The information for organic evolution has somehow been predetermined in the evolving genome in a way comparable to the way in which the necessary information to produce a complete organism is contained within a single cell, the fertilized egg. Davison, John A., biologist, “Prescribed Evolutionary Hypothesis”
From an information perspective, the genetic system is a pre-existent operating system of unknown origin that supports the storage and execution of a wide variety of specific genetic programs (the genome application), each being stored in the DNA. Johnson, Donald E., chemist and computer scientist, “Programming of Life”
The original life plasm of an evolutionary world must contain the full potential for all future developmental variations and all subsequent evolutionary changes and modifications. The Urantia Book (www.urantia.org) INTRODUCTION
The hypothesis of this paper is that the information for the evolution of life was programmed in the original genome. The following are presented as substantiating evidence:
The hypothesis by the Nobel Laureate physicist Erwin Schrödinger that an organic molecule is an aperiodic crystal or quasicrystal in which every atom and group of atoms is arranged in an orderly but non-repeating manner and plays a specific role.
The statement of the physicist Manfred Schroeder that self-similar, i.e., fractal symmetry breeds quasicrystals with five-fold (pentagonal) axis of rotational symmetry.
The demonstration by the mathematical physicist Roger Penrose that a surface can be tiled with pentagon symmetry, heretofore thought impossible, and the subsequent discovery of a crystal exhibiting such symmetry. The relationship between Penrose tiling and quasicrystals is shown.
The assertion by the chemist and computer scientist Donald E. Johnson that to succeed a program must contain formal algorithmic prescriptive information that generates meaning and function.
And the claim by the communication engineer Gerard Battail that error-correcting codes can ensure copies without errors as long as the correcting ability is not exceeded by the errors. The hypothesis of nested codes is proposed as layered structures that protect the oldest, most fundamental information; the example given is the conservation of HOX genes that has ensured from the beginning the preservation of genotypes and matching phenotypes.
FRACTAL GEOMETRY AND FIVE-FOLD SYMMETRY OF ATOMIC ARRANGEMENTS IN ORGANIC MOLECULE
Shape Determines Function
SUMMARY Fat and skinny tiles formed by the two types of isosceles triangles that shape the pentagon, with dimensions based on the divine proportion, are the building blocks that join at the edges according to specific matching rules to form the spherically-shaped, fractal (self-similar) aperiodic atomic structures with pentagon symmetry of organic molecules.
In addition to the specific physico-chemical features, biological molecules exhibit a new, probably emergent, property, i.e. they code for biological information. Thus, in some complex way, the biological information that necessarily codes for a function is also related to the shape because shape is a key feature for implementing such functions. S. Giannerini, statistician D.L. Gonzales, geneticist R. Rosa, statistician
A small molecule might be called the germ of a solid. Starting from such a small solid germ, there seems to be two different ways of building up larger and larger associations. One is the comparatively dull way of repeating the same structure in three directions again and again; that is the way followed by a growing crystal. Once the periodicity is established, there is no definite limit as to the size of the aggregate. The other way is that of building up a more and more extended aggregate without the dull device of repetition. That is the case of the more and more complicated organic molecule in which every atom, and every group of atoms, plays an individual role, not entirely equivalent to that of many others (as is the case in a periodic structure). We might quite properly call that an aperiodic crystal [quasi periodic or quasicrystal] or solid and express our hypothesis by saying: We believe a gene – or perhaps the whole chromosomal fibre – to be an aperiodic solid. … It has always been asked how this tiny speck of material, the nucleus of the fertilized egg, could contain an elaborate code-script involving all future developments of the organism. A well-ordered association of atoms, endowed with sufficient resistivity to keep its order permanently, appears to be the only conceivable material structure that offers a variety of possible (isomeric) arrangements, sufficiently large to embody a complicated system of ‘determinations’ within a small spatial boundary. Indeed, the number of atoms in such a structure need not be very large to produce an almost unlimited number of possible arrangements. p.60-61
In normal crystalline solids (e.g., salt) the atoms are arranged in a lattice which repeats itself regularly in three dimensions with two, three, four, and six-fold rotational symmetry; the information is specified and repetitive and, therefore, very low.
In an aperiodic crystal (quasi periodic crystal or quasicrystal), however, the atoms are arranged in a lattice that repeats itself in 3D in an orderly but irregular yet self-similar or fractal manner; the information content is specified but irregular and, therefore, very high.
Self-similar (Fractal) Symmetry Breeds Quasicrystals
Self-similarity, or invariance against changes in scale or size, is an attribute of many laws of Nature and innumerable phenomena in the world around us. p.2 [S]elf-similarity breeds a new solid state of matter, namely a "quasicrystal" with a five-fold axis of rotational symmetry. p.301 Manfred Schroeder, physicist
Though deemed impossible by the scientific community, pentagonal symmetry in crystals was discovered in an aluminum-manganese alloy by materials engineer Dan Shechtman in 1984.
