Understanding the foundations of biology: A research program

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arXiv:1401.3203v1 [q-bio.OT] 13 Jan 2014

Understanding the foundations of biology: A research program Jean-Louis Sikorav1,∗ , Alan Braslau2 , Arach Goldar3 1 DSM, Institut de Physique Th´ eorique, IPhT, CNRS, MPPU, URA2306 CEA/Saclay F-91191 Gif-sur-Yvette, France. ´ 2 DSM, Service de Physique de l’Etat Condens´ e, SPEC, CNRS URA2464 CEA/Saclay F-91191 Gif-sur-Yvette: France. 3 DSV, iBiTec-S, Service de Biologie Int´ egrative et de G´ en´ etique Mol´ eculaire CEA/Saclay, F-91191 Gif-sur-Yvette, France. ∗ E-mail: [email protected]

Abstract Biology is a scientific discipline based on phenomena derived from observations or experiments, on concepts elaborated to understand them, and on further generalizations of these concepts through theories or laws of nature. We present here a research program seeking to build the foundations of biology in terms of elements, logic and principles, using both the language and the general methods employed in other disciplines. For this, we define four philosophical attitudes towards the concepts of symmetry and asymmetry and of necessity and contingency and explain how they enter into the foundations of knowledge and in the construction of theories. The customary introduction of compound biological entities such as organisms, cells, genes, catalysts or motors, is largely descriptive and relies mostly on inductive reasoning. We endeavor to complement this conventional approach with a more constructive one based on an explicit and more complete use of logical inferences. This program is shown to clarify the philosophical and logical structure of biology and its major theories: the theory of natural selection, cell theory, hereditary theory and the physico-chemical theory of life.

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Summary Background In contrast with other disciplines such as mathematics and physics, biology has not gone through a foundational crisis. Its logical content and its principles remain poorly understood. Furthermore, it is often stated that there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. This raises the question of the roles of necessity and contingency in biology. As a result, compound biological entities such as cells, DNA or proteins are usually described rather constructed. A better understanding of the foundations of biology is expected to clarify these issues.

Methodology/Principal Findings We present a research program seeking to build the foundations of biology in terms of elements, logic and principles, using both the language and the general methods employed in other disciplines, focusing on the concepts of symmetry and asymmetry and of necessity and contingency. The three great biological theories introduced in the nineteenth century, namely cell theory, Darwin’s theory of natural selection, and Mendel’s theory of inheritance were formulated at a time when the atomic structure of matter was still being debated. Following Maxwell, we incorporate atomism in these theories and show how deductive reasoning enters into the elaboration of the concepts of individual living organisms, the struggle for life, natural selection, cells, genes as well as catalysts and motors. A theoretical construction of the genetic material establishes - in a qualified sense - the unique and ideal character of DNA. A similar approach leads to an improved description of amino acids and proteins.

Conclusion/Significance This program contributes to clarify the philosophical and logical structure of biology and its major theories and should ultimately lead to a better understanding of the problems raised by the origin of life, by artificial life, and by system and synthetic biology.

Relation with previously published work We have examined the relationship of the paper with published work with the greatest care for all the topics discussed. This often implied thorough historical investigations, as most of the issues that we address are longstanding ones. The search for the original literature on these issues has thus often led us to cite older publications, which altogether constitute an odd list of references. We shall give below three illustrations of these investigations.

3 1. Our study of the relationship between the concepts of symmetry and asymmetry and necessity and contingency has led us to an in depth analysis of Pierre Curie’s 1894 paper on symmetries. We have found that this work is continually overlooked or, worse, misunderstood as this works points to the necessary character of asymmetries for the existence of phenomena. We believe that this principle is not generally well known, even in the physical sciences, and that its use in biology contributes to clarify the complex issue of the roles of necessity and contingency in this discipline. 2. For the specific issue of the logic of natural selection, we have greatly benefited from the works of Julian Huxley1 in 1942 and of Leigh van Valen2 in 1976. Both authors discuss the role of deductive reasoning in an interesting manner that we believe is improved in our work (in particular through the explicit introduction of atomistic ideas). More recent work, such as the classic book of Mayr3 in 1982 or the articles written by Ayala4 or Gregory5 in 2009 (on the occasion 150 years following the publication of the Origin), discuss the logic of this theory in terms of five major inferences. Whereas these analyses are valuable, they overlook the problem of the logical status of these inferences (deductive, inductive or otherwise) implying that the current understanding of the topic has somewhat regressed today. 3. Our description of the structure of amino acids appears to improve the original description given by Fischer in 1904.

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Huxley, J. (1942). Evolution. The Modern Synthesis. Allen & Unwin, London. Van Valen, L. (1976). Domains, deduction, the predictive method, and Darwin. Evolutionary Theory, 1, 231-245. 3 Mayr, E. (1982) The Growth of Biological Thought: Diversity, Evolution, and Inheritance. The Belknap Press of Harvard University Press Cambridge, MA. 4 Ayala, F.J., (2009) Darwin and the scientific method. PNAS 106, 10033-10039. 5 Gregory, T.R., (2009) Understanding Natural Selection, Evo. Edu. Outreach 2, 156-175. 2

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Introduction Our work investigating the foundations of biology began as a theoretical construction of the genetic material. We observed that the fundamental concept of a material basis to heredity is commonly introduced through a description of the DNA double helix, followed by another description of its replication process. [1, 2] Asking “Why DNA is such as it is and not otherwise?”, we chose to pursue a complementary approach. Our focus was on a construction, establishing a minimal list of requirements that a biological device for information storage should possess. The genetic material emerged from this construction as a transient state in a succession of invariant processes of replication. This work has been slowly mended through presentations to various audiences, both in research seminars, meetings and courses, and has benefited from the criticisms of many people. [3] The construction, even if not fully rigorous, appears to improve our intuitive understanding of the structure and function of DNA. Encouraged by the positive features of this construction, we sought to better understand the nature of the rules upon which it was made. The structure of DNA, when compared to that of the hypothetical genetic material as obtained theoretically, is — in a qualified sense — unique and ideal. This conclusion contrasts with a widely held opinion, according to which there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. It thus raises the broad question of the role of necessity in this discipline. Asking “Why life is such as it is and not otherwise?”, we were inevitably induced to ponder on the foundations of biology, and its connection with the problems of the origin of life, of artificial life and of synthetic biology. Finally, we came to consider the foundations of other disciplines as well. Our initial work on DNA had inflated into an immense inquiry, a research program. We believe that, in this program, the methods used are as important as the first results obtained. It is in this spirit that we present below the approach and only sketch our main arguments and state our major conclusions. The following text is terse and is developed in greater detail elsewhere. [4]

