- ~20 years prior to the discovery of Bicoid, Wolpert and Crick proposed that gradients of biologically active molecules (such as proteins or retinoic acid (RA)) may arise by diffusion from a localized source with degradation balancing production such that the gradients reach steady state. What does this model predict? How does the discovery of Bicoid relate to this model? Which of the results presented are consistent with this model, which ones are not?
- In the simple model, the Bicoid gradient arises by diffusion from a constantly producing source at the anterior pole with spatially uniform degradation. Mathematically, the concentration of Bicoid changes with time at any given position within the embryo according to: dC(x,t)/dt = Dd2c/dx2- kc + Q (1) where c is the concentration of Bicoid, D the diffusion coefficient, Q the production term, and k the degradation rate. At steady state, the solution to (1) is given by: C(x) = C(0)e k/l with l= square root (D/k) What is a steady-state? Why do scientists prefer to work with the steady-state solution rather than the full time-dependent solution? What is the mathematical and what the biological reason?
- Both the length constant l and the diffusion coefficient D were measured. With l= square root (D/k) which life-time/degradation rate do you expect? Over which time does the Bicoid gradient form? Can the gradient be at steady state?
- Two different experiments to measure the diffusion coefficient in the embryo are presented. What do they have in common, where do they differ? Why do the measured diffusion coefficients differ? Which of the 2 diffusion coefficients do you believe more, the one measured with Bicoid or the one measured with biologically inert Dextran molecules? Within the framework of the above-mentioned model, which diffusion coefficient makes more sense?
- How can the stability of the nuclear concentration of Bicoid at a given position be maintained? Do we know for sure how it is stabilized?
- How is the information provided by the Bicoid gradient read by cells? What is cooperativity? How can you test whether there is cooperativity in the Bicoid response? Is the available data consistent with cooperativity?
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