slide1 n.
Skip this Video
Download Presentation
Web-Page for further information:

Loading in 2 Seconds...

play fullscreen
1 / 26

Web-Page for further information: - PowerPoint PPT Presentation

  • Uploaded on

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Web-Page for further information:' - adena-hampton

Download Now 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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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


Web-Page for further information:


Mathematics and the life sciences in the 21st century

  • Selection dynamics
  • RNA evolution in silico and optimization of structure and properties

A  B

B  A

Reactions in the continuously stirred tank reactor (CSTR)


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


Autocatalytic second order reactions are the basis of selection processes.

The autocatalytic step is formally equivalent to replication or reproduction.


Replication in the flow reactor

P.Schuster & K.Sigmund, Dynamics of evolutionary optimization, Ber.Bunsenges.Phys.Chem.89: 668-682 (1985)


Complementary replication as the simplest copying mechanism of RNA

Complementarity is determined by Watson-Crick base pairs:



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


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


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.


City-block distance in sequence space

2D Sketch of sequence space

Single point mutations as moves in sequence space


Mutation-selection equation: [Ii] = xi 0, fi> 0, Qij 0

Solutions are obtained after integrating factor transformation by means of an eigenvalue problem