Methodology Comparing the foundations of disciplines The disciplines of logic, mathematics and physics have gone through foundational crises leading to a deeper understanding of their history, elements, logic and principles. In mathematics, the concept of number (for example, real or infinite) has been revised, novel axioms as well as constructive approaches have been introduced and new measures defined (such as the modern theory of measure). In physics, the concepts of time and of space, of mass and of energy, of temperature, and of identity and of causality have been reconsidered and metrology has been completely renovated. Modern physics has

5 described new elements (such as atoms and subatomic particles), and this has required the elaboration of new logical systems (in statistical physics and in quantum mechanics). The role of probability theory in the logic of science has grown considerably. Logic itself has been transformed by Gödel’s work, showing that certain propositions can neither be proved nor refuted, thus giving an unexpected role to contingency in this discipline, and radically transforming the concept of demonstration. [5,6] Various types of logical systems have developed in the last century: finite or not, discrete or continuous, multivalued or fuzzy, temporal (bearing on past and future, on retrodiction and prediction) or describing other modalities. As a result, the largely illusory a priori character of logic has faded away, the process of differentiation into diverse systems making patent (using the wording of Quine) its naturalization. Lastly, the broad importance of the concept of symmetry has been grasped progressively in logic, in mathematics, in physics, and in the elaboration of theories or laws of nature, as further explained below. From a logical point of view, the disciplines mentioned above appear to have common characteristics: the importance of their deductive content, as well as the key role played by elemental objects in the logical inferences employed. A certain “elemental logic”, bearing on items that are irreducible and invariant [7], is at the heart of many constructive approaches. Biology contrasts today with such disciplines in several ways: It has not gone through a foundational crisis. Its logical content (especially deductive) remains uncertain. It is often claimed that biology is unique, and that contingency reigns, providing the ultimate explanation. Such statements both deny the existence of theories in biology and, more generally, of a unity of knowledge. The three great biological theories introduced in the nineteenth century, namely cell theory, Darwin’s theory of natural selection, [8] and Mendel’s theory of inheritance [9, 10] remain poorly understood and poorly taught. We point out that these theories were formulated at a time when the atomic structure of matter was still being debated, and Maxwell’s conclusion on the need to incorporate atomism in biological thought remains as timely today as it was almost a century and a half ago. [11] This introduction of atomism in biology is required to deduce the existence of individual living organisms (literally, that cannot be divided) and to construct plausible schemes for a process of reproduction. The basic logical tool here is Fermat’s principle of infinite (or indefinite) descent (which, in his terms, can be used both in a negative and in an affirmative manner). [12] The Fermatian inference further rules out reproduction processes based on a constant reduction of the size of living organisms (as in the theory of the homunculus). This was understood by Buffon [13], who, however, could not draw his argumentation to a clear conclusion as the size of atoms were unknown in his days. Another consequence of atomism is that reproduction cannot proceed unbounded under finite resources, pointing to the necessary existence of some sort of competition or struggle for life, a statement which is at the basis of the theory of natural selection (more will be said below). We thus immediately see that the logic of biology relies through atomism on an elemental logic in a manner that is not explicitly recognized.

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Goals and methods The goal of this research program is to investigate these foundations using the language and the methods employed in the investigation of disciplines outside of biology. Our approach is based on a fundamental and general belief in the existence of a unity of human knowledge. This assumption is, nevertheless, constantly held as a heuristic tool, a working hypothesis susceptible of refutation. The question “Why is DNA such as it is and not otherwise?” can be addressed, following Leibniz, using the philosophical principle of sufficient reason, which states that we can always provide an answer to the two questions: “Why does something exist rather than nothing?”, and, if it exists, “Why is it as such and not otherwise?”. But this principle is at once restrained by the observation that most often the reasons remain unknown to us. This limitation illustrates the general finding that fundamental principles never come alone, but always in complementary pairs, in a dialectic manner. Underlying the principle of sufficient reason are the concepts of necessity and contingency and of symmetry and asymmetry. We define four philosophical attitudes towards these two couples of antithetic concepts: One can associate, for instance, symmetry with contingency through the classical point of view according to which contingency arises from ignorance, a lack of information. Conversely, one can associate asymmetry with necessity by observing that a phenomenon, to occur, requires the absence of certain symmetry elements, in other words, the presence of necessary asymmetries; This constitutes Curie’s asymmetry principle. [14] Thirdly, symmetries can be taken as necessary, focusing on simplicity, economy and invariances, and, fourthly, asymmetries can be taken as contingent. We illustrate in Table 1 each of these four attitudes. They can be used to explain how the concepts of necessity and contingency and of symmetry and asymmetry enter in the formation of knowledge: in particular, in the principle of sufficient reason, in the elaboration of theories or laws of nature, and in the processes of teaching and learning. The construction of a theory describing a phenomenon (or a set of phenomena) consists of two steps: The first is the elaboration of appropriate measures aiming at its study. Secondly, from these measures can then be identified the invariants of the phenomenon which include both necessary asymmetries and compatible symmetries. Phenomenal asymmetries can be deemed necessary according to Curie’s point of view. In a complementary manner, the set of all the symmetries compatible with a phenomenon defines its symmetry group. Such symmetries can be viewed philosophically as being either contingent or necessary. The method of construction of a theory that we follow, in the spirit of Lautman, therefore aims both to extract the necessary asymmetries from a phenomenon and to incorporate as many symmetry elements as possible in the symmetry group which describes it. [28] In this approach, we do not construct something that actually exists, but rather an ideal, Platonic structure. We follow a similar approach in the theoretical construction of a compound item. A necessary item is unique and, if it is compound, can

7 be assembled from elementary components using the rules of construction given above. In contrast, an item that is not necessary is called contingent as it could be otherwise; It cannot be constructed, but only described. The claim that everything is contingent in biology raises the philosophical problem of the roots of contingency and of necessity, which we view as having its sources both in logic and/or symmetry considerations. In pure logic, necessity is associated with deductive reasoning (being called an apodictic necessity by Kant). [29] Extending this idea to the natural sciences, we state that the necessary character of inferences made in any scientific discipline is proportionate to their content in deductive reasoning. The inference leading, for instance, to the establishment of a difference between two objects using a measure of sufficient accuracy possesses such a deductive character. It allows us to hold as necessary the conclusion. This can explain, in part, the origin of the necessity expressed by Curie’s asymmetry principle. Another major source arises from the attitude associating symmetry with necessity, at the heart of modern physics. Making symmetry necessary has the consequence to confer a character of certainty to the generalization of induction. We shall now summarize our investigations of the four major theories of biology and the main conclusions drawn from them.

