Schuster et al., J Biol Phys 34:1–17 (2008) Hadas Zur Computational Game Theory Project 2012

Introduction Game Theory and Biochemistry Game Theory and Biophysics Discussion My Project: HGT Game

 Based on assumption that biological systems are optimized biological systems are optimized during evolution during evolution  In line with Darwin’s theory of survival of the fittest of survival of the fittest  Traditional optimization is insufficient for understanding insufficient for understanding biological evolution biological evolution  Evolution is nearly always co-evolution co-evolution

By evolving towards optimal properties Organisms change their environment Which involves, for e.g. competing organisms This, in turn, affects the optimum

 Organisms competing against each other can be considered as players in the sense of game theory  Prisoner's Dilemma: T > R > P > S  Snowdrift Game: T > R > S > P  This changes the situation fundamentally and leads to persistence of cooperation and leads to persistence of cooperation

 Two drivers caught in a blizzard and trapped on either side of a snowdrift  They can either start shovelling (cooperate) or remain in the car (defect)  If both cooperate, they have the benefit b of getting home while sharing the labour c. Thus, R = b - c/2  If both defect, they do not get anywhere and P = 0  If only one shovels, they both get home but defector avoids the labour cost and gets T = b, whereas the cooperator gets S = b – c  If costs are high (2b > c > b > 0), these payoffs recover the Prisoner's Dilemma  By contrast, if b > c > 0, the payoffs generate the snowdrift game, in which the best action depends on the co-player.  This leads to stable coexistence of cooperators and defectors

 ESS is a generalization of NE  A strategy played by a population is evolutionarily stable if it cannot be evolutionarily stable if it cannot be invaded by a rare mutant playing invaded by a rare mutant playing another strategy another strategy  Note that these strategies can be mixed  Each ESS is a Nash equilibrium, but not vice versa  The only ESS of the snowdrift game is mixed.  The only ESS of the PD is the pure strategy of “defecting”

 When two species compete for the same substrate, a typical game- theoretical situation arises  Fitness of either organism depends not only on its own strategy (pathway usage ) but also on the other because both strategies affect the common substrate pool (pathway usage ) but also on the other because both strategies affect the common substrate pool

 Dynamics of 2 competing populations choosing between 2 different pathways can be described: S, substrate concentration, v, input rate of substrate, y, ATPover-substrate yield, N, population density, J, rate of substrate consumption, and d, death rate. S, substrate concentration, v, input rate of substrate, y, ATPover-substrate yield, N, population density, J, rate of substrate consumption, and d, death rate. c denotes the proportionality constant connecting growth rate with ATP formation rate. c denotes the proportionality constant connecting growth rate with ATP formation rate.  The question arises as to what the relevant payoff is

 A payoff matrix with order relation T > R > P > S can be established  Thus, the conditions for a Prisoner’s Dilemma are fulfilled  Although it would be best for both players to opt for respiration (a cooperative strategy), they are tempted to switch to respiro-fermentation(a selfish strategy, PD)  As this applies to both, they end up both using the selfish strategy both using the selfish strategy  This is the NE and ESS of the game

 Assuming that one tree is taller by h, this gives it an advantage in by h, this gives it an advantage in productivity of p productivity of p  The dashed straight lines have the slope p/h, i.e., they depict the gain slope p/h, i.e., they depict the gain in productivity by growing taller. in productivity by growing taller.  The solid straight lines represent the net effect. the net effect.  The evolutionarily stable height, h*, is reached when this net effect is 0 is reached when this net effect is 0 due to investing more into supporting due to investing more into supporting structures, i.e., when the straight line structures, i.e., when the straight line is horizontal. is horizontal.  Clearly, h* is larger than the optimal height, hopt height, hopt

 We have discussed several examples of relevant applications of game theory to biochemistry and biophysics  A difficult issue in the study of optimality properties of biological organisms is to find the relevant optimization principle  The trade-off between rate and yield of ATP production on the basis of evolutionary game theory reveals that paradoxically users’ tendency to maximize their fitness actually results in a decrease of their fitness  The rationality of microorganisms does not stem from reason but from a “choice” of strategies, which can be treated by the same mathematical methods as a deliberate choice by rational beings  An interesting question is whether also interactions between proteins, genes and/or other structures on the molecular level can be described by game theory

Three major steps: 1. Initiation: Properties of the 5’UTR, folding energy, ATG context 2. Elongation: The speed is related to concentrations of tRNA molecules (but also to additional features) Termination

 Codon usage bias refers to differences in the frequency differences in the frequency of occurrence of synonymous of occurrence of synonymous codons in coding DNA. codons in coding DNA.  A codon is a series of three nucleotides (triplets) that nucleotides (triplets) that encodes a specific amino acid encodes a specific amino acid residue in a polypeptide chain residue in a polypeptide chain or for the termination of or for the termination of translation (stop codons) translation (stop codons)  There are 64 different codons (61 codons encoding for amino acids (61 codons encoding for amino acids plus 3 stop codons) plus 3 stop codons) but only 20 different translated but only 20 different translated amino acids amino acids

 HGT, a process in which one organism incorporates genetic material from another incorporates genetic material from another without being its offspring without being its offspring  HGT is a major force in bacterial evolution  Bacteria are under a strong selection to optimize their growth rate by improving optimize their growth rate by improving features related to their codon usage features related to their codon usage  A recent study showed these two forces are coupled: are coupled: (1) codon bias of transferred genes has a strong (1) codon bias of transferred genes has a strong influence on the probability that they will influence on the probability that they will become fixed in the new genome and become fixed in the new genome and (2) frequent HGTs may increase the similarity (2) frequent HGTs may increase the similarity in tRNA pools of organisms within the in tRNA pools of organisms within the same community same community