Quasi-Species ~~ evolution at the speed of light ~~ Signals and Systems in Biology Kushal Shah @ EE, IIT Delhi Quasi-Species : Introduction I Species : Single genotype I Quasispecies I Large group of genotypes with high mutation rate I RNA viruses, Macromolecules like RNA/DNA I Proposed by Manfred Eigen and Peter Schuster in 1970s J. J. Bull et. al., PLOS Computational Biology 1, e61 (2005) C. O. Wilke, BMC Evolutionary Biology 5:44 (2005) Quasi-Species : Introduction I Species : Single genotype I Quasispecies I Large group of genotypes with high mutation rate I RNA viruses, Macromolecules like RNA/DNA I Proposed by Manfred Eigen and Peter Schuster in 1970s J. J. Bull et. al., PLOS Computational Biology 1, e61 (2005) C. O. Wilke, BMC Evolutionary Biology 5:44 (2005) Quasi-Species : Introduction I Species : Single genotype I Quasispecies I Large group of genotypes with high mutation rate I RNA viruses, Macromolecules like RNA/DNA I Proposed by Manfred Eigen and Peter Schuster in 1970s J. J. Bull et. al., PLOS Computational Biology 1, e61 (2005) C. O. Wilke, BMC Evolutionary Biology 5:44 (2005) Quasi-Species : Introduction I Species : Single genotype I Quasispecies I Large group of genotypes with high mutation rate I RNA viruses, Macromolecules like RNA/DNA I Proposed by Manfred Eigen and Peter Schuster in 1970s J. J. Bull et. al., PLOS Computational Biology 1, e61 (2005) C. O. Wilke, BMC Evolutionary Biology 5:44 (2005) RNA Virus I Contains single- or double-stranded RNA as its genetic material I SARS, influenza, hepatitis C, West Nile fever, polio and measles I Retrovirus : Replication process through a DNA intermediate I HIV-1 and HIV-2 I Ribovirus : RNA virus that does not use an DNA intermediate I Very small genome size I RNA Virus ~ 1.7 Kb to 10 Kb I Largest Virus : 1180 Kbp (Mimivirus) I Bacteria ~ 160 Kbp to 13 Mbp I Human ~ 3Gbp I Polychaos dubium ~ 670 Gbp (amoeba) RNA Virus I Contains single- or double-stranded RNA as its genetic material I SARS, influenza, hepatitis C, West Nile fever, polio and measles I Retrovirus : Replication process through a DNA intermediate I HIV-1 and HIV-2 I Ribovirus : RNA virus that does not use an DNA intermediate I Very small genome size I RNA Virus ~ 1.7 Kb to 10 Kb I Largest Virus : 1180 Kbp (Mimivirus) I Bacteria ~ 160 Kbp to 13 Mbp I Human ~ 3Gbp I Polychaos dubium ~ 670 Gbp (amoeba) RNA Virus I Contains single- or double-stranded RNA as its genetic material I SARS, influenza, hepatitis C, West Nile fever, polio and measles I Retrovirus : Replication process through a DNA intermediate I HIV-1 and HIV-2 I Ribovirus : RNA virus that does not use an DNA intermediate I Very small genome size I RNA Virus ~ 1.7 Kb to 10 Kb I Largest Virus : 1180 Kbp (Mimivirus) I Bacteria ~ 160 Kbp to 13 Mbp I Human ~ 3Gbp I Polychaos dubium ~ 670 Gbp (amoeba) RNA Virus I Contains single- or double-stranded RNA as its genetic material I SARS, influenza, hepatitis C, West Nile fever, polio and measles I Retrovirus : Replication process through a DNA intermediate I HIV-1 and HIV-2 I Ribovirus : RNA virus that does not use an DNA intermediate I Very small genome size I RNA Virus ~ 1.7 Kb to 10 Kb I Largest Virus : 1180 Kbp (Mimivirus) I Bacteria ~ 160 Kbp to 13 Mbp I Human ~ 3Gbp I Polychaos