Primordial Sex Facilitates the Emergence of Evolution
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Primordial Sex Facilitates the Emergence of Evolution Sam Sinai1,2,∗, Jason Olejarz1,∗, Iulia A. Neagu1,3, and Martin A. Nowak1,2,4,† 1Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA 2Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 4Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA∗ (Dated: December 11, 2017) Compartments are ubiquitous throughout biology, yet their importance stretches back to the origin of cells. In the context of origin of life, we assume that a protocell, a compartment enclosing functional components, requires N components to be evolvable. We calculate the timescale in which a minimal evolvable protocell is produced. We show that when protocells fuse and share information, the time to produce an evolvable protocell scales algebraically in N, in contrast to an exponential scaling in the absence of fusion. We discuss the implications of this result for origins of life, as well as other biological processes. A defining characteristic of living organisms is their in aqueous conditions [23, 24], forming compartments, ability to replicate and evolve [1]. A major objective of which in this context are known as protocells. research on the origin of life is therefore to find plausi- Protocells alleviate some of the pitfalls that an im- ble chemical systems that are capable of self-replication. pede the transition from prelife to life. The contents of The “RNA world hypothesis” is a leading framework en- protocells are held near each other and share the same compassing theories about the role of RNA in the origin fate. This results in increased interactions within the of life. It postulates that RNA or a similar bio-polymer, protocell and decreased interactions with the outside en- being both an information-carrying molecule, as well as vironment. It also means that the protocell can house an enzymatic one, must have played a central role in a segmented genome, i.e. the information within the initiating self-replication [2–4]. But formidable difficul- protocell need not be stored in one contiguous polymer. ties remain for developing this narrative into a complete It can also dampen the effects of side reactions for any and rigorous theory of the origin of life. Both theoreti- auto-catalytic cycles that may be required to start and cal and experimental investigations show that well-mixed maintain a metabolism [25]. Protocells can also divide populations of RNA or similar bio-polymers often suffer into new protocells that inherit parts of their contents from calamitous pitfalls, including the error catastrophe [26, 27]. These properties of protocells enable them to for replicases [5] and parasitism for cooperative enzymes help in selection for cooperative polymers, in particular [6–9]. Moreover, the complexity of long RNA sequences replicases [6, 7, 28–32]. In addition to enclosing informa- that could serve as efficient catalysts creates a challenge tion and dividing, protocells are able to merge, thereby for explaining their spontaneous prebiotic synthesis [10]. sharing their contents [25, 33–35]. In biology, sharing in- Indeed, despite decades of efforts in prebiotic chemistry formation content between two individuals is considered (and some exciting progress, e.g. [11, 12]), building effi- a defining property of sex. cient, stable, and prebiotically plausible replicases (some- The implications of this information-sharing ability times called the holy grail of the RNA world) has re- among protocells, which is a form of “primordial sex”, mained a challenge [13, 14]. have not received much attention. For reasons outlined arXiv:1612.00825v2 [q-bio.PE] 8 Dec 2017 In modern cells, lipid membranes compartmentalize in the rest of this study, we suggest that the ability for information-carrying and enzymatic molecules akin to these compartments to merge categorically changes the those sought after by RNA world researchers. Hence, at time required to produce an evolvable protocell. Hence, some point in the development of life, either before, dur- we propose that early presence of membranes, possibly ing, or after the emergence of self-replicating genetic el- even before the advent of replication, could have vastly ements, such compartmentalization must have occurred. improved the chances of producing complicated cells by There is evidence in support of the prebiotic availability luck. In such cases it would not be unreasonable to as- of lipid membranes. It has been shown that amphiphilic sume that the starting set of molecules from which an molecules, like simple fatty acids that are building blocks evolvable cell emerges could be large. Almost no origin for the lipid membrane, can be produced in a prebioti- of life models operate on this assumption, because they cally plausible manner [15]. Alternatively, lipids could consider it a probabilistic miracle. have been imported