Abstract
The division of labor between template and catalyst is a fundamental property of all living systems: DNA stores genetic information whereas proteins function as catalysts. The RNA world hypothesis, however, posits that, at the earlier stages of evolution, RNA acted as both template and catalyst. Why would such division of labor evolve in the RNA world? We investigated the evolution of DNA-like molecules, i.e. molecules that can function only as template, in minimal computational models of RNA replicator systems. In the models, RNA can function as both template-directed polymerase and template, whereas DNA can function only as template. Two classes of models were explored. In the surface models, replicators are attached to surfaces with finite diffusion. In the compartment models, replicators are compartmentalized by vesicle-like boundaries. Both models displayed the evolution of DNA and the ensuing division of labor between templates and catalysts. In the surface model, DNA provides the advantage of greater resistance against parasitic templates. However, this advantage is at least partially offset by the disadvantage of slower multiplication due to the increased complexity of the replication cycle. In the compartment model, DNA can significantly delay the intra-compartment evolution of RNA towards catalytic deterioration. These results are explained in terms of the trade-off between template and catalyst that is inherent in RNA-only replication cycles: DNA releases RNA from this trade-off by making it unnecessary for RNA to serve as template and so rendering the system more resistant against evolving parasitism. Our analysis of these simple models suggests that the lack of catalytic activity in DNA by itself can generate a sufficient selective advantage for RNA replicator systems to produce DNA. Given the widespread notion that DNA evolved owing to its superior chemical properties as a template, this study offers a novel insight into the evolutionary origin of DNA.
Author Summary
At the core of all biological systems lies the division of labor between the storage of genetic information and its phenotypic implementation, in other words, the functional differentiation between templates (DNA) and catalysts (proteins). This fundamental property of life is believed to have been absent at the earliest stages of evolution. The RNA world hypothesis, the most realistic current scenario for the origin of life, posits that, in primordial replicating systems, RNA functioned both as template and as catalyst. How would such division of labor emerge through Darwinian evolution? We investigated the evolution of DNA-like molecules in minimal computational models of RNA replicator systems. Two models were considered: one where molecules are adsorbed on surfaces and another one where molecules are compartmentalized by dividing cellular boundaries. Both models exhibit the evolution of DNA and the ensuing division of labor, revealing the simple governing principle of these processes: DNA releases RNA from the trade-off between template and catalyst that is inevitable in the RNA world and thereby enhances the system's resistance against parasitic templates. Hence, this study offers a novel insight into the evolutionary origin of the division of labor between templates and catalysts in the RNA world.
Figures
Citation: Takeuchi N, Hogeweg P, Koonin EV (2011) On the Origin of DNA Genomes: Evolution of the Division of Labor between Template and Catalyst in Model Replicator Systems. PLoS Comput Biol 7(3): e1002024. https://doi.org/10.1371/journal.pcbi.1002024
Editor: Claus O. Wilke, University of Texas at Austin, United States of America
Received: November 28, 2010; Accepted: February 14, 2011; Published: March 24, 2011
This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
Funding: This research was supported in part by the Intramural Research Program of the NIH, National Library of Medicine.
Competing interests: The authors have declared that no competing interests exist.
Introduction
At the core of all biological systems lies the division of labor between the storage of genetic information and the manifestation of genetic information, i.e. the functional differentiation between DNA, which is the information storage medium (template), and RNA and proteins, which are responsible for different aspects of operation (catalyst). This fundamental property of life, however, is believed to have been absent at the earliest stages of evolution. The RNA world hypothesis, which is currently considered to be the most, if not the only, realistic scenario for the origin of life, posits that, in the first, primitive replicating systems, both the storage of genetic information, and chemical catalysis were embodied in a single type of molecules, namely, RNA [1]–[5]. According to this hypothesis, DNA and proteins evolved later as specialized components dedicated to information storage and chemical catalysis, respectively, thereby achieving the division of labor between templates and catalysts. The emergence of this division marks a pivotal event among the major transitions of evolution [6]. The RNA world hypothesis has stimulated extensive studies of reactions catalyzed by natural and synthetic ribozymes which revealed a remarkable, previously unsuspected diversity of catalytic activities of RNA [7]–[10]. The catalytic versatility of ribozymes cannot validate the RNA World hypothesis but clearly is compatible with this scenario.
What selective advantage could there be for the evolution of DNA and proteins in the RNA world? Proteins are obviously superior to RNA as chemical catalysts because of their greater repertoire of chemical moieties and structural flexibility. Conversely, proteins are vastly inferior to RNA for the storage of genetic information because of the absence of mechanisms for template-directed replication. These properties of proteins are compatible with the view that proteins evolved as entities specialized in chemical catalysis owing to their superiority to RNA in that capacity.
The case of DNA appears less straightforward. On the one hand, it remains somewhat unclear what would be the principal driving forces behind the evolution of DNA in the RNA world. DNA is generally a less reactive molecule than RNA thanks to the absence of the 2′-hydroxyl at its sugar moiety. In particular, DNA is markedly more resistant to hydrolysis than RNA [11], especially in the presence of metal ions [12], which would certainly be important components of the RNA world given the ion requirement for most of the catalytic activities of ribozymes. Hence, it is often suggested that DNA has an advantage over RNA as a medium of genetic information storage [13]. However, Forterre recently argued that the greater stability of DNA could not account for the origin of DNA because the advantage of employing DNA for information storage lies in the possibility of evolving a longer genome, which in itself would not provide any immediate selective advantage to the systems that included DNA [14]. The possibility to correct C to U misincorporation is often considered to be another advantage of DNA [13]. However, such correction requires specialized catalytic machinery and so, again, could not provide a short-term advantage within the context of the RNA world. Forterre also proposed an alternative scenario, in which viruses evolved DNA genomes under the pressure to evade defense systems of the hosts [14]. This hypothesis is predicated on the existence of complex RNA cells encoding, among other functions, the defense systems. However, RNA cells might not be a realistic stage in the evolution of life for a variety of reasons [15].
On the other hand, there is no clear experimental evidence demonstrating that DNA is inferior to RNA as a chemical catalyst [16]. DNA molecules that can catalyze various chemical reactions have been successfully produced in in vitro evolution experiments [10], [17]–[19]. Hence, the chemical properties of DNA do not necessarily conduce to the fact that the function of DNA is restricted to information storage.
Given these considerations, we ask: What selective advantage could there be for an RNA-based evolving system to evolve an entity that is solely dedicated to the storage of genetic information, i.e., an entity that is functionally equivalent to DNA?
As a first attempt to answer this question, we consider the evolution of DNA-like molecules in RNA replicator systems, the simplest form of the RNA world that can undergo Darwinian evolution. Our aim is to examine whether there could exist purely population dynamical factors, independent of specific nucleic acid chemistry, which would support selection for DNA-like molecules, i.e., molecules solely dedicated to the storage of information, in RNA replicator systems. To address this question, we construct and investigate minimal computational models of an RNA-like replicator system with a built-in possibility to evolve DNA-like molecules.
Models
There are two types of molecules in the models developed here: “RNA-like molecules” and “DNA-like molecules” (RNA and DNA, respectively, for short). The only difference between the two types of molecules is the presence or absence of the catalytic capacity—all other possible differences are ignored for the sake of simplicity and focus. Thus, an RNA molecule can be both a template for replication and a catalyst that replicates other templates, whereas a DNA molecule can only be a template for replication (to replicate templates is the only catalytic function considered in the models). Moreover, DNA and RNA compete for a common resource (precursors) for replication (this direct competition between DNA and RNA is expected to make the models more conservative with respect to the evolution of DNA). The models do not include protein-like molecules because we intend to investigate the simplest possible scenarios under which the evolution of DNA can be considered (see the “Discussion” section for more on this point).
The two types of molecules give rise to four types of replication reactions, namely:
- RNA-dependent RNA synthesis,
- RNA-dependent DNA synthesis,
- DNA-dependent RNA synthesis,
- DNA-dependent DNA synthesis.
