EFTA01183812.pdf

Primordial sex facilitates the emergence of evolvable protocells Sam Sinai ' ' , Jason Olejarz , lulia A. Neagu , and Martin A. Nowale.b." "Program for Evolutionary Dynamics. HarvaM University. I Brame square. suite 6.02138; hDepanment of Organismic and Evolutionary Biology; `Department of Mathematics; dOepariment of Physics. Harvard University This manuscript was compiled on April x.2016 Membranes, forming protocells, are widely considered beneficial or present in abiotic earth. There is good evidence in support. It even essential to the maintenance of cooperation in early evolution has been shown that amphiphilic molecules, like simple fatty [1-5). Moreover, there are strong arguments from chemistry to sug- acids that are building blocks for the lipid-membrane, could gest that membranes played a critical role in pre-evolutionary dynam- be produced in a prebiotically plausible manner [22]. These ics [6-9). In this study we propose a novel reason why membranes molecules are able to spontaneously assemble into vesicles in are beneficial even before the presence of replication or selection. aqueous conditions [23-25]. Alternatively, lipids could have We argue that the ability of lipid membranes to fuse and share their been imported to earth by chondrite meteorites[26-28]. Hence, contents. "primordial sex", improves the efficiency of finding mini- it is commonly assumed that such molecules were present mal evolvable protocells. We analyze and quantify a model of merg- in sufficient abundances [2-4, 6-9, 12, 24] and could have ing membranes that resembles a sexual repair mechanism known produced lipid vesicles. as multiplicity reactivation in modern viruses [10). We then argue A "lipid world" may have preceded or coexisted with the that this mechanism could shorten the timescale and increase the RNA world [6-9, 29-31]. In a lipid world, protocells can con- probability of finding evolvable combinations of simple functional tain and protect catalytic and information-bearing molecules. elements significantly. This in turn suggests that assembling com- After the onset of replication (on a molecular or cellular level), plicated sets of functions at random may not be as probabilistically a key step in the RNA world, protocells help selection for implausible as it first appears. Hence, in the presence of sex, large cooperative polymers, in particular replicases [3, 4]. Because assemblies and functional networks can form without requiring evo- of the potential benefits of protocells, a multitude of successful lution. Finally, we establish a quantitative framework to analyze how experiments in the past decade have focused on the dynamics parasites, thought to be a serious impediment in early life. affect of simple co-polymerization inside lipid vesicles [32-36]. the accumulation of functions. We show that while parasites may There are several abstract properties of protocells that are hurt the accumulation process, under most circumstances, the ben- of interest. First and most obviously, the contents of protocells efits of sex massively outweigh the risks of exposure to parasitic are held near each other (are "co-localized"), and share the elements. same fate. This results in higher concentrations, increased Origin of Life I Protocells I Origin of Sex I Multiplicity Reactivation interactions within the protocell, and decreased interactions with outside environment. It also means that the protocell can house a "compositional genome", i.e. the information within M enthrones are ubiquitous across all domains of modern life, yet their importance stretches far back to the origins of the very first cells [6-8, Prebiotic chemists [6, 7, 9], as the protocell need not be stored in one (or few) contiguous polymer [11, 37]. It may also dampen the effects of side well as origin of life theorists [2-4, 8, 12), have been interested in understanding the specific roles that membranes, in self- organized lipid vesicles (also referred to as protocells), could Significance Statement have played in early evolution. Protocells are thought to play important roles in the origins of The "RNA world hypothesis" concerns itself with how RNA life. Meanwhile, some propose that sex —sharing informational or similar bio-polymers gave rise to information-coding and content among protocells— provides benefits in early evolution. enzymatic activities that eventually lead to their central role in We use mathematical modeling to