Two faces of entropy and information in biological systems

Journal of Theoretical Biology 359 (2014) 192–198

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Two faces of entropy and information in biological systems Yuriy Mitrokhin The Institute of Problems of Chemical Physics of the Russian Academy of Sciences (RAS), 142432 Moscow region, Chernogolovka, Russian Federation

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Thermodynamic and information entropy are considered as two forms of total entropic process in biosystems. The origination of complexity cannot be compensated only by thermodynamic entropy. When and where in the past the entropy has been produced that is a payment for biological organization at present? The idea is discussed that the genetic information is an instrument of entropy disproportioning in time. The Second Low realization today cannot be without taking into account the information entropy in past generations.

art ic l e i nf o

a b s t r a c t

Article history: Received 14 February 2014 Received in revised form 30 May 2014 Accepted 12 June 2014 Available online 20 June 2014

The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Information entropy Generating of new information Disproportionation of entropy Unsteadiness in genetic systems Compensation for antientropic processes

1. Introduction Discussion about implementation of the Second law of thermodynamics in living systems has always been a collision of diverse points of view, especially when discussing the role of information processes in such fundamental biological phenomena as growth, embryogenesis, ontogenesis and evolution. The fact that genetic information is correlated with the entropy production was expressed in the question: "what is the entropy (and energy) payment for information…" (Romanovskiy et al., 1984). Blumenfeld (1977) wrote: "According to the thermodynamic criteria any biological system is not more ordered than a piece of rock the same weight". However, a few lines later he admitted formalism of his approach: "Orderliness of living matter and the information it contained have a sense". Prigogine and his school developed thermodynamics of open nonequilibrium systems and formulated idea about the

E-mail address: [email protected] http://dx.doi.org/10.1016/j.jtbi.2014.06.018 0022-5193/& 2014 Elsevier Ltd. All rights reserved.

nonequilibrium stationary state which these systems tend to. It is characterized as a state with minimal and constant speed of entropy production in the system. At the same time the total entropy change (dS) for such open systems consists of deS—the inflow (outflow) of entropy due to the exchange of matter and energy between the system and the environment and diS—the entropy production within the system: dS ¼deS þdiS. It should be emphasized that the minimum entropy production is valid in close to equilibrium conditions. The authors extend the theory to growth and development, emphasizing that the processes in biological systems do not contradict the second law of thermodynamics. Ontogenesis is considered as a transition from the less probable state to the more probable (Nicolis and Prigogine, 1990). The last assertion hardly is justified. The more probable state is disorganization, not organization. Organization requires the prescriptive information to temporarily and locally outsmart the Second law of thermodynamics of progressive, relentless disorganization. Interestingly, Prigogine and his colleagues speak exclusively about the thermodynamic entropy in their works and avoid

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discussion of rather evident for every biologist fact that both in a cell and multicellular organism there is a permanent creation of new structures, maintenance of organization. All the pathos of their works focuses on the emergence of structures in non equilibrium dissipative systems which prepared artificially as a rule. It all is true without any doubt, and, apparently, the contribution of this principle–organization out of chaos—was decisive at the very early stages of the prebiotic evolution. But it is not enough for adequate description of the modern biological systems in terms of physical laws. The put forward by Prigogine argument that the outflow of the entropy of the system into the environment deS can compensate for the production of entropy within the system (diS) seems very unconvincing for real cells. Hardly the outflow of heat and low-molecular components (Н2О, СО2, etc.) from the cell, giving a contribution to the positive entropy balance, is sufficient, especially since this outflow is not related to the creation of complex macromolecular structures in the cell. Nonequilibrium structures of biopolymers are not dissipative, as their maintenance does not require any export of entropy and they are conservative structures (Ebeling et al., 2001). In the same vein other attempts to explain the spontaneous generation of the organization in living organisms through the continuous entropy production which accompanies the flow of free energy through the system are made. However, doubts remain. So, Klimontovich (1997) in his work, devoted to the entropy production in open multilevel systems, answers to the question—can we expect that self-organization is the only result of biological evolution—not, as inner aspiration for self-organization is not inherent property of physical and biological systems. He supposes that since the state of full chaos, i.e. thermodynamic equilibrium has not been determined (and is not characteristic of) biological systems, and provided the absence of definition of full order, the systems can be described in terms of ‘chaos norm’ or a relative degree of chaos. The concept more adequately describes the state of genetic systems which are characterized by an acceptable ratio between determinism and randomness (freedom) for combining functional elements of the systems. It is seen that when interpreting specificity of living objects the author considers only thermodynamic entropy as a main factor defining the direction of their evolving. The complexity of the correct interpretation of the efficiency of the Second Law of thermodynamics in biological systems continues to be relevant and sometimes elusive for understanding of the problem. This is reflected in the concluding sentences of the problem analysis which was made by Rubin (2004): "In the center of attention here is the main paradox that the increase in the orderliness of biological systems is accompanied with a spontaneous production of positive entropy". An important step in comprehending a specific role of biological information, its content and consideration for correct interpretation of the Second low of thermodynamics was made by Quastler (1964) who defined two principle moments for its generation: 1—random selection of one of possible versions, and 2—memorization of such selection . Later on, an essential condition was added, which consisted in that new information can be generated in the unsteady-state systems only (Chernavsky, 2001). Among the present concepts of the essence of biological information, two principal viewpoints can be distinguished: in terms of physical reductionism, information is not considered as really existing substance (Wachtershauser, 1997; Boniolo, 2003). The opponents state that the thesis of physicalists about a spontaneous polymerization of information macromolecules in initial chemical (pre-biotic) systems is incorrect, that genes and proteins have never been generated spontaneously. They were synthesized by molecular machines, which physically combine monomers to polymeric chains in accordance with information