To focus on the population dynamical aspect of the problem, we ignore all specific details of the molecular mechanisms [20], [21] of these distinct polymerization reactions and make the following simplification (see the “Discussion” section for more on this point). Regarding the substrate specificity, a replicase is either an RNA polymerase or a DNA polymerase (Rp or Dp, respectively, for short); i.e., the same catalyst cannot produce both RNA and DNA molecules. However, the type of polymerase can be converted from one to another as a result of rare mutations (see below). Regarding the template specificity, a replicase has a potential to discriminate between RNA and DNA. However, for simplicity, it is assumed that replicases do not discriminate between different DNA templates and between different RNA templates (to take account of such discrimination would make the model too complex for the purpose of the current work). It should be noted that, although a catalyst is always RNA, the information on a catalyst can be stored either in an RNA template (which itself is the catalyst) or in a DNA template. Thus, to distinguish between the RNA-form and DNA-form of catalysts, we use superscripts as follows: RpRNA and RpDNA, and DpRNA and DpDNA. When it is preferred not to distinguish between these two forms, catalysts are simply referred to without superscripts.
The replication reaction is assumed to occur in two steps, namely complex formation
between a template and a catalyst (replicase) and actual replication of the
template:where
denotes a replicase;
denotes a template;
denotes a complex
between
and
, and
denotes resource for multiplication;
is the newly produced copy of
, which can be either RNA or DNA depending on the type of
polymerase
(in real replication processes, the template and the product
are complementary to each other; however, for simplicity, the models ignore this, so
is identical to
if no mutation
occurs). Including the complex formation allows us to take into account the fact
that replication is not an instantaneous process [22], [23]. The template specificity of
a replicase is specified by the rate constant of complex formation between
and
. Each replicase is
assigned two parameters:
and
for RNA and DNA recognition, respectively. If
is RNA, the rate constant of complex formation is the value
of
of
; otherwise, it is the
value of
of
. The rate constant of
complex dissociation is set to
and
, respectively.
and
assume values between 0 and 1, ranging from the case of no
complex-formation to the case of no complex-dissociation, respectively. Once a
complex is formed between
and
, replication occurs with the rate constant
. The value of
is assumed to be
identical regardless of the type of a replicase and a template that form a
complex.
A molecule produced by replication () inherits the
properties of the template from which it is produced
(
), but the properties can be modified by mutation, which
occurs with a certain probability during replication. There are four types of
mutations that are mutually exclusive: a change in the value of
(the probability of which is
), a change in the
value of
(
), conversion of the
type of a replicase (
and
), and conversion of a replicase into an inactivated form, a
parasite (
) (see below). A change in
and
is obtained by adding a random number uniformly distributed
in
(
and
are bounded in
; see Text S1 for
details). For simplicity, we set
because this type of
mutation is not required for the evolution of DNA molecules in the present models
(setting
did not qualitatively change the results because the
population of Rp did not go extinct; data not shown).
In addition to the replication reaction, the decay reaction that converts replicators
into the resource occurs with a rate constant :
and
. The decay of complex
molecules is treated as independent decay of the constituent molecules:
and
.
The class of replicators customarily called “parasites” is known to play important roles for the evolutionary dynamics of RNA-like replicator systems [24]–[27]. Parasites are molecules that do not catalyze replication of other molecules but can be replicated by the catalysts, possibly at a faster rate than the catalysts themselves. Under well-mixed conditions, the parasite can bring a replicator system to extinction by (over)exploiting catalysts (e.g., see [22]). Because of this inherent instability of RNA-like replicator systems against the parasite, it is necessary to consider spatial structure in the population of replicators and the discreteness of the population, which can prevent the extinction caused by parasites [28]–[32]. Moreover, if extinction is prevented through spatial pattern formation, the parasite can contribute to the evolution of complexity in RNA-like replicator systems [24].
Given these previous studies, we introduced parasites into the models. The models
assume a special class of molecules, parasites, that have no catalytic activity but
have an increased rate of complex formation with catalysts by a constant factor
; e.g., if a parasite is RNA, the complex formation rate is
, where
(the complex
dissociation rate is unaffected and is
).
The model replicator system specified above was implemented as a spatially extended,
individual-based stochastic simulation model. Two models were constructed: one in
which replicators are assumed to be confined on a surface with finite diffusion (the
surface model, for short) and another in which replicators are compartmentalized by
vesicle-like boundaries that are impermeable to replicators (the compartment model).
In the compartment model, the size of a compartment grows (or shrinks) in proportion
to the number of replicators inside the compartment, and a compartment divides when
its size reaches a threshold given by a parameter . The surface model
does not assume any factors other than the birth, death and diffusion of replicators
and so is simpler than the compartment model. However, the compartment model has an
obvious relevance to the recent experimental efforts to synthesize model
“protocells” (for reviews, [33], [34]).
The two models were implemented as described previously [35] (see Text S1, for
details). Briefly, the surface model was implemented in two-dimensional cellular
automata (CA). One square of the CA contained at most one replicator, and empty
squares were considered to represent the resource (); hence, the number of
replicators the system could sustain was limited both locally and globally. The
dynamics were run by consecutively applying an algorithm that locally simulates the
reactions specified above and diffusion. Interactions occurred only between
molecules that were adjacent to each other on the CA grid. Diffusion was implemented
as exchange of contents between adjacent grid squares, and the rate of diffusion is
given by the parameter
. Both reactions and
diffusion were prohibited to occur across CA and compartment boundaries.
To simulate the dynamics of compartment boundaries, we employed the Cellular Potts
Model (CPM) [36], [37]. The CPM was implemented in two-dimensional CA. Each
compartment consisted of a set of grid squares with identical states. The CPM
algorithm tends to bring the size of each compartment (i.e. the number of squares
that constitute a compartment) closer to its target size while minimizing the number
of contacts between different compartments. The CPM was superimposed onto the
surface model to generate the compartment model. The value of
was increased so that the internal replicator system within
a compartment was relatively well-mixed. The dynamics of compartment boundaries and
those of replicators were coupled by setting the target size of a compartment to be
proportional to the number of replicators present in the compartment with the factor
of proportionality
(see [38], for an
experimental support of this coupling). When the size of a compartment reached the
threshold (
), the compartment was divided along the line of the second
principal component; the internal replicators were distributed between the two
daughter compartments according to their location.
Results
Before presenting the results of the simulations, let us first consider replicator systems consisting of RNA and DNA in general terms. In such a replicator system, there are four replication reactions as listed in the Models section. These four reactions provide for three types of replicator systems, which we denote the self-replication system, the transcription system and the reverse transcription system (Figure 1). The self-replication system consists only of RNA molecules that function both as the templates and as the RNA-dependent RNA polymerases (Figure 1A). This system is “primitive” in the sense that both genetic information and chemical catalysis are provided by a single type of molecules, so there is no division of labor between templates and catalysts. In contrast, the transcription system consists of both RNA and DNA and establishes a division of labor between the template and the catalyst (Figure 1B), where RNA plays the role of the catalyst whereas DNA plays the role of the template. An intermediate case is represented by the reverse transcription system (Figure 1C), which contains DNA molecules but requires RNA molecules to function both as catalyst and as template to complete the replication cycle.
The notation is as follows: Rp and Dp denote RNA polymerase and DNA polymerase respectively. The superscripts to Rp and Dp denote whether the polymerase is in RNA-form (catalyst and template) or in DNA-form (template). The prefixes to Rp and Dp denote the type of templates a polymerase depends on: Rd stands for RNA-dependent, and Dd stands for DNA-dependent. Solid arrows represent the template-product relationship. Broken arrows represent the catalyst-reaction relationship. A: Self-replication system consists of an RNA replicase (RdRp). B: Transcription system consists of a transcriptase (DdRp) and a DNA replicase (DdDp). C: Reverse transcription system consists of a transcriptase (DdRp) and a reverse transcriptase (RdDp).
By comparing the three replicator systems, we can see two effects that can be brought about by the inclusion of DNA molecules into a replication cycle. First, the systems that include DNA are more complex and thus less efficient than the self-replication system. The inclusion of DNA requires the joint action of four types of molecules to complete a replication cycle (RpRNA, RpDNA, DpRNA and DpDNA), regardless of whether replication proceeds via the transcription cycle or via the reverse transcription cycle. Assuming that the total concentration of molecules is constant, this increase in the complexity of the replication cycle leads to a reduction in the concentration of each type of molecules and to the corresponding reduction in the rate of multiplication compared to the self-replication system.
Second, however, there is a converse effect: the division of labor between the template and the catalyst, which emerges in the transcription system, releases the system from a trade-off that exists in the self-replication system. Because replication is not an instantaneous process, a catalyst spends a part of its lifetime replicating other molecules, and during these times, the catalyst itself cannot be replicated [24]. In the self-replication system (the RNA-only cycle), catalysts also serve as templates to be replicated; therefore, the system is hampered by the trade-off between the RNA molecules spending time as templates and as catalysts (the trade-off between template and catalyst for short). This trade-off gives a substantial advantage to a parasite, which spends all of its lifetime being a template [22]. By contrast, the transcription system is free of such a trade-off: the catalysts (RNA) are produced by transcription of the DNA and so do not have to spend any time being templates in order to complete the replication cycle. In the reverse transcription system, however, the catalysts (RNA) also serve as templates in order to produce DNA via reverse transcription. Hence, the reverse transcription system does not establish the division of labor between the template and the catalyst (but, similarly to the transcription system, it suffers from the reduction in the rate of multiplication due to the increased complexity of the replication cycle).