to earth by chondrite meteorites To test this hypothesis, we investigate a simple first- [16–18]. Hence, such molecules were likely abundantly passage process [36, 37]. We assume that in order to be present on the prebiotic Earth [19–23]. These molecules evolvable, a protocell needs to contain a certain number, are able to spontaneously assemble into lipid vesicles N, of component types (i.e., distinct molecules of var- 2 ious complexity) [8, 38–42]. In early life, these could be molecules as simple as ions, activated monomers, molecules that stabilize the membrane, or more compli- cated polymers, like oligo-peptides, and even elementary ribozymes and simple unlinked genes [12, 25, 29, 30, 43– 48]. More precisely, the target set should result in an auto-catalytic network that results in a evolvable cell with non-negligible probability. Such a scheme has been proposed since Oparin, and has been defended more re- cently [48]. We term the smallest set of necessary and sufficient components from which an evolvable protocell can be made a minimal evolvable protocell. We can accordingly represent the functional (or ge- netic) content of each protocell as a binary string of length N. For simplicity, we ignore the redundancy (or dose) of each component in the protocell, and are only concerned with each component’s presence. If a proto- cell contains a particular component i, then the string will have a value of 1 at the ith position and 0 otherwise. Whenever a protocell randomly assembles, we assume that it contains each of the N component types indepen- dently (components do not compete for positions) with FIG. 1. Merging occurs between randomly assembled proto- probability p. I.e. protocell assembly uniformly samples cells. (A) Each color (and a “1” bit at each corresponding each type (with sufficient abundance) from the environ- position on a protocell’s representative binary string) indi- cates presence of one of the four components needed for the ment with probability p. Whenever two protocells merge, protocell to be evolvable (here, N = 4). Randomly assembled the value of the resulting string at every position i is sim- lipid membranes form around the components. (B) When- ply determined by a bitwise OR operation on the ith bits ever two protocells merge, they share their contents. Sharing of the two parent protocells (i.e. if either of the origi- of contents is computed as a bitwise OR operation between nal cells contain a component, the resulting cell will also each of the two parent strings of length N. contain it). This is shown schematically in Figure 1. The dynamical process is as follows. On the first step, the accumulator—the object of our attention—consists number of random assembly and merging events in the of a randomly assembled protocell. If less than N com- accumulation process. ponents are enclosed, then one of two things can happen: The time, Z, needed to form a minimal evolvable pro- With probability δ, the accumulator loses its contents, tocell is thus a random variable that depends on the par- and on the second step, the accumulator consists of a ticular accumulator being tracked. If we track many such new randomly assembled protocell, with the accumula- accumulators, then what is the mean first-passage time, tion process starting over. The accumulator can lose its E[Z], for an accumulator to achieve all N components contents if, for example, its membrane’s integrity is lost, necessary for evolvability? it is infected by a parasite, or it divides, and the param- Begin by considering the simple case δ = 1 (no merg- eter δ accounts for all such possibilities. Or with proba- ing occurs). If the accumulator consists of a randomly bility 1 δ, on the second step, the accumulator merges assembled protocell that has all N components, then the with a randomly− assembled protocell from the environ- minimal evolvable protocell has been achieved. But if ment, possibly gaining additional components. In this there are less than N components, then the accumulator case, if the accumulator still has less than N components is reset without merging. Thus, the expected number of after merging, then one of two things can happen: With such random assembly events required to accumulate all probability δ, the accumulator loses its contents, and on N components necessary for evolvability, Eδ=1[Z], grows the third step, the accumulator consists of a new ran- exponentially with N, i.e., domly assembled protocell, with the accumulation pro- cess starting over. Or with probability 1 δ, on the third 1 N − E [Z]= step, the accumulator merges with another randomly as- δ=1 p sembled protocell from the environment, possibly gaining additional components. This process continues until the For large values of N, the spontaneous generation of a accumulator gains all N components necessary for evolv- minimal evolvable protocell would be a probabilistic mir- ability. The total number of steps (or time units), Z, acle.