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The theory of natural selection

The process of reproduction has two aspects: it is a kind of multiplication, a nonlinear event, and is also the expression of a certain transmission of hereditary information, implying a memory system. Any system involving a memory requires the persistence of this memory through time. This requirement is absolute and cannot tolerate even the smallest interruption, thus relying implicitly on a principle of continuity. Biology, therefore, is based on a pair of seemingly contradictory yet actually complementary principles: of continuity and discontinuity. As shown above, the principle of discontinuity (or atomicity) is central to elemental logical. Continuity, on the other hand, is also present in the theory of natural selection because living organisms are made of a very large number of finite, minute constituents that we perceive as a continuum. This constitutes a second aspect of the principle of continuity illustrating a general principle of fine division. Indeed, many phenomena that we study are complex, involving a large number of elementary components usually interacting in a non-trivial manner. Elements are often few in type yet each is present in large number, an expression of a principle of plenty, complementary to the principle of economy or parsimony. A statistical approach to such systems is appropriate, and their description can be usually made in a purely continuous manner, even though the underlying atomic features are essential for their full understanding. Darwin observed that the reproduction is not an exact invariance, but an approximate symmetry that generates heritable, in general minute, differences. [8] He then generalized by induction this empirical finding to all living organisms. The underlying current ex-

8 planation is that in all living organisms, both the number of hereditary traits and the informational content of each one (expressed as a number of bits) is very large. Consequently, this makes possible the existence of a very large number of variations, slight enough to be treated as infinitesimal, compatible with the use of a continuous description of the reproduction process. Any individual organism must accordingly be thought of as a complex network of interactions between numerous hereditary traits and the environment. (Our present understanding describes this network in greater details in terms of interaction between genes and their products: RNA, proteins and other molecules.) A close look at the logic behind Darwin’s theory of natural selection makes possible the identification of several underlying, complementary principles and of several types of logical inferences: inductive (such as the statement that the reproduction of individuals is not an exact invariance, but an approximate symmetry that generates heritable differences), deductive (the existence of an invariant process called natural selection, leading to the retention of certain living organisms and to the elimination of others is a necessary consequence of the imperfection of reproduction and of the finiteness of available resources) and Bayesian [16] (or abductive in the language of Peirce [30,31]), leading (when augmented by concepts elaborated in cell theory, below) to the parsimonious conclusion of the existence of a unique common ancestor for all living organisms. The inductive as well as the key deductive components of Darwin’s theory were identified long ago by Huxley [32], yet remain poorly understood today. Natural selection defines a second law of interaction between living organisms (reproduction being the first): It provides a constant means of dispersal, acting on all forms of life following the last common ancestor. The existence of this common ancestor, when compared with the immense variety of present living organisms, brings to the fore the action of a principle of divergence underlying natural selection. Natural selection explains in a parsimonious manner the immense variety of living organisms in their totality. Indeed, of all the theories conceived by man to understand the universe, the theory of natural selection stands amongst the simplest in hypotheses and the richest in phenomena. Finally, natural selection operates through a constant search for extremes, both maxima and minima, over all parameters at its disposition. We observe this search of extremes expressed in terms of size, of largeness and minuteness, at the level of entire organisms (with elephants and whales, for example, at one end and prokaryotic single-cell organisms at the other). At the cellular level, the eggs of birds are single cells of macroscopic size; similarly, the largest neurons are of the size of an entire animal and can be several meters long. At the molecular level, natural selection leads to the formation of the giant macromolecules of meter-long chromosomal DNA but also to a constantly increasing repertoire of small molecules such as secondary metabolites. The measure of natural selection, introduced by Fisher, is called fitness and has the dimension of the reciprocal of time. [33] The relative fitness of living organisms is to be understood as an expression a biological principle of fine division.

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Cell theory

Our examination of cell theory also exploits the principle of atomicity, and we construct cell theory starting from the requirements of natural selection: reproduction, imperfect transmission of hereditary information and constant operation of selective pressure. The feasibility of this constructive approach is based on the principle that excludes a division ad infinitum of living organisms. Concomitantly, the theory of natural selection tells us that cells, being complex entities, are themselves assembled from a very large number of elements and can reasonably be described as continuous objects. Our approach is, therefore, semi-continuous. The simplest cellular shape is spherical. The process of reproduction of a cell of minimal size requires cellular growth prior to a binary fission; this combined process of growth followed by division, that we call cell gemination, makes the spherical symmetry of cells only approximate, as observed d’Arcy Thompson [34] and others. Binary fission creates a singular point of contact between two daughter cells at the moment of separation. This point becomes a new pole, and all cells are therefore polarized, both in space and in time, in accordance with the principle of fine division. Cell theory elaborated in this manner is intended to be mostly deductive. It constructs both states and processes. It defines different types of cells: the simplest are those involved in ordinary uniparental or haploid reproduction, the more complex are involved in biparental or diploid reproduction (which are germ cells or gametes in addition to somatic cells). It states that haploid generation preceded diploid generation. Furthermore, the common ancestor of all living organisms was unicellular (a unique biological unit, yet perhaps not an organism as such [35]). Cell theory also defines the state of latent life [36], also called cryptobiosis [37], in which living organisms can survive for extended periods of time as closed or isolated thermodynamic systems in a reversible, dormant stage. Cryptobiosis is both necessary and universal as a potentiality at the cellular level. Thus, at any time, a cell is either living, in a cryptobiotic state, or dead. Cell death is a necessity dictated by natural selection: Every cell living today is connected to the common ancestor by a lineage of cells, all of which have escaped death. The continuity of cellular life thus implies that cell death, although necessary, is not universal. Cell theory also constructs the process of programmed cell death, necessary and universal as a potentiality in living organisms today. Both programmed cell death and cryptobiosis are necessary to ensure the continuity of life across most adverse conditions. In unicellular organisms, programmed cell death is often an intermediate process in a pathway leading to cryptobiosis.

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The informational theory of life

The theory of biological inheritance or informational theory of life envisions living organisms, their structures, their functions and their interactions, in terms of information,

10 stored or transmitted, emitted or received, and involved in regulation or control, in homeostasis as well as adaptation. [38] Biology can be seen as a branch of information and communication sciences, and of cybernetics. [39, 40] Biological information constitutes a fundamental asymmetry of life (to be compared to molecular chirality, first described by Pasteur [41], often itself called the asymmetry of life). Information is a physical concept and is associated with an energy cost. [42, 43] The informational theory of life, as such, includes the study of heredity or genetics, and we focus here on this aspect. The theory of inheritance has its roots, in part, in the work of Mendel in the nineteenth century. [9, 10] The logical basis of this theory, however, was developed mostly starting in the second half of the twentieth century. The work of von Neumann on self-reproducing automata offers a proof of existence of such a logic. [44, 45] The architecture of his six-component automaton is described in Table 2 and compared to the structure of living organisms. The self-reproducing automaton is built from two fundamental, distinct components: a set of instructions and an aggregate of smaller automata. This distinction is required in order to comply with the temporal logic of the process of reproduction. It agrees with the necessary existence of two types of informational biopolymers (explained below) and thus of a genetic code relating their sequences. [46] Wigner’s “no-cloning” theorem of quantum mechanics, furthermore, rules out the possibility of an exact reproduction. [23,47] Shannon’s theory of communication makes possible gradual changes through redundancy and error correction. [19] One can use these ideas to construct a complete theory of inheritance, first for the simplest living organisms reproducing through uniparental, haploid generation, then for the more complex organisms reproducing through biparental, diploid generation. Assuming by simplicity that gametes possess a haploid system of inheritance, one can deduce first the existence of a system of diploid inheritance in zygotes and somatic cells and then establish rigorously Mendel’s law of inheritance.