In the following section, we use the described models to examine whether a replicator system, starting from the simple self-replication (RNA-only cycle), can evolve DNA molecules and the ensuing division of labor between the template and the catalyst.
The surface model
Evolution of the transcription system in the surface model.
The surface model was initialized with a homogeneous population of
RpRNA with arbitrary chosen values of
and
(Table 1, No. 1). A
simulation was first run with the mutation from Rp to Dp disabled. In this
simulation, the system contained a large number of parasites, and the
spatial distribution of catalysts and parasites formed traveling wave
patterns (Figure 2A).
The front of a wave consists of RpRNA, and it expands into an
empty region as the population of RpRNA grows. The back of a wave
consists of parasites, and it contracts, leaving empty regions, in the
direction of wave propagation due to the extinction caused by parasites
[22]
(under well-mixed conditions, the system is unstable as mentioned in the
“Models” section; see
also Figure 9A). When
the evolutionary dynamics reached equilibrium (Figure 2A), the population of Rp
displayed a unimodal distribution of
(Text
S1, Note 1) and a uniform distribution of
(a trivial consequence of the absence of DNA in the
system). After the equilibrium was reached, the mutation from Rp to Dp was
enabled. The system then displayed the following evolutionary dynamics.
Given that the distribution of the
of Rp was
uniform, a mutation (
) could produce
Dp with various values of
. The Dp that
had relatively greater values of
invaded the
system (Figure 2B) and
quickly evolved towards specialization on DNA replication, i.e., increasing
the value of
and decreasing
the value of
(Figure 2C). In other
words, the original, dual specificity Dp that emerged as the result of the
mutation of Rp evolved into a DNA replicase. Upon the invasion of Dp, the
population of Rp diverged into two populations that have markedly different
distributions of
(Figure 2C), where one
population (dual specificity Rp) recognized DNA templates well (high
values), whereas the other population (RNA
replicase) recognized almost only RNA templates (low
values). Subsequently, the dual specificity Rp
evolved towards recognizing only DNA templates by reducing the value of
, i.e., became a transcriptase (Figure 2D). The net outcome is the
evolution of the system into a state in which the two types of replicator
systems, namely, the self-replication system (with the RNA replicase as the
only catalyst) and the transcription system (with two distinct catalysts, a
transcriptase and a DNA replicase), stably coexist with one another and with
parasites.
The model was initialized such that the system consisted of a
population of RNA polymerase (Rp) and parasites. The simulation was
first run with the mutation converting Rp into Dp disabled
().
After the system reached evolutionary equilibrium (panel A), the
mutation was enabled (
), and
the resulting evolutionary dynamics are depicted in panel B to D.
The larger panels depict snapshots of simulations taken at different
times as indicated above panels. The color coding is indicated at
the bottom of the figure. RNA and DNA are not distinguished. The
timescale is scaled such that it has the same meaning as that of the
ordinary differential equation model that describes the replicator
dynamics with the same rate constants as in the CA model (the
timescale is scaled in this manner throughout the paper). The
smaller panels within the larger panels depict a two-dimensional
histogram of
and
. See
the main text for the description for each panel. The parameters
(rate constants) used in this simulation were as follows:
(replication);
(decay);
(diffusion);
(parasite advantage);
(mutation rate of
and
);
(mutation step);
(mutation rate from Rp to Dp);
(mutation rate to parasites). The size of CA was 1024×1024
squares. The boundary had no flux.
Parasites enable the transcription system to coexist with the self-replication system.
Given that every replicator competes for the same resource
(), how can the two replicator systems coexist? To
elucidate the mechanism of the coexistence, we ran the following simulation
(Table 1, No. 2).
A system was initialized with a homogeneous population of an idealized, pure
transcription system (the values of
and
were set to 0 and 1, respectively, for both Rp and
Dp). Mutations were disabled except for those converting catalysts into
parasites. In this simulation, the transcription system displayed a distinct
spatial pattern with numerous “clumps”, which mainly consisted
of DpDNA, and slowly grew, split and occasionally shrank and
disappeared (Figure 3).
The system contained relatively large empty regions
(
) between the clumps (this was the case even when
parasites were absent as becomes obvious from the inspection of the spatial
distribution of parasites in Figure 3). This result indicates that the multiplication of the
transcription system is inefficient, which appears to originate from the
increased complexity of replication cycle through the inclusion of DNA (as
described in the previous section) and from the finiteness of diffusion (see
Text
S1, Note 2, for details). Moreover, the transcription system
contained a far smaller number of parasites compared to the self-replication
system (cf. Figure 2A);
if the influx of parasites through mutation was eliminated, the parasite
soon went extinct under the parameters of this simulation. This indicates
that the transcription system is resistant against parasites. This can be
explained as follows. In the transcription system, the division of labor
between templates and catalysts is established, so that the templates
(RpDNA and DpDNA) do not spend any part of their
lifetimes replicating others, which reduces the advantage of the parasite
over the catalyst (the parasite still has some advantage given that
) (see Text S1, Note 3, for additional
discussion).
The surface model was initialized such that the system consisted of
the transcription system (see below for the parameter values). No
mutation processes were enabled except for the mutation converting
molecules into parasite (). The
color coding is indicated in the figure. The parameters were as
follows:
and
for
both Rp and Dp;
;
; the
size of CA was 512×512 squares; the other parameters were the
same as in Figure
2.
Given the above properties of the transcription system, its coexistence with
the self-replication system can be rationalized as follows. First of all,
the transcription system is more resistant to parasites. In particular, the
parasites that exploit the self-replication system are all RNA templates, so
they cannot exploit the transcription system (which replicates DNA
templates). Hence, when a traveling wave consisting of RpRNA and
the parasite hits a clump consisting of the transcription system, the clump
can remain intact whereas the traveling wave is annihilated because the
expansion of the wave front is impeded by the lack of resource
() in the regions that are already occupied by the
transcription system. However, the transcription system produces large empty
regions in the system due to its inefficiency of multiplication. In
contrast, the self-replication system can multiply faster, so the traveling
waves can propagate into those empty regions before the transcription system
expands into those regions. In this way, the self-replication system can
thrive along with the transcription system. This mechanism of coexistence is
similar to that suggested for grassland ecosystems by Tilman [39],
wherein a faster reproducing species was able to thrive along with a slower
reproducing species. The latter was able to outcompete the faster growing
species locally due to K-selection—in the present models, this is due
to differential resistance against parasites—but which always left
some area in the system unoccupied due to its slower growth and the
occasional local extinction.
The above explanation implies that parasites are one of the key factors
behind the coexistence of the self-replication and transcription systems. To
examine whether this is indeed the case, we conducted the following
simulation (Table 1,
No. 3). A system was initialized with populations of the idealized, pure
self-replication system ( and
were set to 0.4 and 0, respectively) and the
idealized, pure transcription system (
and
were set to 0 and 1, respectively). We compared the
dynamics of the system between the cases with and without parasites, with
all types of mutations disabled. In this experiment, the absence of
parasites caused the extinction of the transcriptase, in support of the
hypothesis that parasites are essential for the coexistence of the two
replicator systems. The DNA replicase did not go extinct in the absence of
parasites because DpRNA can parasitize on the self-replication
system given that its
value is 0 as
is the case for parasites by definition. Thus, the short-term,
“ecological” stability of the transcription system in the
presence of the self-replication system is mediated by the parasites that
exploit the self-replication system (“ecological” pertains to
the absence of mutation processes; below we discuss the long-term,
“evolutionary” stability).
The self-replication system evolutionarily stabilizes the transcription system.
Can the transcription system supersede the self-replication system? In other
words, can a transcription system, assuming that it emerged, be maintained
through evolution in the absence of the self-replication system? The answer
turns out to be negative. To address this question, we continued the
previous simulation, in which the self-replication system and the
transcription system coexisted, by removing the entire population of the
self-replication system (Table 1, No. 4). The result was that the transcriptase evolved
towards improved recognition of RNA templates, thus
“re-inventing” RNA replication (Figure 4ABC). After the transcriptase
evolved into a dual specificity Rp, a subset of its population evolved to
reduce its transcription activity (decreased value of
), becoming an RNA replicase (Figure 4CDE). After the RNA replicase
evolved, the remaining dual specificity Rp evolved into a transcriptase.
