making possible a shortened pathway, by environmental inputs, results in changes of pH and it can regulate the redox balance in the cell. and of other parameters which also promote alter- The origin of the metabolic cycle from the initial native conversions of metabolites. There typically futile cycle determines its essential structure in will be existing enzymes with some non-specific which it is always possible to distinguish between activity toward newly formed compounds. The the two halves (or branchings): the catabolic and genetic redundancy resulting from gene duplica- the anabolic. The catabolic branch is commonly tions and from other genome reconstructions is a oxidative, whereas the anabolic branch can in- precondition for the further specialization of en- clude reduction and condensation. The structure zymes. During evolutionary transformations the of metabolic cycles leads to separate regulation of isozymes acquire specificity to different substrates the two branchings and to differences in their that are similar in structure. The gradients of intensity, so that the outflow of compounds from dynamic information are generated in metabolic one half of the cycle for alternative conversions network at the multiple symmetry-breakings can result. within the overall network of ‘wet symmetries’ The absence of coupling with an energy store in (Marijua´n, 1996b). Functional voids appearing in the oxidative branch, being a precondition of the the system (in this case they are deviations from futile cycle transformation into a metabolic cycle, normal trajectories) precondition the complication can be compensated by the arising of new linkages of structure and of informational capacity of the which decrease the initial dissipation of energy. system, and, in systems capable of evolutionary This is the main reason for the promotion of 8 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 the futile cycle transformation into a metabolic 5. Rhythms and depositions cycle, can be compensated by the arising of new linkages which decrease the initial dissipation of The separation between the direct and reverse energy. This is the main reason for the promotion reactions within the coherent volume of a whole of excessive anabolism by catabolic processes im- system as its dynamically coherent-linked parts portant for biological transformations in ontogen- and their reciprocal regulation lead to the subdivi- esis and evolution. More rapid passage of certain sion in time of the direct and reverse flows and to stages of individual development resulting from the appearance of the internal rhythm within the the elimination of linkages with energetic pools system fed by the external energy supply. The determines the possibility of neothenic processes. direct and reverse metabolic pathways become The acceleration resulting from the ‘reduction’ of connected with the two depots between which the certain stages accompanied by higher dissipation substances can flow with a certain period. Trans- of energy can lead to the formation of new port systems between compartments are necessary metabolic pathways and new morphological struc- for providing these oscillations since the depot tures. These considerations are consistent with the should be compartmentally separated from the ideas of phylogenetic acceleration and of the metabolic part. ‘ontogenetic forestalling of phylogenesis’ (Berg, Every half of the cycle is connected with its 1977). own depot, and oscillations between these depots Arguably, all essential complications in evolu- can be provided by the changes in the balance between the rates of the direct and reverse reac- tion corresponding to the formation of a new tions of the cycle. The generation of oscillations metabolic process are initially energetically disad- can occur only after the emergence of mechanisms vantageous. Therefore the evolutionary process is of reciprocal regulation of the direct and reverse realized more intensively in such environments pathways. Different organizations of rhythms cor- where the dissipation of energy is not strongly respond to different morphologies. Sel’kov (1975) influenced on survival, i.e. in tropical areas showed that two depots (e.g. carbohydrates and (Meyen, 1987). lipids in the organism’s energetic homeostate), The increase of number and diversity of links between which periodic oscillatory changes are within the biosystem leads to the formation of realized, are necessary for stable dissipative oscil- long-lived and stable homeostatic networks. In lations. Energy rich compounds (ATP), being the this connection, the cyclic structures of ‘lateral’ outcome of such a pendulum, provide metabolism are advantageous in maintaining the regulation of intensity of the endogenous rhythm. stable steady non-equilibrium state of a biosys- This corresponds to the model of a pendulum tem. The existence of both cycles and branched with a regulated base. Energy metabolism can be pathways in the network of metabolism is condi- a source of very slow, in particular circadian (of tioned by the parameters of the process of the about a 1-day period) oscillations, which may ‘material flow equilibration’ (Matsuno, 1992) in serve as a basis for the temporal organization of which biological systems change their interaction the cell. with the exterior endogenously so as to maintain It is evident that a stoichiometric cycle is nei- the continuity of their material flow. Metabolic ther a necessary nor a sufficient condition for structures include an abundance of both branches oscillations. For their arising the generator of and cycles, and the formation of branches result- rhythm is necessary, so that the generation of ing from the emergence of initial bifurcation