Kinetics of differentiation/feedback control in a compartmental model.

a. Consider a 6-stage differentiation process (N ¼ 6), in which the last population,X6, produces a cytokine,G, at a per cell rate of qG. This cytokine has a half-life t0:5( ¼ 2 hrs) and influences the growth rate of the stem cells (i.e., u1 ¼ fn([G]), where [G] is the concentration of the growth factor G. Extend the base set of differential equations to describe the dynamics of [G].

b. Incorporate into the equations

where K is the binding constant for the growth factor. What does the function f([G]) describe physiologically

c. Make the equations dimensionless using the growth rate as the scaling factor for time and K for the cell concentration.

d. Describe the meaning of the dimensionless groups and estimate their numerical values.

e. Obtain the numerical values for a simulation starting from a single stem cell. Examine the effect of varying the numerical values of the parameters.

f. Obtain the numerical values for a simulation starting from the steadystate solution and perturb the value of X3 by 20%. Discuss your results.