1 / 23

Mary Jane Richardson and Leah Sauchyn

A Population Genetics Model of Malaria ( Plasmodium berghei ) Resistance in the Mosquito Vector Anopheles stephensi. Mary Jane Richardson and Leah Sauchyn. (http://jhmalaria.jhsph.edu/Faculty/jacobs_lorena/documents/jacobs.htm). Mendelian Genetics. Example: Flower Colour.

cwen
Download Presentation

Mary Jane Richardson and Leah Sauchyn

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Population Genetics Model of Malaria (Plasmodium berghei) Resistance in the Mosquito Vector Anopheles stephensi Mary Jane Richardson and Leah Sauchyn (http://jhmalaria.jhsph.edu/Faculty/jacobs_lorena/documents/jacobs.htm)

  2. Mendelian Genetics Example: Flower Colour genotype - the genetic makeup of an individual PP Pppp first allele second allele (http://www.janbiro.com/images/01-mendel-himself_1_.jpg) gene - portion of genetic material coding for a functional unit – eg. a protein - in diploid organims there are 2 alleles/gene in each individual - P => purple (dominant) - p => orange (recessive) phenotype: the outward expression of the genotype Purple Orange PP Pppp

  3. Transgenic Malaria-Resistant Mosquitoes A – allele that prevents malaria development in the mosquito (dominant) Phenotype: transgenic wild Genotype: AA Aa aa (homozygous (heterozygous transgenic) transgenic) Relative fitness (W): WAA WAa Waa Where: WAA = (1+b)*(1-c) WAa = (1+b) Waa = 1 three different relative fitnesses acts as a three phenotype system with respect to selection b = benefit to being transgenic c = cost to being homozygous transgenic (Marrelli et al., 2007)

  4. Plasmodium berghei life cycle Blood meal oocyst (n) in blood sporozites (n) in salivary gland sporozites (n) in blood ookinete (2n) in midgut sporozites(n) in liver Gametocyte-producing strain merozites (n) in red blood cells zygote (2n) in midgut schizont (n) in red blood cells ♀gamete ♂ gamete gametocytes (n) in blood meal gametocytes (n) in blood Blood meal Infected Mosquitoes (Anopheles stephensi) Infected Rodent (Grammomys surdaster) (http://www.tufts.edu/tie/tci/images/climatechange/Aedes%20mosquito.jpg) (http://www.lumc.nl/1040/research/ malaria/model02.html) Transgenic allele (A) SM1 peptide Gametocyte-deficient strain

  5. Hardy-Weinberg Equilibrium p q p = frequency of allele selected for (A) q = frequency of allele selected against (a) p p2 pq p + q = 1 q pq q2 • At equilibrium, the genotypic frequencies are the squared expansion of the allelic frequencies: • (p+q)2 = p2 + 2pq + q2 = 1 • equilibrium is established after one generation (i.e. ‘children’ are in H-W equilibrium) • sexual reproduction does not change equilibrium frequencies • a dynamic equilibrium - a new equilibrium is established following reproduction if allelic frequencies are changed

  6. Transgenic Malaria-Resistant Mosquitoes: A Model b = benefit to being transgenic = 0.5 c = cost to being homozygous transgenic = 0.35 Relative fitness: Homozygous transgenic (WAA) = (1+b)*(1-c) = 0.975 Heterozygous transgenic (WAa) = (1+b) = 1.5 Wild type (Waa) = 1 Transgenic Mosquitoes (http://www.nature.com/embor/journal/v7/n3/images/7400643-f1.jpg) Average relative fitness: Wavet = pt2WAA + 2ptqtWAa + qt2Waa (Marrelli et al., 2007)

  7. Transgenic Malaria-Resistant Mosquitoes: A Model Genotypic frequencies in adult population after selection and before reproduction: freqAAt+1/2 = pt2WAA Wavet freqAat+1/2 = 2ptqtWAa Wavet Transgenic adult (http://www.jichi.ac.jp/idoubutsu/Yoshida%20publication.html) freqaat+1/2 = qt2Waa Wavet (Marrelli et al., 2007)

  8. Transgenic Malaria-Resistant Mosquitoes: A Model Allelic and genotypic frequencies in offspring after reproduction and before selection: Allelic frequencies: pt+1 = freq(A)t+1 = 1*freqAAt+1/2 + ½*freqAat+1/2 + 0*freqaat+1/2 qt+1 = freq(a)t+1 = 1-pt+1 Genotypic frequencies In Hardy-Weinberg Equilibrium freqAAt+1 = pt+12 freqAat+1 = 2pt+1qt+1 Freqaat+1 = qt+12 Transgenic juvenile (http://www.jichi.ac.jp/idoubutsu/Yoshida%20publication.html) (Marrelli et al., 2007)

