Quasi_species_Error_Threshold_and_Hypercycles

,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Quasi-species, Error Threshold and Hypercycles,A Model for,Molecular,Evolution,Mor Dolev,Jan Ihmels,Introduction,Darwinian evolution: diversity of species,Starting point: cell,Cell: molecular mechanisms, complex machinery,highly conserved,Origin of life : processes that lead to emergence of the cell,Eigen+Schuster: molecular evolution,Do we need living things for evolution?,Conditions for Natural Selection,Metabolism:,Spontaneous, independent formation and degradation far from equilibrium,Self-reproduction:,Ability to instruct own synthesis (autocatalysis), conservation of information,Mutability:,Limited fidelity of self-reproductive process,Ribonucleic Acid,Satisfies requirements for natural selection,Eigen&Schusters candidate for the origin of life,Dynamics of Selection,Simplest model:,Reproducible global conditions:,Dynamics of Selection,System at constant overall concentration:,where,Quasi-species,Single species are,coupled,.,Competition, but co-operation between related species.,Reorganize: N species N quasi-species.,Transformed equation:,Quasi-species,Steady state:,Natural selection: one quasi-species survives,Target of selection: quasi-species (distribution), not single molecular species,Characterized by master sequence,Example: RNA Clones,Wild type:,average,sequence,Species is a distribution,Model Summary,Natural selection of inanimate objects,Open questions:,Darwinian diversity vs. prebiotic unity,Can we have integration of several functions?,Error threshold,The error threshold,-the relative concentration of the master sequence. -the relative concentration of all the others.,We can simplify our equations:,The error threshold,We want to have a steady state,at which,Solving the equations we get:,Demanding , we get:,The error threshold,Where s is the superiority of the master sequence.,Let q be the replication fidelity per digit. Then:,The maximal length of a molecule is limited by the error rate, 1-q .,The maximal length of a genome is inversely proportional to the error rate:,The error threshold:,Is there a correlation between error rate and genome size?,The error catastrophe,In RNA replication without a replicase the error rate is around 0.01. This allows a maximal length of not more than 100 nucleotides.,To increase the fidelity of replication, an enzyme is needed.,Eigens paradox:,no enzyme without a large genome, and no large genome without enzymes.,How can we increase the amount of information maintained in the system, without an increase in the error rate?,A single long molecule vs. two short ones:,If we could have a stable coexistence of more than one quasi-species in the system, this system would keep more information.,The problem: competition between quasi-species prevents a stable coexistence.,The Hypercycle,Organized arrangement of catalytic molecules,Catalyst:,Catalytic cycle:,Autocatalyst,Hypercycle,Next higher order:,Catalytic hypercycle,Cyclic linkage of,Self-replicative units,Intermediates I,n,are,Catalytic cycles,Properties,Allows collective growth of cooperative system (Eigens paradox).,Competition between member species is switched off.,Three basic types of growth rates:,Constant: coexistence.,Linear: exponential growth.,Higher than linear: once for all time-selection.,Properties,Entire ensemble capable of expansion and optimization.,Replacement is difficult.,Genetic code, mechanisms, chirality.,Hypercycles exhibit hyperbolic growth:,An example for a hypercycle: RNA-phage infection:,Hypercycles are all around us,Problems With Hypercycles,Mutants in hypercycles,A,B,A,B,A,A”,Selfish:,Better Target,Altruistic:,Better Replicase,Large (4) cycles fluctuate greatly: instability,Short cuts can destroy cycles,Parasites can destroy hypercycle,Compartments,Eigen suggests compartments,Functional advantages can be selected for,Feedback from phenotype to genotype,Compartments,Improved replicase mutations can be selected for,Do we still need hypercycles?,Summary,Quasi species: Simple molecular evolution,Error Catastrophe: Eigens paradox,Hypercycles as a solution:,Cooperation between quasi-species,Can overcome error threshold,Once and for all-selection,Problems of the hypercycle:,no selection favoring “,altruistic” mutants,need for compartments,References,M. Eigen, P.Schuster, The Hypercycle, Springer-Verlag, 1979,M. Eigen, “Steps towards life : A Perspective on Evolution”, Oxford Univ Press, 1996,J. Hofbauer, K. Sigmund, “The theory of evolution and dynamical system” , Cambrige Univ Press, 1988,J. M. Smith, Hypercycles and the origin of life, Nature 20:445-6, 1979,J. M. Smith, E. Szathmary “The major transitions in evolution”, W.H. Freeman, 1995,