Inevitability of the emergence and persistence of genetic parasites caused by thermodynamic instability of parasite-free states

Genetic parasites, including viruses and mobile genetic elements, are ubiquitous among cellular life forms, and moreover, are the most abundant biological entities on earth that harbor the bulk of the genetic diversity. Here we examine simple thought experiments to demonstrate that both the emergence of parasites in simple replicator systems and their persistence in evolving life forms are inevitable because the putative parasite-free states are thermodynamically unstable.

thanks to multiple defense strategies that include parasite exclusion, innate immunity and 48 adaptive immunity [18][19][20][21][22][23]. The SAGE respond with counter-defense mechanisms that range 49 from simple mutational escape from defense to dedicated multigene systems that specifically 50 inactivate host defense systems. Notably, defense systems and SAGE including their counter-51 defense machineries are tightly linked in evolution. Enzymes involved in the mobility of SAGE,52 in particular, transposons are often recruited by host defense systems for roles in parasite genome 53 inactivation and other functions, and conversely, SAGE recruit components of defense systems 54 that then evolve to become agents of counter-defense [24][25][26]. 55 Thus, the arms race, along with cooperation, between genetic parasites and their hosts are 56 perennial features of the evolution of life. Why is this the case? Why do the parasites emerge in 57 the first place? And, could some cellular organisms actually get rid of the parasites through 58 highly efficient defense systems? Empirically, the answer to the latter question seems to be 59 negative. Conceivably, the general cause of the inability of the hosts to eliminate the genetic 60 parasites is the unescapable cost of maintaining sufficiently powerful defense systems [27][28][29][30]. 61 Analysis of theoretical models of parasite propagation suggests that an important source of this 62 cost, perhaps the primary one in microbes, could be that efficient anti-parasite defense has the 63 side effect of curtailing horizontal gene transfer (HGT), which is an essential process in 64 microbial evolution that allows microbes to avoid deterioration via Muller's ratchet [31,32]. 65 Another major factor could be the effectively unavoidable autoimmunity [29,33,34]. However,66 what about the first, arguably, the most fundamental question: why do genetic parasites evolve to 67 begin with? Again, empirically, there is a strong impression that the emergence of such parasites 68 is inevitable. Not only are they ubiquitous in cellular life forms but they also evolve in various 69 computer simulations of replicator system evolution [35][36][37][38][39]. Furthermore, it appears intuitive: 70 genetic parasites can be considered cheaters, in game-theoretical terms, and as soon as, in a 71 replicator system, there is a distributable resource, such as a replicase, cheaters would emerge to 72 steal that resource without producing their share of it [40]. These, however, are informal 73 considerations. Here we ask the question: is it possible to develop a theoretical framework that 74 would allow a formal demonstration of the inevitability of the emergence of genetic parasites in 75 evolving replicator systems, or else, that parasite-free replicator systems are after all possible? 76 77 Thermodynamic instability of parasite-protected replicators 78 Let us try, as a gedunken experiment, to construct a self-replicating entity that is strictly resistant 79 to parasites. Consider a simple system consisting of a replicator, serving as a template for itself, 80 and the replicase it encodes (Figure 1). The replicator is assumed to contain the replicase-81 encoding signal (RES) (the replicase could be a protein, a ribozyme, under the RNA World 82 model, or, in theory, any other entity capable of catalyzing replication of a template) and the 83 replicase recognition signal (RRS).

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Evolvability is a fundamental and inescapable property of such a replicator-replicase system 85 [41]. To be evolvable, a system must possess three basic properties: 1) heredity (whereby the 86 location of progeny in the phenotype space is correlated with that of the parents), 2) variability 87 (whereby the progeny is not identical to the parents), and 3) differential reproduction (whereby 88 the capability of a replicator to leave progeny is part of the phenotype). Heredity is ensured by 89 replication with fidelity above the error catastrophe threshold. The replicator theory that was 90 developed primarily by Eigen and colleagues demonstrates that, under simple fitness landscapes, 91 there exists a replication fidelity threshold, below which the master sequence in a population of 92 replicators cannot be efficiently passed across generations, so that the entire population collapses 93 [42,43]. Elucidation of the molecular mechanisms of primordial replication that could provide 94 for crossing the error catastrophe threshold remains a daunting task that is central to the entire 95 origin of life field. However, for the purpose of the present discussion, we assume that a 96 sustainable replicator system with a minimally acceptable fidelity has evolved.

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Variability is ensured because, at any temperature above 0 K, any process is subject to entropy-98 increasing fluctuations and, therefore, replication is inherently error-prone, under the second and 99 third Laws of Thermodynamics.

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Differential reproduction ensues from the fact that the replicator encodes the replicase that, in 101 turn, copies the replicator itself. Mutations in both RES and RRS can affect the efficiency of 102 replication.