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matrixes and codes. Thus, proteins and genes are molecular ‘artifacts’ (Barbieri, 2012). We suppose that this statement opposes cause to effect and violates the principle of holism. A disputable is attribution of information to the class of physical essences, though the author states that specificity of biological sequences cannot be measured quantitatively. Therefore, it is not clear—is information a phenomenon of life or that of human consciousness. In other words, does this concept reflect objective reality or not? An interesting information concept was proposed by Battail (2009) who considers it as one of the main essences of the physical world, along with the matter and energy. However, unlike them, the information exists only in the world of living beings where it can be generated and multiplied (where it can proliferate) and may at the same time be annihilated (lost). The author introduces the notion of potential information to denote the information which exists in the form of some immaterial essence in nonliving world. I the living world, potential information turns into symbolic one through materialization into the form of the base sequence of genomes. At the next stage of its passage it looks as structural information of functional macromolecules and structures of cell metabolism . I can agree with the notion of potential information, not in the prebiological world but rather in the world of ideas that exist in the person's head. It is no mere chance physicists find not place for information in the strict system of physical laws. One of such attempts was made in the well-known works by Haken (1988) in the new interdisciplinary filed called synergetics. Using several model systems the author found the appearance of information from observing the effects of ordering or even self-organization. When the known one-stage order emerges from chaos in laser or any other model system, it resembles crystallization at a moment of attaining required temperature rather than the appearance of organization. The existence of special intangible essence in biological objects was comprehended by Schröedinger (1944) when 10 years prior to the discovery of DNA structure he attributed mutation effects transfer through generations with the effect of a certain nonphysical law . Barbiery justly supposes that now genetic information should be considered as new observable physical entity, which is present in living objects along with other fundamental physical entities. However, a more precise definition should be given. Information and human consciousness as a derivative of information processes in neuron networks appear as new non-physical realities emerging parallel to the germination of life and becoming of human being. They acquire sense only in the process of information transfer and reception by a receiver, subsequent re-coding and generation of a biological function or thought. The value of potential information equals zero similarly to rest mass of elementary particles. We suggest the following definition of the sense of information for natural biological systems, namely, certain observed essence consisting in a sequence of monomers of genetic macromolecules, which provided carriers transfer to molecular recoding devices, unambiguously realizes one of multiple possible sequences of elements when building functional molecules of another nature in a genetic system. Probability of such event out of an organized biological system is close to zero even in the presence of messenger. Thus, information is nonphysical essence, which arises inside a pre-biological physico-chemical system at a stage of life origin, evolves from generation to generation and is present in living systems as long as they are such. These definitions are have been made to show that information is not coming to the system from without. It comes into existence, becomes a reality in a primary physical-chemical system when the succession of the following events spontaneously encloses to a cycle: minimal polynucleotide—primary recoding device—polypeptide showing presumably polymerase activity—replication of