Atoms of Quasicrystals Pack Space with Pentagonal Symmetry Based on PHI
PHIΦ, the golden ratio or divine proportion, the proportion of beauty, is an irrational number named after the Greek architect Phidias who designed the Parthenon. It is the division of a line with any given length into a large part and a small part so that the ratio of the whole line to the large part is the same as the ratio of the large part to the small part. This occurs only when the whole is 1.618033 times the large part and the large part is 1.618033 times the small part.
A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. [Q]uasicrystals can be constructed from a single repeating cluster of atoms and…the rigid [arrow edge-]matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. P. J. Steinhardt, physicist
Ten years before the discovery of the aluminum-manganese alloy, Penrose had shown that a surface could be tiled with pentagonal symmetry with two sets of tiles each of which is the combination of the PHI-based isosceles triangles forming the pentagon.
The tiling [on the right] is composed of two tiles, fat and skinny rhombi, that repeat with incommensurate frequency. … To force the tiles to make a quasiperiodic tiling, one must introduce matching rules for how any pair of tiles can join edge-to-edge. P. Steinhardt
Penrose tiling, the first aperiodic tiling constructed by two types of rhombic tiles. The entire pattern is generated by a local joint rule referred to as the ‘‘matching rule’’, which requires each of the tiles to complete types and directions of the arrowheads on the tile edges, as shown in the figure. The pattern appears to be complicated, but there are only eight local environments (vertex symmetry), as indicated by the black dots. E. Abe, materials engineer
Quasicrystals are Three-Dimensional Analogues of Penrose Tilings
The surface area of a protein molecule is known to determine many of its physical properties. ... The surface corrugation can be analyzed by using fractal theory. p.180 K.S. Birdi, chemist
Protein locations in a capsid (nucleus) of bovine papilloma virus (with fractal pentagonal symmetry) O.V.Kuznetsova, chemist; S.B.Rochal, physicist; V.L.Lorman, physicist
A=adenine T=thymine C=cytosine G=guanine U=uracil
A chain of specific codons translates into a chain of specific amino acids to form specific proteins
Protein Synthesis SequenceA Transfer RNA [tRNA] is an adaptor molecule composed of RNA, typically 73 to 94 nucleotides in length, that serves as the physical link between the nucleotide sequence of nucleic acids [mRNA] and the amino acid sequence of proteins. Each tRNA is charged with the proper amino acid via a covalent ester bond at its 3′ end by a family of enzymes called aminoacyl-tRNA synthetases. bass.bio.uci.edu/
SUMMARY Changes in inorganic matter occur spontaneously according to physical and chemical laws, but changes in organic matter occur only by means of codes. The genome stores and executes a wide range of specific programs for all developmental stages of the organism with codes that contain formal algorithmic prescriptive information that generates meaning and function.
The genes and proteins of the first cell had to have biological specificity, and specific molecules cannot be formed spontaneously. They can only be manufactured by molecular machines, and their production requires entities like sequences and codes that simply do not exist in spontaneous processes. That is what really divides dead from living matter. All components of matter arise by spontaneous processes that do not require sequences and codes, whereas all components of life arise by manufacturing processes that do require these entities. It is the sequences and codes that makes the difference between living and dead matter. It is semiosis (symbol translation system) that does not exist in the inanimate world, and that is why biology is not a complex form of chemistry. Quote by Donald E. Johnson, p.21
The great evolutionary biologist George C. Williams has pointed out that animals with complicated life cycles need to code for the development of all stages in the life cycle, but they have only one genome with which to do so. A butterfly genome has to hold the information needed for building a caterpillar as well as a butterfly. A sheep liver fluke has six distinct stages of its life cycle, each specialized for a different way of life. Quote by Donald E. Johnson p.31
The main distinctive features of living beings are their extreme complexity and… the obvious but still overlooked fact that besides matter and energy, they receive and transmit information, and that life heavily relies on information transfer and conservation. p.32
Omics refers to the collective technologies used to explore the roles, relationships, and actions of the various types of molecules that make up the cells of an organism.