suggest that even before living organisms [13-15]. However, well-mixed populations of the emergence of replication (and evolution). sex could have such molecules often stiffer from well-known pitfalls, including been enormously beneficial. In particular. we show that while the error catastrophe for replicates [16, 17] and parasitism for assembling protocells with a desired set of components is cooperative enzymes [1, 2, 5, 12]. Further, despite decades of nearly impossible if the number of components is large, sex effort in prebiotic chemistry, and some exciting piseess (e.g. would improve the efficiency of making such cells by orders of [18, 19]), building efficient, stable, and prebiotically plausible magnitude. We quantify how much this primitive sex (which replicases (sometimes called the "holy grail" of the RNA world) also appears in viruses) "speeds up the inception of evolvable in lab has remained a challenge [20]. Population assortment protocells. and once evolution begins can further increase the through dividing membranes seems to alleviate the parasitism speed at which complexity arises. problem [2-5, 12]. Apart from mathematical reasons, chemists also argue that membranes play a crucial role (e.g. producing SS-J.0.. M.A.N. doomed rosaanth. S.S. 10- tA.N. MAN. paterned ear.oatch.S S JO IA.N an electro-chemical gradient) in maintaining a metabolism in MANanalyzed data. S.S.. J.Q. IAN. AAR solo true papa.. early cells [6, 7, 9, 21]. The =has declare no cocain al intwesl While early presence of membranes has many potential IS.S. and J.O. oanlrb.ned equal?, to thirintk. benefits, it is prudent to consider whether they could have been 2 Martin Nest [email protected](lu ‘vettreas.orgeodoviotoratteati0000000cxx PNAS I Apr14,2016 I vol. )3fX I no. XX I 1-7 EFTA01183812 reactions for auto-catalytic cycles that may be required to start and maintain a metabolism [1]. Seoond, protocells can divide into daughter cells that inherit parts of their contents [38]. This property is at the heart of many group selection models, like the stochastic corrector [12], that alleviate problems arising from parasitism[3, 4, 39-41]. Third, protocells are able to merge and share their contents under certain conditions. While this property of protocells has been scrutinized before [1, 42, 43], it has received far less attention relative to division mechanisms. Nonetheless, there has been recent experimental success in protocell fusion models, suggesting that fusion may play a role in the development of early cells [21]. Note that some of these properties are also exhibited by other non-organic boundaries. For instance, bubbles [44] and porous materials [45] (where fluids flow through small holes and pipes) can increase local interactions, divide material, and merge them. In this study, we primarily focus on merging and its role in constructing evolvable protocells, keeping in mind that our results are general and are applicable to many processes that exhibit such properties. Fig. I. Merging occurs between randomly assembled cal s. A pro- We assume that in order to be evolvable, a protocell needs tooel consisting of all of the necessary functionalibes could be constructed by (A) to contain a certain number of functions (molecules of various random assembly or (8) merging. Each merging event can be seen as a bdwise complexity). In early life, these could be molecules as simple OR operation between strings of length n that represent protocell contents. Here as ions, co-factors, and nutrients, or more complicated poly- each color represents a functionality (and so does each position on the representative stems). A cell arch all the functions would be represented by a string of all Is. mers, like oligo-peptides, and even elementary ribozymes and simple unlinked genes [I, 19, 32-34, 46-48]. Similar models of functional assemblies have been employed successfully in the past [2, 11, 12, 37, 49-51] and simple examples have been functionalit ies. We use the number of operations for each experimentally observed [21, 52]. We call the smallest set process. relative to the number of functions we need to reach, of functions from which an evolvable protocol' can be made as our measure of complexity. A process that takes fewer steps a minimal evolvable protocell. More precisely, the target set to finish is considered more efficient. This approach allows us should result in an auto-catalytic network that results in an to analyze the processes