Thus, the system eventually returned to the original state through
re-evolving the self-replication system. To summarize the results of this
simulation, the self-replication system is required for the stable
evolutionary maintenance of the transcription system: when the
self-replication system is eliminated, the transcription system evolves the
self-replication system via the evolution of a dual specificity Rp from the
transcriptase, which results in the stabilization of the transcription
system.
After the surface model reached evolutionary equilibrium (Figure 2D), the
whole population of the RNA replicase (i.e. the self-replication
system) was removed from the system (Figure 4A), and the simulation
was continued. The resulting evolutionary dynamics are depicted
(Figure
4B–F). The figure has the same format as that of
Figure 2.
See the main text for the explanation of each panel. The parameters
where as follows: ; the
size of CA was 512×512 squares; the other parameters were the
same as in Figure
2.
How and why does the presence of the RNA replicase cause the evolutionary stabilization of the transcriptase? The RNA replicase has two distinct effects on the transcription system:
- The catalysts of the transcription system (transcriptase RpRNA and DNA replicase DpRNA) are directly replicated by the RNA replicase;
- If the transcriptase evolves into a dual specificity Rp, it will replicate the RNA replicase RpRNA.
To determine which of these two effects causes the evolutionary stabilization
of the transcriptase, we modified the model such that interactions between
the RNA replicase and the transcriptase were prohibited. The following three
cases were investigated: 1) The RNA replicase does not recognize the
transcriptase as a template; 2) the transcriptase does not recognize the RNA
replicase as a template (both RNA and DNA given that it can evolve into a
dual specificity Rp); 3) the RNA replicase and the transcriptase do not
recognize each other (a combination of 1 and 2). For each of these three
cases, we continued the previous simulation that had reached the
evolutionary equilibrium. The results showed that the evolutionary
stabilization of the transcriptase was obtained only in case 1. In this
case, the modification did not qualitatively change the behavior of the
system although the transcriptase went extinct after a long time due to
fluctuation. In case 2, the transcriptase evolved into a dual specificity
Rp, which out-competed the original RNA replicase, and which then underwent
speciation into the RNA replicase and the transcriptase, re-establishing the
original system as we saw before (note that the model allowed interactions
between the descendants of the original transcriptase). In case 3, the
transcriptase evolved into a dual specificity Rp, which went extinct after
its value of exceeded that
of the RNA replicase. Therefore, the evolution of the transcriptase into a
dual specificity Rp is prevented because a dual specificity Rp replicates
the RNA replicase RpRNA. This duality makes the dual specificity
Rp selectively inferior to the transcriptase which does not waste time and
resource (
) on replicating RNA replicase RpRNA. (See
Text
S1, Note 4, for additional information.)
The transcription system induces the evolution of parasites.
As shown above, parasites mediate the coexistence between the
self-replication system and the transcription system. Does this mean that
the evolution of Dp was caused by parasites? To analyze the cause and effect
relationship between the parasite and the evolution of the transcription
system, the model was modified to exclude parasites that are explicitly
defined as a class of non-catalytic replicators with an advantage
() for the recognition by catalysts (Table 1, No. 6). In this
model, the difference between catalysts and parasites is continuous as it is
determined by the value of
and
. Thus, only quantitative distinction can be made
between catalysts and parasites: the catalysts that recognize templates less
well are “more parasitic” than those that recognize templates
better. As before, the simulation was first run until it reached equilibrium
with the mutation converting Rp into Dp disabled. In this simulation, the
system did not develop a traveling wave pattern; instead, it exhibited
continuous production and refilling of small empty spots (Figure 5A). Moreover, the
RNA replication activity of the Rp (
) was
distributed around a single peak; hence, there was no sharp boundary between
catalysts and parasites. The RNA replication activity was significantly
lower than that which evolved when the system contained parasites as can be
seen from the comparison of the value of
between Figure 2A and Figure 5A (Text
S1, Note 5).
The surface model was initialized with a population of Rp (no
parasites were introduced in the system). The simulation was run in
the same manner as in Figure 2 with the mutation converting molecules into
parasites disabled (). The
format of the figure is the same as that of Figure 2. For the explanation of
each panel, see the main text. The parameters were as follows:
; the
size of CA is 512×512 squares; the other parameters were the
same as in Figure
2.
We then enabled the mutation converting Rp into Dp. The resulting system
displayed the following evolutionary dynamics. Dp quickly invaded the
system, evolving into a DNA replicase (Figure 5B). Upon the invasion of Dp, the
population of Rp that had higher transcription activity (greater values of
) out-competed the population of Rp that had lower
transcription activity (smaller values of
) (compare
Figure 5A and Figure 5B). This is in
contrast to the model containing explicitly defined parasites, in which the
population of Rp underwent speciation with respect to the distribution of
the values of
(Figure 2BC). After the
evolution of the DNA replicase, the remaining population of Rp evolved
towards increasing RNA replication activity (Figure 5C). After Rp increased the RNA
replication activity sufficiently (i.e., it evolved into a dual specificity
Rp), a subpopulation of it started to evolve towards decreasing
transcription activity, becoming an RNA replicase (Figure 5DEF). After the RNA replicase
evolved, the remaining dual specificity Rp evolved towards decreasing RNA
replication activity, becoming a transcriptase (Figure 5FGH). Interestingly, the
population of the evolved RNA replicase displayed a broad distribution of
the
value (Figure 5G; cf. Figure 2), and subsequently diverged into two populations with
markedly different distributions of
(Figure 5H). Among these
two populations, one population had the values of
that were significantly higher than the values of
which Rp evolved in the beginning of the simulation
(compare Figure 5A and
Figure 5H). This
population, therefore, resembles the RNA replicase that evolved in the model
that included explicitly defined parasites (compare Figure 2D and Figure 5H). By contrast, the other
population of the RNA replicase had the values of
that were lower than the value of
which the Rp evolved in the beginning of the
simulation, and it turned out that these values were too small for Rp to
survive through self-replication. Thus, this population effectively
consisted of parasites. It is most likely that these parasites mediated the
coexistence between the RNA replicase and the transcription system.
To summarize, even though this model did not include explicitly predefined
parasites as a separate class of molecules and thus did not allow the
emergence of parasites with an advantage () in the
recognition by catalysts, the system evolved a DNA replicase and a dual
specificity Rp, which then caused the evolution of an effectively parasitic
species. Consequently, the system reached an equilibrium state that was
essentially identical to the equilibrium state of the model with explicitly
predefined parasites. This result demonstrates the robustness of the
equilibrium state observed in the original model. Moreover, it elucidates
the cause and effect relationship between the evolution of the transcription
system and the evolution of parasites. On the one hand, the parasites
provide for the evolution of the transcription system by mediating the
coexistence with the self-replication system. On the other hand, the
transcription system also allows the evolution of the parasites when the
model does not include explicitly predefined parasites, by causing the
subdivision of the population of the RNA replicase (see the discussion in the next section).
Interpretation of the surface model results.
The results described above show that the transcription system can evolve in the surface model because the division of labor between the template and the catalyst, which is made possible by the inclusion of DNA molecules in the replication cycle, increases the resistance of the transcription system against parasites compared to the self-replication system.
In addition to this main conclusion, the above results also revealed two general points worthy of note. First, there are two distinct regimes in the stabilization of a certain species by another species, namely, ecological (short-term) stabilization and evolutionary (long-term) stabilization. The results showed that, on the one hand, parasites enabled the transcription system to coexist with the self-replication system. In theoretical ecology, this is known as predator-mediated coexistence [40], [41]. In this regime, the mediation occurs on a short timescale at which each species does not change its character through evolution, hence ecological stabilization. On the other hand, the RNA replicase generated a selection pressure for the transcriptase not to evolve into a dual specificity RNA polymerase. In this regime, a species exerts a selection pressure on the other species so as to maintain its identity on a long timescale at which the other species would have the potential to evolve new features if the stabilizing species was absent, hence evolutionary stabilization.