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parent polynucleotide (Eigen and Schuster, 1979; Eigen, 2000). Essentially, all events of the primary information cycle and its metabolic maintenance are possible in minimal volume limited by a lipid membrane. Then the system can be reproduced due to division and evolve by the Darwinian mechanism. Therefore, it cannot be considered as a pure software as Chaitin, 2012 which defines life as ‘evolving software’. The system evolves as a single whole including all the above cycle elements. Any spontaneous random changes in the primary nucleotide sequence are accompanied by changes followed in elements of the organized system and, hence, are materials for selection. Abel (2009) has recently justified the notion of "Prescriptive information" (PI) whose main essence is prescription (instruction) of the method of particular functions appearance in biological systems. PI is an absolutely necessary working element contained in the genome structure which ensures creation and support of deterministic relations in the physical and chemical chaos of the cell. The prescribed selection of the amine acid sequence in the forming molecule of the enzyme or other functional agent determines the choice of the passageway of any metabolic chain (Abel and Trevors, 2005; 2006). The idea of two forms of information — descriptive and prescriptive, as well as the idea about two forms of entropy —thermodynamic and informational, developed in this article, are not connected with each other by content but reflect the complicated nature (duality) of the considered basic essences —information and entropy. I would like to show in the article that PI arises not out of information entropy (nothing may arise out of entropy) but thanks to its existence. Information entropy, being the internal property of genetic systems, violates the existing stable condition; this results in the appearance of modified sequences in genomes whose carriers will become objects of selection. In cognitive semiosis, the appearance of PI is considerably reduced and even not mandatory. Another image of semantic information, "Descriptive information", dominates here, which is typical for information system of symbols on the basis of neuronal network of the higher animals and human. But this is a subject for a separate article. If in addition to the thermodynamic entropy in every cell we consider а coming in evolutionary time scale mutation process, — a peculiar another face of entropy which accompanies the occurring in the genetic material processes, —the result is known to be a violation of genetic programs and, as a consequence, deterioration of cellular and organismic functions. Thus, information entropy as if has no relation to the emergence of complexity, orderliness and progressive evolution of biological systems. But, as it is shown below, exactly this kind of entropy is the one responsible. Thus, a conclusion can be drawn on that an obvious contradiction between continuous generation of entropy in a metabolic system on one hand and the emerging biological organization on other hand does not vanish. Apparently that is going on because in the total entropy balance does not provide for information entropy —a motive force for mutational process in genetic systems in course of their reproduction and functioning in generations. Namely an acceptable part of information chaos, which exists in real genetic systems, allows a random search for new combinations of informational elements of genome, which can be selected for a new step of evolution. In effect, only separate authors, for instance (Rubin, 2004), paid attention to the existence of this paradox but did not try to interpret the mutation process in genetic systems as the process of information entropy production that should be taken into consideration to evaluate the general entropy balance in the evolving biosphere. In this article we try to correlate (ideally, of course) all the known positive entropic processes which have taken place both in the past and today in the metabolic and genetic cell systems, and antientropy processes which include both the processes of

formation (origination) of the new elements of biological organization and the process of retention of existing ones, i.e. selected and forming a functioning biological system elements. At the same time it is intended that this correlation is lawful only if there is a direct causal physical link between these two opposite classes of processes, even if the mapped events spaced in time and space. Real basis for giving a comprehensive biological sense to such a correlation is a well-established fact of conjugated positive entropy of biochemical transformations of substances of food with high content of free energy and thermodynamically impossible without such conjugating processes of formation of various macroergic equivalents, synthesis of complex organic molecules, biopolymers etc. We consider that continuous mutation process in genetic systems during the evolution is the process of information entropy production. The resulting unsteadiness in the genetic information system is a necessary condition for the generation of new information. Transfer of gene complexes to the next generation that is supported by the selection and provides better information, is that causal physical link between the positive entropy events in the past generations and antientropy processes in their descendants. In fact, this speculative correlation between entropy and antientropy processes is that attempt to overcome the paradox of contradictions between the emerging biological organization and the growth of entropy. The problem is complex and cannot be described by a simple formula.