in the same framework, and compare evolvable cell with non-negligible probability. their efficiency. It is possible to map this measure to physical In the absence of evolution through replication, a protocell time or energy cost in a continuous chemical process, depend- will need to collect all of those functions through some random ing on the problem of interest. Here we concern ourselves with process. If the number of necessary functions that have to a protocell's abstract properties. co-occur in a protocell is large, this process is very inefficient in a landscape where there is no evolution and replication. In order to mathematically measure the number of opera- The absolute worst case scenario would be that out of pure tions, we represent the functional (or genetic) content of each luck, a membrane is formed around all the required functions protocell as a binary string of length n (a beckon conjunction at once, and results in an evolvable protocell. As this is used similarly in [54]). For simplicity, and without loss of gen- incredibly unlikely, it is used as a criticism against approaches erality, we ignore the redundancy (or dose) of each function in that require many components (or in some scenarios "genes") the protocol', and are only concerned with their presence. If a at inception [1]. However, as we show in the following section, protocell contains a particular function i, then the string will alternative random mechanisms of accumulation are made have a value of I at the ilk position and 0 otherwise. We as- possible by protocells. These mechanisms may reduce the sume that the probability for the presence of each component probabilistic burden significantly enough, that even under no (component frequency) in a sample is p (and define q E 1 — p). evolution, the target set of functions may be achievable for We also assume that p is identical across components, as this large number of functions. simplifies our model but is not a key issue for our conclusions. A process begins with an empty protocell that we track, Model and Results called the accumulator. The accumulator then collects func- The goal of our study is to compare the efficiency of mecha- tions by "sampling" protocells and updating its own contents. nisms that lead to construction of a minimal evolvable proto- Sampling is defined as picking random strings from the en- cell, in terms of the information it contains. While we take an vironment. We can measure the average-case trajectory of algorithmic perspective (see [53] for a related discussion), the the accumulator protocell by calculating the expected num- results can be interpreted biologically. Our target set would ber of independent samples required so that the accumulator entail a lipid membrane that encloses all the necessary func- acquires all a functions. We can now model an accumulation tions for starting a simple metabolism (e.g. an auto-catalytic algorithm within this framework. The methods used here cycle) and eventually a replication process. are commonplace in analysis of random algorithms and have We study the average-case trajectory of single cell in the also been applied to evolutionary processes [55]. The detailed population of protocells until it accumulates all the necessary calculations for the following results are provided in the SI. 2 I weiwooes.orstgvoovio.vmenaam00000cxxx Sinai el al EFTA01183813 Random assembly. In a world in which protocells cannot fuse, finding a string that has a 1 at every position, by sampling and material transport across the membrane is insignificant, many strings and merging them with the current accumulator. protocells are constructed by spontaneous formation of a mem- The hitting time of this process brane around a random set of functions. In this world, proto- cells keep the set of functions they already contain. A full set is only generated when all the required functions happen to En (1")'" boa 1—qt [2] be enclosed within a membrane upon formation. Under the random assembly process, for each step, the accumulator takes This function is O(logn) (intuitively, grows no faster than the value of the latest sample. Hence, each new sample repre- At log n as n oo for some constant k). This captures the idea sents a protocell brining around a random set of molecules. A that you start from many protocells and merge them together protocell produced in this way will contain X functions, where to arrive at all n functions. Further, it