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The physico-chemical theory of life

The physico-chemical theory of life seeks to understand the process of natural selection at the most elementary level. This includes molecular biology (and extends into the infra-molecular level, as both nuclear and electronic properties have to be considered, as well as into the supra-molecular level). This theory tries to explain the high rates, high yields and high specificity of biochemical reactions and how efficient transport processes operate. It is through the study of the biochemistry, physical chemistry and biophysics of nucleic acids in particular that we came to study the general questions raised here. Indeed, we described methods coupling chemical reactions and phase transitions that increase the rates of nucleic-acid hybridization and cyclization by many thousand-fold. These investigations fostered our initial interest in heterogeneous biochemistry and for

11 a principle of fine division underlying biochemical fitness. This principle of fine division is expressed in terms complementariness, of heterogeneity (such as phase heterogeneity), anisotropy (such as molecular chirality) and of fine division of time. This principle can be understood as an extension of the Carnot principle for heat engines [26] to other sources of energy. Catalysis (a concept introduced by Berzelius and developed by Ostwald, Fischer, Pauling, among others) operates through a tight complementariness between the catalyst and a transition state conformation occurring in the chemical reaction. A catalyst is an invariant transforming a virtual process allowed by the laws of thermodynamics, but which will not necessarily occur, into a phenomenon observable within a finite time. In a Carnot cycle, for instance, the motor itself is a catalyst and is not consumed; In another example, a carbon nucleus serves as the catalyst in the cyclic process of energy production in stars. [48,49] Catalysis (as perceived by Berzelius) illustrates a certain unity of knowledge as it unifies (among others) the fields of engineering, chemistry and biology. Beyond the field of biochemistry, Mitchell’s chemiosmotic theory endeavors to unite transport and metabolism into a vectorial metabolism. Osmoenzymes (in the language of Mitchell [50, 51]), now called biological motors, perform various types of mechanical work, improving, in particular, the transport of compounds beyond that facilitated by Brownian motion, a necessary component of selective advantage. Secondly, the theory physico-chemical of natural selection must also explain the extraordinary stability of the components of living organisms in the state of cryptobiosis. The necessary existence of informational biopolymers, whether catalysts, motors or devices for the storage of hereditary information, can then be established deductively. Such approaches will explain the necessary and unique character of essential biological structures and functions, leading, in particular, to a clearer, intuitive understanding of the structures of proteins and nucleic acids, described below.

Results of the construction The structure of the genetic material The theoretical structure of the genetic material obtained through our construction must be a heteropolymer made of at least two types of monomers in order to contain information. This heteropolymer must be both copied and transported efficiently to the two daughter cells during cell division, raising, simultaneously, problems of transport and metabolism. These problems of vectorial metabolism are solved by catalysts and by motors, introduced progressively in the step-by-step construction. The requirement of efficient transport leads to assert the existence of motors, called translocases, able to translocate along the chain (or to translocate the chain if the motor remains immobile). The interaction between a translocase and the polymer will be more efficient if it involves a repetition of identical steps (of translation and rotation). Thus,

12 the heteropolymer as seen by the motor must present a repetitive structure and be able to adopt at least transiently a regular, helical structure. For the translocation to be efficient, each monomer must contain the same chemical group used for the interaction with the motor. We call this group a vertebra. To this vertebra is attached one of more possible side-chains, specific for the two monomers, separated from the vertebra by a chemical group used as a spacer so as not to interfere with the action of the translocase. The vertebra is also used to connect the monomers between themselves to form the polymeric chain; It is therefore trifunctional. The chain of vertebrae is called the backbone of the heteropolymer. The motor must also be able to move in a constant direction along the backbone. This implies that the motor can dissipate energy anisotropically when it interacts with a vertebra which must have a polar (directional) structure. To the polarity of the vertebrae is associated a polarity of the backbone, and, thus, a polarity of the genetic information encoded by the sequence of the monomers. This polarity appears as an expression of the principle of fine division: the mechanical efficiency of the translocase is based on a fine, one-dimensional orientation of matter. Each monomer contains a trifunctional, chiral vertebra: two of the functions are present in a polar, oriented backbone and the third connects this backbone to specific achiral side chains or residues, held outside of the reach of the motor. The monomers are homochiral compounds and the polymers are isotactic chains. In order to be copied efficiently, the heteropolymer must contain its own complement, and thus be two-stranded, replicated through a semi-conservative process. The final structure obtained is that of a transient, semi-flexible, compact (globular), circular, two-stranded heteropolymer built with two types of complementary monomers. The two strands are topologically linked. They form a plectonemic double helix in which one monomer on a given strand is associated through non-covalent interactions with the complementary monomer on the other strand. Complementary rules also introduce the redundancy required to allow an efficient copy error-correction process. The separation of the two strands occurring during the replication process must be assisted by motors (called helicases), disrupting the non-covalent bonds between them, and by enzymes performing strand-passage reactions through cut and paste operations which contribute to decrease their topological linking number to zero. (We call these enzymes dianemases, following the recommended nomenclature for naming biological catalysts; Those acting on DNA have been called topoisomerases.) The genetic material is a carrying information device fully oriented in time and in space as required by the principle of fine division. The efficiency of the interaction with motors results both from asymmetries (polarity and chirality) and symmetries (helical: homochirality, isotacticity; two-fold rotation axes). The structure is characterized by necessary asymmetries: it contains information and this information is encoded both spatially and temporally. The spatial encoding is expressed by the sequence of monomers and by the fact that each strand is a fully oriented polymer, both spatially (through polarity and

13 chirality) and temporally, as there exists a temporal order along each strand, albeit imperfect, the monomers being assembled by a directed, out of equilibrium polymerization. The temporal ordering is also found at the level of the double helix, where one strand, which we call the C strand, used as a template in the previous round of duplication, is older than the complementary, younger W strand. This last asymmetry is a consequence of the necessary semi-conservative nature of the replication process. The structure obtained is ideal, having been systematically saturated with compatible symmetries: helical symmetry, homochirality, isotacticity, plectonemicity, two-fold rotation axes, circularity, globularity, complementarity, parity and redundancy, achiral side groups. None of these symmetries are exact, but only nearly so. Temporal asymmetries express the historicity of the double helix. The asymmetry between the old and the new strand makes possible their labeling through certain chemical modifications, called epigenetic, used for example in DNA repair. In a general manner, epigenetic phenomena result from necessary asymmetries, not only in DNA but also in cell membranes, where the existence of new poles following cell division can be exploited similarly.