Second, exploration of the model showed that removing any of the three components of the system, namely, the self-replication system, the transcription system and the parasite, at the evolutionary steady state resulted in the restoration of the deleted component through the evolution of the remaining components (Figure 6BCD). Moreover, there was a mutual dependence among the three components with respect to the ecological or evolutionary stability (Figure 6A); e.g., the parasite enabled the evolution of the transcription system through mediating its coexistence with the self-replication system, whereas the transcription system enabled the evolution of the RNA replicase into a parasite-like species. Thus, the causal relationship among the evolutionary fates of the components—i.e. which species causes the evolution of which species—does not form a linear chain, but rather a cycle (Figure 6A). This circularity is in a sharp contrast with the linear structure of the evolutionary history of the species (Figure 6BCD). Therefore, the analysis of an evolutionary trajectory (history) from a single initial condition may not fully elucidate the cause and effect relationships among the evolutionary fates of the species.
Dual-Rp denotes a dual specificity Rp. In B, C and D, the evolutionary dynamics progress from top to bottom. For the explanation, see the main text.
The flow of information.
Given the evolution of the transcription system, it is interesting to consider the separation between template and catalyst in terms of the flows of genetic information. In particular, is the line of descent continued through the replication of DNA in the transcription system? To address this question, we conducted the following experiment. The previous simulation (Table 1, No. 1) was continued after having reached evolutionary equilibrium with the mutation converting Rp into Dp disabled. At the beginning of the simulation, each individual replicator was labeled according to whether it was RNA or DNA. A new individual inherited this label from the template from which it was produced regardless of whether the new individual was RNA or DNA. The simulation was run until the entire populations of the RNA replicase, transcriptase and DNA replicase each descended from either RNA molecules or DNA molecules (not necessarily from one molecule). Then, each molecule was re-labeled, and the simulation was continued: this cycle was repeated 200 times. The result showed that the entire population of the transcriptase was descended from DNA templates of the transcriptase in more than 98% of the simulations. Given that the mean fraction of DNA molecules in the population of the transcriptase was 65%, the origin of this line of descent was significantly biased towards DNA. Likewise, the entire population of the DNA replicase was descended from DNA templates of the DNA replicase in 100% of the simulations whereas the mean fraction of DNA was 78%. These results show that, in the transcription system, the flow of genetic information is unidirectional from DNA to RNA. Therefore, the transcription system established the separation between the template and the catalyst in terms of the flows of genetic information across generations. By contrast, the entire population of the RNA replicases descended from RNA templates in less than 92% of the simulations. Given that the fraction of RNA among the RNA replicases was 95.5% averaged over time, this line of descent was not significantly biased towards RNA templates.
The Central Dogma of molecular biology states that the flow of genetic information is unidirectional from nucleic acids to proteins [42]. In the strict chemical sense, the Dogma is unrelated to the unidirectional flow of information exhibited by the transcription system in the present model. However, the Dogma may be recast in generalized terms, to assert that the flow of genetic information is unidirectional from templates to catalysts. Under this extended interpretation, there seems to be an analogy between the Central Dogma and the unidirectional flow of information from templates (DNA) to catalysts (RNA) exhibited by the transcription system in the present model.
The compartment model
Evolution of a transcription-like system in the compartment model.
As in the surface model, the compartment model was initialized with a
homogeneous population of RpRNA (Table 2, No. 1). The simulation was first
run with the mutation converting Rp into Dp disabled. When the system
reached equilibrium, Rp displayed a uniform distribution of
—a trivial consequence of the absence of DNA
molecules—and a unimodal distribution of
(Figure
7A). The distribution of
is balanced at
some intermediate value by the selection pressure of two opposing
directions. The selection pressure at the level of intra-compartment
dynamics tends to reduce the value of
because of the
trade-off between templates and catalysts. In contrast, the selection
pressure at the level of inter-compartment dynamics tends to increase the
value of
because of the positive coupling between the growth
of compartments and the multiplication of internal replicator systems.
The compartment model was initialized, and the simulation was run in
the same way as in Figure 2. The model was initialized such that the system
consisted of a population of Rp enclosed in a compartment. The
simulation was first run with the mutation converting Rp into Dp
disabled ().
After the system reached evolutionary equilibrium (Figure 7A), the
mutation (
) was
enabled. The resulting evolutionary dynamics are depicted in panel B
to E. The left picture of each panel shows a snapshot of the
simulation taken at different times as indicated above panels. The
color coding is indicated in the upper left corner of the figure.
DNA and RNA are not distinguished. The insets depict two-dimensional
histogram of
and
. The
right picture of each panel shows a snapshot with a different color
coding, which indicates the value of
.
Distinction is not made between Dp and Rp and between DNA and RNA.
The insets depict a histogram of
with
the same color coding as in the larger pictures that contain them.
For the explanation of each panel, see the main text. The parameters
were as follows:
(the
volume threshold for division of compartments);
(the
target volume is set to the number of internal replicators
multiplied by
);
; the
size of the CA is 512×512 squares; the other parameters were
the same as in Figure
2.
After the system reached equilibrium, the mutation converting Rp into Dp was
enabled. As a result, the Dp with a high activity in DNA replication (a high
value of ) quickly invaded the system (Figure 7B). However, this Dp did not
immediately evolve into a DNA replicase, maintaining a moderate reverse
transcriptase activity. After the invasion of Dp, the Rp evolved a high
transcription activity and a slightly increased RNA replication activity
(Figure 7B). The
system remained in this state for a long period of time. The existence of Dp
at this stage required a continual influx of Dp through mutations because Dp
went extinct if the mutation converting Rp into Dp was disabled after the
invasion of Dp. Later on, in a subpopulation of compartments, Dp evolved
towards decreasing reverse transcription activity (i.e. decreasing the value
of
) (Figure 7C). Concomitantly, Rp in the same compartments evolved
towards increasing RNA replication activity (i.e. increasing the value of
) (Figure 7D). As a result, compartments containing a replicator
system which consists of a DNA replicase and a dual specificity RNA
polymerase appeared in the system (Figure 7D). This replicator system is
henceforth referred to as the transcription-like system. The compartments
containing the transcription-like system quickly out-competed the other
compartments (Figure
7E). After the transcription-like system was established, the model
displayed the invasion of compartments that contained only RpRNA,
which arose through the chance loss of Dp in compartments containing the
transcription-like system (Figure 8A). The compartments containing only RpRNA
quickly increased its population size, locally out-competing the
compartments containing the transcription-like system (Figure 8B). However, the compartments
containing only RpRNA displayed the rapid evolution of their
internal replicator system, whereby the Rp evolved towards reducing RNA
replication activity (Figure
8C). Consequently, the compartments containing only
RpRNA were eventually out-competed by those containing the
transcription-like system (Figure 8D). This cycle of invasion and extinction was observed
repeatedly. The next section describes why the system displays this complex
population dynamics.
The figure depicts the same simulation and in the same format as in Figure 7. The time is reset to zero at an arbitrary moment after the time in Figure 7E. For the explanation of each panel, see the main text.
Compartments containing the transcription-like system experience slower evolutionary deterioration of the internal replicator system than compartments containing only RpRNA.
To elucidate the causes of the results described above, the simulation was
continued with mutations modifying the values of
and
disabled. The
result showed that compartments containing only RpRNA appeared
and quickly out-competed compartments containing the transcription-like
system. The same result was obtained when the mutation rate was reduced by
an order of magnitude (Table
2, No. 3).
The above two results, the repeated cycle of invasion and extinction of compartments containing only RpRNA and the extinction of compartments containing the transcription-like system under sufficiently reduced mutation pressure, have two implications. Firstly, compartments increase their fitness by losing the DNA replicase (i.e., when RpRNA remains the only catalyst in a compartment). Secondly, however, compartments containing only RpRNA experience faster evolutionary deterioration of the internal replicator system than compartments containing the transcription-like system, an effect that confers a selective advantage onto the compartments containing the transcription-like system under sufficiently strong mutation pressure.
To investigate the first effect, we directly measured the fitness of
compartments as follows. The model was modified to make the boundaries of
the compartments completely unchangeable so the model contained compartments
but no compartment dynamics. The model was initialized in a configuration
where the size of the compartments was equal to the threshold above which
compartments divide in the original model (). Two
simulations were conducted. In the first simulation, compartments were
filled with a population of RpRNA, RpDNA,
DpRNA and DpDNA in equal proportion. The values of
and
were set such
that the transcription-like system was established
(
and
for Rp;
and
for
Dp—these values were obtained from the system depicted in Figure 7E). In the second
simulation, compartments were filled with a population of RpRNA
alone (
and
were the same
as before). The simulations were run with all mutations disabled (all the
other parameters were the same as in Figure 7). We then measured the rate at
which the compartments lost all internal replicators (i.e. the death rate of
compartments) and the density of the replicators in the surviving
compartments (directly related to the growth rate of compartments). The
result was that the compartments indeed increased fitness by losing the DNA
replicase (for the compartments containing the transcription-like system,
the death rate was
, and the
average density of internal replicators was 0.81; for the compartments
containing only RpRNA, the death rate was 0 within the timescale
of measurement, and the average density of internal replicators was 0.94).