is possible to show that X is a random variable, distributed binomially with param- the distribution of the number of merges is reasonably tight eters ut, p. Therefore, on average np functions are contained around the mean (see SI). inside the protocell when it is assembled at random. However, Note that in the limit where p = 1/n, each new merging if we need all a functions to co-occur in the same cell, then protocell contains a single function on average. We call this TR(n), the expected hitting time, grows exponentially in n: limit the "membrane transport" process as each operation entails absorption of a single function from the outside envi- ronment into the protocell. The reader may notice that this Ta(a) = ( 1 " [1] characterization is identical to the coupon collector's problem This calculation lays the foundation for our model as it [58]. In this limit, the hitting time is: provides a point of reference for the performance under the worst-case scenario. Ts(a) = nHn [3] Here H„ is the a-th harmonic number. More intuitively, Merging. As we can see from above, most of the cells generated this function is G(n logn). As a nice check, we can see that by random assembly will contain a subset of n possible func- the formula provided for the merging model (setting p = I/n) tions. However, if merging is allowed, we can intersect their is a good approximation to the hitting time predicted by contents to produce the desired set. In order to model this the coupon collector process. This is indeed the case, and a process we merge the accumulator protocell with random sam- verification is provided in the SI. ples taken from the environment while counting the number The membrane transport process is a special case of the of merges. merging process. Both processes are far more efficient that the prohibitively slow random assembly. As an aside, note Table 1. Merging protocells efficiently produce cells with f, compo- nents. that our analysis of merging membranes easily maps to other membrane transport phenomena such as heat-cycles, where Number 04 Random Assembly Merging Merging protocells become more permeable to surrounding material in Functions (n) (Eqn 2.) (Simulation) a periodic manner [59]. In such a case, T(n) would capture (Err I.) the number of cycles that the protocell undergoes to capture 10 1020 291.93 291.16 ± 5.24 all n functions (assuming there is net inflow). 25 1054 380.18 381.96 ± 5.47 SO 10100 448.17 448.48 ± 5.55 Loss of functions. We observed above that in an ideal setting, 100 10200 516.64 516.22 ± 5.53 where all samples can be incorporated into the accumulator 250 10500 607.51 608.32 ± 5.41 without interruptions, merging significantly reduces the num- ber of steps it takes to reach the target set. Obviously, while As an example. fixing the concentration parameter at p = 0.01. we functions are being accumulated, membrane integrity may be compare the number of steps it takes to accumulate a functions lost, the protocell may get infected by a parasite, or the proto- through random assembly. and that of the merging process. While cell may simply divide. Hence, the key test of the performance finding sets of a functions by random assembly grows exponentially fast in a. if those same randomly assembled protocells were able to of the merging process is to understand if it can accumulate merge, target compositions can be found with very few merges. We functions efficiently even in cases where it is regularly set back also verify the model numerically. The Monte Carlo simulation results by events like division or death. are the mean hitting times over 2000 trials (with corresponding 95% confidence interval). To address this question, which is the main contribution of our study, we consider the possibility of a restart in the If protocells are able to merge with each other, and gener- accumulator. A restart can be total or partial. A total restart ate a new protocell that encloses all the functions from the is equivalent to protocell death; i.e., all functions are lost, and two original cells, then their contents are the union of the the accumulation of functions starts anew. A partial restart parental cells that are generated by random assembly. Like occurs if a protocell divides and loses some—but not all—of before, merging occurs with samples that contain X functions, its functions. Obviously, division performs better than death where X is binomially distributed. Hence, a sampled string in the