  9. Transgenic Malaria-Resistant Mosquitoes: A Model WAa>Waa>WAA Inital condition 2pq = 0.5 and p2 = 0 2pq+p2 increases until p and q are at equilibrium according to the relative fitnesses (W) (Marrelli et al., 2007)

  10. Transgenic Malaria-Resistant Mosquitoes: Allele Frequency Equation pt+1 = 1*freqAAt+1/2 + ½*freqAat+1/2 + 0*freqaat+1/2 pt+1 = 1*(pt2*WAA/Wavet) + ½*(2ptqt*WAa/Wavet) + 0*(qt2*Waa/Wavet) pt+1 = 1*pt2*WAA + ½*2ptqt*WAa + 0*qt2*Waa Wavet pt+1 = 1*pt2*WAA + ½*2pt(1-pt)*WAa + 0*(1-pt)2*Waa pt2*WAA + 2pt(1-pt)*WAa + (1-pt)2*Waa (de Vries et al., 2006; Marrelli et al., 2006)

  11. Stability Analysis

  12. Stability Analysis is stable if WAa<Waa is stable if WAa<WAA is stable if WAa>WAA,Waa

  13. Possible Outcomes of the Allele Frequency Equation p1* = 0 unstable p2* = 1 stable Case 1: WAA>WAa>Waa

  14. Possible Outcomes of the Allele Frequency Equation p1* = 0 stable p2* = 1 unstable Case 2: WAA<WAa<Waa

  15. Possible Outcomes of the Allele Frequency Equation p1* = 0 unstable p3* = Waa-WAastable WAA-2WAa+Waa p2* = 1 unstable Case 3: WAa>WAA>Waa OR WAa>Waa>WAA

  16. Possible Outcomes of the Allele Frequency Equation Case 4b: WAa<WAA<Waa Case 4a: WAa<Waa<WAA

  17. Possible Outcomes of the Allele Frequency Equation Case 4a and Case 4b: p1* = 0 stable p3* = Waa-WAaunstable WAA-2WAa+Waa p2* = 1 stable

  18. Transgenic Malaria-Resistant Mosquitoes: Allele Frequency Equation p*3 = 0.4878 p*3 = Waa – WAa WAA – 2WAa + Waa WAA= (1+b)*(1-c) = 0.975 WAa = (1+b) = 1.5 Waa = 1 WAa>Waa>WAA p never becomes fixed - mosquitoes that transmit malaria will not be eliminated from the population as long as heterozygous transgenics are more fit than homozygous transgenics (de Vries et al., 2006; Marrelli et al., 2007)

  19. How long does it take to reach p3*? 682.5 days 577.5 days 472.5 days 367.5 days Assuming a generation time of 1.5 weeks it takes 1 year, 10 months , and 17 days to reach p3* from p = 0.01

  20. Conclusions • In general: • the relative fitness of the genotypes determines the stability of the fixed points • Malaria model: • the heterozygote transgenic has the greatest relative fitness • the transgenic allele (p) will never become fixed in the mosquito population • wild type (q) persists in heterozygote • how applicable is this system? (Cohuet et al., 2006) • Plasmodium berghei is a parasite of muric african rodents • Anopheles stephensi is a laboratory vector

  21. Literature Cited Cohuet, A., Osta, M., Morlais, I., Awono-Ambene, P., Michel, K., Simard, F., Christophides, G., Fontenille, D., Kafatos, F. (2006). Anopheles and Plasmodium: from laboratory models to natural systems in the field. EMBO reports 7(12): 1285-1289. de Vries, G., Hillen, T., Lewis, M., Mϋller, J., and Schönfisch, B. (2006). A course in mathematical biology: quantitative modeling with mathematics and computational methods. Society for Industrial and Applied Mathematics, Philadelphia, PA. Janse, C. and Waters, A. (2006). The life cycle of Plasmodium berghei in: The Plasmodium berghei research model of malaria. Leiden Univeristy Medical Center. http://www.lumc.nl/1040/research/malaria/model.html. Accessed on May 9th, 2007. Marrelli, M.T., Li, C., Rasgon, J.L., and Jacobs-Lorena, M. (2007). Transgenic malaria- resistant mosquitoes have a fitness advantage when feeding on Plasmodium- infected blood. PNAS 104(13): 5580-5581. All images from Google Images accessed on May 10th, 2007.

  22. Acknowledgments We wish to thank Gerda de Vries and Frank Hilker for much needed guidance and patience, Drew Hanson for being a pillar of strength during a time of need, the University of Alberta, the Centre of Mathematical Biology and the Pacific Institute for the Mathematical Sciences. Gerda Frank

  23. Questions?

More Related