The structure of nucleotides and nucleic acids The theoretical construction allows one to better understand the structure of nucleic acids; we focus here on the primary structure of DNA and RNA, shown in Figures 1 and 2. They are heteropolymers made of four monomers (rather than the predicted, minimal number of two). The monomers, called nucleotides, consist of a trifunctional handle to which is attached one out of five planar, achiral nucleobases. The molecular vertebra contains a trifunctional deoxyribose or ribose, to which are attached the 50 and 30 phosphates: these two links account for the polarities of the vertebra and of the heteropolymeric chains. The vertebra is both polar and chiral as expected, but its structure is not minimal (that is consisting of a single stereogenic carbon): instead, the three stereogenic carbons located in the pentose ring are associated each with one of the three specific functions of the vertebra, being associated to the 30 end (for C03 ), to the 50 end (for C04 ), or to the lateral base (C01 ). The planar side groups are always connected in the same manner, forming an isotactic chain. RNA contains a fourth chiral C02 , lowering its symmetry, thus decreasing its stability. This additional asymmetry is associated with novel phenomena, as the attached hydroxyl group is a catalytic component of several ribozymes. The phosphorus atom as well as all non-chiral carbon atoms are prochiral (with the exception of the methyl group of the thymine base of DNA). All atoms attached to tetravalent phosphorus and carbon atoms are thus discernible. Similarly, the two faces defined by (trigonal) trivalent carbons and their attached groups are distinct, illustrating again the principle of fine division. Lastly, both in DNA and RNA, the common vertebra extends, in fact, into the planar nucleobases. Indeed, four atoms are common in all bases, not only the nitrogen linked to the deoxyribose or ribose, but also two carbon atoms connected to this nitrogen

14 and an additional hydrogen atom. (To emphasize this fact, we have drawn the structure in Figures 1 and 2 using different colors for the atoms belonging to the backbone, common to all monomers, shown in black, and for the atoms of the bases specific to each residue, colored in blue.) The geometry of the common atoms associated with the backbone only differ minimally by the angles of six- or five-atom heterocyclic ring structures of the purines and pyrimidines (60◦ versus 72◦ ). The differences of chemical structure between the four nucleobases arise by specific substitutions of reactive groups in the pyrimidines cytosine, thymine (and uracil) as well as in the purines guanine and adenine. The minimal number of monomers required to synthesize informational polymers is two. The existence of four bases, thus of two distinct types of complementary base pairs having different bond strengths (involving two versus three hydrogen bonds), can be explained as follows: The secondary structure of the DNA double helix shows a sequencedependent stability, a phenomenon of central importance in replication, transcription and recombination. [52] This would be impossible to observe in a double helical polymer made of only two types of monomers, thus of a single type of pair. Indeed, the stability of such a double helix would be that of a homopolymer. The additional asymmetry makes possible the orientation of the secondary structure of DNA as well as novel phenomena in the tertiary structure of chromosomes, for example, or in the interaction with catalysts.

The structure of amino acids and proteins Proteins are heteropolymers that are assembled by a motor called the ribosome which must translocate efficiently during the polymerization steps. This implies that one can apply the analysis leading to the conclusions reached above concerning the genetic material to understand the structure of amino acids and proteins. Proteins must be assembled from monomers containing trifunctional vertebrae that are polar, chiral and to which side groups are attached; The side groups should be achiral, spatially separated by a spacer from the molecular vertebra (to avoid direct contact with the motor). Finally, polymers assembled from these monomers, polypeptides and proteins, must also be able to adopt, at least transiently, a helical conformation. (We shall discuss the secondary and tertiary structure of these polymers elsewhere.) The structure of the twenty proteinogenic amino acids obeys these basic rules. The standard representation of these amino acids and of the polypeptidic chain is due to Fischer. It is based on the concept of the side group, denoted R, specific for each amino acid and attached to the asymmetric C∗α atom, as illustrated for the monomer in Figure 3 (top, left) and written below for a two amino acid peptidic chain: [53] NH2 .C∗ HR.CO.NH.C∗ HR.COOH We propose a refined representation of these amino acids, shown in Figure 3 (top, right) which emphasizes the existence of a Cβ H spacer group. The structure minimizes the amount of matter required to build a vertebra: the three-point, chiral, handle consists of

15 a single chiral carbon to which is attached a hydrogen atom and the constitution of the spacer consists of a single methyne group. These structures cannot be further reduced. One can describe this simplicity in terms of atom economy or biological perfection. This economy results from the high energetic cost of the synthesis of proteins (the cost of nucleic acid synthesis is in comparison much lower, and appears compatible with their more opulent sugar-phosphate-aromatic vertebra). The molecular vertebra consists of a single, trifunctional asymmetric C∗α atom to which are also attached hydrogen, carboxyl and amino reactive groups. The description of the molecular vertebra now includes a methyne spacer, which can be removed from the conventional specific residues or side groups. The Cβ atom of this spacer is predicted and observed to be achiral (isoleucine and threonine are exceptions to this prediction, and the absolute configuration is S for Ile and R for Thr in the Cahn-Ingold-Prelog notation). Table 3, listing the twenty proteinogenic amino acids sorted by decreasing molecular weight, details the simpler residues that consist of two groups R0 and R00 . The second residue R00 is a single hydrogen atom except for isoleucine, threonine and valine (where R00 = CH3 ). Glycine is special as it is achiral and lacks a methyne spacer group. However, the side group of glycine, being a simple H atom, causes no steric clash with a molecular motor and glycine often plays the role of a flexible junction in the construction of protein chains. Note that the carbon atom of glycine is prochiral and that the two hydrogen atoms attached to it are discernible. Table 3 also lists the molecules obtained when a hydrogen atom would be added to the separated active residue R0 in place of the spacer bond (in the case of proline, where the side group is cyclically attached to the backbone, a second terminating hydrogen atom is included). This permits to identify sixteen trimmed specific active side groups. The functional properties of the trimmed side groups are more readily grasped than when the Cβ H spacer is included in the residue: the specific side group H − R0 of tryptophane is thus indole (instead of skatol), that of tyrosine is phenol, that of phenylanine is benzene, and that of histidine is imidazole. The structure of these amino acids appears minimal if one wants to employ the corresponding functional groups. In contrast, this is not the case for other amino acids: for instance, lysine with 1-propylamine or arginine with Nethylguanidine, where the functional group (amine or guanidine) could be attached using a short spacer. Altogether, eleven out of the twenty amino acids appear to possess minimal side groups (Trp, Tyr, Phe, His, Met, Asp, Asn, Cys, Ala and Gly). The novel representation that we present here does not aid our understanding in the case of short side chains (alanine, cysteine and serine), as the removal of the methylene group leaves the residue without a carbon atom. Here, it is be better to associate the spacer with the functional side group, leading to the molecules methane, methylmercaptan and methanol (instead of dihydrogen, hydrogen sulfide and water). The major role of proteins as catalysts implies, in contrast to the relative simplicity of the genetic material, that proteins should contain the main functional groups of organic chemistry, such as acid and base, alcohol and thiol, or aromatic (benzene, indol and

