How does a replicator change the nature of stability




















As many a systems chemist has learnt to his or her sorrow, the simplest molecular replicators can be quite finicky. You need fancy labs, specialised equipment and dedicated researchers to get them to replicate and, even then, it can be hit or miss. By contrast, biological replicators — living things — are extraordinarily robust. Consider some of the simplest life forms, bacteria. These highly complex entities can survive and prosper pretty well anywhere — some deep within the Earth, some high in the atmosphere, some in boiling water, some in nuclear reactors, no labs, equipment or human assistance required.

The inordinate complexity of all living things has emerged for one reason alone — to facilitate the replicative function, thereby enhancing the stability of the replicating system. How, then, did that extraordinary complexity come about? The answer, of course, is: one step at a time. Gerald Joyce, professor of chemistry at the Scripps Research Institute in La Jolla, California, recently demonstrated how a single replicating RNA molecule, on its own, is a relatively inefficient replicator.

In contrast, a two-molecule RNA replicating network, in which each RNA molecule catalyses the formation of the other, is far more effective. The two-molecule system is more effective for the same reason that picking up an object with two fingers is a lot easier than with just one, and nature has exploited that fundamental design principle.

So complexity and function go hand in hand. Animate and inanimate forms came about because there are two mathematical engines of stability. Boltzmann showed us the more familiar thermodynamic one, but the other is traceable to the English cleric Thomas Malthus.

After all, it was Malthus, studying the economics of famine in the s, who first recognised the profound consequences of exponential growth in a biological context. Of course, once we recognise the existence of two distinct stability kinds, one based on probabilities and energy, the other on exponentially driven self-replication, the reason for the teleological character of all living things becomes obvious. That drive has a thermodynamic manifestation, as expressed through the ubiquitous Second Law, but it also has a kinetic manifestation — the drive toward increasingly persistent replicators.

Two mathematics, two material forms. This distinction does not trace the dividing line between living and dead matter precisely — but it does explain it, and many of the other riddles of life into the bargain. Space exploration. Instead of treating Mars and the Moon as sites of conquest and settlement, we need a radical new ethics of space exploration. Ramin Skibba.

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For one entity to be a copy of another, it must be the output of a process whose biofunction is to conserve function. The function of copying is to produce from one token another token which is similar in the relevant respects. Genes fit this definition, but so do lots of examples of non-genetic transmission; e.

In the nineteenth century development was an extremely active research program. The next great discoveries in biology were going to be in the area of development. It was not to be. First Mendelian genetics and then a version of evolutionary theory centered on population genetics took over biology, and they did so while avoiding development. Everyone knew that development was central to both evolution and reproduction, but no one could see how to integrate the masses of developmental data available into the emerging synthesis of evolutionary biology and genetics.

Considering how central development actually is in metazoan and metaphyte biology, the advances made while ignoring it are staggering. Even so, developmental biology continued on its course until at long last we seem to understand development well enough to begin integrating it into the rest of biology.

On the most conservative view, current versions of evolutionary theory can remain largely unchanged as development is grafted onto them. On a second view, both perspectives are likely to require some modification to bring off this integration. Finally, at the other extreme, development will all but replace evolutionary theory. In their more exuberant moments, some advocates of Developmental Systems Theory hereafter DST seem to be claiming just that. Just as some molecular biologists think that molecular biology is rapidly replacing all the rest of biology, some advocates of DST argue that developmental theories will simply replace current versions of evolutionary theory.

In fact, no element of the developmental matrix plays any privileged causal role—not genes, not organisms, not the environment, not anything.

Everything counts as a resource, albeit in particular situations certain resources will play more important roles than other resources. In rejecting any privileged role for genes, advocates of DST are especially skeptical of one particular role supposedly played by genes—the transmission of information.

According to some, information is central to developmentalism, but genes are not the only mechanisms for information transfer. According to others, information plays no role in the emerging developmentalist perspective. The developmental system as a whole is the unit of selection [see the entry on units and levels of selection ]. If genes have no special role and whole developmental cycles are replicators, as some developmental- systems theorists argue, the distinction between replicator and interactor becomes blurred.

