# Chemical games and the origin of life from prebiotic RNA

From bacteria to vertebrates, life — as we know it today — relies on complex molecular interactions, the intricacies of which science has not fully untangled. But for all its complexity, life always requires two essential abilities. Organisms need to preserve their genetic information and reproduce.

In our own cells, these tasks are assigned to specialized molecules. DNA, of course, is the memory store. The information it encodes is expressed into proteins via messenger RNAs.Transcription (the synthesis of mRNAs from DNA) and translation (the synthesis of proteins from mRNAs) are catalyzed by polymerases necessary to speed up the chemical reactions.

It is unlikely that life started that way, with such a refined division of labor. A popular theory for the origin of life, known as the RNA world, posits that life emerged from just one type of molecule: RNAs. Because RNA is made up of base-complementary nucleotides, it can be used as a template for its own reproduction, just like DNA. Since the 1980s, we also know that RNA can act as a self-catalyst. These two superpowers – information storage and self-catalysis – make it a good candidate for the title of the first spark of life on earth.

The RNA-world theory has yet to meet with empirical evidence, but laboratory experiments have shown that self-preserving and self-reproducing RNA systems can be created in vitro. Little is known, however, about the dynamics that governed pre- and early life. In a recent paper, Yeates et al. (2016) attempt to shed light on this problem by (1) examining how small sets of different RNA sequences can compete for survival and reproduction in the lab and (2) offering a game-theoretical interpretation of the results.

### RNA cocktails

The Azoarcus tRNA intron, found in the nitrogen-fixing Azoarcus bacteria, can be split into two or more sequences that can spontaneously reassemble in a controlled environment. Yeates et al. (2016) make use of this property by splitting the intron into two pieces, labelled WXY (a polymer made up of three chains W, X, and Y) and Z (single-chain). Modifying one of the first or last three nucleotides of the W chain results in a different WXY genotype. The authors generate 16 such genotypes and observe their catalytic rates when combined with Y, alone and alongside other WXY variants.

Yeats et al choose the autocatalytic rate constant parameter as the measure of the contribution of RNA-catalysis to the reaction. Cross-assembly rates for genotype pairs are observed via doping: a genotype in relatively large concentration is combined with another genotype in relatively small concentration (the dopant). Both genotypes are used as a dopant for each other, resulting in the following matrix of autocatalytic rate constant parameter for each pair:

 Genotype 1 Genotype 2 Genotype 1 a = rate when genotype 1 is the only WXY reactant b = rate with both genotypes, genotype 1 is the dopant ( [genotype 1] <<<  [genotype 2 ]) Genotype 2 c = rate with both genotypes, genotype 2 is the dopant ( [genotype 2] <<<  [genotype 1]) d = rate when genotype 2 is the only WXY reactant

I lay out the experimental details because the a, b, c and d measures in the above table are used throughout the paper. Note that the authors do not measure cross assembly rates for all of the 120 possible two-genotype combinations, choosing instead “a few that would include competitions between both rapid and slow self-assembling RNAs”.

Yeates et al. pick out seven genotype pairs representative of various a, b, c, d patterns (e.g. a >b > d > c) and run new contests for several bursts, starting with a fresh solution, diluting the contest solution and adding to it a mixture of X and WXY variants – in similar concentrations this time – at 5-minute intervals, for 8 bursts.

In parallel, the authors construct an ordinary differential equation (ODE) system to model the experiment,  taking into account the handy fact that RNA replication rate linearly depends on abundance. This model is a continuous approximation of serial dilution:

With x as the frequency of genotype 1 and y as the frequency of genotype 2.

\begin{aligned} \dot{x} & = ax + by - \theta x \\ \dot{y} & = cx + dy - \theta y \end{aligned}

where $\theta = (a+c)x + (b+d)y$ is the dilution term which ensures that $\dot{x} + \dot{y} = 0$ so that probability is conserved. It is used to account for the fact that the solution is diluted at each burst.

Yielding the equilibrium proportion:

$x^* = \frac{(a - 2b - d + \sqrt((a-d)^2 + 4bc))}{2(a+c-b-d)}$

Yeates et al’s ODE model is a good fit: given a, b, c, and d obtained from the single-round contests, the model accurately predicts the outcome of all contests.

Four patterns emerge: selfishness, such that the rates of self-assembly for both genotypes are greater than the rates of cross-assembly; dominance, where a > c and b > d; cooperation, such that cross-assembly outpaces self-assembly for both genotypes; and last but perhaps most interesting, counter-dominance, where the genotype with the lower self-assembly rate ends up dominating the faster self-assembling variant (a >d , c > a and d > b).

In previous posts, Artem touched upon the challenges facing experimental scientists trying to uncover replicator dynamics in the petri dish. He highlighted the importance of restricting definitions of fitness to what can be measured, and of trying to distinguish the role of the medium from that of interactions with other players. He also deplored that experimental data is often left unexplored, without models to fit the data. Yeates et al. clearly separate what Artem calls “medium-mediated” fitness from interaction effects. They also work out a fairly convincing EGT model to the data, as the following explains.

### RNA dynamics and game theory

Chemical games often consider the rate at which molecules replicate. In particular, the replicator equation is a fixed-strategy, non-innovative system of ordinary differential equations wherein the replication rate depends on the population frequencies. In the present context, the datum of interest is not replication but assembly (WXY + Z -> WXYZ), yet the framework is similar. To look at the experiment with the lens of game theory, Yeates et al. draw an analogy between their catalytic rate matrices and payoff matrices. Each cell of the catalytic rate matrix can be interpreted as the payoff to the row and column genotypes when both interact.

Take the “counter-dominance” pattern, where genotype 1 (G1) has a higher self-assembly rate than genotype 2 (G2): a > d. In the corresponding matrix, c > a, meaning that G2 can boost G1+Z assembly. However, d > b, meaning that the payoff to G2 for “helping itself” exceeds that of interacting with G1. Rings a bell? It’s a prisoner’s dilemma! Here, the strategy that would benefit the group (i.e., yield the highest overall assembly rate) is selected against at the individual level.

Interestingly, Yeates et al were also able to reproduce the well-known “rock-paper-scissors” (RPS) pattern, in which three strategies successively become dominant. In RPS, pitting any of the three strategies against any of the other two would yield a clear winner. Adapting the serial dilution experimental to three genotypes, the authors were able to generate an instance rock-paper-scissors dynamics in the laboratory, as well as successfully predict equilibrium catalytic rates of the RNA variants with ODEs.

Yeates et al. take an original approach to biological game theory, adapting a common model, the replicator equation, to a new problem. The problem in question is of tremendous significance: it concerns the dynamics that led to life, in the hot soup our planet was 4 billion years ago. How did isolated organic molecules come together to form the first molecular communities? Cooperation, selfishness, dominance – those very dynamics that underpin economic decisions, social structures and board games – may have played just as important a role in the rise of life.

Yeates JA, Hilbe C, Zwick M, Nowak MA, & Lehman N (2016). Dynamics of prebiotic RNA reproduction illuminated by chemical game theory. Proceedings of the National Academy of Sciences of the United States of America, 113 (18), 5030-5 PMID: 27091972