ABSTRACT. The ability of systems of molecular reactions to be simultaneously autocatalytic and sustained by some ambient 'food source' of simple molecules may have been an essential step in the origin of life. In this paper we first describe a polynomial-time algorithm that determines whether any given set of molecules, reactions and catalysations contains a subsystem that is both autocatalytic and able to be sustained from a given subset of the molecules. We also describe some combinatorial properties of this algorithm, and show how it can be used to find irreducible auto-catalysing and sustaining subsystems. In the second part of the paper we use the algorithm to investigate random catalytic networks -in particular a model described by Kauffman. Using simulations and some analytic techniques we investigate the rate of catalysis that is required for the emergence of autocatalytic and sustaining subsystems.

Trees, Qualitative characters, Compatibility, Resolved quartets, Clusters, Strict consensus tree,

Archaebacterial halophiles (Haloarchaea) are oxygen-respiring heterotrophs that derive from methanogens-strictly anaerobic, hydrogen-dependent autotrophs. Haloarchaeal genomes are known to have acquired, via lateral gene transfer (LGT), several genes from eubacteria, but it is yet unknown how many genes the Haloarchaea acquired in total and, more importantly, whether independent haloarchaeal lineages acquired their genes in parallel, or as a single acquisition at the origin of the group. Here we have studied 10 haloarchaeal and 1,143 reference genomes and have identified 1,089 haloarchaeal gene families that were acquired by a methanogenic recipient from eubacteria. The data suggest that these genes were acquired in the haloarchaeal common ancestor, not in parallel in independent haloarchaeal lineages, nor in the common ancestor of haloarchaeans and methanosarcinales. The 1,089 acquisitions include genes for catabolic carbon metabolism, membrane transporters, menaquinone biosynthesis, and complexes I-IV of the eubacterial respiratory chain that functions in the haloarchaeal membrane consisting of diphytanyl isoprene ether lipids.LGT on a massive scale transformed a strictly anaerobic, chemolithoautotrophic methanogen into the heterotrophic, oxygen-respiring, and bacteriorhodopsin-photosynthetic haloarchaeal common ancestor.H alophilic archaebacteria (Haloarchaea) require concentrated salt solutions for survival and can inhabit saturated brine environments such as salt lakes, the Dead Sea, and salterns (1). In rRNA and phylogenomic analyses of informational genes, Haloarchaea always branch well within the methanogens (2-4). Haloarchaea can thus be seen as deriving from methanogen ancestors, but the physiology of methanogens and halophiles could hardly be more different. Methanogens are strict anaerobes, most species are lithoautotrophs that use electrons from H 2 to reduce CO 2 to methane (obligate hydrogenotrophic methanogens), thereby generating a chemiosmotic ion gradient for ATP synthesis in their energy metabolism, although some species can generate methane from reduced C 1 compounds, or acetate in the case of aceticlastic forms (5-7). Their carbon metabolism involves the Wood-Ljungdahl (acetyl-CoA) pathway of CO 2 fixation (5-7). In contrast, Haloarchaea are obligate heterotrophs that typically use O 2 as the terminal acceptor of their electron transport chain, although many can also use alternative electron acceptors such as nitrate in addition to light harnessing via a bacteriorhodopsin-based proton pumping system (8). The evolutionary nature of that radical physiological transformation from anaerobic chemolithoautotroph to aerobic heterotroph is of interest.Many individual reports document that lateral gene transfer (LGT) from eubacteria was involved in the origin of at least some components of haloarchaeal metabolism. These include the operon for gas vesicle formation, which allows Haloarchaea to remain in surface waters (9), the newly identified methylaspartate cycle of acetyl-CoA oxidation (10), vario...

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It is nearly 20 years since the landmark paper (Saitou and Nei 1987) in Molecular Biology and Evolution introducing Neighbor-Joining (NJ). The method has become the most widely used method for building phylogenetic trees from distances, and the original paper has been cited about 13,000 times (Science Citation Index). Yet the question "what does the NJ method seek to do?" has until recently proved somewhat elusive, leading to some imprecise claims and misunderstanding. However, a rigorous answer to this question has recently been provided by further mathematical investigation, and the purpose of this note is to highlight these results and their significance for interpreting NJ. The origins of this story lie in a paper by Pauplin (2000) though its continuation has unfolded in more mathematically inclined literature. Our aim here is to make these findings more widely accessible.