In the continuing debate over developmental versus traditional theories of evolutionary biology, Sterelny et al. They agree with the developmentalists that genes play no privileged role in the development of phenotypes from genotypes. Genes do play a role in this process, only simply not a privileged role. Genes can serve as a causal bridge from phenotype to phenotype, but other entities can do so as well.

Genes are not the only replicators in biological evolution. The repeated cycles in inheritance include many different sorts of constancies and repetitions—genes, cellular machinery, phenotypic traits including behaviors, and social structures. Information remains central to selection processes, but genes are not the only carriers of such information.

Genes predict phenotypic characters only in the same sense that environmental factors predict them. Sterelny a has argued that developmental considerations require no fundamental reevaluation of evolutionary conceptions along the lines of DST. Ever since Darwin, a number of authors have proposed that for evolution by natural selection to occur three conditions or ingredients are necessary.

A population should exhibit 1 variation, that 2 leads to differences in fitness between the entities forming the population [see the entry on fitness ], 3 which are heritable reviewed in Godfrey-Smith The most famous version of these recipes is the one provided by Lewontin Another difference between the two approaches, is that under the classical approach replication is not required for evolution by natural selection to occur.

In fact, as long as heritability is positive, and the two other conditions are satisfied, then evolution by natural selection can occur but will not necessarily do so, cf. Godfrey-Smith Godfrey-Smith concurs:. From this point of view, we can see the replicator analysis as picking out a special case of what is covered or supposed to be covered by the classical view.

To see why a lack of replication does not prevent evolution by natural selection from occurring, suppose a population of entities exists with different sizes, as presented in Figure 3 a , in which there is selection for larger entities. We assume that the entities reproduce asexually in discrete generations and that there is no environmental variation. After one generation, although there is no high-fidelity replication, the average size of the population has changed, due to the effect of natural selection.

This simple example demonstrates quite straightforwardly that replication is not required for evolution by natural selection to occur. We said earlier that replication would imply a heritability of exactly 1 in the absence of environmental variation. Although this is correct, the reverse is not true. In fact, take again a similar population as in Figure 3 a , but this time assume a different pattern of inheritance for the two types of entities as displayed in Figure 3 b.

With this pattern of inheritance, although there is no replication, entities, on average, have the exact same character as their parent.

Rather, it is evolution by natural selection mixed with some other evolutionary processes. A rationale for this claim is that the fact offspring do not resemble their parent introduces some variation in the population of which the origin is not natural selection.

In abstract terms, the introduction of variation can be regarded as a form mutation. Understood that way, the two approaches do not necessarily need to be opposed. One premise of this argument is that some form of natural selection must have occurred on entities that initially were not replicating, perhaps not even reproducing. The idea that evolution by natural selection can occur without reproduction has been argued by Bouchard , ; see also Doolittle , Bourrat Evolution by natural selection occurs.

Figure 3. Illustration of the idea that evolution by natural selection can occur without replication. If modern biological systems evolved from molecules that did not have the ability to reproduce, let alone replicate, one might ask, what is the simplest case of evolution by natural selection? It is a case in which different types of entities have different persistences but do not produce any offspring.

In this model, the types with the property of persisting longer represent an increasing frequency of the total population over time. One problem though in a model of persistence alone, is that each time one entity goes out of existence, it is not replaced by another entity, so that over time the population size tends towards zero. Although this does not mean that evolution by natural selection cannot occur in such populations, this poses important constraints on the evolutionary dynamics of this population.

Furthermore, it is possible to regard the ability for a population to maintain its size or increase its size as a primordial form of adaptation. To see this one can imagine different populations of entities at different locations, some with the ability to produce some entities or multiply, others without.

It is clear that the populations with the ability to maintain or increase their size would out-compete those that are unable to do so. The ability for a population to sustain its population size might thus be regarded as a primordial form of adaptation. In such a situation the size of a population could be maintained. The most extreme form of that would be to imagine a population of two types in which each type has the same probability to produce an offspring of the other types than its own type.

