4.1. The Number of Species Is Essential for High Growth Rate
Cells with diverse species can increase their growth rates by utilizing a greater variety of resources. This mechanism explains the advantage of increasing the number of molecular species. However, how the catalytic network expands its diversity over generations is not fully explored in our previous publication [20
Before investigating the process of diversification, we first noted that the number of molecular species is essential to convert a greater variety of resources for cell growth. The network structure itself is not necessarily essential to the growth rate as long as every species has a catalyst for its replication.
When resources are abundant, the diversity of intracellular components is decreased to realize a higher growth rate. Thus, the catalytic cycle is typically composed of a minimum three to four species. If there are multiple disjoint cycles, the cells select only a single cycle with the highest replication rate and exclude the others. Accordingly, all the nodes are connected as a single network.
When resources are limited, a single connected network itself is not essential for high growth rate. To demonstrate this, we consider a simple model in Figure 3
A. We consider two types of cells. Both types are composed of four molecular species. In type 1, the molecular species form two sets of mutually catalytic cycles. In type 2, the molecular species form a single cycle. The other parameters are identical for the two types. Thus, type 1 has two independent cycles and type 2 has a single network. For this simple illustration, the direct mutual catalytic relation (
) is allowed here, instead of the three-component loop in the previous section. The same argument as presented here is applied for comparison between the two disconnected three-component hypercycles and one six-component loop.
The growth rates of the two types are equal when resources are limited. Because the number of molecular species is essential for the growth rate, the structure of the catalytic network is not relevant. Thus, there is no selective advantage for a single joint network. In fact, survival of cell types is by chance, in direct competition between the two types (Figure 3
B). Even the stochastic reactions result in the dominance of the population by either type, no difference is observed in selection preference between the two types. The result of this simple model suggests that the joint network is not an absolute requirement for higher growth rate.
4.2. Cells Diversify Their Molecular Species by Adding Species One by One to the Existing Network
As shown in the previous Section 4.1
, a single joint network is not an absolute requirement for the growth rate. For example, in a huge variety of catalytic networks, one may naively expect that a set of disjoint networks can have the same growth rate as the joint network in Figure 2
B. However, it is generally observed as a result of diversification in which all the nodes (species) are connected (Figure 2
We argue here that the joint network is obtained as an outcome of the evolutionary pathway to diversify the molecular species. In our simulation, a novel molecular species appears by errors in replication (“mutation”). The appearance of a new species by error is not sufficient for it to be fixed. The species has to increase its copy number. Otherwise, the species is diluted out by the growth of the cell.
To successfully increase its copy number, the new species should have its catalyst in the cell. Fixation of the new species is then possible if the remaining species can catalyze this new species. Thus, the catalytic network diversifies its molecular species so that it connects the new species to the existing catalytic network.
To attest this, we perform a simulation when the resources are limited (). In the initial condition of the simulation, each of the cells has only three molecular species , and . The three species form the minimum hypercycle: , , and .
From the minimum hypercycle, we trace the content of cells as shown in Figure 4
to examine how the cells diversify their molecular species. At cell division, the contents of a cell are taken over by the two daughter cells (Figure 4
A). By coloring the daughter cells in red, we identify a single ancestor cell in the initial condition from which all the
cells at the final stage are originated. In Figure 4
B, all the cells are marked in red by the division events 3500. Here we also trace the content of cells along a branch of such progeny cells from the ancestral cell (up to the 2500 division events; colored blue in Figure 4
A shows the number of major species in the cells along the branch. Other than the initial three molecular species (
), the major species is defined such that its copy number is greater than ten. The total species (magenta) indicates the number of such species. It increases from the beginning and eventually reaches a steady-state value (≈15 of this value of D
). By looking at the catalytic network formed by the major species, we also show the number of host (red), sub-host (green), and parasite (blue) species. The host species indicate the member of an auto-catalytic hypercycle. Other than the host species, the sub-host species are defined such that they catalyze the replication of at least one other species in the major species, but do not belong to any auto-catalytic hypercycle. The parasite species indicate that their replication is catalyzed by other species, but they do not catalyze any other in turn.