This result is understandable because, as discussed above, the inclusion of
DNA in a replication cycle leads to a fourfold increase in the number of the
types of molecules required for multiplication and so reduces the efficiency
of multiplication and increases the chance of stochastic loss of essential
molecules. Therefore, compartments increase their fitness by losing the DNA
replicase.
To assess the second effect, we compared the evolutionary deterioration rates
between the self-replication system and the transcription-like system (Table 4, No. 1 and 2).
To simplify the comparison, we considered a large, well-mixed replicator
system. The greater size of the replicator system reduced the effect of
random drift in the population dynamics of replicators and so allowed us to
focus on the deterministic aspect of the evolutionary deterioration process
over a sufficiently long time (note that selection pressure is a
deterministic factor). To this end, we modified the model such that
interactions between molecules occur globally (i.e. interactions can occur
independent of the locations of molecules) so that the system was
effectively well-mixed. Again, two simulations were conducted. In one
simulation, the system was initialized with a population of
RpRNA, RpDNA, DpRNA and DpDNA in
equal proportion. The value of and
were set such that the replicator system was the
idealized, pure transcription-like system (to be precise,
and
for Rp;
and
for Dp). In
the other simulation, the system was initialized with a population of
RpRNA alone (
and
).
The result was that the system consisting only of RpRNA rapidly
deteriorated, with the value of quickly
decreasing, and eventually went extinct (Figure 9A). The
of RpRNA underwent neutral evolution
because of the absence of DNA molecules (Figure 9A). This rapid deterioration of
the replication activity is expected because it is selectively
disadvantageous to be a catalyst in a well-mixed self-replication system
with complex formation [22]. In contrast, the transcription-like system
displayed evolutionary deterioration that was qualitatively
indistinguishable from neutral evolution (compare Figure 9B and Figure 9A). Although the
transcription-like system also went extinct eventually, this took much
longer time than for the self-replication system (time≈105).
This qualitative difference in the rates of evolutionary deterioration of
catalysts supports the argument that compartments containing the
transcription-like system experience slower evolutionary deterioration of
the internal replicator system (the origin of this difference will be
elucidated in the next section).
The model was modified such that interactions between molecules
happen globally regardless of the location of molecules (the system
is effectively well-mixed). The model was initialized with a
population of RpRNA in panel A, with a population of
RpRNA, RpDNA, DpRNA and
DpDNA in equal proportion in panel B and C, and with
a population of RpRNA, RpDNA and
DpRNA in equal proportion in panel D. The initial
value of Rrec and Drec were set as indicated in the figure (at
time = 0). The parameters were as follows:
(effectively); the size of the CA is
512×512 squares; the other parameters were the same as in
Figure
2.
If the advantage of compartments containing the transcription-like system
lies in the slower evolutionary deterioration of internal replicator
systems, it is expected that altering the severity of evolutionary
deterioration would modulate the evolvability of the transcription-like
system. Decreasing the mutation rate of replicators, obviously, delays
evolutionary deterioration. Thus, if the mutation rate is sufficiently
reduced, the advantage of the transcription-like system must be so
insignificant that compartments containing the transcription-like system are
unable to out-compete those containing only RpRNA. In fact, this
has already been seen in one of the simulations described above (Table 2, No. 3).
Moreover, the severity of evolutionary deterioration also depends on the
population size of the internal replicator system (i.e. the size of
compartments, ) because the
population size determines the level of random drift in the evolutionary
dynamics, which disturbs the deterministic force of selection and,
consequently, generates greater variation among the compartments, on which
the compartment-level selection operates. Thus, if the size of compartments
is smaller, the evolutionary deterioration of the internal replicator system
should be slower [35]. Therefore, it is expected that, if the size of
compartments is sufficiently small, compartments containing the
transcription-like system are unable to out-compete those containing only
RpRNA. These expectations were indeed confirmed by additional
simulations (see Text S1, Note 6, for details).
To summarize, the transcription-like system can confer both advantage and disadvantage to a compartmentalized replicator system compared to the self-replication system: it impedes the evolutionary deterioration of the internal replicator system but hampers the efficiency of multiplication of that system. The disadvantage due to the reduced efficiency of multiplication is significant regardless of the parameter values because it is a necessary consequence of an increase in the complexity of replication cycle brought about by the inclusion of DNA. In contrast, the advantage due to the slower evolutionary deterioration depends on how fast the evolutionary deterioration proceeds if compartments contain the self-replication system, which, in turn, depends on the mutation rate of individual replicators and the size of compartments (or more precisely, the population size of the internal replicator system). If the rate of the evolutionary deterioration of compartments containing the self-replication system is sufficiently high, the advantage of the transcription-like system more than compensates for the disadvantage, and the evolution of the transcription-like system becomes possible.
The presence of transcription and the absence of reverse transcription prevents the evolutionary deterioration of catalysts in the internal replicator system.
We next consider the reason why, in the compartment model, the
transcription-like system displays slower evolutionary deterioration than
the self-replication system. As already mentioned, in the self-replication
system, catalysts gain a selective advantage by decreasing the time they
spend replicating templates (i.e. by decreasing the value of
and
) because of
the trade-off between templates and catalysts. By contrast, in the
transcription system, the catalysts do not function as templates, so there
is no selective advantage for catalysts to reduce the time spent on
replicating templates. However, in the transcription-like system, Rp
maintains a high RNA replication activity, which raises the question whether
this impairs the release from the trade-off.
To address this question, we consider an ordinary differential equation (ODE)
which simulates the population dynamics of the internal replicator system of
compartments in the compartment model (Table 3). Although the ODE model does not
fully reflect the evolutionary dynamics of the internal replicator system,
it captures the deterministic aspect of the dynamics under idealized
conditions where random drift and mutations play no role. This
simplification makes it easier to investigate the deterministic stability of
replicator systems. The first ODE model we constructed described the
population dynamics of one species of RNA polymerase and one species of DNA
polymerase (see the equation in Text S1). The strategy of the analysis
was to use the idealized transcription system (i.e.
and
for both Rp
and Dp) as a reference point and then consider the effect of adding RNA
replication (i.e. setting
for Rp) and,
for the purpose of comparison, reverse transcription (i.e. setting
for Dp) to the transcription system.
The ODE model was numerically solved for various initial conditions. The results showed that the transcription system could survive under well-mixed conditions if the initial ratio of RpDNA to DpDNA was neither too large nor too small (Table 3, No. 1). In the transcription system, there is symmetry between Rp and Dp because of the assumption that catalysts do not discriminate between different templates of the same molecular type. Because of this symmetry, the steady state ratio of RpDNA to DpDNA and that of RpRNA to DpRNA are determined by the initial ratio of RpDNA to DpDNA (i.e., there is structural instability in the system).
We next considered the effect of adding either RNA replication or reverse transcription to the transcription system. Before describing the results, it is worth noting that adding either of these processes introduces asymmetry into the system. For instance, adding RNA replication makes RpRNA play both the role of catalysts and templates for RNA replication, whereas DpRNA plays only the role of templates. Of course, DpRNA also plays the role of catalysts for DNA replication, but so does RpRNA for transcription—there is no asymmetry between Dp and Rp with respect to reactions involving DNA molecules. Due to the above asymmetry, DpRNA will be replicated by RpRNA more often (per molecule) than RpRNA is replicated by RpRNA assuming that the initial condition is symmetric with respect to Dp and Rp. This can be seen from the fact that three times more RpRNA is required than DpRNA in order to produce an equal amount of the two complex molecules (i.e. that between RpRNA and RpRNA and that between RpRNA and DpRNA) [22]. It is easily seen that adding reverse transcription likewise introduces asymmetry into the transcription system.
