A cellular protein, Protein X, is translated during interphase and undergoes proteolysis during mitosis. Which formula describes the intracellular Protein X concentration?
(x is the independent variable, and a, b, and c are constants, and e is Euler’s constant)
a) [Protein X] = a(x+b)
b) [Protein X] = asin(bx+c)
c) [Protein X] = a(x+b)2
d) [Protein X] = aeb(x+c)
Explanation
Protein X is described as undergoing synthesis and destruction along with the cell-cycle. The correct formula describing the concentration must oscillate. Choice a) is linear, choice b) oscillates, choice c) climbs or descends parabolically, and choice d) exhibits exponential growth or decay. Only choice b) provides the correct qualitative behavior.
a) [Protein X] = a(x+b), incorrect, This choice is linear.
b) [Protein X] = asin(bx+c), correct.
c) [Protein X] = a(x+b)2, incorrect, This choice is parabolic.
d) [Protein X] = aeb(x+c), incorrect, This choice is exponential.
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