Question
Binding of insulin to its receptor. Figure $27.19$ shows the binding of insulin to the insulin receptor in a detergent solution. Use the Langmuir model to estimate the binding constant.
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In this case, the surface is the insulin receptor, and the molecules are insulin. The model assumes that there is a fixed number of binding sites on the surface, and that each site can only bind one molecule. The binding constant, K, is a measure of the affinity Show more…
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A glucose solution is administered intravenously into the bloodstream at a constant rate $r .$ As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at that time. Thus a model for the concentration $C=C(t)$ of the glucose solution in the bloodstream is $$\frac{d C}{d t}=r-k C$$ where $k$ is a positive constant. (a) Suppose that the concentration at time $t=0$ is $C_{0 .}$ Determine the concentration at any time $t$ by solving the differential equation. (b) Assuming that $C_{0} < r / k,$ find $\lim _{t \rightarrow \infty} C(t)$ and interpret your answer.
APPLICATIONS OF INTEGRATION
Differential Equations
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