Contributions of a modified electrodynamics to the molecular biochirality

In this paper, we investigate the physical basis behind the molecular biochirality from the computation of a parity violation energy difference (PVED) in enantiomers of organic molecules (e.g., amino acids, which occur as levogyrous-type in nature), by considering the influence of fundamental interactions beyond the standard model of elementary particles and interactions. Particularly, we study the role of a 4-D Chern-Simons theory at the origin of this PVED, the Carroll-Field-Jackiw electrodynamics, which violates both Lorentz and parity symmetries. Then, we consider terrestrial and Jovian scenarios where the influence of a modified (effective) magnetic field generated by the planets on the molecules is taken into account in the calculation of PVED. Besides this quantity, we also calculate the relative quantity excess of an enantiomer over the other in a thermal bath. Finally, we compare the obtained results with those ones from other models based on fundamental interactions.

Possible Physical Basis of Mirror Symmetry Effect in Racemic Mixtures of Enantiomers: From Wallach’s Rule, Nonlinear Effects, B–Z DNA Transition, and Similar Phenomena to Mirror Symmetry Effects of Chiral Objects

Effects associated with mirror symmetry may be underlying for a number of phenomena in chemistry and physics. Increase in the density and melting point of the 50%L/50%D collection of enantiomers of a different sign (Wallach’s rule) is probably based on a physical effect of the mirror image. The catalytic activity of metal complexes with racemic ligands differs from the corresponding complexes with enantiomers as well (nonlinear effect). A similar difference in the physical properties of enantiomers and racemate underlies L/D inversion points of linear helical macromolecules, helical nanocrystals of magnetite and boron nitride etc., B–Z DNA transition and phenomenon of mirror neurons may have a similar nature. Here we propose an explanation of the Wallach effect along with some similar chemical, physical, and biological phenomena related to mirror image.

Сhiral and Racemic Fields Concept for Understanding of the Homochirality Origin, Asymmetric Catalysis, Chiral Superstructure Formation from Achiral Molecules, and B-Z DNA Conformational Transition

The four most important and well-studied phenomena of mirror symmetry breaking of molecules were analyzed for the first time in terms of available common features and regularities. Mirror symmetry breaking of the primary origin of biological homochirality requires the involvement of an external chiral inductor (environmental chirality). All reviewed mirror symmetry breaking phenomena were considered from that standpoint. A concept of chiral and racemic fields was highly helpful in this analysis. A chiral gravitational field in combination with a static magnetic field (Earth’s environmental conditions) may be regarded as a hypothetical long-term chiral inductor. Experimental evidences suggest a possible effect of the environmental chiral inductor as a chiral trigger on the mirror symmetry breaking effect. Also, this effect explains a conformational transition of the right-handed double DNA helix to the left-handed double DNA helix (B-Z DNA transition) as possible DNA damage.

Spontaneous symmetry breaking of population: Stochastic Lotka-Volterra model for competition among two similar preys and predators

The celebrated Lotka-Volterra (LV) model is vastly used to describe the simple competition between prey and predator populations. The stochastic LV model, for its turn, considers the competition among two similar prey and two similar predator populations, with each group being described by identical mathematical equations. However, each of these groups differs in stochastic fluctuations, which are interpreted as small variations in each species' specimens (Genetic Diversity and Phenotypic Expression Diversity) and environmental conditions. The relative statistical variation presented is inversely proportional to the square root of the amount of specimens in each population. The model begins with two prey and two predator groups and, after a transient time, is reduced to one element of each group, returning to the classic LV system. That is, the model ends in asymmetric states despite starting from an initial symmetric condition without population excess. Spontaneous population symmetry breaking without population excess was obtained using the stochastic method. For its turn, the deterministic method could be used to analyze such breaking by forcing a perturbative fluctuation or adding little excess to one population, but the stochastic method can simulate such break in symmetry naturally.

Stochastic chiral symmetry breaking process besides the deterministic one

In chiral symmetry breaking, populations with initial enantiomeric excess (EE) are probabilistically favored if statistical fluctuation is present, as in nature. Stochastic methods correctly describe chiral symmetry breaking by taking into account the quantitative enantiomeric difference (excess or deficiency) and the statistical fluctuation amplitude, which is inversely proportional to the absolute size of the populations involved. From this, we obtain a law, which indicates that such a favoring probability decreases exponentially [P(EE) = 1/(e^αEE + 1)] with an initial enantiomeric deficiency mediated by statistical fluctuation. Obviously, chiral symmetry breaking equally favors populations without enantiomeric excess [P(0) = 1/2]. However, if deterministic methods are considered, chiral symmetry breaking will strictly favor the population with an initial enantiomeric excess (EE). To study these stochastic chiral symmetry breaking processes the autocatalytic Frank model was considered. Summarizing, our results show that the initial enantiomeric excesses are not entirely responsible for the final state configuration of autocatalytic finite systems.