Critical phenomena in evolutionary dynamics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 118-128).This thesis consists of five essays on evolutionary dynamics. In Chapters 1 and 2, we study the evolution of trust from the perspective of game theory. In the trust game, two players have a chance to win a sum of money. The "investor" begins with one monetary unit. She gives a fraction of that unit to the "trustee." The amount she gives is multiplied by a factor greater than one. The trustee then returns a fraction of what he receives to the investor. In a non-repeated game, a rational trustee will return nothing. Hence, a rational investor will give nothing. In behavioral experiments, however, humans exhibit significant levels of trust and trustworthiness. Here we show that these predispositions may be the result of evolutionary adaptations. We find that when investors have information about trustees, investors become completely trusting and trustees assume the minimum level of trustworthiness that justifies that trust. "Reputation" leads to efficient outcomes as the two players split all the possible payoff from the game, but the trustee captures most of the gains: "seller" reputation helps "sellers" more than it helps "buyers." Investors can capture more of the surplus if they are collectively irrational: they can demand more from trustees than is rational, or their sensitivity to information about trustees can be dulled. Collective investor irrationality surprisingly leads to higher payoffs for investors, but each investor has an incentive to deviate from this behavior and act more rationally. Eventually investors evolve to be highly rational and lose the gains their collective behavior had earned them: irrationality is a public good in the trust game. Next, we describe two evolutionarily robust mechanisms for achieving efficient outcomes that favor the investor while still compensating trustees for the value of their agency. In the first mechanism, "comparison shopping," investors compare limited information about various trustees before committing to a transaction. Comparing just two trustees at the beginning of each interaction is enough to achieve a split desirable to the investor, even when information about trustees is only partially available. In the other mechanism, a second layer of information is added so that trustees sometimes know what rates of return investors desire. The trust game then becomes similar to an ultimatum game, and positive investor outcomes can be reached once this second type of information is sufficiently pervasive. In Chapter 3, we study the origin of evolution and replication. We propose "prelife" and "prevolution" as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting "prevolutionary dynamics" have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this "originator equation" gives the classical selection equation. In the other limit, we obtain "prelife." There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to "reversals" in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence. We continue our study of replication in Chapter 4, taking a more concrete, chemistry-oriented approach. Template-directed polymerization of nucleotides is believed to be a pathway for the replication of genetic material in the earliest cells. Adding template-directed polymerization changes the equilibrium structure of prelife if the rate constants meet certain criteria. In particular, if the basic reproductive ratio of sequences of a certain length exceeds one, then those sequences can attain high abundance. Furthermore, if many sequences replicate, then the longest sequences can reach high abundance even if the basic reproductive ratios of all sequences are less than one. We call this phenomenon "subcritical life." Subcritical life suggests that sequences long enough to be ribozymes can become abundant even if replication is relatively inefficient. Our work on the evolution of replication has interesting parallels to infection dynamics. Life (replication) can be seen as an infection of prelife. Finally, in Chapter 5, we study the emergence of complexity in early biochemical systems. RNA biochemistry is characterized by large differences in synthetic yield, reactivity to polymerization, and degradation rate, and these properties are believed to result in pools of highly homogeneous, low complexity sequences. Using simulations of prebiotic chemical systems, we show that template-directed ligation and the mass-action effect of sequence concatenation increase the average complexity and population diversity in pools of RNA molecules. We verify these theoretical results with experiments showing that ligation does enhance complexity in real RNA systems. We also find a correlation between predicted RNA folding energy and complexity, demonstrating the functional importance of this measure. These results contrast with previous assumptions that fine-tuning of the system is the only way to achieve high complexity. Our work shows that the chemical mechanisms involved in nucleic acid polymerization and oligomerization predispose the RNA world towards a diverse pool of complex, energetically stable sequences, setting the stage for the appearance of catalytic activity prior to the onset of natural selection.by Michael L. Manapat.Ph.D

The Basic Reproductive Ratio of Life

Template-directed polymerization of nucleotides is believed to be a pathway for the replication of genetic material in the earliest cells. We assume that activated monomers are produced by prebiotic chemistry. These monomers can undergo spontaneous polymerization, a system that we call “prelife.” Adding template-directed polymerization changes the equilibrium structure of prelife if the rate constants meet certain criteria. In particular, if the basic reproductive ratio of sequences of a certain length exceeds one, then those sequences can attain high abundance. Furthermore, if many sequences replicate, then the longest sequences can reach high abundance even if the basic reproductive ratios of all sequences are less than one. We call this phenomenon “subcritical life.” Subcritical life suggests that sequences long enough to be ribozymes can become abundant even if replication is relatively inefficient. Our work on the evolution of replication has interesting parallels to infection dynamics. Life (replication) can be seen as an infection of prelife.MathematicsOrganismic and Evolutionary Biolog

Originator Dynamics

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose “prelife” and “prevolution” as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting “prevolutionary dynamics” have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this “originator equation” gives the classical selection equation. In the other limit, we obtain “prelife.” There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to “reversals” in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.MathematicsOrganismic and Evolutionary Biolog

Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences

During the origin of life, the biological information of nucleic acid polymers must have increased to encode functional molecules (the RNA world). Ribozymes tend to be compositionally unbiased, as is the vast majority of possible sequence space. However, ribonucleotides vary greatly in synthetic yield, reactivity and degradation rate, and their non-enzymatic polymerization results in compositionally biased sequences. While natural selection could lead to complex sequences, molecules with some activity are required to begin this process. Was the emergence of compositionally diverse sequences a matter of chance, or could prebiotically plausible reactions counter chemical biases to increase the probability of finding a ribozyme? Our in silico simulations using a two-letter alphabet show that template-directed ligation and high concatenation rates counter compositional bias and shift the pool toward longer sequences, permitting greater exploration of sequence space and stable folding. We verified experimentally that unbiased DNA sequences are more efficient templates for ligation, thus increasing the compositional diversity of the pool. Our work suggests that prebiotically plausible chemical mechanisms of nucleic acid polymerization and ligation could predispose toward a diverse pool of longer, potentially structured molecules. Such mechanisms could have set the stage for the appearance of functional activity very early in the emergence of life

Inhibition of Bacterial Conjugation by Phage M13 and Its Protein g3p: Quantitative Analysis and Model

Conjugation is the main mode of horizontal gene transfer that spreads antibiotic resistance among bacteria. Strategies for inhibiting conjugation may be useful for preserving the effectiveness of antibiotics and preventing the emergence of bacterial strains with multiple resistances. Filamentous bacteriophages were first observed to inhibit conjugation several decades ago. Here we investigate the mechanism of inhibition and find that the primary effect on conjugation is occlusion of the conjugative pilus by phage particles. This interaction is mediated primarily by phage coat protein g3p, and exogenous addition of the soluble fragment of g3p inhibited conjugation at low nanomolar concentrations. Our data are quantitatively consistent with a simple model in which association between the pili and phage particles or g3p prevents transmission of an F plasmid encoding tetracycline resistance. We also observe a decrease in the donor ability of infected cells, which is quantitatively consistent with a reduction in pili elaboration. Since many antibiotic-resistance factors confer susceptibility to phage infection through expression of conjugative pili (the receptor for filamentous phage), these results suggest that phage may be a source of soluble proteins that slow the spread of antibiotic resistance genes