Stem cell Math/modelling question. Please help!

Sean megason at fas.harvard.edu
Wed Jul 8 10:14:45 EST 1998


Hi all,
I'm actually a developmental biologist but I thought people that follow
this newsgroup might be more helpful in answering my question. I'm trying
to come up with some equations that describe stem cell proliferation.
Imagine a stem cell can divide in two ways: it can divide to give rise to
two new stem cells, or it can give rise to one stem cell and one
differentiated cell (which can never again divide). Lets call the first
type of division proliferative and the second type differentiative. Let:
   S=number of stem cells
   Si=the initial number of stem cells
   D=number of differentiated cells
   t=time
   l=cell cycle length
   p=probability of proliferative type of division

Also assume the cell cycle of the population of stem cells is asynchronous
(random phase but equal length) and the initial number of differentiated
cells is zero.

What I'm trying to figure out are equations giving the number of stem
cells, S(t), and differentiated cells, D(t), at a given time.

I have  S(t) = Si * 2^(tp/l)  but I'm not sure this is correct. I don't
have anything for D(t).

Any help would be greatly appreciated. Thanks.

Sean Megason
megason at fas.harvard.edu




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