2. Entropic processes in the system of metabolism Having once begun, biological systems reproduce themselves continuously and evolve, carrying a rather large but limited set of standard chemical reactions, many of which cannot proceed spontaneously and need to be conjugated with spending of free energy and require the presence of catalysts formed in the same system. During the evolution of living systems this set of chemical reactions has become more complicated, and, apparently, long time ago it has reached some reasonable limit and the degree of perfection that provided the evolution of organisms, speciation and stable existence of species for long periods of time over 3.5  109 years. It is considered that on the metabolic level of living systems there are spontaneous processes of all the biochemical transformations in conditions of minimum entropy production in the system and its simultaneous substantive growth in the environment. In the system of conjugated biochemical transformations, the processes of thermodynamically prohibited reactions are provided by the fact that the part of the free food energy irreversibly lost on the production of heat (i.e. entropy member of balance) decreases, and the saved energy is used for positive work in the construct process, for example, in any biosynthesis reactions etc. The total balance of entropy production should be positive. It is a requirement for the process. Thus, the process of conjugated transformations becomes thermodynamically allowed (Galimov, 2001; Opritov, 1999). In fact, here we are dealing with underproduced entropy. And in this sense, the part of the free food energy which could be dispersed for heat production is used for creating "the organization" in the cell, i.e. the organization is partially paid for by the underproduction of entropy. Making these speculative qualitative estimations of the entropy production balance on physicochemical level, we should always remember that the conclusion of the spontaneity of biochemical processes is something largely apparent. Indeed, thermodynamic constraints are overcome through the mechanism of conjugated positive entropy and antientropy reactions (if they are regarded separately). However kinetic limitations are so great that they

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would be the same insurmountable barriers, if it were not for the intervention of higher-level organization of the cell, if the system did not have enzymes and other sophisticated infrastructure. As being terminal links of an information transfer chain from genes to effectors of proteins in a cell, ferments and other protein structure realize the function of "guidance", direction of biochemical reactions in the cell. The term «induced processes» was proposed by Zotin in order to distinguish them from verily spontaneous (Zotin and Zotina, 1993). Thus, in relation to the events of the metabolic level, the positive balance of entropy production that accompanies biochemical transformations is not the only condition of these processes. It is a necessary but not sufficient condition. Rethinking Schröedinger (1944) thesis that the organization is supported removing the "orderliness" from the environment, today we can say that the organization of living systems, orderliness, its structures, system maintenance in the stationary, far from equilibrium condition with minimal entropy production is provided at the expense of realization of genetic information contained in DNA. As discussed here, the positive balance of the thermodynamic entropy should be considered only "accounting" of the process, but not the driving force. The author of the book devoted to information and the theory of evolution wittily said: “Life does not use negentropy for food like the cat which licks sour cream” (Yockey, 2005). Indeed, the degree of orderliness of substances entering the cell from the environment is not too high. They are more carriers of free energy which can be freed, become accessible for a cell and be used for the processes of thermodynamically prohibited reactions. Both for the thermodynamic and information entropy the main content of the concept is the internal inherent in the system aspiration to the chaotization, the disruption of the structure, the dispersion of part of the free energy in the form of heat, i.e. in fact, the direction to the balance, to the more probable state. And if, contrary to this system inner desire but conjugated with it, opposite events occur, such as the complex biosynthesis, the storage of available free energy in ATP, the biosynthesis of macromolecules and, finally, the emergence of new information, then, apparently, this process needs some additional driving force, and manufactured in the system entropy is the only evidence of flowing process spontaneity. The driving factor in this process is the genetic information.

3. Entropy and the genetic information Consider another level of organization of living systems (namely multicellular organism) in terms similar to those that we used at the description of physiochemical intracellular processes. Leaving aside the physiochemical transformations of matter and energy in every cell, try to qualitatively evaluate the directivity of the actual processes in the cell which we now regard as the emergence of a new biological system (the organism). It seems quite clear that exclusively the processes of а developing system structure complication, improvement and increase of an organization degree take place during the entire period of full organism formation (embryonic period). Following the terminology proposed by Schröedinger (1944), during this process there is a growth of the level of orderliness of elements composing the system and only an entropy decrease are observed that is not accompanied with its any parallel growth in the related parts of the system. It must be remembered that we are talking only about the events on the cellular level (in this case we do not consider what happens in every cell). So, the formation of a multicellular organism seems to be not accompanied with the entropy increase about which we spoke above describing the metabolic processes in cells; the impression is that at this level there is not some