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If the resources that are available to the system are limited (i.e. the system does not support 104 unlimited growth of all possible constituent parts), competition between individual replicators 105 ensues and selection arises. In a system with finite memory storage, all information exchange, 106 transfer and utilization processes carry memory clearing cost of at least kTln2 J/bit, where k is 107 Boltzmann constant and T is temperature (the existence and value of this minimum information 108 cost is known as Landauer's principle that is a corollary of the Second Law of 109 Thermodynamics); in all known systems, this cost is many orders of magnitude higher [44][45][46]. 110 Therefore, selection for cost reduction acts not only on the constituent parts of the system, but 111 also on the information transfer processes themselves, effectively ensuring an upper limit on the 112 fidelity of information recognition.

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(eliminating replicators that are inefficient as templates, e.g. are poor replicase-binders), but 115 these two selection processes act on the replicator through physically different agents (the 116 replicator-encoded replicase and the replicator itself, respectively).

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The dual nature of the replicator (acting as both the template and, directly or indirectly, as the

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Under the scheme in Figure 3, parasites emerge as long as the information content of the RRS is 128 less than that in the full replicator, i.e. when the RRS is at least partially separable from the RES.

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If this is the case, a replicator containing the full RRS, but omitting at least some of the RES 130 (RRSp ≡ RRS, RESp -> 0; the subscript 'p' denotes the respective signals in the parasite), would 131 not only serve as a template as efficient as the original replicator, but would also enjoy an 132 evolutionary advantage because replication of the smaller replicator is faster and requires less 133 resources (building blocks, such as nucleotides, and energy). This makes the parasite-free 134 equilibrium point of the replicator-parasite system unstable because deletion of any part of the 135 RES yields more efficient replicators (Figure 4). Therefore, the system is vulnerable to parasite 136 invasion, and moreover, such an invasion is inevitable under a non-zero parasite emergence rate 137 (see Appendix for a more formal demonstration).

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It appears that, under this scheme, the only way to render the replicase-producing replicator 139 parasite-protected is to make the RRS to include the entire RES (Figures 2 and 4). Such 140 RRS ≡ RES configuration evidently rules out the emergence of a parasite because any mutation 141 of the RES would also inactivate the RRS and prevent replication.

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However, such a parasite-protected state is subject to the aforementioned instability ( Figure 4). 143 In the absence of parasites, perfect protection does not carry any benefits, but incurs a greater 144 cost than less protected states. Given that the system is evolvable, an RRS < RES state will 145 inevitably arise and outcompete the RRS ≡ RES progenitors that are, as shown above, prone to 146 emergence of genetic parasites (RRSp ≡ RRS, RESp -> 0).

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From a more abstract perspective, the fully protected RRS ≡ RES system corresponds to the 148 maximally constrained, i.e. minimum entropy, state. The second law of thermodynamics 149 effectively guarantees that it evolves into a higher entropy state, such that RRS < RES, and at 150 least some parts of the RES can be mutated or deleted without compromising replication. The 151 ensemble of higher entropy states is obviously more robust than the unique RRS ≡ RES state. In  It should be noted that, because, at least in the simplest replicator system, the replication rate is 171 inversely proportional to the genome length, the parasite have an intrinsic advantage in the arms 172 race. In the well-mixed case, the preferential replication of parasites drives the host to extinction 173 which, obviously, results in the collapse of the entire system (no replicase is produced anymore) . The thought experiment described above also answers the question whether a perfect defense 192 system can exist. A perfect self vs non-self discrimination, whereby a replicator possesses the 193 means to reject or destroy any potential cheater, that is, any sequence other than a perfect copy of 194 itself, is nothing but the same parasite-protected system with recognition based on the complete 195 information on the self, i.e. RRS ≡ RES. We have already shown above that such a system is 196 evolutionary unstable from pure thermodynamic considerations because it provides no benefit in 197 the absence of parasites, and will inevitably devolve to an RRS < RES configuration ("leaky" 198 defense).

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The existence of an unavoidable cost implies that maintenance of any form of defense is subject 200 to a cost-benefit tradeoff. Notably, a recent quantitative assessment of the selection coefficients 201 (a measure of fitness cost) associated with different classes of genes in microbial genomes has 202 shown that defense systems are as costly as the more benign SAGEs, such as transposons [30].   (2) Thus, at least some parts of the RES can be deleted without inactivating the RRS. Hence 228 genetic parasites emerge.

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(3) The shorter the genome sequence of a genetic element the more efficient its replication is.

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Hence parasites accumulate in a replicator system and may bring it to collapse in a well-mixed 232 case.

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(4) A perfect defense system should, in the least, be able to recognize parasitic elements, i.e.  The more general model that we consider here also includes the existence of a (potentially 273 costly) defense system: where R and P are the concentrations of the replicator and the parasite particles, respectively, eR 277 and eP are the corresponding decay rates and K is the environment carrying capacity (the 278 replicator growth rate is taken to be 1 without loss of generality). The parasite enjoys an 279 evolutionary advantage that is manifested in two ways: it both replicates faster and consumes 280 fewer resources by the same factor q (the simple conceptual model of this effect is based on an 281 RNA molecule that is shorter than the replicator by a factor of q