Threshold Models of Intracellular Calcium Release
Stephen Coombes

Among all the regulators of cellular signalling, Calcium ranks as one  
of the most important.  In many cell types Calcium signalling is  
associated with the generation of waves.  In this talk I will present  
a bidomain fire-diffuse-fire model that facilitates mathematical  
analysis of such propagating waves in living cells.  Modelling Calcium  
release as a threshold process allows the explicit construction of  
travelling wave solutions to probe the dependence of Calcium wave  speed 
on physiologically important parameters.  A linear stability  analysis 
identifies the newly discovered 'Tango waves' as a dynamic  instability 
of propagating pulse solutions.  Furthermore, I will use  the bidomain 
model to shed some light on recently discovered  sensitisation waves in 
ventricular myocytes.  Moving next to atrial  myocytes, I will describe 
the development of a computationally  efficient framework to investigate 
stochastic Calcium release and  propagation in a realistic 
three-dimensional cellular geometry.