Abstract
The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.
Highlights
Investigations o f s ymmetries in in herited b iological structures are an important co mponent of biomechanics, biophysics, bi ochemistry, a nd ot her s ciences of living matter
In the genomes of higher and lower organisms, an important rule for the recurrent organization of DNA nucleotide sequences was d iscovered; t hese s equences serve for the transfering genetic information [2, 3]. This hyperbolic r ule for th e r elationship o f o ligomer sums i s associated with a long-known harmonic progression (1): 1/1, 1/2, 1/3, 1/4, ...., 1/n
Let us present some of the possibilities we have studied of us ing t he mathematical p roperties o f h armonic progression ( 1), which i s a ssociated with t he organization of genomes of higher and lower organisms, for modeling i nherited b iological s tructures a nd processes
Summary
Investigations o f s ymmetries in in herited b iological structures are an important co mponent of biomechanics, biophysics, bi ochemistry, a nd ot her s ciences of living matter. In the genomes of higher and lower organisms, an important rule for the recurrent organization of DNA nucleotide sequences was d iscovered; t hese s equences serve for the transfering genetic information [2, 3] This hyperbolic r ule for th e r elationship o f o ligomer sums i s associated with a long-known harmonic progression (1): 1/1, 1/2, 1/3, 1/4, ...., 1/n (1). Our studies of the properties of genetic inheritance of biological structures and the possibilities of their algebraic modeling are based on the well-known mathematical formalisms of matrix and tensor analysis, recurrent sequences, the theory of information noise-immune coding, as well as on known academic information about genetic and other biological structures
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