RNA World Modeling: A Comparison of Two Complementary Approaches

Abstract

The origin of life remains one of the major scientific questions in modern biology. Among many hypotheses aiming to explain how life on Earth started, RNA world is probably the most extensively studied. It assumes that, in the very beginning, RNA molecules served as both enzymes and as genetic information carriers. However, even if this is true, there are many questions that still need to be answered-for example, whether the population of such molecules could achieve stability and retain genetic information for many generations, which is necessary in order for evolution to start. In this paper, we try to answer this question based on the parasite-replicase model (RP model), which divides RNA molecules into enzymes (RNA replicases) capable of catalyzing replication and parasites that do not possess replicase activity but can be replicated by RNA replicases. We describe the aforementioned system using partial differential equations and, based on the analysis of the simulation, surmise general rules governing its evolution. We also compare this approach with one where the RP system is modeled and implemented using a multi-agent modeling technique. We show that approaching the description and analysis of the RP system from different perspectives (microscopic represented by MAS and macroscopic depicted by PDE) provides consistent results. Therefore, applying MAS does not lead to erroneous results and allows us to study more complex situations where many cases are concerned, which would not be possible through the PDE model.

Keywords: RNA world; multi-agent systems; partial differential equations.

Figure 1

For y < yC, the system behaves like a pendulum with friction; it oscillates around the equilibrium, but these oscillations become weaker over time. Eventually, y becomes stable.

Figure 2

With y being past the critical point, the Q function becomes positive, thus increasing the velocity. y diverges to infinity, which means that the replicases die off (y is the inverse density of replicases).

Figure 3

The waves formed in multi-agent systems. They represent various populations in different phases of the cycle. Replicases are gray, whereas parasites have colors denoting their reaction rate, with replicases ranging from red (very high) to yellow, green, blue, and purple (very low) [41].

Figure 4

Waves for the diffusion constant equal to 5 and mutation rate equal to 0.1. Replicases are gray; parasites are purple.

Figure 5

Waves for the diffusion constant equal to 5 and mutation rate equal to 0.2. Replicases are gray; parasites are purple.

Figure 6

Waves for the diffusion constant equal to 10 and mutation rate equal to 0.1. Replicases are gray; parasites are purple.

Figure 7

A well-mixed system, where replicases and parasites peacefully coexist. Replicases are gray; parasites are blue.

Figure 8

The evolution of y (the inverse of the number of replicases multiplied by 10,000 for readability) over time is very similar to the results obtained from Equation (46). The value of y begins to oscillate, but this oscillation is quickly slowed down.

Figure 9

The evolution of aP at one particular point in space. This oscillated between values of $0.4$ and $0.6$.

Figure 10

The waves formed in differential equation simulation, when inequality (27) is not fulfilled. Dark areas are devoid of replicases, whereas white areas have a high density of them.

Figure 11

Scenario 12: the density of replicases and parasites. Replicases dominated the system because parasites had a lower reaction rate.

Figure 12

Scenario 13: the densities of replicases and parasites were equal, so the two graphs actually overlap.