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inherent in the system potential which determines the spontaneous course of the process. This logical impasse will be overcome, if we apply macromolecular or genetic level of biological systems, especially since all the events of this level occur within the described system. The causal connection between the events of these two levels is not in doubt. Remaining within the limits of the natural science in describing the phenomena and processes, we must, as before, in the case of the description of intracellular physico-chemical transformations, find the force that determines the direction of the spontaneously flowing embryogenesis. Without delving into details of embryogenesis we will try to highlight this biological phenomenon from the point of view of the requirements of the second law of thermodynamics. Positive thermodynamic entropy balance in each cell of a multicellular organism is not associated directly with the emerging and growing organization, orderliness of this higher level in the hierarchy of a multicellular organism. Obviously, without the cells possessing of some properties which are necessary for the formation of a multicellular organism, the embryo will not occur and the result is just a larger number of cells, although each of them has an obligatory positive entropy production balance. Apparently, it is actually not the thermodynamic entropy produced in the cells of the developing embryo. It does not determine the direction of the events of the considered hierarchy's level of living systems. The acquisition of certain properties that gives to dividing cells the ability to remain connected to each other is apparently relevant to the implementation of the new genetic information which originated in the evolving eukaryotic cells—the predecessors of multicellular organisms. Its generating processed in genetic systems of these cells which possess acceptable degrees of volatility and the possibility of mistakes when replicating the nucleotide sequences of genes (Chernavsky, 2001). It was the first and may be the most decisive step on the path of the multicellular origination. Each of these countless steps was an act of a new information birth. The second, not less important event in the germ cells of primary multicellular organisms was, obviously, origination in the genomes of these cells of absolutely new, specific genes whose activity modulated features of the hereditary cells phenotype in such a way that in a growing embryo the cells with different functional specificity began to originate. There is no doubt that this became possible when the original genome of zygote was enriched with a considerable set of genes— new genes which did not exist in free-living eukaryotic cells. The formation of a wide spectrum of phenotypically different cellular elements in the developing embryo was (and is) based on the same initial genome. Eukaryotic cells have acquired an extremely useful evolutionary innovation which allows them rational and sustainable use of the resources of their actually large genome converting certain genes in silence state or returning them in active one. We discussed it more elaborately in the work (Mitrokhin, 2013). The process of new genetic information generating is directly conjugated with the changes of entropy (both thermodynamic and information) but, however, it should be recognized that there is a fundamental difference between the thermodynamic entropy and the information one in probabilities of occurrence of elementary events which make sense of each entropy type. The growth of the thermodynamic entropy results in processes of biochemical transformations which are accompanied with the dispersion of part of the free energy of the participants (presented in the system or entering into it). The probability of elementary acts is very high because the reactions of this type come with the release of energy. Part of this energy is retained and will be then implemented for the processes of thermodynamically improbable events, such as the synthesis of universal macroergic compounds.

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On the contrary, information entropy which we want to characterize as a source of subsequent, related changes is the result of very improbable events, because these events (mutations) occur in macromolecular, highly organized systems which have largely deterministic character of consecutive reactions process. This kind of entropy in no way affects the physical orderliness of the nucleotide sequences (only the semantic!) and, therefore, does not contribute to the change of thermodynamic entropy of the system (they are something like immiscible substances). Information entropy contributes to the implementation of the ranges of freedom which are possessed by the carrying genetic information nucleotide sequence. Time of waiting for occurrence of the elementary entropy events of this kind significantly (many times) exceeds the time of the occurrence of such events for the thermodynamic entropy—the other face of entropy as a physical phenomenon. Owing to this modest contribution to the overall entropy balance which is the driving force of biological systems evolution it becomes possible to overcome determinism of strict sequence of DNA replication events and the generating of new information motives. Produced in a cell thermodynamic entropy compensates for the reproduction of the physical component of the genetic information system—chemistry and physics of structures which transfer and implement information, i.e. compensates for current events of the metabolic level but not the events of the evolutionary process. Now we need to understand how the system became what it is; we need to understand how it was complicated, acquired new properties and how it progressively evolved. The possibility of mistakes in nucleotide sequences during their reproduction should be considered as implementation of the immanent aspiration of the information system to state of chaos and information distortion, i.e. as the information entropy growth. One important feature of every occurring in the genetic system entropy event should be noted: it is remained in memory, in contrast to the elementary thermodynamic events or, for example, the breakdown of proteins and more complicated cellular structures. These kinds of mutation lead to nothing. They are forgotten. As a general rule, they are not transferred to the next generation. The situation is quite different with the fate of DNA mutations. As positive entropy events (i.e.—causing chaos, disorganization) in relation to the information content of DNA sequence, mutations practically do not have an impact on thermodynamic entropy balance of this system. From this point of view, they have zero cost. As a rule, they do not change the amount of the Shannon information which, in principle, can be measured in known units. They change the quality of the information, its content. In this connection the information entropy in genetic systems is an analog Shennon's concept of entropy in artificial communicative systems (Shannon, 1948). But in this systems the new information is not be originated. It is come down only. Of course, we should not forget about the energy spending on this new information that is paid with the constantly going thermodynamic entropy production in the cells. Genetic system remains in memory everything that has overcome replicative and drafting mechanisms which save the original information. The true cost of new acquisitions will be detected only after the selection performs its function. In this context, it is permissible to focus somewhat passive role of natural selection in the evolution of the genetic system. Real, active creativity occurs in the information system the physical structure of which allows it to combine its elements in periods of instability and remain in memory detected variants. Everything that has been changed in the genome after overcoming cellular repair mechanisms and correction remains in memory. The selection performs a simply passive function, so to speak; and it occurs at later stages. It eliminates nonviable organisms (phenotypes) with their altered gene complexes and leaves viable ones (Brooks, 2000).