Formal algorithmic prescriptive information is key to any successful computer program, including the program within life. Prescriptive information instructs or directly produces nontrivial function. Prescriptive information either tells us what choices to make, or it is a reminder of wise choices already made. It not only describes, it generates meaning and function, providing a functional algorithm. p. 39
When it comes to instructions, messages and cybernetic programs, grammar rules cannot be isolated from message meaning and message function. Grammar rules without meaning lack function. Thus prescriptive information requires all three categories of symbols [syntactics, semantics, pragmatics] and their meaning (semiotics) to communicate shared meaning and function between source and destination. p. 40
From an information perspective, the genetic system is a pre-existent operating system of unknown origin that supports the storage and execution of a wide variety of specific genetic programs (the genome application), each being stored in the DNA. p.48
SUMMARY In terms of geological time, the memory of the genome is rather short and the replication of information may contain errors. However, error-correcting codes can ensure faithful replication of information as long as the ability of the codes is not overwhelmed by the errors. The oldest information in the genome is "nested" with several protective layers as is demonstrated by the conservation of HOX genes which have ensured from the beginning the preservation of genotypes and matching phenotypes.
Excerpt from Abstract – Faithful conservation of genomes can be ensured only if they involve error-correcting codes. Then the genomes can be recovered with a small probability of error, provided the interval between successive generations is as short (on the time-scale of geology), to always avoid that the number of accumulated errors exceeds the correcting ability of the code. G. Battail, p. 299Abstract: As semiotics itself, biosemiotics is concerned with semantics. On the other hand, the scientific study of communication engineering led to the development of information theory, which ignores semantics. For this reason, many biologists thought that it would be useless in their disciplines. It turns out however that problems of communication engineering are met in biology and thus can only properly be dealt with using information theory. As an important example, the faithful transmission of genetic information through the ages is a difficult problem which has been overlooked by biologists. Cumulated errors in the DNA molecule due to radiations and even to its own indeterminism as a quantum object actually perturb its communication through time. A simple information-theoretic computation shows that, contrary to the current belief, the genomic memory is ephemeral at the time scale of geology. The conventional template-replication paradigm is thus not tenable. According to a fundamental theorem of information theory, error-correcting codes can perform almost errorless communication provided certain conditions are met. Faithful conservation of genomes can thus be ensured only if they involve error correcting codes. Then the genomes can be recovered with an arbitrarily small probability of error, provided the interval between successive generations is as short (at the time scale of geology) as to almost always avoid that the number of cumulated errors exceeds the correcting ability of the code. This paper presents an intuitive outline of information theory and error-correcting codes, and briefly reviews the consequences of their application to the problem of genome conservation. It discusses the possible architecture of genomic error-correcting codes, proposing a layered structure referred to as ‘nested codes’ which unequally protects information: the older and more fundamental it is, the better it is protected. As regards the component codes of this system, we notice that the error-correcting ability of codes relies on the existence of constraints which tie together the successive symbols of a sequence. It is convenient in engineering to use mathematical constraints implemented by physical means for performing error correction. Nature is assumed to use to this end ‘soft codes’ with physico-chemical constraints, in addition to linguistic constraints that the genomes need for directing the construction and maintenance of phenotypes. The hypotheses that genomic error-correction means exist and take the form of nested codes then suffice to deduce many features of the living world and of its evolution.
Turbo codes have a performance close enough to the theoretical limit of the channel capacity [the largest amount of information which can be communicated in the average by a symbol] to be considered as almost optimal, at least from a practical point of view. p. 317-18
A subsidiary hypothesis is that Nature uses ‘nested codes’, a system which combines several codes as follows: A first information message is encoded according to some code. Then, a second information message is appended to the codeword which resulted from the first encoding, and the resulting message is encoded again using another code. This process is repeated several times, the last information message being left uncoded. The resulting nested system is the fortress metaphor where each code is represented as a wall which encloses the information message it contains.
The hypothesized nested structure is plausible if we notice that certain parts of the genome like the HOX genes are conserved with astonishing faithfulness in many animal species, with the consequences that the organization plans of the corresponding phenotypes are very faithfully conserved. p. 329
Probably the most important contribution is the statement that the paradigm of genome replication by copying a template is wrong and should be replaced by that of genome regeneration based on its intrinsic error-correcting properties. Although we established that the existence of error-correcting codes is an unavoidable consequence of the faithful conservation of genomes, almost nothing is known as yet as regards the error-correcting means that nature actually implements. The multiplicity of codes combined in the hypothesized nested structure hints at a variety of encoding constraints and regeneration processes. p. 343
The PHI-based, pentagon-shaped, aperiodic and fractal atomic structure of organic molecules containing, within a minute space, specific and non-repetitive information in a vast number of genetic programs bearing algorithmic prescriptive codes for directing the construction and maintenance of phenotypes; the specific sequential steps taken by DNA to synthesize proteins in a cell; the faithful replication of individual genetic information by means of error-correcting codes; and the preservation of genes that have ensured from the beginning the conservation of genotypes and matching phenotypes are indicative that the original genome was programmed and the evolution of life was, therefore, prescribed.
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