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Lack of Evolvability in Self-Sustaining Autocatalytic Networks Constraints Metabolism-first Scenarios for the Origin of Life

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Lack of Evolvability in Self-Sustaining Autocatalytic Networks Constraints Metabolism-first Scenarios for the Origin of Life Lack of evolvability in self-sustaining autocatalytic networks constraints metabolism-first scenarios for the origin of life Vera Vasasa,b, Eörs Szathmárya,b,c,1, and Mauro Santosa,d aCollegium Budapest, Institute for Advanced Study, H-1014 Budapest, Hungary; bInstitute of Biology, Eötvös University, H-1117 Budapest, Hungary; cParmenides Center for the Study of Thinking, Munich D-80333, Germany; and dDepartament de Genètica i de Microbiologia, Grup de Biologia Evolutiva, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain Edited by Gerald F. Joyce, The Scripps Research Institute, La Jolla, CA, and approved December 3, 2009 (received for review November 3, 2009) A basic property of life is its capacity to experience Darwinian reactions that may deplete certain reactants (12) and dynamical evolution. The replicator concept is at the core of genetics-first aspects of autocatalytic cycles if they are assumed to coexist in theories of the origin of life, which suggest that self-replicating abstract space (13). Even if we ignore such hurdles, the key oligonucleotides or their similar ancestors may have been the first question still remains: Was a network of chemical reactions able to “living” systems and may have led to the evolution of an RNA increase in complexity and eventually undergo Darwinian selec- world. But problems with the nonenzymatic synthesis of biopol- tion as assumed by their advocates? A basic condition for any ymers and the origin of template replication have spurred the nascent Darwinian process in a population of self-reproducing alternative metabolism-first scenario, where self-reproducing systems is that they must have a sort of hereditary transmission and evolving proto-metabolic networks are assumed to have pre- which requires, in turn, becoming familiar with a lesser-known and dated self-replicating genes. Recent theoretical work shows that absolutely different form of replication than the well-known “compositional genomes” (i.e., the counts of different molecular template-dependent replication: ensemble replication of molec- species in an assembly) are able to propagate compositional infor- ular networks (12). So far, the strongest support for such a possible mation and can provide a setup on which natural selection acts. scenario comes from theoretical work carried out by Doron Lancet EVOLUTION Accordingly, if we stick to the notion of replicator as an entity that and collaborators (14–16). They have proposed the thoughtful passes on its structure largely intact in successive replications, graded autocatalysis replication domain (GARD) model (which those macromolecular aggregates could be dubbed “ensemble utilizes chemical kinetics to simulate the behavior of mutually replicators” (composomes) and quite different from the more catalytic sets) as an alternative to alphabet-based inheritance. A familiar genes and memes. In sharp contrast with template- basic feature in GARD is that noncovalent, micelle-like molecular dependent replication dynamics, we demonstrate here that repli- assemblies capable of growing homeostatically (i.e., buffered fi cation of compositional information is so inaccurate that tter enough as to maintain stability) according to the assembly’s con- compositional genomes cannot be maintained by selection and, stitution store compositional information that can be propagated therefore, the system lacks evolvability (i.e., it cannot substantially after occasional fission (i.e., assembly splitting). depart from the asymptotic steady-state solution already built-in Here we analyze the putative evolvability of those macro- in the dynamical equations). We conclude that this fundamental molecular aggregates dubbed “ensemble replicators.” The chief limitation of ensemble replicators cautions against metabolism- reason for our undertaking is that such compositional genomes fi rst theories of the origin of life, although ancient metabolic sys- (composomes) apparently fulfill the required conditions as to be tems could have provided a stable habitat within which polymer considered units of evolution (17), thus suggesting a pathway from replicators later evolved. pre-Darwinian dynamics to a minimal protocell. The remainder of the paper is organized as follows. First, we provide the back- autocatalysis | graded autocatalysis replication domain model | ground of the GARD model. Then, we derive an Eigen equation units of evolution that allows analyzing the deterministic dynamics of the growth- splitting process in GARD and investigate the mechanisms nce beyond the abiogenic synthesis and accumulation of a behind the observed quasistationary