Quantum Similarity in our DNA, and in DNA Storage

Symmetry: Culture and Science, 2019

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. Correspondingly the article is devoted to some phenomenological symmetries in probabilities of components in long DNA sequences and to opportunities of their modelling by means of formalisms of quantum informatics. Using binaryoppositional traits of DNA nitrogenous bases, a notion "genetic qubit" is proposed and used for such modelling. Presented results support thoughts of many authors about quantum computing in biological organisms.

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G = Z5 H where H = Z2.S4 ∼ = 2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G = Z5 GL(2, 3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed. Arxiv: q-bio.OT, quant-ph, math.GR, math.AG

Journal of Molecular Structure: THEOCHEM, 1998

A comprehensive survey of the theoretical foundations and de®nitions associated with quantum similarity is given. In this task care has been taken to determine the primary mathematical structure which can be associated with quantum similarity measures. Due to this, the concept of a tagged set is de®ned to demonstrate how molecular sets can be described systematically. The de®nition of quantum object, a notion introduced by our laboratory and employed for a long time in quantum similarity studies, is clari®ed by means of a blend involving quantum theory and the tagged set structure formalism, and used afterwards as the cornerstone of the subsequent development of the theory. In the de®nition of quantum objects, density functions play a fundamental role. To formally construct the quantum similarity measure, it is very interesting to study the main algorithmic ideas, which may serve to compute approximate density forms, accurate enough to be employed in the practical calculation of nuclear, atomic and molecular quantum similarity measures. Thus, the atomic shell approximation is de®ned accompanied by all the implied computational constraints and the consequences they have in the whole theory development as well as to the physical interpretation of the results. A wide and complex ®eld appears from all these ideas, where convex sets play a fundamental role, and a new de®nition emerges: one associated with vector semispaces, where the main numerical formalism of quantum similarity seems perfectly adapted. Applications of this development embrace quantum taxonomy, visual representation of molecular sets, QSAR and QSPR, topological indices, molecular alignment, etc., and among this range of procedures and ®elds, there appears with distinct importance the discrete representation of molecular structures. q 1998 Elsevier Science B.V. All rights reserved.

Springer eBooks, 2011

During the last decade we have worked extensively on quantum computation in universe with special reference to biological organisms. We have given several hypotheses in the above mentioned area. This article presents an integrated perspective of our hypotheses presented during the last ten years.

2003

The degree of molecular quantum similarity (MQS) between different quantum objects can be expressed in different ways, depending on the operator used in the MQS equation. The most intuitive one is based on the integrated overlap between the electron densities of both quantum objects. The evaluation of the MQS requires the quantum objects to be placed in the same coordinate system; in other words the molecules must be aligned in some way. Up to now this was mostly done via topogeometrical methods. It will, however, be shown that molecular alignments based on maximization of the QSM offer important advantages.

DNA Decipher …, 2011

and theoretical work from several sources are described in this work. It is suggested that: (1) The evolution of biosystems has created genetic "texts", similar to natural context dependent texts in human languages, shaping the text of these speech-like patterns; (2) The chromosome apparatus acts simultaneously both as a source and receiver of these genetic texts, respectively decoding and encoding them, and (3) The chromosome continuum of multicellular organisms is analogous to a staticdynamical multiplex time-space holographic grating, which comprises the space-time of an organism in a convoluted form. Thus, the DNA action (as theory predicts and experiment confirms) is that of a "gene-sign" laser and its solitonic electro-acoustic fields, such that the gene-biocomputer "reads and understands" these texts in a manner similar to human thinking, but at its own genomic level of "reasoning". It is asserted that natural human texts (irrespectively of the language used), and genetic "texts" have similar mathematicallinguistic and entropic-statistic characteristics, where these concern the fractality of the distribution of the character frequency density in the natural and genetic texts, and where in case of genetic "texts", the characters are identified with the nucleotides. Further, DNA molecules, conceived as a gene-sign continuum of any biosystem, are able to form holographic pre-images of biostructures and of the organism as a whole as a registry of dynamical "wave copies" or "matrixes", succeeding each other. This continuum is the measuring, calibrating field for constructing its biosystem.

Biosystems, 2008

A model for the information transfer from DNA to protein using quantum information and computation techniques is presented. DNA is modeled as the sender and proteins are modeled as the receiver of this information. On the DNA side, a 64-dimensional Hilbert space is used to describe the information stored in DNA triplets (codons). A Hamiltonian matrix is constructed for this space, using the 64 possible codons as base states. The eigenvalues of this matrix are not degenerate. The genetic code is degenerate and proteins comprise only 20 different amino acids.

1998

Quantum similarity is a useful tool to establish comparisons between elements of a quantum object set and, so far applied successfully to molecular physics, is applied here to atomic nuclei. Quantum Similarity Measures (QSM) and Indices (QSI) are introduced to study an arbitrary set of 20 nuclei. From this study, relationships between nuclear overlaplike self-similarities and size-like properties are found. A bidimensional projection of the set is performed, and Mendeleev conjecture is invoked to predict qualitatively some nuclear ground-state properties, such as total binding energy per nucleon, nuclear radius, nuclear volume, total and partial energies, etc.

Progress of Theoretical Physics Supplement

Inspired by Ikemura conjecture about electron transfer in DNA playing an important role in information exchanges, the field theoretical approach is applied to π-electrons and phonons inside DNA. Under some approximations, three-dimensional string action is derived. The DNA string model is applied to formulate the three phenomena-luminescence quenching, eletric current through DNA and absorption of light.