Hox Gene Collinearity May Be Related to Noether Theory on Symmetry and Its Linked Conserved Quantity

Abstract

Hox Gene Collinearity (HGC) is a fundamental property that controls the development of many animal species, including vertebrates. In the Hox gene clusters, the genes are located in a sequential order Hox1, Hox2, Hox3, etc., along the 3’ to 5’ direction of the cluster in the chromosome. During Hox cluster activation, the Hox genes are expressed sequentially in the ontogenetic units D1, D2, D3, etc., along the anterior–posterior axis (A-P) of the early embryo. This collinearity, first observed by E.B. Lewis, is surprising because the spatial collinearity of these structures (Hox clusters and embryos) correlates entities that differ by about four orders of magnitude. Biomolecular mechanisms alone cannot explain such correlations. Long-range physical interactions, such as diffusion or electric attractions, should be involved. A biophysical model (BM) was formulated, which, in alignment with the biomolecular processes, successfully describes the existing vertebrate genetic engineering data. One hundred years ago, Emmy Noether made a fundamental discovery in mathematics and physics. She proved, rigorously, that a physical system obeying a symmetry law (e.g., rotations or self-similarity) is followed by a conserved physical quantity. It is argued here that HGC obeys a ‘primitive’ self-similarity symmetry. In this case, the associated primitive conserved quantity is the irreversibly increasing ‘ratchet’-like Hoxgene ordering where some genes may be missing. The genes of a vertebrate Hox clusterare located along a finite straight line. The same order follows the ontogenetic unitsof the vertebrate embryo. Therefore, HGC is a manifestation of a primitive Noether Theory (NT). NT may be applied to other than the vertebrate case, for instance, to animals with a circular topological symmetry. For example, the observed abnormal Hox gene ordering of the echinoderm Hox clusters may be reproduced by a double-strand break of the circular Hox gene ordering and its subsequent incorporation in the flanking chromosome.

Hox Gene Collinearity with Pulling Physical Forces Create a Hox Gene Clustering in Embryos of Vertebrates, Invertebrates, Complete or Split Clutters

“…Besides the obvious external symmetries in Space and Time, there appeared in the last century the need to introduce several internal symmetries and particularly in the field of elementary particles where these material constituents are given exotic names like bosons, quarks, charmed particles, mesons etc [22,23]. Historically, in 1932, W. Heisenberg was the first who introduced such esoteric terms (e.g.…”

“…According to Noether's theory such a symmetric system is necessarily followed by a conserved quantity -in this case it is the momentum. [22,23].…”

Physical Laws Shape Up HOX Gene Collinearity

“…, . , 6, 5) is forbidden because it represents a gene reversal mutation which is not allowed [36].The abnormal spontaneous mutant of Antennapedia in the Drosophila is an example where, in the location of antennas, legs are growing as a result of an abnormal reversal of the corresponding Hox genes [37]. These mutations are named Homeotic.…”

Physical Laws shape up HOX Gene Collinearity

“…For instance, the wild type Pg ordering [1, 2, , , 5, 6,...] is allowed. In contrast, the ordering [1, 2, , ,6, 5,…] is forbidden because it represents a gene reversal mutation which is not allowed [36].…”