With entities of the two types having different persistence, a modest form of evolution by natural selection is still possible.

Since there is, on average, no more resemblance between an offspring with its parent than any other entity of the parental generation, and evolution by natural selection is still observed in such a scenario, one might think that heritability is, strictly speaking not a necessary condition for evolution by natural selection.

Wilkins et al. Recent work in biochemistry has added strength to that suggestion Altstein Hence, given that no replicator is required for selection in this case, chemical , replicator molecules can be seen as the outcome of selective evolution, not a necessary prior condition for it. Bourrat , further developed this idea into a series of agent-based models. He showed that replication is an attractor in populations lacking heritability once small random mutations increasing or decreasing the fidelity of character inheritance is introduced.

Reproduction is a composite process of development and progeneration, leading to objects that are themselves capable of development and progeneration. Thus, the reproducer concept extends the notion of a developmental system. Here inheritance is a system property, not a property of parts, unless they are also reproducing systems, and is developmentally acquired.

Organisms do not arise already capable of reproduction in the main, but must undergo orderly transitions before they may reproduce. The relation between reproducers, and replicators and interactors, varies according to author.

Griesemer treats replication as the terminal form of reproduction, once coding mechanisms have been evolved, which is itself an evolved form of multiplication Griesemer a: However, replication arises when material overlap evolves progeneration, and progeneration evolves a codical inheritance system, as Figure 4 indicates.

Figure 4. Others, particularly Jablonka and Lamb , , think that reproducers are distinct from replication, and that some epigenetic inheritance systems are reproducers without being replicators. Chem Rev , 1 — Pross A, Pascal R: The origin of life: what we know, what we can know, what we will never know. Open Biol , 3: Article Google Scholar. Pross A: What is life?

How chemistry becomes biology. Forterre P, Gribaldo S: The origin of modern terrestrial life. HFSP J , 1: — Shapiro R: Small molecule interactions were central to the origin of life. Q Rev Biol , — Luisi PL: The emergence of life: from chemical origins to synthetic biology. Book Google Scholar. Popa R: Between necessity and probability: searching for the definition and origin of life.

Berlin: Springer; Fry I: The emergence of life on Earth. The physical aspects of the living cell. Pascal R: Suitable energetic conditions for dynamic chemical complexity and the living state.

J Syst Chem , 3: 3. Monod J: Chance and necessity. New York: Random; Mayr E: Toward a new philosophy of biology. Cambridge: Harvard University Press; Pross A: Toward a general theory of evolution: Extending Darwinian theory to inanimate matter. J Syst Chem , 2: 1. Chem Eur J , — Pross A: Stability in chemistry and biology: Life as a kinetic state of matter. Pure Appl Chem , — Pross A, Khodorkovsky V: Extending the concept of kinetic stability: toward a paradigm for life. J Phys Org Chem , — Pross A: The evolutionary origin of biological function and complexity.

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London: Printed for Johnson J, in St. Science , — Current Biol , RR Angew Chem Int Ed , Furthermore, the changes in the lengths of the replicators show that the complete set of evolved RNA strands falls within the 35—45 nt range, and they are synchronized independently on the coded enzyme types. This fact also emphasizes the importance and the effectiveness of the local group selection mechanism that keeps the system coexistent.

Another aspect of the exceptional robustness of the system is that in the qualitative sense it is surprisingly insensitive even to replicator mobility D and length penalty b 2 : we do not find conspicuous differences between the four parameter sets in this respect. Compare Fig. S3 , the first with high D — high b , the second with low D — high b.

The two other combinations not shown give similar results. Some of the subtle quantitative differences will be touched upon in the Discussion. The daughter sequence is the complement of the mother if no mutation occurs, obviously resulting in a different secondary folded structure with the rare exception of the mother being a palindrome.

