Polymerization kinetics and equilbria

Dr E. Buxbaum EB15 at le.ac.uk
Wed May 21 05:40:35 EST 1997

lhom at nature.berkeley.edu (Louis Hom) wrote:
>There is a cellular protein called actin that polymerizes into filaments
>called F-actin (the monomeric form is called G-actin).  These filaments
>have nonequivalent ends, the (+) end -- sometimes called the fast-growing
>end -- and the (-) end -- which would be the slow-growing end. 
>	But it's not just that the kinetics of addition are different for
>each end;  the (+) end has a higher affinity for monomers than the (-) end.
>	So my question is this:  is it the case that addition to the (+)
>end is faster simply because it is further away from the equilibrium
>concentration?  if one wanted to study this, how would one approach it?

You could do some computer simulations with this problem. If the effect 
were due to the different Kd's, with Vmax being the same at both ends, 
then you could use the Henry-Michaelis-Menten equation to describe the 
speed of association. A more complicated model would also allow for 
dissociation, using a system of differential equations to describe 
association and dissociation at both ends. The Euler algorithm should be 
sufficient for numerical interation of this system, alternatively a 
Runge-Kutta could be used. 

If the model does not give results in reasonable agreement with observed 
facts, then change to a model were the Vmax is different at both ends 
and see what you get. 

You may whant to read for example "Computer Modells in Biology" by Spain 
to get some information on modelling techniques. "Numerical Recepies in 
[Pascal, C, Fortran]" by Press et al. is very good once you have 
understood the general approach.

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