is oscillations can occur only after the emergence of only a precondition for metabolic cycle formation the mechanisms of reciprocal regulation of the which can be realized when it leads to the ultimate direct and reverse reactions which provide coher- network stability. Realization of a new cycle is ent modes of oscillations. Such a dynamical non- therefore a realization of a new dynamical coher- equilibrium mechanism is important for robust ent structure. adaptation in signal transduction network which A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 9 is a consequence of the network connectivity and The formal model of oscillations connected does not require the ‘fine-tuning’ of parameters with the operation of two isozymes has been (Barkal and Leibler, 1997). developed (Li and Goldbeter, 1989). It shows how the kinetic differences between the two enzymes give rise to complex oscillatory phenomena. In 6. Isozymes and metabolic channeling this model the coexistence of two simultaneously stable oscillatory regimes (birhythmicity) is ob- Isozymes can be considered as a result of ge- served, and bifurcations can arise leading to the netic redundancy and gene duplication. Multiple formation of a stable small-amplitude limit cycle molecular forms of enzymes can also appear via which coexists with the stable, large-amplitude the alternative splicing or post-translational mod- cycle. ifications of enzyme molecules. Isozymes are char- The other aspect, non-studied yet, is the coher- acterized by different turnover rates and different ent correspondence of different isozymes to differ- values of the Michaelis constant. Small alterations ent metabolons. Some indication of that can be in the molecular structure can lead to changes in the data of Comorosan (1976) showing that the time intervals of enzyme–substrate interactions isozymes related to different metabolic pathways and consequently to the alterations of isozyme are characterized by the different time periods of affinities to the substrates and inhibitors. These activation during illumination of substrates, but changes should be definitely different for the di- they reveal a similar mode of substrate activation rect and reverse reactions. In the latter case, after with other enzymes of the same metabolic path- the appearance of a new isoform, the previously way. This may be connected with the induction of linear metabolic pathway is split, and this be- particular characteristic frequencies resulting in comes a possible precondition for the formation resonant electromagnetic energy transfer (Ciblis of new metabolic pathway; the preferential partic- and Cosic, 1997). ipation of different isozymes in different The presence of isozymes is a very important metabolic pathways is generated. If more specific precondition of complex spatial and temporal or- but slower conversion of a substrate is preferen- ganization of metabolic network. The formation tial, the slower isozyme operates in this pathway; of complexes between the certain isozymes local- if less specific but rapid substrate turnover is ized in one tissue and participating in the same important, the faster isozyme operates. It seems to metabolic pathway was shown by MacGregor et be the case that the appearance of novel isozymes al. (1980). This is based on the specific isozyme– leads to the internalization of bifurcations, i.e. to isozyme interactions and excludes the shuttle of their genetic fixation. common intermediates between opposing path- The presence of different isozymes in biological ways. It may be very important for the kinetic systems leads to significant consequences for perfection of the system and for realization of metabolic organization. If a substrate is converted computation. into a product by two (iso)enzymes with different An important role of isozymes in metabolic turnover rates, reversible or irreversible transi- channeling is elucidated (Ureta, 1991). Metabolic tions are possible after changing of reaction channeling is an important integrative factor for parameters, and non-linearity can arise (Herva- maintaining whole dynamic organization (Welch gault and Cimino, 1989). It was also shown that and Easterby, 1994) and it can be considered as a the competition for a common substrate can cause basis for coherent (‘dissipation less’) events in oscillations and trigger phenomena in metabolism metabolic networks, and simultaneously it reduces (Sel’kov and Shevelev, 1989). We can state that the number of spurious ‘outputs’ in the system, the presence of different isozymes with even small thereby expanding the configurational domain of differences in kinetic properties generates branch- the useful ‘computation’ part of metabolic ma- points in metabolic network, and represents a chinery (Welch, 1996). Diffusion is a dissipative possibility for its evolutionary complication. phenomenon, whereas channeling prevents dissi- 10 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 pation of energy and provides efficient informa- erty of a genome essential for its reconstruction tional transfer within the whole network. may be its uncertainty (Ogryzko, 1997) which can Isozymes provide the conditions in which multiple be based on quantum non-local superpositions. pools of intermediates may be kept in functional Uncertainty on a genetic level may be provided compartments. Thus they maintain branching by base tautomery, transitions of a proton from structure of metabolism in which common inter- one place of nucleotide to another, etc. (Topal mediates do not shuttle between the opposing and Fresco, 1976). But the main uncertainty pathways. which is reduced in the irreversible process is The presence of isoforms in biosystems is not a connected