Discovery of Power-Laws in Chemical Space

Abstract

Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank/ frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80/20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases.

Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations

“…The power-law α-distributions have been frequently observed and noted in some systems away from equilibrium, such as the space plasma at a high energy [20], the solar flares [27], the chemical processes and reaction-diffusion processes [12,13,18], the trapped ion collisions with heavy neutrals [9], and elsewhere.…”

Inhibition of Highly Productive HIV-1 Infection in T Cells, Primary Human Macrophages, Microglia, and Astrocytes by Sargassum fusiforme

“…Abundances of expressed genes in human normal and cancer tissues were found to be Zipfdistributed [31]. In the chemical world, a recent study shows that the distributions of such features as rigid segments, ring systems and circular substructures of small, organic molecules follow power law [32]. The Zipf distribution of the weights of the TCM formulas and herbs may therefore suggest TCM treatment as a dialect, with herbs as words and formulas as phrases, in the communications to the human body.…”

The power-law reaction rate coefficient for an elementary bimolecular reaction

“…(3) is reduced to a BG distribution if the ν-parameter is set ν →1, where the parameter 1 ν ≠ measures a distance away from the equilibrium and it is a function of the energy [4]. The power-law distributions in complex systems have been found and noted prevalently in the processes such as single-molecule conformational dynamics [8,9], reaction-diffusion processes [10], chemical reactions [11], combustion processes [12], gene expressions [13], cell reproductions [14], complex cellular networks [15], and small organic molecules [16] etc. In these processes, the reaction rate coefficients may be energy-dependent (and/or time-dependent [17,18] ) power-law forms [19,20], which are beyond the scope of conventional TST reaction rate formulae with a BG exponential law.…”