Transcript hadas presentationx

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
during evolution
 In line with Darwin’s theory
of survival of the fittest
 Traditional optimization is
insufficient for understanding
biological evolution
 Evolution is nearly always
co-evolution
By evolving towards
optimal properties
Organisms change
their environment
This, in turn, affects
the optimum
Which involves, for e.g.
competing organisms
 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
 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
invaded by a rare mutant playing
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
 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.
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
 This is the NE and ESS of the game
 Assuming that one tree is taller
by h, this gives it an advantage in
productivity of p
 The dashed straight lines have the
slope p/h, i.e., they depict the gain
in productivity by growing taller.
 The solid straight lines represent
the net effect.
 The evolutionarily stable height, h*,
is reached when this net effect is 0
due to investing more into supporting
structures, i.e., when the straight line
is horizontal.
 Clearly, h* is larger than the optimal
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) ...
3. Termination
 Codon usage bias refers to
differences in the frequency
of occurrence of synonymous
codons in coding DNA.
 A codon is a series of three
nucleotides (triplets) that
encodes a specific amino acid
residue in a polypeptide chain
or for the termination of
translation (stop codons)
 There are 64 different codons
(61 codons encoding for amino acids
plus 3 stop codons)
but only 20 different translated
amino acids
 HGT, a process in which one organism
incorporates genetic material from another
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
features related to their codon usage
 A recent study showed these two forces
are coupled:
(1) codon bias of transferred genes has a strong
influence on the probability that they will
become fixed in the new genome and
(2) frequent HGTs may increase the similarity
in tRNA pools of organisms within the
same community