16 phenol). Proteins, furthermore, are to be produced in greater quantities then the genetic material itself and, therefore, must involve an economical use of matter (atoms). The conclusion reached above that eleven out of the twenty proteinogenic amino acids possess minimal side groups implies that the necessary number of functional groups is greater than the number of strict minimal structures. These investigations suggest that it will be eventually possible to explain why the proteinogenic amino acids, their common vertebra and their specific side groups are such as they are and not otherwise.

The necessity of both nucleic acids and proteins Why do two types of informational biopolymers, nucleic acids and proteins, exist rather than only one? Both heteropolymers are informational storage devices. However, they fulfill mostly different functions: nucleic acids forming the genetic material providing a memory having long-term stability and reliability and proteins holding structural roles or serving as biochemical catalysts. As explained above, no more than four monomers are required in the constitution of nucleic acids, whereas at least eleven monomers are necessary in proteins. This difference in roles and in requirements for their structures, reflects a certain division of labor between nucleic acids and proteins, the genetic material and catalysts. It thus offers a plausible explanation for the necessary existence of the two types of biopolymers. It also points to the likely uniqueness of the logical solution offered by von Neumann for self-reproduction.

Concluding remarks On the unity of knowledge. Our approach tries to adapt the methods used in the investigation of other disciplines to biology, and our emphasis is on the methods themselves as much as on results. Underlying this approach is a conviction of the existence of a unity of knowledge, which finds its main expression in a science of research (Leibniz Ars inveniendi [54] or Peirce’s Economy of Research [55]), shared by all disciplines. The unity of knowledge can be seen as a specific expression of a more general principle of unity called monism. Yet, the tree of knowledge also grows through the many disciplinary branches, the existence of which can be explained in terms of an increased efficiency associated with a division of intellectual labor at the basis of economical thought. We find here again fundamental principles coming as complementary pairs: a principle of diversity expressing a pluralism coupled with a principle of unity. The unity of human knowledge is also expressed in the foundations of biology, which are found here to rely on elementary phenomena, on pairs of complementary principles (of continuity and discontinuity or atomicity, of symmetry and asymmetry, of necessity and contingency, of parsimony and plenty...), and on logic, in the same manner as do

17 other sciences of nature. The foundations of biology will provide this discipline both with elements and laws of interaction, making possible a deductive formulation of the concept of natural selection and then of cells, genes, catalysts and motors. They will explain in a plausible manner the necessary and unique character of essential biological structures and functions and contribute to a better understanding of the problems raised by the origin of life, by artificial life, and by system and synthetic biology.

Acknowledgments The present work summarizes an ongoing research program initiated a few years ago. Previous versions of it have been presented to sundry audiences: Cargèse School on DNA and Chromosomes, in 2004, 2006, and 2009; Gent Fantom Research School on Symmetries and symmetry violation in 2004 and 2007; Lectures on the Foundations of Molecular Biology, Evry in 2004; Lectures on Elements of Biology, Ecole Polytechnique Fédérale de Lausanne in 2008; Lectures on Foundations of Biology, University Pierre and Marie Curie, Paris 2008-2013; Meeting “From Base Pair to Body Plan”, Cold Spring Harbor Laboratory in 2013. We have greatly benefited from the comments of their participants. We wish to thank for discussions Roger Balian, Sydney Brenner and Theo Odijk, as well as Albert Libchaber, Marie-Claude Marsolier-Kergoat and Edouard Yéramian for the critical reading of the manuscript.

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18 7. Russell B (1911) Le réalisme analytique. Bull Soc Fr Philo 11: 53–61. 8. Darwin C (1859) On the Origin of Species by Means of Natural Selection, or The Preservation of Favoured Races in the Struggle for Life. London: John Murray. 9. Mendel G (1866) Versuche u ¨ber pflanzen-hybriden. Verh Natur Vers Br¨ unn 4: 3–47. 10. Bateson W, Mendel G (1902) Mendel’s Principles of Heredity. A Defence, with a Translation of Mendel’s Original Papers on Hybridisation. Cambridge: Cambridge Univ. Press. 11. Maxwell JC (1875) Atom. In: Encyclopedia Britannica, Edinburgh: A & C Black, volume 3. 9 edition, pp. 36–49. 12. Fermat P (1894) Correspondance. In: Tannery P, Henry C, editors, Oeuvres de Fermat, Paris: Gauthier-Villars, volume 2. pp. 431–436. 13. Buffon GLL (1749) Histoire Naturelle Générale et Particulière, avec la Description du Cabinet du Roy, volume 2. Paris: Imprimerie Royale. 14. Curie P (1894) Sur la symétrie dans les phénomènes physiques: symétrie d’un champ électrique et d’un champ magnétique. J Phys (Paris) 3ème série 3: 393– 415. 15. Simon HA (1981) The Sciences of the Artificial. Cambridge, MA: MIT Press, 2 edition. 16. Laplace PS (1820) Théorie Analytique des Probabilités. Paris: Madame Veuve Courcier, 3 edition. 17. Keynes JM (1921) A Treatise on Probability. London: Macmillan. 18. Gibbs JW (1902) Elementary Principles in Statistical Mechanics. New York: Scribners. 19. Shannon CE (1948) A mathematical theory of communication. Bell Sys Tech J 27: 379–423, 623–656. 20. Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106: 620–630. 21. Weyl H (1952) Symmetry. Princeton: Princeton Univ. Press. 22. Weyl H (1949) Philosophy of Mathematics and Natural Science. Princeton: Princeton Univ. Press.