dubium ~ 670 Gbp (amoeba) RNA Virus I Contains single- or double-stranded RNA as its genetic material I SARS, influenza, hepatitis C, West Nile fever, polio and measles I Retrovirus : Replication process through a DNA intermediate I HIV-1 and HIV-2 I Ribovirus : RNA virus that does not use an DNA intermediate I Very small genome size I RNA Virus ~ 1.7 Kb to 10 Kb I Largest Virus : 1180 Kbp (Mimivirus) I Bacteria ~ 160 Kbp to 13 Mbp I Human ~ 3Gbp I Polychaos dubium ~ 670 Gbp (amoeba) Natural Selection The process by which traits become more or less common in a population due to consistent effects upon the survival or reproduction of their bearers. ~~ Survival of the fittest ~~ Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Fitness (natural selection) vs. Mutation rate I Consider a group of genotypes existing together I If mutation rate is low, natural selection works I If mutation rate is high, the idea of ‘fittest’ becomes meaningless I 2 genotypes could just have a difference of 1 nucleotide I Equilibrium between various genotypes I Error catastrophe I Loss of a fitter genotype in a population due to high mutation rate I Mutagenesis : Increase the mutation rate of viruses using drugs I Extinction : All genotypes become extinct Simple case of 2 genotypes Quasispecies : Mathematical Model Assuming discrete time-steps 0 n1 = n1w1 (1 − m1) + n2w1m3 0 n2 = n1w2m1 + n2w2 (1 − m2) N0 = MN where w1 (1 − m1) w1m3 M = w2m1 w2 (1 − m2) n1 N = n2 w ≥ 0 and 0 ≤ m ≤ 1 Quasispecies : Mathematical Model Assuming discrete time-steps 0 n1 = n1w1 (1 − m1) + n2w1m3 0 n2 = n1w2m1 + n2w2 (1 − m2) N0 = MN where w1 (1 − m1) w1m3 M = w2m1 w2 (1 − m2) n1 N = n2 w ≥ 0 and 0 ≤ m ≤ 1 Quasispecies : Mathematical Model Assuming discrete time-steps 0 n1 = n1w1 (1 − m1) + n2w1m3 0 n2 = n1w2m1 + n2w2 (1 − m2) N0 = MN where w1 (1 − m1) w1m3 M = w2m1 w2 (1 − m2) n1 N = n2 w ≥ 0 and 0 ≤ m ≤ 1 Quasispecies : Mutation-Selection Balance w1 (1 − m1) w1m3 n1 M = N = w2m1 w2 (1 − m2) n2 N0 = MN At equilibrium, N0 = lN ) MN = lN If m3 = 0, N1 w1 (1 − m1) − w2 (1 − m2) l1 = w1 (1 − m1) = N2 w2m1 l2 = w2 (1 − m2) N1 = 0 w1 (1 − m1) = w2 (1 − m2): Error Threshold Quasispecies : Mutation-Selection Balance w1 (1 − m1) w1m3 n1 M = N = w2m1 w2 (1 − m2) n2 N0 = MN At equilibrium, N0 = lN ) MN = lN If m3 = 0, N1 w1 (1 − m1) − w2 (1 − m2) l1 = w1 (1 − m1) = N2 w2m1 l2 = w2 (1 − m2) N1 = 0 w1 (1 − m1) = w2 (1 − m2): Error Threshold Quasispecies : Mutation-Selection Balance w1 (1 − m1) w1m3 n1 M = N = w2m1 w2 (1 − m2) n2 N0 = MN At equilibrium, N0 = lN ) MN = lN If m3 = 0, N1 w1 (1 − m1) − w2 (1 − m2) l1 = w1 (1 − m1) = N2 w2m1 l2 = w2 (1 − m2) N1 = 0 w1 (1 − m1) = w2 (1 − m2): Error Threshold Quasispecies : Mutation-Selection Balance w1 (1 − m1) w1m3 n1 M = N = w2m1 w2 (1 − m2) n2 N0 = MN At equilibrium, N0 = lN ) MN = lN If m3 = 0, N1 w1 (1 − m1) − w2 (1 − m2) l1 = w1 (1 − m1) = N2 w2m1 l2 = w2 (1 − m2) N1 = 0 w1 (1 − m1) = w2 (1 − m2): Error Threshold Quasispecies : Mutation-Selection Balance w1 (1 − m1) w1m3 n1 M = N = w2m1 w2 (1 − m2) n2 N0 = MN At equilibrium, N0 = lN ) MN = lN If m3 = 0, N1 w1 (1 − m1) − w2 (1 − m2) l1 = w1 (1 − m1) = N2 w2m1 l2 = w2 (1 − m2) N1 = 0 w1 (1 − m1) = w2 (1 − m2): Error Threshold w1 > w2 m1 = km m2 = m k > 1 l1 = w1 (1 − m1) l2