02:25

Physical Biology of the Cell

In the estimate on cell-to-cell variability in the chapter, we learned that the standard deviation in the number of molecules partitioned to one of the daughter cells upon cell division is given by

$$\left\langle n_{1}^{2}\right\rangle-\left\langle n_{1}\right\rangle^{2}=N p q$$

(a) Derive this result.

(b) Derive the simple and elegant result that the average difference in intensity between the two daughter cells is given by

$$\left\langle\left(I_{1}-I_{2}\right)^{2}\right\rangle=\alpha I_{\mathrm{tot}}$$

where $I_{1}$ and $I_{2}$ are the intensities of daughters 1 and 2 respectively, and $I_{\text {tot }}$ is the total fluorescence intensity of the mother cell and assuming that there is a linear relation between intensity and number of fluorophores of the form $I=\alpha N$