The results of the numerical calculation indicated that adding RNA
replication did not adversely affect the survival of the system (Table 3, No. 2). In
contrast, adding reverse transcription led to the extinction of the system
(this was the case even when the value of was very
small, e.g. 0.01; Table
3, No. 3). To determine the origin of this difference, we
searched for a factor(s) that dampened the asymmetry generated by RNA
replication and a factor(s) that amplified the asymmetry generated by
reverse transcription. Let us first consider the case of reverse
transcription. If there is no reverse transcription, the initial condition
determines the ratio of RpDNA to DpDNA which itself
determines the ratio of RpRNA to DpRNA. Let us suppose
that the system is initially symmetrical between Rp and Dp. Now, by adding
reverse transcription, RpDNA is produced at a slightly higher
rate than DpDNA due to the aforementioned asymmetry in reverse
transcription, so that the ratio of RpRNA to DpRNA
increases through transcription, which, in turn, leads to the further
increase of the RpDNA to DpDNA ratio, hence an
amplifying factor. Next, for the case of RNA replication, assuming a
symmetric initial condition again, adding RNA replication slightly increases
the ratio of DpRNA to RpRNA. However, the change of
the DpRNA to RpRNA ratio has no effect on the
DpDNA to RpDNA ratio because there is no reverse
transcription. Thus, transcription tends to bring the DpRNA to
RpRNA ratio back to the DpDNA to RpDNA
ratio, hence a dampening factor. To summarize, provided the absence of
reverse transcription, the transcription of DNA molecules tends to bring the
population composition of RNA molecules towards that of DNA molecules and so
dampens the bias in the population composition of RNA molecules generated by
the asymmetry in RNA replication. In other words, the population of DNA
molecules serves as a buffer to the population of RNA molecules.
The above argument implies that in the absence of reverse transcription,
transcription prevents the evolutionary deterioration of catalysts because
the selective advantage a catalyst would obtain by increasing the time it
spends being a template is effective only in the RNA population, and such a
selective advantage would be counteracted by the transcription of DNA
molecules. To examine whether this is indeed the case, we extended the ODE
model to include the population of an additional species of Rp, which we
refer to as Rp′. The strategy of the analysis was to treat Rp′
as a mutant of Rp and examine whether Rp′ could out-compete the
original Rp when the small amount of Rp′ was introduced into the
system, which mimicked the mutation of Rp into Rp′. The value of
and
were set to
yield the idealized transcription-like system
(
and
for Rp, and
and
for Dp). The
system was initialized such that it was symmetrical with respect to Rp and
Dp, and the population size of Rp′ (both RNA and DNA) was set to 0.
After the system reached equilibrium, the population size of Rp′ (both
RNA and DNA) was increased by a small amount (0.001), and the system was
allowed to reach a new equilibrium. The result showed that even if Rp′
completely lost its catalytic activity (i.e.
and
), Rp′ was unable to out-compete Rp (the
population size of Rp′ remained small; Table 3, No. 4). Thus, in the absence of
reverse transcription, transcription impedes the evolutionary deterioration
of catalysts.
The above argument shows that the release of catalysts from the
template-catalyst trade-off depends not only on the presence of
transcription but also on the absence of reverse transcription, i.e.
blockage in the flow of information from catalysts (RNA) to templates (DNA).
To investigate this issue, we conducted a simulation of the type shown in
Figure 9, i.e. the
examination of evolutionary deterioration process in a large, well-mixed
replicator system (Table
4, No. 3). The system was again initialized with the
transcription-like system; however, this time, reverse transcription
activity was added to the system (i.e. the of Dp was set
to 1). The result of this simulation showed that addition of reverse
transcriptase greatly accelerates the evolutionary deterioration of
catalysts (Figure
9C).
Information flow.
As shown above, breakage in the flow of information from RNA to DNA (elimination of reverse transcription) is an important factor underlying the advantage of the transcription-like system in a compartmentalized replicator system. However, although reverse transcription activity was much reduced in the transcription-like system, it was not completely absent due to the mutation pressure. Moreover, the transcription-like system maintained a high rate of RNA replication (Rp was dual specific). Therefore we were interested to find out in which direction the information was transmitted among replicators in the long run: from RNA to DNA, or from DNA to RNA, or both? To address this question, we conducted the same simulation as for the surface model in order to trace the line of descent over generations. This simulation showed that the population of the dual specificity Rp was always descended from its DNA templates (i.e. RpDNA). Therefore, from the actual flows of genetic information, the division of labor between the template and the catalyst was established for the dual specificity Rp despite the fact that it maintained a high RNA replicase activity. However, the situation differed for the DNA replicase. The simulation showed that two populations of compartments quickly arose in the system: in one of these populations, the Dp was descended from DpDNA, whereas in the other population the Dp was descended from DpRNA. Because of the finiteness of the system, the entire population of Dp was eventually descended either from DpRNA or from DpDNA, with the choice determined by chance.
To further examine the case of Dp, we completely removed reverse
transcription activity from the model (i.e. the value of
for Dp and its mutation rate were set to zero). The
simulation showed that DpDNA was eventually lost from the system
whereas DpRNA remained (Table 2, No. 2). This is possible because
DpRNA can be amplified through RNA replication by the dual
specificity Rp. In the absence of DpDNA, the equilibrium value of
of Dp was slightly decreased (data not shown). This
seems to occur because DpRNA was maintained through RNA
replication, so the trade-off between template and catalyst set in and
caused selection pressure on DpRNA towards decreasing
. This interpretation was supported by a simulation
of the type shown in Figure
9, i.e. examination of evolutionary deterioration in a large,
well-mixed replicator system (Table 4, No. 4). The system was initialized with the
transcription-like system without DpDNA, and reverse
transcription activity was completely removed in the same way as above. This
simulation showed that Dp evolved towards decreasing DNA replication
activity much faster than did the transcription-like system (Figure 9D; compare with
Figure 9B). This
result gives further support to the conclusion that DNA molecules can
prevent or at least slow down the evolutionary deterioration of catalysts.
Moreover, this simulation shows that the survival of DpRNA does
not require the existence of DpDNA (because of dual-specificity
Rp), which can explain why the line of descent for Dp was not always
continued through DNA replication in the original compartment model (Table 2, No. 2). (See
Text
S1, Note 7, for additional discussion.)
Models without complex formation
The preceding sections argued that the evolution of DNA-like molecules is driven
by the ability of the division of labor between the template and the catalyst to
eliminate the advantage of parasites originating from the trade-off between
template and catalyst. To further test this argument, we removed the complex
formation from the models and instead assumed that the replication reaction is
an instantaneous process: . This is expected
to significantly reduce the effect of the trade-off (but see below). Examination
of the models without complex formation showed that Dp did not evolve under
various parameter combinations (Table 1, No. 7; Table
2, No. 5). This result is in accord with the above argument. However,
deviation from this outcome was observed under conditions that were not
considered in the original models. Specifically, in the surface model without
complex formation, if the decay rate of DNA was substantially lower than that of
RNA and if the diffusion rate
was sufficiently
low, Dp could be evolutionarily maintained (i.e. Dp survived if the system
initially consisted of the transcription system and the self-replication system,
but it could not evolve if the system initially consisted of the
self-replication system only). In the compartment model without complex
formation, Dp evolved when the diffusion of molecules across compartment
boundaries was enabled and the system included an explicitly predefined
parasite. However, it has to be kept in mind that assuming instantaneous
replication does not completely remove the trade-off between template and
catalyst in RNA-like replicators because, if a catalyst replicates other
templates, this leads to local depletion of the resource under finite diffusion,
decreasing the chance of the catalyst itself being replicated. This
interpretation was supported by analysis of the compartment model in which the
complex formation was removed and compartment boundaries were immobilized. In
this model, when
(diffusion), which
was the value used in the compartment models to achieve a relatively well-mixed
condition in the internal replicator system, the self-replication system evolved
towards decreasing RNA replication activity. Thus, assuming instantaneous
replication is not a perfect control experiment with respect to the trade-off
between template and catalyst. Nevertheless, the finding that Dp did not evolve
in the model without complex formation under the conditions considered in the
original models (i.e. no difference between DNA and RNA other than the
presence-absence of catalytic ability and no diffusion across compartment
boundaries) implies the importance of the trade-off enhancement by complex
formation for the evolution of DNA.