with combinatorial transformations us- result of an adaptive evolutionary process. It itself ing molecular addresses at all levels of informa- promotes the complication of metabolic structure tional transfer (mobility of genome, splicing, and the generation of new metabolic flows which posttranslational processing). During this process, can lead to the appearance of new properties coherent events corresponding to realization of possessing the adaptive significance and to the interacting individual programs form a percolat- formation of new ecological niches. ing network, and this leads to a concrete spatial (morphogenetic) pattern. This pattern should cor- respond to the condition of optimality, i.e. should 7. Hypercycles and the dynamics of information be constructed using an optimal coordinate scale which is built mostly by non-local transfer (perco- When a certain subset of a substrate set of a lating coherent events, fluctuons, mobile proton catalytic system realizes the function of a matrix states, etc.). Coordinate scale is a manifestation of which determines the formation and reproduction dynamics which generates different forms in dif- of this catalytic system, a self-reproducing ferent coordinate systems (Thompson d’Arcy, metabolic system arises defined as a hypercycle. 1917). The transition of a biosystem in a new Different nucleotides serve as cosubstrates (coen- condition allows some of the components of the zymes) of many enzymes, and their association superposition to amplify irreversibility, and this is into nucleic acids generates matrices for the repro- a basis for the selection in the potential field in duction of enzymes themselves. When cosub- addition to the common Darwinian selection of strates serve as allosteric effectors, they form actual forms. The directed mutations phe- reflective arrows in metabolic networks leading to nomenon may be explained by this consideration the formation of a switching network possessing (Ogryzko, 1997). an internal intrinsic logic. Polymerization of co- The ‘central dogma’ of molecular biology is substrates into nucleic acids generates a self-refer- based on the irreversible expense of price of ac- ential set of arrows for the set of catalysts, tion on realization of programs by means of resulting in the appearance of the digital informa- optimal molecular devices (Liberman and Minina, tion of the genetic code forming the internal 1996). The quantum superpositions in the genome programmable structure of biosystem. may be reversible, and during the reduction corre- The hypercycle structure seems to be the main sponding to the internal measurement they enter or even the sole condition for the internalization into an irreversible process. Coherent events at of metabolic bifurcations which is preconditioned the genetic level return us to the ideas of Gur- by the autonomic recombination between symbols witsch (Gurwitsch, 1923) who considered the non- based on the mobility and redundancy of genetic equilibrium macromolecular constellations as a systems consisting of the possibility of gene dupli- possible source of biological informational space cation, amplification and horizontal transfer. The (Gurwitsch and Gurwitsch, 1959). DNA itself changes in regulative systems during evolution as may be a source of coherent photon storage, and promoted by the epigenetic reconstructions, besides the genetic information it can be a carrier makes possible the novel readings of previously of the information for ‘pattern recognition’ existing genetic texts. The other important prop- (Popp, 1989). This may be a not quite different A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 11 property of DNA: the specific recognition and replication is an emergent property arising from molecular complementarity being the basis of bio- local interactions in systems that can be much logical information processing, according to the simpler than it generally believed (Reggia et al., ideas discussed above, can be based on condensed 1993). But this property cannot be programmably coherent bosonic fields. DNA itself can be a vehi- deduced from the set of system’s elements: state- cle for the self-assembly model of computing, ments of metalanguage reflecting the ways of since even here the conformational dynamics can configuration change cannot be given indepen- change in distinctly different ways in response to dently from the configurations themselves different input signals (Conrad and Zauner, (Kampis and Csa´nyi, 1987; Kampis, 1991). 1998). The origin of the genetic code may be based on The newly generated metabolic pathway or cy- the mapping from biosynthetic pathways of cle, being induced by environmental inputs, for its amino acids (Di Giulio, 1997). The mode of map- conservation should be fixed genetically and this ping seems to be explained by some principle of fixation can be realized by different ways, al- optimality: it is the best compromise that can be though the number of these ways can not be achieved between biosynthetic cost and biological infinite: in hypercycle formation only a limited return in respect of the rate of protein evolution number of variants based on mutations and natu- (Dufton, 1997). It can be provided by minimal ral selection for providing optimal solutions can price of action during calculation (realization of be realized, as it was shown for adaptive au- the program) (Liberman, 1979). tomata by Kauffman and Smith (1986). It is explained by the fact that the operation of every gene depends on the state of neighboring elements 8. Informational field and morphogenesis which determines a system’s dynamics. Molecular complementarity based on specific correspondence The genetic information defines the