The consequential constraint of any replicator probably returning to the same secondary structure in just every second generation is a strict one on the MCRS, because the system requires that all the metabolically necessary enzyme activities be present within the same metabolic neighbourhood for replication to occur at all.

We expect there to be strong selective forces shaping the evolution of the replicators to multiply as fast as possible while maintaining as efficient a local metabolism as possible. Specifically, the frequencies of sequences harbouring any subset of the three different enzyme activities E 1 , E 2 and E 3 were recorded for all the pairs of complementary replicator strands present in the lattice in all generations Fig.

A replicator sequence i. Dynamics of ribozyme activity distribution on complementary strands. The complementary strands may be E 1 blue , E 2 red , or E 3 green ribozymes or parasites grey. Complementary pairs are identified by their enzymatic activities; darker shades of red represent more frequent activity pairs.

Dominant activity pairs are denoted by black frames. The majority of the evolved sequences are trans -promiscuous ribozymes, single-activity ribozymes or parasitic sequences without any catalytic activity, almost irrespective of the actual model parameters. S5 , which is why they are not shown in Fig. The typical absence of cis -promiscuity is easy to understand by considering that cramming more than a single catalytic motif into a short sequence is heavily punished by impaired functionality at all active sites of the molecule due to steric constraints cf.

Supplementary Equation S2. Supplementary Fig. S6 shows the ribozyme activity distributions of the complementary pairs after 2.

An interesting aspect of the stability of the system is that the metabolic replicator populations evolve into single clusters or cluster pairs in sequence space Supplementary Fig. S8 , which form quasi-species in a loose sense of the term. At any point in time during the later phases of the simulations we observed such definite clusters and cluster pairs in the PCoA Principal Coordinate Analysis diagrams based on the Hamming distances of ten thousand sequences taken at random from the replicator community.

The solitary clusters were dominated by nearly palindromic ribozymes, along with a substantial number of parasitic sequences present within the clusters. The cluster pairs tend to occupy two symmetric positions and take similar shapes in the space of the PCoA, and they were formed by trans-promiscuous ribozymes of complementary sequences which admitted different primary structures in every generation, and thus they alternated between the clusters of the pair.

The two related clusters, together with the parasites mutated from them, constituted the quasi-species of the complementary pair of ribozymes. S8 shows that parallel simulations tend to evolve into similar PCoA patterns, but this is not always the case. Regime shifts may reorganize the PCoA patterns just as they do the frequency distribution of catalytic activities cf.

Different parameter settings may result in seemingly different cluster patterns, but they preserve the quasi-species structure in all cases. The dynamical feasibility criteria of origin-of-life scenarios require any prebiotic system to be stable in both the ecological and the evolutionary sense, while still remaining evolvable and capable of maintaining sequence diversity. We discuss the dynamics of the MCRS with regard to these fundamental criteria in the following sections, starting with the notion that a distinctive feature of the model is the low number of its parameters which, as well as the striking insensitivity of the dynamics to the actual parameter values, is a corollary of the fact that the dynamical parameters of the replicators are calculated from basic laws of physics and the feasible chemical consequences thereof — i.

Since the system is coexistent, the time-averages of the growth rates must be equal and at the stationary state they must precisely be equal to zero, otherwise one of the replicators would displace all the others Fig. S3 and the system would collapse. The equivalence of the average growth rates is enforced by the common regulation 30 of the entire replicator community through the mutual dependence of the growth of any one replicator type on the presence of all the others due to their metabolic coupling.

The stabilizing effect of this regulatory mechanism is so efficient that the system remains robust under any reasonable parameter setting: it is highly insensitive to changing the values of its key parameters. The extreme stability of the sequence explicit MCRS is maintained by two direct and an indirect dynamical effect that RNA structure exerts on replicator fitness. The direct effects on the growth rates are realized through mutational changes affecting degradation and replicability, both of which are functions of folding energy and sequence length cf.