Discussion
It has been customarily assumed that the evolution of DNA should be explained by some advantageous properties of DNA as template, e.g., the higher stability of DNA compared to RNA. However, the current study shows that, in RNA-like replicator systems, the lack of catalytic activity in DNA-like molecules in itself can give rise to a selection for the emergence and fixation of DNA molecules. In the surface model, DNA allowed the evolution of the division of labor between the template (DNA) and the catalyst (RNA), which mitigated the adverse effect of parasites arising from the trade-off between templates and catalysts. In the compartment model, DNA could cause the retardation of the evolutionary deterioration of the internal replicator system of compartments by eliminating the advantage of RNA molecules being non-catalytic, i.e. evolving into parasites, which originated from the aforementioned trade-off. This retardation required the presence of transcription and the absence of reverse transcription. In other words, the information must flow from DNA-like molecules (template) to RNA-like molecules (catalyst) but not vice versa. This unidirectionality of the information flow is also a form of division of labor between the template and the catalyst. Therefore, both models effectively yield the same conclusion: DNA can nullify the disadvantage of RNA functioning as a catalyst—and hence the advantage of parasites—through establishing the division of labor between the template (DNA) and the catalyst (RNA). This advantage can more than compensate for the disadvantage due to the reduced efficiency of multiplication caused by the increased complexity of the replication cycle.
Although the transcription system avoids the trade-off between template and catalyst through establishing the division of labor between the template and the catalyst, it generates the trade-off between replication and transcription whereby a template (DNA) must spend a part of its lifetime being transcribed in order to produce catalysts (RNA), and during these times, the template cannot be replicated. The latter trade-off causes a selection pressure for templates to evolve towards decreasing the rate of transcription in exchange for increasing the rate of replication. In the present models, however, this selection pressure does not affect the evolution because the models do not allow templates to evolve their affinities towards Rp and Dp so as to differentiate between replication and transcription. To examine the effect of the replication-transcription trade-off on the evolution of DNA, we slightly modified the models to allow templates to distinguish between Rp and Dp (see Text S1 for details). The results showed that, although the effect of the trade-off between replication and transcription was non-negligible as the models exhibited the evolution of templates to reduce transcription, it was not large enough to qualitatively change the main results obtained with the original models. This result corresponds to a well-known fact from the group selection theory [43] that the condition required for the evolution of “weak altruism” (the action that is beneficial to the individual that performs it but gives greater benefits to the other individuals of the same “group”) is much less strict than the condition required for the evolution of “strong altruism” (the action that gives no benefit but a cost to the performer of the action). Thus, everything else being equal, the selection against strong altruism is stronger than the selection against weak altruism. Indeed, in the trade-off between template and catalyst, when a catalyst replicates templates, this gives no benefit to the catalyst itself and so corresponds to strong altruism. By contrast, in the trade-off between replication and transcription, when a template (DNA) is transcribed, this gives a benefit not only to the other templates but also to the template that is transcribed through the production of catalysts, hence weak altruism. Therefore, the suppression of the template-catalyst trade-off should more than compensate for the generation of the transcription-replication trade-off.
Although the order of appearance of different types of biopolymers during primordial evolution is still debated [44], [45], the universality of the translation machinery in all domains of life suggests that proteins most likely evolved in the RNA world before DNA (e.g., [46]). If RNA molecules functioned predominantly as templates in the RNA-protein world, the division of labor between templates and catalysts was established before the emergence of DNA. The basic tenet of the present study, namely, that dedicated templates (DNA) can release catalysts (RNA) from the trade-off between template and catalyst through establishing the division of labor between templates and catalysts, seems to be also applicable to the evolution of proteins in the RNA world. Indeed, the relegation of the catalytic functions to proteins so that RNA molecules turn into dedicated templates might achieve an effect similar to the effect of the separation of functions between DNA (template) and RNA (catalyst) in the present models. In the RNA-protein world, the trade-off between RNA replication and RNA translation becomes relevant as the same RNA molecule is used both for replication and for translation. However, this trade-off implies weak altruism as opposed to the strong altruism implicit in the template-catalyst trade-off, so the separation of functions is likely to be beneficial for the replicator system (see above).
The question arises whether there could be advantages associated with the emergence of DNA (irrespective of its chemical properties) in the RNA-protein world. In this case, DNA can release RNA from the trade-off between replication and translation so that RNA can be dedicated to translation. This effect might cause a substantial reduction in the selective advantage of parasitic templates because the suppression of RNA replication due to translation would be more severe than the suppression of DNA replication due to transcription assuming equal rates of protein production (the rate of DNA transcription can be smaller than that of RNA translation, so DNA transcription would impede DNA replication less than RNA translation impedes RNA replication). Moreover, if a high rate of protein production is selectively advantageous to the system, releasing RNA from the replication function and so allowing it to be dedicated to translation might be a substantial advantage to the system, causing strong selection pressure for the evolution of DNA.
The present models assume that Dp can emerge from Rp through a one-step mutation.
This simplification was made because the central question of the current study was
whether there could be any selective advantage for an RNA-based evolving system to
produce DNA-like molecules independent of specific nucleic acid chemistry. It
appears that our main conclusion on the existence of such a selective advantage
should be valid independent of specific assumptions on the mutation. To further
assess the validity of this conclusion, we also investigated the models under two
different assumptions on the effects of mutations. Under the first assumption, the
distinction between Rp and Dp was continuous. Each replicase is assigned two
parameters that determine the product specificity: and
, the rate constants of RNA and DNA production, respectively.
The ratio
assumed non-negative values with the constraint that
and could be modified by mutations (in the original model,
this ratio was either 0 or infinite). Under this assumption, DNA evolved in both the
surface model and the compartment model. The population of catalysts consisted of
only one species that catalyzed both RNA and DNA production. Moreover, the surface
model displayed the evolution of both product and template specificity toward DNA:
and
. In contrast, the
compartment model displayed only the evolution of template specificity toward
DNA—
and
, probably because of
the between-compartment selection that tends to increase the number of catalysts
(RNA) within compartments. Under the second assumption on the mutation, a replicase
was either Rp or Dp as in the original model, but there was a continuous range of
catalytic capacity associated with each polymerase:
assumed a value
between 0 and 1 and could be modified by mutations. When Rp mutated into Dp (through
a one-step mutation), the value of
was set to
. When
, the surface model
showed qualitatively the same result as the original model, whereas the compartment
model did not display the evolution of DNA—a result indicating the greater
robustness of the results with the surface model. To summarize, these experiments
with (partially) continuous mutation effect models revealed the evolution of DNA and
so appear to validate our main conclusion on the intrinsic advantage of the
template-catalyst separation.
Kaneko and Yomo [47] proposed that molecules must be a minority to display hereditary properties in a protocell (see [47], for the exact meaning of “hereditary properties”). In their study, it is conceived that the hereditary molecule emerges not as a result of Darwinian evolution due to the selective advantage it confers to a protocell but as a physical consequence of factors that are not necessarily related to the hereditary properties (such as higher-order catalysis and kinetic asymmetry). By contrast, in the present compartment model, DNA evolved due to a selective advantage conferred to the respective protocells (compartments). Moreover, DNA molecules constituted 30–40% of the total population of internal replicators and so were not a small minority.
Zintzaras et al [48] investigated the consequence of the trade-off between catalytic activity and template affinity to RNA polymerase in ribozymes and proposed that the complete absence of competition between two species of ribozymes could lead to the evolutionary divergence where one species functions slightly more efficiently as a catalyst and the other functions more efficiently as a template. Despite the superficial similarity, this form of divergence crucially differs from the division of labor between template and catalyst discussed here. In the model of Zintzaras et al., the two species were not templates for each other, so both ribozymes must function as templates to transmit information to subsequent generations. In the present models, DNA allows RNA (ribozyme) to not function as template at all and releases it from the template-catalyst trade-off. In addition, the division of labor between template and catalyst evolved without assuming reduced competition between replicators.
We previously noted an interesting difference between the concepts of genotype as applied to modern cells and protocells conceived as vesicle-like compartments containing replicators [35]. A common assumption is that the genotype of an individual is static on the timescale of an individual's lifetime. Although valid for modern cells, this assumption might be invalid for the protocell because the internal replicator system of a protocell—the population of which can be viewed as the genome—undergoes evolutionary deterioration over time comparable to the lifetime of a compartment due to the within-compartment selection [35]. The current study has shown that the division of labor between template and catalyst can prevent such rapid evolutionary deterioration. The evolutionary stabilization of the internal replicator system caused by DNA can be considered a step toward the evolution of the modern-type, relatively stable genotype in protocells.
Supporting Information
Text S1.
The text contains notes to the main text, the implementation details of the surface model and the compartment model, the ODE models and the description of the models that take account of the trade-off between replication and transcription.
https://doi.org/10.1371/journal.pcbi.1002024.s001
(PDF)
Author Contributions
Conceived and designed the experiments: NT PH. Performed the experiments: NT. Analyzed the data: NT. Contributed reagents/materials/analysis tools: NT. Wrote the manuscript: NT PH EVK. Interpreted the results: NT PH EVK.
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