Information-theoretic approach in allometric scaling relations of DNA and proteins

Allometric scaling relations can be observed in between molecular parameters. Hence, we looked for presence of such relation among sizes (i.e., lengths) of proteins and genes. Protein lengths exist in the literature as the number of amino acids. They can also be derived from the mRNA lengths. Here, we looked for allometric scaling relation by using such data and simultaneously, the data was compared with the sizes of genes and proteins that were obtained from our modified information-theoretic approach. Results implied presence of scaling relation in the calculated results. This was expected due to the implemented modification in the information-theoretic calculation. Relation in the literature-based data was lacking high goodness of fit value. It could be due to physical factors and selective pressures, which ended up in deviations of the literature-sourced values from those in the model. Genome size is correlated with cell size. Intracellular volume, which is related to the DNA size, would require certain number of proteins, the sizes of which can therefore be correlated with the protein sizes. Cell sizes, genome sizes, and average protein and gene sizes, along with the number of proteins, namely the expression levels of the genes, are the physical factors, and the molecular factors influence those physical factors. The selective pressures on those can act through the connection between those physical factors and limit the dynamic ranges. Biological measures could be prone to such forces and are likely to deviate from expected models, regardless of the validity of assumptions, unless those are also implemented in the models. Yet, present discrepancies could be pointing at the need for model improvement, data imperfection, invalid assumptions, etc. Still, current work highlights possible use of information-theoretic approach in allometric scaling relations' studies.