From Molecules to Life: Quantifying the Complexity of Chemical and Biological Systems in the Universe

Abstract

Life is a complex phenomenon and much research has been devoted to both understanding its origins from prebiotic chemistry and discovering life beyond Earth. Yet, it has remained elusive how to quantify this complexity and how to compare chemical and biological units on one common scale. Here, a mathematical description of molecular complexity was applied allowing to quantitatively assess complexity of chemical structures. This in combination with the orthogonal measure of information complexity resulted in a two-dimensional complexity space ranging over the entire spectrum from molecules to organisms. Entities with a certain level of information complexity directly require a functionally complex mechanism for their production or replication and are hence indicative for life-like systems. In order to describe entities combining molecular and information complexity, the term biogenic unit was introduced. Exemplified biogenic unit complexities were calculated for ribozymes, protein enzymes, multimeric protein complexes, and even an entire virus particle. Complexities of prokaryotic and eukaryotic cells, as well as multicellular organisms, were estimated. Thereby distinct evolutionary stages in complexity space were identified. The here developed approach to compare the complexity of biogenic units allows for the first time to address the gradual characteristics of prebiotic and life-like systems without the need for a definition of life. This operational concept may guide our search for life in the Universe, and it may direct the investigations of prebiotic trajectories that lead towards the evolution of complexity at the origins of life.

Keywords: Biogenic unit; Biomolecule; Chemical complexity; Evolution; Life-like system.

Fig. 1

Molecular complexity C _m calculated for the structures of various small molecules in a universal complexity scale. The graphic representation is given in a logarithmic scale

Fig. 2

Quantification of molecular (C _m) and information complexity (C _i) for various types of biogenic units. a Chemical structures of DNA, (R)-GNA, and PNA and calculated complexity values for an arbitrary model sequence (ATGTGA). b Information complexity plotted against molecular complexity for arbitrary protein sequences of different alphabet sizes (1 aa to 10 aa) as function of length. B: nucleobase, aa: amino acid

Fig. 3

Complexity values calculated for various biogenic units. a Lower range of complexity of biogenic units and b complexity of larger units such as multimeric proteins, genomes, and an entire virus particle

Fig. 4

Universal complexity scale plot with representative biogenic units of Earth’s biosphere