PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Biophysics & Medical Physics · Genetic circuits, regulation and biological information
Forces, Machines and Signals, Ch Genetic circuits and biological pattern
Problem
Cells divide every tdiv=25min, so every protein is diluted at rate γdil=ln2/tdiv. A gene's product is additionally tagged for active degradation with a chosen half-life t1/2,deg, and γ=γdil+ln2/t1/2,deg (with the degradation term omitted for a stable, untagged protein). Calculate the response half-time ln2/γ for each of the following degradation tags, keeping tdiv=25min fixed throughout:
((a)) no active degradation (stable protein)
((b)) degradation half-life 30min
((c)) degradation half-life 10min
((d)) degradation half-life 3min
((e)) Find the degradation half-life that makes the response four times faster than dilution alone, and the factor by which the promoter's production rate must rise to keep the same steady level pss.