Common sense dictates that the selection selects neither the best genes (Dawkins, 2006) nor the most successful populations and species (Shcherbakov, 2005a, 2005b) – a successful combination of genes is selected as the information subsystem of the whole, i.e. cells (in the world of unicellular) or the organism (in the world of multicellular). On the other hand, a successful combination of genes which ensured this successful phenotype is not retained in sexual reproduction of new generations and is not selected, so to speak. But the genes included in it are retained, i.e. selected for the following generations. This approach to the concept of «selection» is consistent with the concept of «holism» according to which the inheritance is implemented not only by the transmission of genes, but it is provided by a certain integrity of the composing the system elements (Shcherbakov, 2012). Information entropy which accompanies acts of information transfer to the new generations has regularly contributed its share to the general entropy expenditures required for maintaining of the nonequilibrium state and falls on the scale which has a positive sign (i.e. towards the equilibrium state). These rare fluctuations transfer the system in an unsteadiness state only for a short time and it is accompanied with the birth of a new information motive. The information entropy which accompanies this simple event can in no way influence the general entropy balance in a separate cell. But it is summed with the whole array of similar events on an evolutionary time scale and assures us that the Second law of thermodynamics is adhered to. The system's return in a stable state allows maintained a significant nonequilibrium state characterized by high level of organization. The memorization mentioned above is not a birth of new information yet. It will become the same only when it is sent, i.e. it will be reproduced in the new generation and will be implemented in the form of any particular cell function and the survival of this generation descendants will not worse than that of the ancestors, maybe even better. It is possible only in systems with three obligatory properties: metabolism, self-reproduction and mutability, i.e. in living systems. Eygen and Shuster defined these properties as "prerequisites for feasibility" in capable of selective self-organization systems (1979). The birth of "organization out of chaos",—the formula of expression of the new class of physical phenomena,—is possible exactly in these systems. Apparently, this formula was implemented at the earliest stages of the information emergence - at the origin of life. However, in the process of the new information emergence there were equally the events the meaning of which is «determinism and steadiness». And here in the first place is a unique structure of DNA which provides long-term retention of genetic information by chemical stability of the structure and the ability to enzymatic matrix selfreproduction. However, there is a possibility of new sequences as a result of random errors in replication. In addition, here we can talk about the genetically provided evolution of the genome; it begins to be implemented in the more complex genomes which have new genes whose products form an apparatus that enhances the genetic instability and provides advanced combinatorics of genetic material and the origination of new genes (Carroll, 2002). Amazingly, this enzymatic apparatus is not an independent structure performing function of mutability increase, although the existence of such special evolutionarily supported apparatus is postulated in some works (Radman, 1999; Earl and Deem, 2004) that is hardly justified. Shcherbakov (2005a, 2005b) rightly noted that selection of the mutagenesis high rate seems absurd. The mentioned above apparatus is an integral part of replicative complex of genome and at the same time the mechanism of recombinational DNA repair (Paques and Haber, 1999. Both of structural-functional features of the genome originated in it and were supported by the selection as they