Furthermore, the major molecular species in a cell are displayed in Figure 5
B. Initially, the three species 1, 2, and 3 are present (hereafter, we denote the species by its number i
, instead of
) and form a minimum hypercycle. Thus, the three species work as hosts and are marked by red points. Shortly thereafter, the species 17 appears as a parasite (with a blue point). Then, the species 106 also appears as a parasite. The third species 8 is fixed as a sub-host (with a green point) as it catalyzes the replication of 17. Simultaneously, the species 106, originally a parasite species, changes its role to a sub-host because it catalyzes the replication of 8 (the color of the points at species 106 changes from blue to green by the appearance of the species 8 in Figure 5
As the diversity increases by fixing the parasite and sub-host species, a change in host species occurs. By the emergence of species 161, several species change their role to host species (at around 500 division events). Even though the initial three species are almost simultaneously lost from the cells, the number of host species increases by successive transformation to host species from parasites. Then, most of the new species afterward are fixed and keep their role (shown with red and blue arrows), whereas some of them can be lost.
At the initial stage, all the new species start as a parasite or a sub-host species (as shown with magenta and light-blue arrows). In fact, most of the new species initially emerged as parasites. To start as a host species, the new species has to catalyze the replication of existing host species. However, the diversity of the host species is initially low due to which the probability of the new species catalyzing the host species is quite low. Hence, the new species has to start as a parasite species to the existing host species, or as a parasite to a sub-host species, i.e., a parasite to the original parasite species.
One can roughly estimate the probability with which a new species can be initially introduced as a host species. The catalytic reaction path is assigned with probability p (which was fixed at 0.1) for each pair of and . Thus, the new species can catalyze one of the remaining host species with a probability on average (the factor 1/2 is added because only one of the two reactants works as a catalyst). By denoting the number of remaining host species as , the probability that the new species can catalyze at least one host species is estimated as .
After fixation of species 161 in Figure 5
B, the number of host species (
) was approximately 5 or 6 between the division events 600 and 900. Thus, the probability
is estimated as 0.25–0.3. In fact, one species (78) is introduced as a host whereas three species (5, 85, 18) are introduced as parasites. Thereafter, fixation of 102 further increases the number of host species to eight, which increases the probability of the appearance of host species later.
To further visualize the process of diversification, we show the effective catalytic network by coloring the existing molecular species in Figure 6
. The underlying catalytic network is formed by 23 potential molecular species, which appeared at some generation in Figure 5
B. Here, the absent species at each generation are represented by white nodes.
As explained above, the new species initially appear and work as a parasite or sub-host species (Figure 6
(1) to (3)). As diversity increases, several species turn to be host species and a change of the “core” network occurs [(4)]. With a successive increase in host species, the molecular species further diversify and a complex joint network evolves [(5) to (6)].
From this example, one can see that the cells fix their new species one by one to simultaneously meet the requirements of growth and diversification. This evolutionary constraint suggests a potential of “parasitic” molecules. Typically, such species are considered cheaters because they are not beneficial for maintaining the “core” network. On the other hand, the species could be considered a stepping-stone toward diversification when the resources are limited. Here, we explained how diversification progresses using an example. This process of evolution through parasites is general as far as we checked five examples in the present simulation. We also show another example in a Supplementary figure.
Here, the emergence of a new species is less plausible in a disjoint network. Such fixation requires construction of another catalytic cycle from scratch. To keep the number of the new molecules against decreases by cell dilution, another mutation that catalyzes it is necessary, which hardly occurs. Then, the mechanism of connecting the species is more plausible than constructing an auto-catalytic cycle from scratch. In other words, a single connected network is more evolutionarily achievable than disjoint networks, even if their fitness (growth rate) is identical.