class 2010-2011

Class : Modeling the dynamics of the cell nucleus

David Holcman

WHEN : Oct-Feb 2010-2011

Wed. 10h-13h.

Starting date : Sept. 29 2009

WHERE "Salle Conference" : 46 rue d’Ulm, 75005 Paris

General description : Eukariotic cell are characterized by an envelop that separates the genetic material from the other organelles. Chromosomes are not randomly positioned but they seem to occupy some specific positions.

My goal is to present the physical rules that have been discovered that can explain and predict the chromosome organization in various conditions. We will particularly focus on telomere organization (ends of the chromosomes). We will present a novel aggregation-dissociation model of clusters.

Finally, we will then study how mARN or fundamental proteins are transported in the nucleus. We will present some models of gene activation by a transcription factor and finally the dynamics of dsDNA repair.

Syllabus :

- Overview

PDF - 4.5 Mo

General theory

- Brownian motion, Ito calculus.
- Dynkin’s equation, Fokker-Planck equation, Short and long time asymptotics, ray methods.
- Mean first passage time Equations, conditional MFPT, distribution of exit points.
- The small hole theory, no potential, with an attracting and a repulsive potential.
- Small hole in a narrow domain.
- The case of one and several holes.
- Minimization of MFPT, consequence hole distribution.
- MFPT in random environments.
- Narrow escape time for a switching particle.
- Homogenisation theory with many small holes.
- Modeling diffusion of shaped object, law of reflection, polymer dynamics using Rouse model.

- Aggregation-dissociation of telomeres, formation and stability of the telomere cluster. Mean encounter time, Markov description of clusters. Dissociation scenario of cluster. Recurrent time of 2 telomeres, dissociation time from a cluster. Asymptotic estimations.

- Dynamics of diffusion of chromosomes and polymers Stochastic dynamics of anisotropic objects in confined microdomains.

- Gene activation by transcription factors.
- Dynamics of the double strand DNA break repair.

Requirements : notions of partial differential equations, probability, cellular biology.

Evaluation : small projects.

References :

Basics :
- Molecular Biology of the Cell, B. Alberts, et al,4rd ed., 2002.
- D. Holcman, Computational challenges in synaptic transmission, AMS Contemporary Mathematics : Proceedings of the Conference on Imaging Microstructures : Mathematical and Computational Challenges, Edited by H. Ammari and H. Kang. 2009
- Schuss, Z., 1980, Theory and Applications of Stochastic Differential, New York, Wiley.

Advanced :

- D. Holcman, Z. Schuss. 2004. Diffusion of receptors on a postsynaptic membrane:exit through a small opening, J. of Statistical Physics, 117, 5/6 191-230.
- A. Singer Z, Schuss, D. Holcman, Narrow Escape I, II and III, in J. of Statistical Physics, 2006, Vol 122, N. 3, p 437 - 563. -D. Holcman A. Singer, Z. Schuss, Narrow escape and leakage of Brownian particles. PRE 78:051111 (2008).
- D. Holcman, Z. Schuss. 2005. A theory of stochastic chemical reactions in confined microstructures, Journal of Chemical Physics 122, 114710, 2005.
- Reingruber D. Holcman, Narrow escape for a switching state Brownian particle
- A. Taflia D. Holcman, The Optimal PSD of synaptic transmission
- J. Reingruber and D. Holcman, Diffusion in narrow domains and application to phototransduction, Phys Rev E 2009 ;79(3 Pt 1):030904.
- T. Lagache E. Dauty D. Holcman, Physical principles and models describing intracellular virus particle dynamics, Current Opinion in Microbiology, 12,4 (2009).
- D. Coombs and R. Straube M Ward Diffusion on a Sphere with Localized Traps : Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points (SIAM J. Appl. Math., Vol. 70, No. 1, (2009), pp. 302-332.)
- S. Pillay, A. Peirce, and T. Kolokolnikov, M. Ward, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems : Part I : Two-Dimensional Domains (SIAM Multiscale Modeling and Simulation, (March 2009), 28 pages.)
- A. Cheviakov and R. Straube M. Ward, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems : Part II : The Sphere (SIAM Multiscale Modeling and Simulation, (March 2009), 32 pages.)