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performed conserving function; they provided memory and accuracy of the genome duplication in generations (Shcherbakov, 2005a, 2005b; Rice and Chippindale, 2001). The primary nucleotide sequence is strictly retained but larger elements of the genome (genes, complexes genes, promoters and other elements) are shuffled. Impressive recent achievements of comparative genomics prove this observation. Deep conservatism of nucleotide sequences of genes contrasts with higher mobile gene composition of genomes and, to higher extent, evolution instability of genome architecture, i.e. arrangement of genes in genome (Koonin, 2009, 2012; Novichkov et al., 2009; Koonin and Wolf, 2010). It provides (especially in gametogenesis) with the origination of new, unexpected genetic combinations. This process goes in parallel with the regular (evolutionarily more primitive), ancient mutagenesis at the level of single nucleotide substitutions. At the stage of selection there is no any creativity about which, for example, Ayala, 2007. There is either "applause" or "stunned silence". The creativity took place on the scene of life when emerged in genetic information system new information realized in an unexpected turn of events in the cell, in the modified phenotype. If we see natural selection only as its final stage, i.e. elimination of nonviable forms, and at the same time we are aware of the fact that this process does not require the functioning of any mechanisms and is implemented on its own, then we lose sight of the two first and the most important stages of Darwin's natural selection that he defined as «the nature of the organism». In other words, a creative role is played not by the last stage of the whole selection process, but by its first phase – evolving information systems.

4. Concluding remarks We observe in a living cell several parallel conjugated processes the driving force of which is accompanying these processes entropy in two forms: thermodynamic entropy and information one. The processes of metabolism providing the formation of necessary substrates and macroergic equivalents proceed due to spontaneous oxidation of food substances which possess the free energy and are accompanied with the production of a considerable degree of thermodynamic entropy. This type of entropy compensates for those conjugated antientropic processes (such as muscle contraction, active transport of substances, the biosynthesis of all polymers etc.) that cannot proceed spontaneously. Basic events of the metabolic level are sequence of physicochemical transformations of small molecules and determine the system's aspiration system for the most probable state—thermodynamic equilibrium. However, it does not occur for the reason that the system is open for matter and energy and contains an internal source of information—genetic system of cells which is a macromolecular complex and requires the constant reproduction of its structure for current information cell maintenance and for transfer of information to the future generation. Process of operations on genetic material includes two essentially different components. The elementary acts of polymerization of the predecessor monomers which possess a considerable reserve of free energy flow spontaneously and are accompanied with the production of thermodynamic entropy. The resulting molecular orderliness (i.e. the process of polymerization) is evidence of the decrease of the entropy balance member which reflects its production within the system. This first component of the genetic system elements reproduction provides the formation of its physical and chemical structure. The second aspect—its informational content, its specific sequence which provides the functional organization of the system is inherited to the newly synthesized descendant