parameters of certain macromolecular structures (Root-Bern- of morphogenetic processes but it cannot give stein and Dillon, 1997) may provide a limited much for understanding morphogenesis: limits of number of variants of evolutionary transforma- sequences of computable numbers are generally tions and explain the ‘nomothetic’ (Berg, 1977) non-computable (Kak, 1996). The self-assembly aspect of evolution. of atoms shares non-algorithmic properties: even Besides metabolic bifurcations, the processes of some crystals grow not in accordance with the protein degradation and apoptosis become infor- classical picture of local adding of atoms, there mationally determined (programmed) within hy- must be a non-local quantum–mechanical ingre- percycles. Appearing functional voids (Marijua´n, dient to their assembly. Many alternative atomic 1996a) become an important precondition of the arrangements must coexist in evolving complex development and informational growth within the linear superposition, and then become singled out system. Internalization of a void becomes possible as the ‘actual’ arrangement (quantum reduction) because of the parallel process of genetic recombi- (Penrose, 1989). The selection of an appropriate nation. In hypercyclic structure, void becomes a solution of reduction of a wave function should ‘creative misunderstanding’ (Kampis, 1996) which satisfy certain limit conditions provided by the can be encoded due to a redundance and combi- interfering bosonic fields. Penrose proposes the natorial dynamics of the genetic matrices. participation of gravity (curvature units) in this The emergence of reflectively autocatalytic sets process: superpositioned states each have their of peptides and polypeptides is considered by own space–time geometries which collapse to a Kauffman (1986) to be an essentially inevitable single state when the degree of coherent mass–en- collective property of any sufficiently complex set ergy difference reaches a threshold related to of polypeptides. The participation of nucleic acids quantum gravity. As soon as a ‘significant’ provides new means to select for peptides with amount of space–time curvature (equal to one useful properties. It becomes evident that self- graviton) is introduced, the rules of quantum 12 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 linear superposition must fail: one of the alterna- possible because the phenomena of the specific tives existing potentially actually takes place. recognition and molecular complementarity are of The flow of alternative realizations (of sequen- a quantum mechanical nature and based on the tial non-demolition measurements) generates dy- condensed coherent bosonic fields. namic unfolding of morphogenetic structures: Cytoskeleton is an important milieu for provid- time separates contradictory points and creates ing coherent events being the basis for acoustic/ non-algorithmic phenomena. Coordinate scales in phononic transmission and quasiparticle biological space–time are formed therefore by processes, i.e. quantum coherence may be realized percolating coherent events which generate curvi- within it (Penrose, 1989). This corresponds to the linear structures according to Thompson d’Arcy ideas of Gurwitsch about the mitogenetic rays. (1917). The role of gravity in self-consistency dy- The position of many multienzyme complexes on namics of biosystems is analyzed by Conrad cytoskeleton is an important precondition for (1996) who emphasizes that the motions of mani- their self-according operation. fest particles alter curvature and curvature con- An important role in morphogenetic processes trols the way manifest particles move. Vacuum belongs to the heterogeneities which participate in density structure is isomorphic to the space curva- the process of self-organization and realize coher- ture of general relativity, and decoherence (wave ent events as energy-driven self-consistent dynam- function collapse) depends on that density matrix ics. Biomembranes provide the deposition of (space–time curvature). charges and determine the transport of ions and As we mentioned above, DNA may be a source metabolites which results in the intracellular au- of coherent photon storage. Besides the genetic toelectrophoresis, i.e. to the polarization of the information it can be a carrier of the information cell being an important precondition of morpho- for ‘pattern recognition’ (Popp, 1989). This may genetic processes. Electromechanical alterations be based on entangling photons with atoms and sensibilized by plasmalemma precede biochemical realized via coherent interactions in DNA-se- changes leading to cellulose biosynthesis and cell quence-specific biophoton transfer. The coherence wall formation. Morphogenesis is not only a of biophotons may form ‘Gestalt’—information chemical, but it is a mechanochemical process in essential for morphogenesis. An ultraweak or which heterogeneities, phase boundaries and me- even ‘non-force’ (according to the quantum chanical tensions play an important role (Be- Aharonov–Bohm effect) three-dimensional field, loussov, 1998). provided by different topological structures in The underlying structure can provide operation DNA, is proposed for explanation of structure of bound enzyme systems in which the reversible generation (Zhvirblis, 1993). In morphogenesis desorbtion of enzymes takes place. The membrane the principle of optimal prediction (Liberman and can be regarded as a device allows for coherent Minina, 1996) in operation of hypercycles works: events. The water-membrane interface is consid- inequality of different coordinate systems is real- ered to be a substrate for a proton superflow ized in the selection in the potential field. In based on the