1 / 26

Web-Page for further information: tbi.univie.ac.at/~pks

adena-hampton
Download Presentation

Web-Page for further information: tbi.univie.ac.at/~pks

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. Some Mathematical Challenges from Life SciencesPart IIPeter Schuster, Universität WienPeter F.Stadler, Universität LeipzigGünter Wagner, Yale University, New Haven, CTAngela Stevens, Max-Planck-Institut für Mathematik in den Naturwissenschaften, LeipzigandIvo L. Hofacker, Universität WienOberwolfach, GE, 16.-21.11.2003

  2. Web-Page for further information: http://www.tbi.univie.ac.at/~pks

  3. Mathematics and the life sciences in the 21st century • Selection dynamics • RNA evolution in silico and optimization of structure and properties

  4. A  B B  A Reactions in the continuously stirred tank reactor (CSTR)

  5. Reversible first order reaction in the flow reactor

  6. Autocatalytic second order and uncatalyzed reaction in the flow reactor

  7. Autocatalytic third order and uncatalyzed reaction in the flow reactor

  8. Pattern formation in autocatalytic third order reactions G.Nicolis, I.Prigogine. Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations. John Wiley, New York 1977

  9. Autocatalytic second order reactions are the basis of selection processes. The autocatalytic step is formally equivalent to replication or reproduction.

  10. Replication in the flow reactor P.Schuster & K.Sigmund, Dynamics of evolutionary optimization, Ber.Bunsenges.Phys.Chem.89: 668-682 (1985)

  11. Selection in the flow reactor: Reversible replication reactions

  12. Selection in the flow reactor: Irreversible replication reactions

  13. Complementary replication as the simplest copying mechanism of RNA Complementarity is determined by Watson-Crick base pairs: GCandA=U

  14. Reproduction of organisms or replication of molecules as the basis of selection

  15. Selection equation: [Ii] = xi 0 , fi> 0 Mean fitness or dilution flux,(t), is a non-decreasingfunction of time, Solutions are obtained by integrating factor transformation

  16. s = ( f2-f1) /f1; f2 > f1 ; x1(0) = 1 - 1/N ; x2(0) = 1/N Selection of advantageous mutants in populations of N = 10 000 individuals

  17. Changes in RNA sequences originate from replication errors called mutations. Mutations occur uncorrelated to their consequences in the selection process and are, therefore, commonly characterized as random elements of evolution.

  18. The origins of changes in RNA sequences are replication errors called mutations.

  19. Chemical kinetics of replication and mutation as parallel reactions

  20. City-block distance in sequence space 2D Sketch of sequence space Single point mutations as moves in sequence space

  21. Mutation-selection equation: [Ii] = xi 0, fi> 0, Qij 0 Solutions are obtained after integrating factor transformation by means of an eigenvalue problem

  22. The molecular quasispecies in sequence space

  23. The quasispecies on the concentration simplex S3=

  24. Quasispecies as a function of the replication accuracy q

More Related