Vancomycin W and Evolutionary Dynamics”

Vancomycin W and Evolutionary Dynamics” • Iwamoto • Typical Feature of Vancomycin W (revisited) • Why and how the ratio of W1and W2is controlled • Evolutionary Dynamics and Games • W1 and W2 again

Typical feature of Vancomycin W (revisited) Experimental findings: W1 and W2 are Connected with large-scale flip-flop inversion!! Requirement to theory: Determination of flip-flop probability, which was performed by extended Lotka-Volterra equation for the growth curve

Fitting to S-colony start data (extended Lotka-Volterra equation)

Fitting to L-colony start data (extended Lotka-Volterra equation)

The flip-flop probability determined are: • 1. The value of wsl =3.0x10-5 (per 1 doubling) • 2. In the S-colony start specimen, wl s =2.0x10-1 • (per 1 doubling) • In the L-colony start specimen, wls =2.0x10-2 • (per 1 doubling). • The remarkable results are: • Flip-flop probability is much larger than the mutation • probability. • 2. Flip-flop probability is strongly state-dependent. • What do these data tell us?

2. Why and how the ratio of W1 and W2 is controlled There are several items which might be closely related to this phenomena of W1 and W2. • Quorum sensing: Quorum: minimum number of members required to be present at an assembly or meeting（定足数） Bacteria communicate with one another using chemical signal molecules (autoinducer). As in higher organism, the information supplied by these molecules is critical for synchronizing the activities of large group of cells.Bacteria monitor the environment for other bacterial and alter the behavior on a population-wide scale in response to changes in the number and/or species present in a community.

S.aureus uses a biphasic strategy to cause disease: At low cell density, the bacterial express protein factors that promote attachment and colonization, whereas at high density, the bacteria repress these traits and initiate secretion of toxins and proteases that are presumably required for dissemination. Bistability: Phase variation 1. chromosomal inversion 2. contingency loci (slipped strand mispairing) Other type of bistability Persistercell Genetic competence Sporulation and cannibalism Swimming and chaining

An example : Growth of hipA7 bacteria (E. coli against Ampicillin) hip : high persistencemutant N. Q. Balaban et al., Science 305, 1622 -1625 (2004)

Fig. 3. Measurements of the dynamics of persister (p) and normal (n) subpopulations in batch cultures N. Q. Balaban et al., Science 305, 1622 -1625 (2004)

Another example: Cooperation and conflict in quorum-sensing bacterial populations, S.P.West et al., Nature 450 (2007) 411 • Pseudomonas aeruginosa (QS controls biofilm development, swarming and motility, production of virulence factor, …) • Focus on the las QS pathway, which controls the rhl system • Mutation in las QS results in a general abolition of QS in P. aeruginosa To examine the costs and benefits of QS, three strains are chosen 1. Wild strain 2. Signal-negative mutant (lasI) that does not produce auto-inducer but still responds to signal 3. Signal-blind mutant (lasR) that does not respond to extra-cellular signal

QS-controlled publicgoods Proteases are a group of exoproduct controlled by QS. Examined are the growth of three types, wild, signal negative, signal blind, in a medium in which the ability to make proteases (elastase) is required for growth.

QS-dependent cooperation is costly Comparison of the growth yield of the mutants and wild type in nutrient-rich Luria-Bertani broth, in which the exoproducts produced by QS are not needed for growth.

Do quorum-sensing cheats spread in a population? Initiate populations of wild-type with a small population (1-3% ) Of one of the two mutants. Growth in QSM over 48h results in frequency change from 1% to 45% (signal-blind) and 3% to 66% (signal negative). Fitness of cheats decreases Significantly when it is more Common.

Quorum sensing is a social trait, susceptible to exploitation and invasion by cheats. Why is QS maintained in natural population? QS is favoured by higher relatedness. If the neighbouring cells tends to be close relatives they will have a shared interest in communicating honestly and cooperating.

3. Evolutionary Dynamics and Games Big contribution from John Nash Nash Equilibrium

Evolutionary game theory Peter Taylor Josef Hofbauer Karl Sigmund Martin Nowak

payoff =reward - cost A: cooperator (C) B: defector (D) c > a > d > b : prisoner’s dilemma For example, c=5,a=2,d=0,b=-3 (reward=5,cost=3)

Nash equilibrium, evolutionarily stable strategy (ESS) Let’s assume the following payoff matrix C D C D C: cooperator D: defector Strategy D is Nash equilibrium: If both player choose C, then one player can improve his payoff by switching to D. If both play D, then neither player can improve his payoff by switching to C. C is dominated by D. John Maynard Smith invented the concept of “evolutionary stable strategy”, which is closely related to Nash equilibrium.

Fig. 1. Without any mechanism for the evolution of cooperation, natural selection favors defectors M. A. Nowak Science 314, 1560 -1563 (2006)

Repeated games Direct reciprocity This equation is equivalent to Lotka-Volterra equation!!

Fig. 3. Five mechanisms for the evolution of cooperation M. A. Nowak Science 314, 1560 -1563 (2006)

4. W1 and W2 again 1. Extended Lotka-Volterra equation (including flip-flop) is equivalentto replicator-mutator equation, which is the most general form of equation used in evolutionary dynamics. It was discussed in application to the evolution of language by M.Nowak but not for the evolution of life. 2. Collaborator-defector relation is not always competitive. From the observation that mixture of cheater (defector) is rather common in natural (bacterial) group, this mixture raises the fitness of the group as a whole, like the wild-persister mixture. (Is prisoner’s dilemma no more dilemma?) 3. W1 and W2, both are definite mixtures of small- and large-colony-forming bacteria, both are quasi-stable, are controlled by the special quorum sensing mechanism (state-dependent flip-flop rate). This is a “refined” form of the bistability. 4. “Natural cooperation ( and defection )” will play an important role for the evolution of life, in addition to “mutation” and “natural selection”

Vancomycin W and Evolutionary Dynamics”