martin3

martin3 - (maximum Phi ). Sequence space Error threshold If...

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A quasispecies is a population of RNA or DNA molecules: ATCAGGACTCA ATC G GGACTCA ATCAGGA A TCA …. Manfred Eigen & Peter Schuster 1977
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The Quasispecies equation i ji n j j j i x x Q f x x ) ( 1 r f - = = Frequency of type j Fitness of type j Mutation from j to i Average fitness i i i x f x = ) ( v f 1 = i i x
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The Quasispecies equation i i ji n j j i x f Q x x + = = 1 ji n j j j i Q f x x = = 1 &
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Mutation matrix ) and between mutations point of number ( distance Hamming ... length genome ... bit per rate n ...mutatio ) 1 ( j i H L p p p Q ij H L H ij ij ij = - = -
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Sequence space 00 01 10 11 Hamming (or Manhattan) metric L= 2 dimensions
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Sequence space 000 001 110 111 010 011 100 101 L=3 dimensions
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Fitness landscape Each point in sequence space is assigned a number. Sequence space
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Evolution … is adaptation of the quasispecies on the fitness landscape. Sequence space
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Search process Not a single sequence, but the a whole ensemble of sequences explores the fitness landscape.
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Survival of the quasispecies Not the fittest sequence (maximum a ), but the fittest quasispecies is selected
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Unformatted text preview: (maximum Phi ). Sequence space Error threshold If the mutation rate is to high, the quasispecies cannot maintain genetic information. Advantageous mutants disappear. Error threshold f f 2 2 2 1 1 2 1 1 1 1 ) 1 ( Mutants Wildtype x x f Q x f x x Q x f x-+-=-= & & 2 1 if survives Wildtype f Q f Error threshold implies a maximum genome length p L / 1 < mutation rate per base genome length Error threshold Adaptation is only possible if the mutation rate is below a certain threshold. Localization L p / 1 < Applications of quasispecies theory n origin of life n in vitro evolution n viruses n bacteria n cancer Extensions n More complicated mutation operator (insertion, deletion, recombination, etc) n Stochastic formulation (finite population)...
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martin3 - (maximum Phi ). Sequence space Error threshold If...

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