19 23. Wigner EP (1967) Symmetries and Reflections. Bloomington: Indiana Univ. Press. 24. Lee TD (1981) Particle Physics and Introduction to Field Theory. Contemporary concepts in physics. Chur: Harwood Academic Publishers. 25. Wiener N (1923) Differential space. J Math and Phys 2: 131–174. 26. Carnot S (1824) Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance. Paris: Bachelier. 27. Perrin J (1909) Mouvement brownien et réalité moléculaire. Ann Chim Phys 8ème série 18: 1–114. 28. Lautman A (1946) Symétrie et dissymétrie en mathématique et en physique. Le problème du temps. In: Actualités scientifiques et industrielles. Essais philosophiques 3, Paris: Hermann. pp. 9–22. 29. Kant I (1883) Prolegomena and Metaphysical Foundations of Natural Science. London: G. Bell. Translated by E. B. Bax. 30. Peirce CS (1878) Illustrations of the logic of science. Sixth paper – deduction, induction, and hypothesis. Popular Science Monthly 9: 470–482. 31. Peirce CS (1934) Pragmatism and pragmaticism. In: Hartshorne C, Weiss P, editors, Collected Papers of Charles Sanders Peirce, Cambridge, MA: Harvard Univ. Press, volume 5. p. 455. 32. Huxley J (1942) Evolution: The Modern Synthesis. London: George Allen and Unwin. 33. Fisher RA (1930) The Genetical Theory of Natural Selection. Oxford: The Clarendon Press. 34. D’Arcy Thompson (1942) On Growth and Form. Cambridge: The Univ. Press, a new edition. 35. Woese C (1998) The universal ancestor. Proceedings of the National Academy of Sciences 95: 6854–6859. 36. Bernard C (1878) Le¸cons sur les Phénomènes de la Vie Communs aux Animaux et aux Végétaux, volume I. Paris: J.-B. Baillière et fils. 37. Keilin D (1959) The Leeuwenhoek lecture — the problem of anabiosis or latent life history and current concept. Proc Roy Soc London series B-Biol Sci 150: 149–191.

20 38. Cannon WB (1929) Organization for physiological homeostasis. Physio Rev 9: 399–431. 39. Wiener N (1961) Cybernetics or Control and Communication in the Animal and in the Machine. Cambridge, MA: MIT Press. 40. Ashby WR (1960) Design for a Brain. New York: Wiley, 2 edition. 41. Pasteur L (1848) Recherches sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire. Annales de Chimie et de Physique, 3ème série 24: 442–459. ¨ 42. Szilard L (1929) Uber die entropieverminderung in einem thermodynamischen system bei eingriffen intelligenter wesen. Z Phys 53: 840–856. 43. Szilard L (2003) On the decrease in entropy in a thermodynamic system by the intervention of intelligent beings. In: Leff H, Rex AF, editors, Maxwell’s demon 2: Entropy, classical and quantum information, computing, Bristol: Institute of Physics. pp. 124–133. Translated by A. Rapoport and M. Knoller. 44. von Neumann J (1951) The general and logical theory of automata. In: Jeffress LA, editor, Cerebral Mechanisms in Behaviour – The Hixon Symposium, New York: Wiley. pp. 1–41. 45. von Neumann J (1966) Theory of Self-Reproducing Automata. Urbana: Univ. Illinois Press. 46. Crick FHC (1958) On protein synthesis. Symposia of the Society for Experimental Biology 12: 138–163. 47. Wigner EP (1961) The probability of the existence of a self-reproducing unit. In: Shils E, editor, The Logic of Personal Knowledge: Essays presented to Michael Polanyi on his seventieth birthday, 11th March 1961, London: Routledge & Paul. p. 231. 48. Bethe HA (1939) Energy production in stars. Phys Rev 55: 103–103. 49. Bethe HA (1939) Energy production in stars. Phys Rev 55: 434–456. 50. Mitchell P (1979) The ninth Sir Hans Krebs lecture. Compartmentation and communication in living systems. Ligand conduction: a general catalytic principle in chemical, osmotic and chemiosmotic reaction systems. European Journal of Biochemistry 95: 1–20. 51. Mitchell P (1991) Foundations of vectorial metabolism and osmochemistry. Bioscience Reports 11: 297–344.

21 52. Yeramian E (2000) Genes and the physics of the DNA double-helix. Gene 255: 139–150. 53. Fischer E (1904) Synthese von polypeptiden. II. Berichte der deutschen chemischen Gesellschaft 37: 2486. 54. Couturat L (1901) La logique de Leibniz: d’après des documents inédits. Paris: Alcan. 55. Peirce CS (1976) Parts of the Carnegie Application (L 75). In: Eisele C, editor, Mathematical Philosophy, The New Elements of Mathematics, The Hague: Mouton, volume 4. pp. 13–73.

22

Figures NH2 O

H CH3 C

𝟓′ O

P ⊖

CH2 O

O

∗

HH ∗ O O

P ⊖

N NH C T

C

H

O

C

O

N

C

∗

O

HH

O NH2

H

N

H

C

O CH2

∗

HH ∗ O

O

C

C N

∗

HH

NH N

C N

G A

C NH2 H

H

𝟑′

Figure 1. Structure of nucleotides and primary structure of polynucleotides. I Deoxyribonucleic acid. Two consecutive monomers are shown. The planar nucleobases (C: cytosine, T: thymine, G: guanine, and A: adenine) include atoms drawn in black belonging to the backbone, being common to all of the bases; the atoms that differ are drawn in blue and constitute the specific residues. The magenta arrow indicates the polarity of the backbone. The three chiral carbon atoms are indicated by red asterisks.

23

NH2 O

H NH C

𝟓′ P

O ⊖

N NH C U

C

H

O

CH2 O

O

∗

HH ∗

O ⊖

C

N

O

HH

∗

O

OH

P

O

O

C

∗

O NH2 H

N C

CH2 O

∗

HH ∗ O

C

C N

∗

HH ∗

NH N

C N

G A

C NH2 H

OH

𝟑′

Figure 2. Structure of nucleotides and primary structure of polynucleotides. II Ribonucleic acid. The same convention is used as in Figure 1, with U designating uracil. The backbone contains a fourth chiral carbon atom and a reactive hydroxyl group.

24

R″

R′ H

R C ∗α ⊕

O C

NH3

⊖

H ⊕

O

O

CH2 C

NH3

Gly

⊖ O

O C

⊖ O

C𝛽 H2 H C ∗α

CH2 ⊕

C ∗α

NH3

CH2

⊕

H

C𝛽

O C

NH2

Pro

⊖ O

Figure 3. Chemical structure of proteinogenic amino acids. Top, left: conventional generic representation of the amino acids showing a residue R (in blue) attached to the asymmetric C∗α atom; Top, right: refined generic representation, emphasizing the presence of a prochiral spacer group Cβ H (in red) to which are attached two residues R0 and R00 (in blue). See also Table 3. Bottom, left: glycine is achiral and lacks a methyne spacer group. Bottom, right: proline is also somewhat an anomaly since its side group cycles back to the amino group of the vertebra.

