In the course of evolution, cell–cell interactions, including possible exchange of membrane lipids ( Reed, 1968 Pagano and Huang, 1975 ), might have allowed the emergence of a pool of shared membrane lipids in their plasma membranes. Formation of this boundary, the plasma membrane of a cell, was driven by self-aggregation of amphipathic molecules that also subsequently led to intracellular compartment formation, resulting in a eukaryotic cell. Appearance of the first single cell(s), unit(s) of life, required a boundary enclosing a “system” separated from the surrounding environment. Self-aggregation/assembly of amphipathic molecules was a crucial step in the origin of life ( Monnard and Deamer, 2002 Rasmussen et al., 2009 Chen and Walde, 2010 ). Thus, in spite of the importance of amphipathic lipid molecules in formation of compartments as whole cells and within cells, emphasis on the essential “third” component (i.e., amphipathic lipid molecules) has been limited. Only a few scattered reports comment on the evolution of eukaryotic membranes, and those are also based largely on membrane proteins and biosynthetic pathways in cells ( Pereto et al., 2004 Daiyasu et al., 2005 Mulkidjanian et al., 2008 Lombard and Moreira, 2011 Lombard et al., 2012a ). The majority of these studies are based on genomics and proteomics data. On the other hand, the two-merger theory supports the presence of amitochondriates ( Fuerst and Webb, 1991 ). Literature on the one-merger theory indicates that early eukaryotes (e.g., Trichomonas foetus) are not amitochondriates and contain organelles, called hydrogenomas, that are analogous to mitochondria ( Lindmark and Muller, 1973 ). 2) Two-merger theory: the merger of archaea and eubacteria first formed the nucleus of the eukaryotic cell around 2.7 Ga another alpha-Proteobacteria was later engulfed to produce mitochondria around 2 Ga ( Margulis et al., 2006 ). There are two basic schools of thought: 1) One-merger theory: the merger of eubacteria and archaea led to the formation of the nucleus and mitochondria at the same time (around 2 giga-annum Hartman and Fedorov, 2002 ). The majority of these models are based on the merger of two prokaryotes to form ancient eukaryotic cells. To date, there are a number (more than 20) different models to explain the origin of eukaryotic cells ( Martin and Muller, 1998 Martin, 2005 Martin and Koonin 2006 Moreira and Lopez-Garcia, 1998 Vesteg and Krajcovic, 2006 Forterre, 2011 Baum and Baum, 2014 ). On the other hand, the universal tree of single-stranded rRNA clusters eukaryotes near to archaea ( Woese, 2000 ). While genes involved in replication, transcription, and translation indicate similarity between archaea and eukaryotes, metabolic genes indicate eukaryotes are closer to eubacteria ( Rivera et al., 1998 ). Over the years, the evolutionary origins of eukaryotic cells have been studied with respect to two key components in living systems-nucleic acids and proteins. Further inspection of membrane lipid structures affecting physicochemical properties of plasma membranes provides the first evidence (to our knowledge) on the symbiotic origins of eukaryotic cells based on the “third front” (i.e., lipids) in addition to the growing compositional data from nucleic acids and proteins. This indicates the presence of interaction(s) and/or association(s) in lipids forming plasma membranes of eubacteria and eukaryotes but not for those in archaea. This statistical paradox, called Simpson's paradox, was absent for lipids in archaea and for lipids not common to plasma membranes of the three domains. However, mutually exclusive subsets of same data show exactly the opposite-the number of carbon atoms in lipids of eukaryotes was higher than in eubacteria. For lipids common to plasma membranes of the three domains, the number of carbon atoms in eubacteria was found to be similar to that in eukaryotes. In this work, rigorous compositional analyses of ∼5000 plasma membrane lipid constituents of 273 species in the three life domains (archaea, eubacteria, and eukaryotes) revealed a remarkable statistical paradox, indicating symbiotic origins of eukaryotic cells involving eubacteria. Compositional analyses of nucleic acids and proteins have shed light on possible origins of living cells.

Statistical anomaly