merging process, as the accumulator gains a head start will on average contain np functions, not all of which are nec- on the number of functions. Therefore, calculating the hitting essarily new additions to the accumulator. Note that when time by assuming a total restart (death) provides us with an two protocells merge, the value of the resulting string at every upper bound on the performance of the merging process with position i is simply determined by a bitwise Oft operation (an protocell division. Oft operation on the ith bit of the original protocells taken I A read, Win Vdefoil in effpriinme may rectoint Ibis resun as the expeled help l01a woes- together). Now, the problem can be seen as the probability of blis12 skp 151 arm n elemealS156.571 SEIM Nat. PNAS I Apr114, 2016 I vol. XXX I na XX I 3 EFTA01183814  We introduce a new parameter, 8, which denotes the prob- Comparison of the model, approximation, and simulation ability of death at any given step. The accumulator makes a data for p=0.0I and varying step (samples another protocell) with probability 1— cf. Given — Model 48, we can revisit the mechanisms introduced above and incor- x x Simulation porate the death parameter into them. For random assembly, ono Approx (Eq. (5)) = 1, i.e. either all functions are accumulated on the first 000 Approx (Eq. (6)) step, or the process restarts. We now turn our attention to 0 the cases where 0 < 6 < 1 (with arbitrary 0 < p < I) and extend the results that we obtained in the previous sections for merging. To calculate the hitting time, we define a sequence as a series of merging events starting from a randomly assembled protocell V y that terminates either by accumulating all a functionalities or by being reset due to death. After each death event, a new sequence begins. Denote by F the probability that a given sequence results in all n functionalities being accumulated without being reset. We have: 22 23 2a 25 26 2' 23 Number of functions (n) F = (!— 8).-1[(1- qz)" — - ez-In Fig. 2. Numerical verification of the merging process with death. For chtferenl values of me death parameler 6. we show the number of samples required soot to read, a minimal evolvable prdocell. Simulation results and the approximations in Denote by P(z) the probability mass function for the num- Eq. (5) and Eq. (6) are provided for comparison. ber of samples, z, needed to accumulate all n functionalities when starting with a randomly assembled protocell given that required to reach the target set of functions. Remarkably, the all it functionalities are accumulated before death. We have: merging process achieves a complete set of functions in low- order polynomial time for a sizable segment of the parameter — (1 r ( 1 — sr -1 [Ci — qt in space. For example. for .5 < p, the upper bound on the growth P(z) = F of T(n) is O(n). As another example, for 1 — S > (1 — p)2, Similarly, denote by A(z) the probability mass function for the upper bound on the growth of T(n) is O(n2). As long as the number of samples, z, taken before the protocell is reset < 1—i.e.. while there is merging of protocells—the merging to having no functionalities when starting with a randomly process accumulates a complete set of functions in polynomial assembled protocoll given that the protocell dies. We have: time. 718 clarify this further we provide a visualization for the A(z) — so - Sy-,o - - eysi growth of T(n) with respect to p and tS in Figure 3. 1— F Discussion Hence, the expected number of samples needed to accumu- Membrane merging, and sharing of informational content, late all n functionalities is given by the exact result: could be seen as a primitive form of sex. The idea that z[FP(z) + (1 - F)A(z)] sex (or a similar fusion and genetic sharing mechanism) may T(n) z=1 [4] have existed since the RNA world has been discussed for F decades [1, 30, 42, 43, 60], but, to our knowledge, the time We show a numerical verification for Eq. (4) in Figure complexity of this process has not yet been quantified. We 2. We can calculate the expected number of steps exactly offer a simple model in the previous and use it to quantify through Eq. (4). However to understand the trade-off between the time complexity of the accumulation processes that result component frequency p, death S, and the number of functions n in functional or genetic assemblies (akin to compositional better we provide the following approximations. For arbitrary genomes [11, 37] or auto-catalytic sets [50]). These results values p,S E (0.1) and large it. the expected number of steps establish the quantitative scale of improvement that is possible has the following asymptotic behavior: through merging (and transport across a membrane), in terms of number of operations. The time 7'(n) required to assemble a —(1 — 6) 40 — p)nk log(1 — 6) protocell with all the necessary functionalities is reduced from T(n) , where k = [5] an exponential number of attempts to a low-order polynomial 62F(k) log(1 — p) by the merging process. Critically, our observations remain There are many possible cases to consider. For example, relevant even if the protocells undergo division or death during we can simplifyEq. (5) further for small p,S (hence k 8/p), this process or if they are infected with parasites. This is and if 8 is not too large relative to p. In this case, we can the key result of this analysis. If merging is possible, the approximate the growth of T(n) by: idea of cells with many co-occurring functions is no longer a probabilistic miracle, but sometimes even inevitable. /Lk There are conjectures that in the primordial world, genomes T(n) - [6] may have been segmented and a lot of mixing and reassert- This equation is also plotted and verified via simulation in ment may have taken place [1, II, 61, 62]. Our results take the Figure 2. Using Eq. (5) and Eq. (6) we can see that the ratio k benefits of sex to even before evolution (self-replication of com- is the primary factor in determining the number of operations ponents or protocells) started. In other words, the population 4 I wonv.pnas.ctestglidS/10.1073.epnasJ0O30CXXXXX Sins el al EFTA01183815  an analytical framework to quantify the trade-off between abundance of parasites and performance gain provided by merging. The merging model developed here also has similarities to well-known biological phenomena in modern viruses. The first, Multiplicity Reactivation (MR) [10, 65], is captured by our model. It is a process to generate an infectious particle by combining multiple non-functional mutant viruses of the same strain. In experiments, the viral particles would be subject to S intense radiation such that they accumulate too many dele- oPP SO., e terious mutations and would not be able to replicate in their host. However, if several of these mutants were introduced on 045 04 into the same host cell, the mutant particles would "cover" >. 40 on each other's loss-of-function mutations, and ultimately result °” ) in a functioning virus. Our calculations complement the early g of models proposed by Luria and Baricelli [10, 65]. They can on el also be used to calculate the expected multiplicity of infection 42 014 on required for sexual repair in viruses, given any level of genetic 0 damage (or mutation). Second, in multi-compartment viruses E 01 V 001 00S multiple distinct components need to co-infect the same host SJSOSOS O SI S „I* Je O .0 in order to produce a new virion. In many plant viruses, such Death 4 Death .4 as the genus 1Vrnovirus, the infection occurs when two or Number of steps more functionally distinct virions infect the same host [66, 67]. =SEPOPE.M . Similarly, some viral satellites and virophages need to co-infect ≤n n n n n /I a host in the presence of their target organism in order to reproduce [68]. These satellites are thought to transfer genetic Fig. 3. Target protocells are found within polynomial number of and functional material between their hosts. These processes steps through merging with death. The bur panels provide a general could serve as modern examples of similar mechanisms in early oveSew of the Interplay between the probability of component per sample p prob. abildy of death 6. and multiple examples of n (number of functions). The colors life. The fact that this type of combinatorial reproduction is represent the number of steps 7 (n) as a function of ri. present in many RNA viruses, which are thought to be ancient [62], is consistent with the suggestion that such mechanisms could have been present for a long time. If one assumes a structure, and operations proposed here, improve the efficiency virus-early point of view [61, 69, 70], we can readily see how of finding an evolvable cell, without the need for any selection this process could have contributed to the increase in complex- or explicit replication. The process only requires protocells, or ity of cellular life. There are in fact several suggestions that a similar