25

Tables Table 1. Four attitudes towards necessity and contingency, symmetry and asymmetry Contingency

Necessity “Symmetrism” Principle of “Incompletism” simplicity or Principle of economy bounded Principle of rationality [15] symmetry Principle of Symmetry Conservation indifference laws, selection [16, 17] rules, Principle of symmetries as maximum “nonentropy [18–20] observables” [21–24] “Inventism” “Phenomenism” Gedanken Principle of experiments of asymmetry physics [14] Asymmetry Mathematical Heat Brownian engines [26] motion [25] Brownian Sciences of the motion [27] artificial [15]

26

The four attitude may be viewed as forming a modified modal square of opposition (yet we stress their complementary — and not their contradictory — nature). Incompletism associates symmetry with asymmetry, in a principle of “non-sufficient” reason or indifference. Both in physics and in information theory, ignorance, viewed as a lack of information, can prevent the establishment of the uniqueness of a phenomenon. This is treated through a maximization of the relevant (Gibbs-Boltzmann or Shannon) entropies. Phenomenism associates asymmetry with necessity. Carnot, for instance, shows that the macroscopic heat engine requires (1) a transfer between two reservoirs differing in temperature (a space heterogeneity), (2) an absence of time reversibility (time orientation) and (3) an oriented heat flow from the hot to the cold reservoir. This Carnot principle can be viewed as an expression of a principle of division of the simplest type relating division with efficiency. A Curie analysis of the phenomenon of the Brownian motion of a colloidal particle in a fluid similarly reveals two fundamental asymmetries: a granularity of the surrounding fluid, establishing its discrete, atomic structure (and, therefore, the disruption of a symmetry of scale invariance), and the constant motion of this fluid (in agreement with the kinetic theory of heat). Symmetrism asserts the necessity of symmetry at the foundations of laws of nature. It arises first through the principle of simplicity or economy: when several laws can describe the same phenomenon, we must retain the one that is the simplest, most parsimonious, devoid of redundancy. Here phenomena are not described through necessary asymmetries, but instead through a group of compatible symmetries, either continuous or discrete, and the focus is on conservation laws or selection rules. Symmetries are called “non-observables”, and, accordingly, asymmetries become associated observables as in phenomenism. Inventism associates asymmetry with contingency. Here, one decides to suppress some of the necessary asymmetries of phenomenon, treating them as contingent. It releases imagination and contributes to creative thinking at large. Gedanken (thought) experiments of physics lead to the prediction of phenomena, thus to conjectural asymmetries. It can also be found in all disciplines that are not constrained by natural phenomena such mathematics or the sciences of the artificial. Mathematical Brownian motion (also called a Wiener process) can be obtained as the continuous limit of a discrete random walk on a lattice and possesses the property of unbounded scale and time invariance. Yet both scale and time invariance are incompatible with the phenomenon of Brownian motion and thus mathematical Brownian motion does not describe physical reality.

27

Table 2. The self-replicating automaton of von Neumann Component Function in the automaton ID A B C D E

Structural counterpart in living organisms The instruction describing automaton DNA D Constructing automaton Transcription and translation machinery Copying automaton DNA replication machinery Controlling automaton Regulation of replication and gene expression The aggregate A + B + C A cell without its genetic material The aggregate A + B + C + ID The cell, the simplest living organism

The automaton of von Neumann consists of five automata and one instruction. This instruction ID is an aggregate of elementary parts and acts as the tape in a Turing computing automaton. The automaton B makes a copy of ID : “the copying mechanism B performs the fundamental act of reproduction, the duplication of the genetic material, which is clearly the fundamental operation in the multiplication of living cells.” [44] When the constructing automaton A is furnished with the instruction ID , the controlling automaton “C will first cause A to construct the automaton which is described by this instruction ID . Next C will cause B to copy the instruction ID referred to above, and insert the copy into the automaton referred to above, which has just been constructed by A. Finally, C will separate this construction from the system A + B + C and ‘turn it loose’ as an independent entity.” [44] In order to function, the aggregate D = A + B + C must be furnished with the instruction ID describing this very automaton D, thus forming the self-reproducing automaton E. “E is clearly self-reproductive. Note that no vicious circle is involved. The decisive step occurs in E, when the instruction ID , describing D, is constructed and attached to D. When the construction (the copying) of ID called for, D exists already, and it is in no wise modified by the construction of ID . ID is simply added to form E. Thus there is a definite chronological and logical order in which D and ID have to be formed, and the process is legitimate and proper according to the rules of logic.” [44]

Table 3. The proteinogenic amino acids H−R −R00 skatole 3- −H methylindole 2 Y Tyr Tyrosine 181.188 −CH2 C6 H4 OH 4-methylphenol −H 4-cresol 3 R Arg Arginine 174.201 −(CH2 )3 NHC(NH)NH2 N−H propylguanidine 4 F Phe Phenylalanine 165.189 −CH2 C6 H5 toluene −H 5 H His Histidine 155.155 −CH2 C3 H3 N2 4−H methylimidazole 6 M Met Methionine 149.211 −(CH2 )2 SCH3 ethyl methyl −H sulfide 7 E Glu Glutamate 147.129 −(CH2 )2 COOH propionic acid −H 8 K Lys Lysine 146.188 −(CH2 )4 NH2 1-butylamine −H 9 Q Gln Glutamine 146.144 −(CH2 )2 CONH2 propionamide −H 10 D Asp Aspartate 133.103 −CH2 COOH acetic acid −H 11 N Asn Asparagine 132.118 −CH2 CONH2 acetamide −H 12 L Leu Leucine 131.173 −CH2 CH(CH3 )2 isobutane −H 13 I Ile Isoleucine 131.173 −CHCH3 CH2 CH3 butane −CH3 14 C Cys Cysteine 121.158 −CH2 SH methanethiol −H methyl mercaptan 15 T Thr Threonine 119.119 −CH(OH)CH3 ethanol −CH3 16 V Val Valine 117.146 −CH(CH3 )2 propane −CH3 17 P Pro Proline 115.130 −(CH2 )3 − propane −H (H − R − H) 18 S Ser Serine 105.093 −CH2 OH methanol −H 19 A Ala Alanine 89.093 −CH3 methane −H 20 G Gly Glycine 75.067 −H dihydrogen ∅ Amino acid 1 W Trp Tryptophan

Mw (Da) −R (conventional) 204.225 −CH2 C8 H6 N

−R0 −C8 H6 N

H − R0 indole

−C6 H4 OH

phenol

−(CH2 )2 NHC(NH)NH2 N-ethylguanidine −C6 H5 −C3 H3 N2

benzene imidazole

−CH2 SCH3

dimethylsulfide

−CH2 COOH −(CH2 )3 NH2 −CH2 CONH2 −COOH −CONH2 −CH(CH3 )2 −CH2 CH3 −HS

acetic acid 1-propylamine acetamide formic acid formamide propane ethane hydrogen sulfide

−OH −CH3 −(CH2 )2 −

water methane ethane (H − R0 −H) water dihydrogen ∅

−OH −H ∅

28