Levels of description of random evolutions, and applications in cell biology
28.03.2012 Seminaris  -  Curs de matemàtica avançada a càrrec de Reinhard Illner. Els dies 11 i 13 d'abril.

Títol:

 Levels of description of random evolutions, and applications in cell biology
Speaker Reinhard Illner
Tentative schedule: Wednesday 11 and Friday 13 April, from 15:00 to 17:00
Room: C1/028, CRM
Contents: Many processes in cell biology are driven by interactions between protein compounds and the DNA; because of the microscopic scales, the activation or deactivation of genes by such compounds are best described by random processes. I will begin by showing an example of such a process which gives rise to a random evolution known as a "transcriptional-translational oscillator  (TTO). It will be explained how TTOs can possibly interact to explain the origin of circadian rhythms in organisms.
In a highly oscillatory regime TTO models turn (formally and rigorously) into ordinary dynamical systems, and there the oscillatory behaviour is easily seen to be the result of a Hopf bifurcation. This high oscillatory limit is  a second level of description and is common in the math biology literature.
Kolmogorov master equations for the original random evolution are the most complete level of description, and they allow (in principle) computing probabilities to find the system in a certain state at a certain time. These master equations are the third level of description, and they provide a link to kinetic theory, as they are simply linear kinetic equations. Close to the high frequency limit the random switchings in the DNA behaviour lead to inherent noise, and this noisy behaviour can be modelled via a diffusion approximation, derived from the Kolmogorov equations with the Chapman-Enskog expansion. This is the fourth and last level of description which will be shown.
More information: If interested, please contact carrillo@mat.uab.es
 
Anar a Notícies

Arxiu de notícies

Des de
Fins a
Paraula clau

Departament de Matemàtiques
Edifici C Facultat de Ciències
08193 Bellaterra (Barcelona)
TEL +34 93 581 13 04
FAX +34 93 581 27 90

d.matematiques@uab.cat
 

 

 

2025 Universitat Autònoma de Barcelona