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molecules without spending of additional energy and without change of thermodynamic entropy. This becomes possible owing to matrix mechanism of complementary DNA duplication. This is true both for the cell cycle process and for the process of a multicellular organism reproduction (embryogenesis). The mentioned above positive balance of thermodynamic entropy production which accompanies and compensates for occurring in the cell negative entropic processes is typical for the periods of steady state of the system. The cell with the most possible precision duplicates genetic material and transfers it to the next generation. Thus, the driving force of the entire set of processes in the cell and in the multicellular organism in selected periods (i.e. periods of ontogenesis) is continuously generating in them thermodynamic entropy. However, this positive entropy balance describes only the energy side of intracellular processes in their steadiness periods. This is a necessary but not sufficient for the process of progressive evolution condition. The information component is equally important and has its source of those rare events in genetic systems of individual cells that we call mutations. Basically, this is a demonstration of another face of entropy as a physical phenomenon; it is inherent in the system aspiration to the chaotization, to the disruption of largely deterministically determined elementary events in the genetic system. In those rare cases when internal fluctuations overcome sustainable condition of the genetic system, in the genome emergence of new information motives occurs. They are tested by the selection on the viability and can be transmitted in a series of generations. Transfer of new genetic information supported by the selection in the mode of steady state of the system is fully compensated with the production of the thermodynamic entropy in the process of energy maintenance of macromolecules synthesis. However, the origination of these new information motives in the genome of the cells and the following implementation of the new organizational structure which was not until then is perceived by the observer as a violation of the entropy balance (apparent) that is especially evident, for example, during embryogenesis. At this moment we forget about the information entropy which found itself in all periods of the life's evolution in the form of random fluctuations in generating these information motives. We would like to discuss the idea that in living systems there is the phenomenon of disproportionation of entropy in time. It should be understood as a kind of conjugation of positive entropy events in the genetic material of cells of past generations with the formation of highly organized structures in modern organisms; and this conjugation can be considered a way of implementation of the Second law of thermodynamics in uninterrupted living systems with a very long lifetime. Of course, we are aware of the fact that the information entropy which was produced in the genomes of past generations in no way can be taken to the entropy balance of current cell. This would contradict the principle of obligatory physical conjugation between two processes going on in the thermodynamically opposite directions. The proposed term "disproportionation of entropy in time" is intended to emphasize that genetic information physically transmitted in generations was created and improved during the evolution in really existing genetic information systems which experience continuous entropy pressure transforming these systems into an unstable state. Darwinian selection in this process performed and still performs a passive function,—it only eliminates the whole vast array of failed (nonviable) phenotypes and the corresponding with them combinations of genes emerging as a result of mutagenesis (Brooks, 2000). Nothing like that occurs with the thermodynamic entropy. It is simple and clear: the implementation of each event (for example, the synthesis of peptide bond) is achieved owing to conjugate ongoing process of hydrolysis of ATP and is

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accompanied with a release of energy and entropy production which is sufficient for the synthesis of this peptide bond. The next amino acid needs new entropic spending. But it is impossible to make a new protein molecule only at the expense of current thermodynamic spending without presentation of information. Feeling of elusive sense of the phenomenon is reproduced in question first articulated by Schröedinger (1944): "In accordance with which such a well-known physical law a random, chaotic event of molecular level occurred, perhaps, 109 years ago in some place of genome of that time, today determines the specific phenotypic attribute which has macroscopic form and in some cases we can measure it quantitatively. We may assume that living matter obeys a new type of physical law. Or we should call it nonphysical". These sentences written 10 years before the discovery of the DNA structure and formulation of ideas about genetic information are striking for its vision. Thermodynamic entropy produced in cells is not enough to compensate for all the processes which accompany the growth and development, —definitely antientropic processes, the processes of creation of organized biological structures. It is clear that this entropy is only a constant replenishment, "the electric current to a moving train". Transfer of information is essentially a way of relating entropy and antientropy processes which we mentioned in the introduction; it with a logical inevitability arises from the requirements of the Second law of thermodynamics in accordance with which the organization created in the organisms must be compensated with an excess with the respective amount of positive entropy. Poplavskiy arrays a relationship between entropy and information in the following line: "Thermodynamics of information processes explores the transformation of entropy into information, and the last one—into negentropy" (Poplavskiy, 1981). Summing up, we note again that the two faces of entropy correspond with two fundamentally different periods of biological systems existence. Production of the thermodynamic entropy in the metabolic system provides maintenance of steady state and reproduction of already existing information. This is evolution towards the most probable state in periods of ontogenesis. Production of the information entropy in the genetic system accompanies the transformation of a system into an unstable state and is a condition for the generation of new information. These events correspond with the evolution of the system to a less probable state which is formed from the unlikely events (mutations) in the genetic information system, and it becomes possible only with the participation of selection in the process of phylogenesis and memorization of the selected sequence (information motives). Modern organization of the evolving biological system is mainly payable in the payments, in a variety of past evolution moments, in the acts of the birth of new information fixed by the selection. At that time there was also entropy production—information entropy which broke "the order" in those moments. Its disproportionation in time, its today's accounting weaken the tension caused by the existence of a paradoxical contradictions between the evident increase of orderliness of living systems and the production of positive entropy. References Abel, D.L., Trevors, J.T., 2005. Three subsets of sequence complexity and their relevance to biopolymeric information. Theor. Biol. Med. Model 2 (29), 1–16. Abel, D.L., Trevors, J.T., 2006. Self-organization vs. self-ordering in life-origin models. Phys. Life Rev. 3, 211–228. Abel, D.L., 2009. The biosemiosis of prescriptive information. Semiotica 174, 1–19.

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