Use the continuum approach to show that in a steady state the number of cells pr

Question

Use the continuum approach to show that in a steady state the number of cells produced during a differentiation process that involves replication but no apoptosis (a=0) is

and is thus primarily a function of the ratio a/u. a=0 is the completely undifferentiated state and a=1 is the completely differentiated state. What is Xout if u and g are the same orders of magnitude and if g is 10 times slower? Which scenario is a more reasonable possibility in a physiological situation?

Note : if the rates are comparable, only two mature progeny will be produced. On the other hand, if the differentiation rate is ten times slower than the replication rate (probably close to many physiologic situations, i.e. 20 h doubling time, and 200 h=8 days differentiation time) then about one million cells will be produced. Thus, overall dynamic state tissue is strongly dependent on the relative rates of the cellular fate processes.

Explanation / Answer

As here the rates are comparable, only two mature progeny will be produced. Note that differentiation rate is ten times slower than the replication rate( 20 h doubling time, and 200 h=8 days differentiation time) then about one million cells will be produced. Thus, overall dynamic state tissue is strongly dependent on the relative rates of the cellular fate processes.

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