pairing of mobile hydrogen bonds non-living systems the reduction is casual (proba- by propagating electronic oscillations in polar side bilistic), in living systems it is driven by the selec- groups of the membrane (Conrad, 1987). It was tion of optimal coordinate scales. The main also proposed that the region of water surround- problem of morphogenesis can be determined as a ing the cell is a dynamically ordered non-linear problem of deterministic actualization based on coherent optical device (Jibu et al., 1997) which the optimality principle. Both bosonic fields and provides that cells can receive electromagnetic dynamical coherence may work together in gener- signals consisting of evanescent photons tunneling ation of spatial forms. The participation of bo- through the dynamically ordered region of water. sons in realization of calculations in natural Multienzyme systems are formed correspond- systems was proposed by Liberman and Minina ingly to the symmetry of underlying structure. (1996). The biological information processing is The organized charged milieu, such as a mem- A.U. Igamberdie6 / BioSystems 50 (1999) 1–16 13 brane, plays an important role in generating func- there is no syntactic operation which takes us tional long-distance interactions between bound from simple systems to complex ones. enzymes. This spatial organization of enzymes can Thus, morphology is a result of the temporal lead to the generation of cooperativity in behavior and spatial organization of matter and energy of enzymes which follow Michaelis–Menten ki- flows in biosystems. Morphological transforma- netics. Membranes may provide the accommoda- tions occur via changes of organization of these tion of antagonistic enzyme reactions resulting in flows, and this results in the transformations of the avoidance of futile cycles (Ricard et al., 1992). coordinate scales describing biological forms The charged membrane can transform the futile (Thompson d’Arcy, 1917). The degree of curvilin- cycle into organized long-distance structure with earity of the ‘space of biological forms’ is deter- feedback and feedforward regulations. This is the mined by the periods of cycles’ turnover and by precondition of morphogenetic events. The model the differences in the rates of reactions providing of such a construction of morphology was pro- depositions from cycles. If the deposited com- posed by Ricard (1987) who described the cyclic pounds can turn in reverse transformations, oscil- structure involved in the ionic regulation and lations are possible, but if they turn into the building up the plant cell wall. The fixed negative insoluble form, they participate in the construc- charges in this model modify the activity of bound tion of rigid skeletons. The formation of morpho- multienzyme systems, and the coupling emerges logical structures is a result of interference among between the diffusion of reactants and enzyme concentration oscillations of compounds partici- reactions. This coupling between very simple reac- pating in structure formation, in this process non- tions, the joint operation of which in the solution local coherent phenomena of non-algorithmic leads to the futile dissipation of energy, after the nature are important. compartmentalization provided by membrane or Morphology is a projection from the multi-di- cell wall, generates complex dynamic events which mensional space of kinetic equilibria and pro- are regulated cooperatively and prevent futile re- cesses into the three-dimensional space possessing cycling. Many enzymes associated with mem- an epimorphic (many-to-one) reflective structure branes are kinases and dehydrogenases realizing which cannot be modeled programmably, and non-local proton transfer. A number of them are regulatory. may only satisfy certain limiting conditions for its Kinetic parameters correspond to spatial geo- realization. Alterations of the time intervals of the metric effects, and structures can be considered as cycles can lead to the changes of such projections morphological fixations of dynamical processes. which results in modifications of morphology. The biochemical cycle being a system of incomes The morphogenetic field operates in the space of and outcomes of certain compounds can be con- physical fields and metabolic cycle being a pri- sidered as an axis of symmetry relative to which mary morphological generator providing the con- biological structures are organized (Petukhov, ditions of structure formation. 1986). Even insignificant changes in the parame- Regulatory products of metabolism, e.g. hor- ters of cycles can lead to essential morphological mones, affect bifurcations and therefore realize reconstructions. Morphology is formed by the morphological transformations. Most of them are stable trajectories of the formation and deposition regarded to be mild uncouplers between different of compounds formed in biochemical cycles. The processes connected with energy conservation formation of new cycles leads to the overbuilding (Skulachev, 1996). It seems evident that regulators of new metabolic trajectories, and this corre- of growth and development via influence on bifur- sponds to morphological changes. This process is cations make it possible for the system to trans- highly context-dependent generic phenomenon, form into a new state (to undergo a metasystem and it may recall the operation of taking of limits transition). Under their influence the system be- (Rosen, 1991). It cannot be represented algorith- comes more dissipative (consequently less stable) mically, as computability itself is non-generic: and can more easily be transformed. 14 A.U. Igamberdie6 / BioSystems 50 (1999) 1–16

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