compositional genomes. Ovariety of complex organic compounds on Earth took place Finally, we describe the results from computer simulations and (1), the conceivable paths toward life’s emergence have been discuss the implications of our findings in relation to the genetics- dominated by two fundamentally different views in origin-of-life or metabolism-first scenarios of the origin of life. research: the genetics- or replication-first approach (2), and the metabolism-first scenario (3). Both schools acknowledge that a Background critical requirement for primitive evolvable systems (in the The GARD model was originally based on computer simulations Darwinian sense) is to solve the problems of information storage using Gillespie’s algorithm (18, 19) for chemical reactions and and reliable information transmission (4, 5). Disagreement intended to provide a quantitative tool for detailed analyses of starts, however, in the way information was first stored. All inheritance without information-carrying polymers. It involves present life is based on digitally encoded information in poly- discrete stochastic changes in noncovalent assemblies dictated by nucleotide strings, but difficulties with the de novo appearance of the differential equations oligonucleotides and clear-cut routes to an RNA world (but see ref. 6), wherein RNA molecules had the dual role of catalysts and information storage systems (7, 8), have provided continuous Author contributions: V.V., E.S., and M.S. designed research; V.V., E.S., and M.S. per- fuel for objections to the genetics-first scenario (9, 10). formed research; V.V. and M.S. analyzed data; and V.V., E.S., and M.S. wrote the paper. As emphasized by Kauffman (11), metabolism-first theories The authors declare no conflict of interest. suggest that life, in a deep sense, crystallized as a collective self- This article is a PNAS Direct Submission. reproducing metabolism in a space of possible organic reactions. A 1To whom correspondence should be addressed. E-mail: [email protected]. critical property of such systems must be the capacity for robust This article contains supporting information online at www.pnas.org/cgi/content/full/ self-maintenance, but problems arise when considering side 0912628107/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.0912628107 PNAS Early Edition | 1of6 Downloaded by guest on September 24, 2021 tribution of all possible Ω assemblies (a total of 220 under our dn 1 ¼ i ¼ ηG ¼ðρ − Þ þ ∑j NG β ; Fi ikiN k − ini 1 j¼1 ijnj characterization) can be obtained by constructing an Eigen dt N [1] (4) equation, i ¼ 1; 2; ...; NG ‘ Ω X ¼ðrk − EÞXk þ ∑ ¼ μ Xl; k ¼ 1; 2; ...; Ω; [3] G k l 1 kl where η is an NG − long vector; NG is the molecular repertoire ρ ‘ of environmentally available prebiotic compounds; i is the where Xk (with prime for time derivation) is the density of ¼ − 2 − 1 η10 μ external concentration of molecular species i; ki 10 sec assembly k ; rk is a self-reproduction term; and kl is the ¼ − 5 − 1 η10 η10 and k − i 10 sec are uncatalyzed forward and backward mutation rate from l to k (i.e., the fraction of growth-split- rate constants assumed to be equal for all molecules for sim- ting processes leading to the kth daughter assembly from plicity [they differ in their mutual rate enhancement properties parental l). The rate of exact self-reproduction arises as the sum ð < Þ ¼ ∑NG (14)]; N N NG is the assembly size given by N i¼1ni, with of all processes that after growth and splitting give rise to the ni indicating the count of molecular species i (i.e., the internal same assembly that we started with. ηG ; ; ...; Þ β molecular counts of vector are n1 n2 nNG and ij is an The overall excess productivity element of the NG × NG positive matrix that defines the network À Á ¼ ∑ þ ∑ μ [4] of mutually catalytic interactions governed by a statistical for- E k rkXk l klXl ηG malism (see below). Given two compositional assemblies p and ηG fi q , their degree of similarity is de ned as the scalar product is built-in so as to ensure that G G ∑ ¼ : [5] η η kXk 1 HðηG; ηGÞ¼ p : q ; [2] p q jηGj jηGj p q In short, we are explicitly dealing here with compositional space η10 ¼ in which for any assembly k with initial size Nmin 3 all jηGj jηGj ¼ where p and q are Euclidian norms (H 1 represents per- accessible daughter assemblies of the same size are calculated. fect similarity, and H ¼ 0 indicates orthogonality). The reason Death rates were not incorporated and empty assemblies were for assuming N < NG is that information transfer becomes trivial avoided by allowing splitting of assemblies into two offspring of for large assemblies (15). equal size but otherwise random composition (sampling without At time t, a GARD assembly contains a subrepertoire of replacement). These assumptions do not, however, hamper the molecular types out of NG, and the time-dependent trajectory of conclusions obtainable by the analysis of
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