I-AIM Interdisciplinary Seminar
(Institute for Applied and Interdisciplinary Mathematics)
3:10 PM April 5, 2006
Foields Institute, room 230
The combination of fluorescence microscopy techniques and mathematical modelling facilitates the study of the spatio-temporal dynamics of nuclear proteins in living cells. In this talk, I will highlight ongoing modelling work on two related aspects, namely (1) the quantitative assessment of the mobility of the proteins, and (2) their spatial organization within the nucleus. The work is the result of a collaboration between applied mathematicians and an experimental cell biologist.
(1) The mobility of proteins is characterized experimentally by fluorescence recovery data. In the past, diffusion models were fit to the data to extract an effective diffusion coefficient for the proteins of interest. I will show that simple reaction-diffusion models and compartmental models can provide a much better fit to the data, suggesting that such models are more appropriate to describe the behaviour of diffusive proteins undergoing binding events. A perturbation analysis of the models leads to an elegant explanation of two important limiting types of behaviour exhibited by fluorescence recovery data, namely reduced diffusive and biphasic behaviour.
(2) The spatial organization of splicing factors (proteins which play an important role in RNA processing) within the nucleus can be described by a fourth-order aggregation-diffusion model, derived from a random walk analysis. A linear stability analysis of this model reveals the emergence of spatial patterns under conditions that are in accordance with experimental observations.