Supplementary Equations S3 and S5 , whereas the indirect effects come from the local metabolic support that neighbouring replicators provide for the local production of monomers. We consider the changes in replicator traits determining these direct and indirect effects in turn. S4 , so that the vast majority of persistent replicators are folded into a compact structure.

Consequently, their degradation rates are also nearly uniform. As the lengths of the evolved strands follow a spiky distribution as well in our specific case ranging from 35 to about 40 nucleotides in most simulations; cf.

S3 , the replicability distribution of the evolved RNA population, which depends on folding energy and strand length, must be rather uniform as well. That is, the traits directly affecting replicator fitness i. Distribution of Gibbs free energies. Note that the relative frequency scales are different on the two panels. Replicators have an indirect effect on their own fitness through contributing to the local metabolic efficiency of the system, i.

Figure 3 and Supplementary Fig. S3 illustrates that the E 2 and E 3 activities converge to the same value, but E 1 does not; E 1 is 1. This is the only exception from the almost universal convergence in fitness-related properties, which, however, is the result of a hard arbitrary constraint enforced on the system: the E 1 activity of any sequence is binary 0.

This is yet another proof of its dynamical robustness: the system can withstand even such a crude arbitrary constraint. That is, wherever a consistent trait convergence is prevented by a hard constraint, the system tunes other features by evolutionary means in order to compensate destabilizing effects. Notice that in this case compensation is possible precisely because the replicators exist in complementary pairs of sequences.

A substantial fraction of the parasites of the system appear as the complements of metabolically functional replicators, which is why they cannot lose nucleotides to become shorter and thus to be copied faster: they have to yield functional ribozymes as their own copies if they are to survive the next few rounds of replication. Replicators with their complementary strands both parasitic are kept in check by their own adverse effect on the local metabolism wherever they become abundant.

That is, the system does not allow highly destructive, short parasites with a slack secondary structure to persist and spread for long.

Both the ecological and the evolutionary stability of the MCRS are attained by evolutionary optimization acting on the complementary strands of each metabolic replicator simultaneously, but possibly aimed at different targets. The trivial target of optimization is replicability R as it directly contributes to the fitness of the replicators.

This evolutionary pressure tends to decrease replicator lengths and increase their free energy so that they become short and loosely folded, i.

An indirect pressure acts in the opposite direction to evolve them into efficient metabolic enzymes in order to make them capable of supplying themselves with monomers for their own replication by contributing to an efficient local metabolism. The actual lengths and folding energies of the strands are the results of a compromise between the evolutionary responses to these counteracting selective pressures: the optimal strands are long and folded into a sufficiently compact secondary structure to be good enough ribozymes, but short and loose enough to be copied relatively fast.

In addition, the individual optimizations of all metabolic replicator species must to be balanced in such a way that neither ribozyme species excludes any other. The evolutionary dynamics of the sequence-explicit MCRS seems to be highly efficient in finding solutions to this delicate optimization problem. Although the solutions obtained in different parallel simulations with the same parameter set may differ in some detail such as the finer structure and the actual regime shift pattern of the evolved replicator community cf.

S5 , the diversity and the ecological and evolutionary stability properties of the resulting systems are always the same. The evolved convergence of the dynamical traits of the constituent replicators renders the MCRS exceptionally robust. One of the most important properties of the sequence-explicit MCRS model is that it does not require parametric fine-tuning to be persistent, evolutionarily stable and evolvable Most of the dynamical parameters of the replicators are derived from their nucleotide sequence and the corresponding secondary structural folding properties, which are in turn calculated from the physical-chemical characteristics of polymerized RNA nucleotides on a statistical physical basis.

This is why a few dynamically straightforward parameters can define the replicability, degradation rate and enzymatic functionality of the replicators, along with all the well-known trade-off relations between them 21 , The dynamical parameters of the model are emergent from simple statistical physical rules, and they provide ecological stability to the system through the nearly infinite flexibility of the evolutionary process tuning them.

The common features of the simulated activity patterns Fig. S5 , S6 ultimately depend on the arbitrary choices of the catalytically active structures for E 1 , E 2 and E 3.



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