compartmentalization agent that is capable of fusion. RNA viruses with segmented genomes may be very ancient, Of course, the same results could equally apply to protocell and in fact may have undergone some form of mating [61, 62]. interactions after the emergence of replication. Excitingly, recent experiments have invoked fusion success- In that case, these results may suggest that among other fully in vitro in order to produce "self-sustaining" protocells benefits that sex could provide for protocells, like allowing for three generations [21]. Kurihara et al. used "conveyer good combinations to form, select for good "mixers" [63], and protocells" (which correspond to our samples) to restore the repairing lost functionalities [42], it could have also played a chemical composition of their "giant vesicle" (accumulator), role in finding them quickly. Under such scenario, primordial and thereby produced a recursive mechanism by which pro- sex through merging and content sharing preceded primor- tocells can grow and divide for multiple generations. Our dial replication (or "prelife" [64]) and lasted throughout early results indicate that not only can such an approach be used evolution. Obviously, these results are applicable if mem- to construct the basic accumulator from scratch, and further branes, or similar compartments, appear early and in sufficient provide it with metabolic nutrients, but also it can be used abundance, and the number of functions is not trivially small. to efficiently increase the genetic and functional information A well-recognized pitfall of early life dynamics is the prob- content of a complex vesicle. lem of parasitism [2, 4]. In particular, sex increases the possi- The insights we gain through this analysis could prove bility of exposure to parasitic elements [I, 43]. However, our useful ill progress towards synthetic genomes. A "minimal results show that while parasites do harm the efficiency of bacterial cell" may require a few hundred genes in order to the process significantly, even in their presence the merging self-sustain [71-73]. Current attempts at making such cells use process remains tractable and reasonably efficient for a large a reductionist approach, where non-essential genes are pruned set of parameters. Notably, here we assume that merging with by trial and error to the point that all remaining genes are a single parasite is sufficient to kill the cell, which is a strictest required for a cell to grow in a stress-free environment at a possible bound. In other words, barring relatively high prob- reasonable rate. Recall that in our model the ratio between ability of encountering a parasite at each merging, in most frequency of fatal outcomes 45 and proportion of components regimes, it is beneficial for the protocell to fuse with others (to p (in this case genes) that carry essential functions in a given gather functions). Hence, while the issue of parasites cannot context is the key factor that determines the efficiency of the be ignored, we address the issue at its heart by establishing process. If this ratio is small (8/p A. I) in this case, it means Sinai ef . PNAS 1 Agree, 2016 I vol. XXX I no. XX I S EFTA01183816 that it is possible to construct genomes by random samples of 21. KUlhala K M S. (2015)A reCistne vOSIC10-0440(1M0(1016.0t00(41*(th a 901144.4 model Cell genes from pools of simple genosnes within a feasible number cycle. Nature cornmuncastos 6. 22. Ph:GOICM TM. Meer 0. Simonet BR (19991 UOI0 'lanese under hydroneemd COndliOnil by of trials. fischertropschtypa reactcna Ofirs ot Laaand Evoiboon of Moticeohare2912)153-166. We hope that in light of our results, the role of protocell 23. Yamamoto S. Maruyarna Y. Hyodo Sa (20021 Despalin pW1d0 dynamics study d span lanfrOura veSide *MEMO d amsepasc MC10Culeit The JOternd 01 dental pathos fusion in pre-life and early life is revisited and further con- I16113):510/2-5849. sidered both by theoreticians and experimentalists. In this 24. DearDer DW (19861 Role 01 amPlfM110 Compounds in the evolution d membrane tauttuie study, we have shown that merging significantly improves the en me °any earth. Ofigies or Ut.rodEvOtbliOn Mme Saphen? 1711)'.3-25. 25. Mated F. Lust Pl. 11996) AliapalabC set.roproduong vesicles: a simples] isnotc model. plausibility of producing protocells with a high number of com- The Journalof PhystalCrierterlry 103(41)1 6603-16607. ponents through a random process. Our results are applicable 26. Wen 0.13blit N.Des Magni CM. Chang (1984)CarbOn Osage compositkon ellar molecular to assemblies of molecules before and after the onset of evolu- weight hydrocarbonsand monocarbonlic apish= murtheon metconto. 27. Lanless JO. Wen GIJ (1979) OuarridaillOn d MOMairbOxyliC acids In me niobium OM- tion. We have also provided a clear quantitative model that tonaceol.c meteorite. captures the effects of parasites (or other fatal causes) on the 29. Deemer DV/ 11996) Boundary atlases are tamed by organic co/monads of ono murchson efficiency of the merging process. Finally, we hope that these CarbOnASOuti 011000110. 29. Russel IN al.(2014) The two to lb on as andicyworlds. Psychology 14141:309-343. results can be useful in analyzing viral mechanisms such as 30. Halel8110J13341929)Tteorltan 0 Be. ROMAN Annual 148:3-10. multiplicity reactivation, reassortment, and their evolutionary 31. Operin Al. et al. 11957rfhe oritin Of 110 on V* earth The onoln Oa* On Int EWA (3r0 Ed). 32. Mansy SS cial.(201:01Ternplatodredeci symhesisol a gore polymer in a model protocell. backgrounds. Mtun745417200):122-125. 33. btu TF. Stanek .1W (2009) Coupled growth and dvbion of model protocol membranes. Joum nal of the Amencan Chemical Soo* 131(1515705-5713. Materials and Methods 34. Ekdn I. Detnain A 520510 JW 12012) COMM*80M-Olven woe* °IMO& MOSOcell Men,. banes. Journalof the Arnercan Chemical Society 134151120912-20919. Models were vet flied using Monte Carlo simulations written in 35. Adamala K. SZCI4104N 12013) Nearan2yMOC larmialetkecied ma °reheats moo, model Mathematica and Python. Each simulated mean is generated from laotocens Scianee3e2(6162):10S6-1100. 2000 independent trials, and confidence intervals are calculated 36. Hanczyc MM. Fulliawa SPA. Szoszak AV 12003) ENtormontal models 01 FdrelaVO cellular COIrObilMeaS: eowsolaltn. yore,. and dMslan. 36010•302(5645)1318-622. using the t-Procedure. Simulation code can be provided by request 37. Segni O. Lancet D. Kadin O. Pipet Y(19911, Graded amacalalysis roplcalion domain (paid': from the authors. kinetic anaheis of sadrephcation in mutual., cameo sets. Onpins oft* and Eldtgal OF ale aiospnene 28(44)501-514. 39. Madmen A. Scrams A. Peters* K van Santo R. Fibers P (200/1 Lipid-based mocha. ACKNOWLEDGMENTS. We thank Krishnendu Chatterjee for Name fOr veljele liKJOn. The JOurnef d Pertoia Cheeesfry13 111(20)5719-5725. technical comments on the manuscript. We also thank Leslie Valiant 39. SUMO B. ROCMIKJA.0044:41M 12013) TO.WRIS a general theory Ol group 99100/01. &Ob. and Scott Linderman for helpful comments in the initial phases of ion 67(61:1561-1572. this project. We thank Robert Israel for pointing us to related liter- 40. tuween A. Seocem N. NOMA MA (2008) Asasoso MEOW la iniviOutl and crag seieclion ature. We thank Jeffrey M. Gerold, Carl Veller, Michael Nicholson, d any intensity. Bataan or Inachomatica boxy 70(5):1410-1424. Ben Adlam, Nicolas Freiman, and Tibor Antal for helpful discus- 41. Traisen A. Now* MA (20051 Evolution of cooperation by imblevel a:exam Proceochnos of me Nadenal Academy 0So:iron 103(29)10952-10955. sions. This research was conducted using the resources provided 42. Bernston H. B)ttly HC. Hopi FA. Mithod RE (19641 00pn of sex. Journal of Pworctical by the Program for Evolutionary Dynamics at Harvard University. MAW 110/3)323-351. PED is supported by the John Templeton Foundation and in part 43. Se/405kt Zemzems E. Statinary E(2003)Origin Of Sex feeltded. Or1pVs Of LW and EsOkr. by a grant from B Wu and Eric Larson. ton aline Biosphere 33(441%05-612. 44. Russel W. HMI A (1997) The °magenta Mlle from Iron M0009.4)440 Outdate at 8 ilutena. I. SUMMary E. SONGS M. FerreMO (2005) EvOlutkinary poeenlial and feekileMentS ke *n- and protocols n Preadt Chemistry. ISisnngen. pp 167-211. Me hOrotherrnal redo( and ph tort Journal oldie Geefopcal Society 15443)277-402. 2. SUMMary E. DOOM& I. (19071 Oroup election d easy replied:OM and the origin oe lire. 45. Elamite P el at 12007) Enron. accurn.Mm of nucleotides in simulated hydrothermal core J04.anel d theoretics, NOV), 12814463-48B SWIMS. Procayangs Of MeNefienalACKIenly M Sciences I04(22)9346-9351. 3. barters G. 21.00 K. Chen (A. Nook MA(20131 Solecism for replicas:isin protocols. PLoS 46. FeNcis PA (2007) Steps toads tie famaton of a protect the possible rote of anon pop compursvois(5i e100X61. SOK GPM of EXe endEaWtgn 8.01.phenfl 37(6):537-553. 4. Markvoat AJ. Sinai S. Nowak MA '2014) Compiler simulatio