Physical Biology of the Cell

Rob Phillips, Jane Kondev, Julie Theriot

Chapter 2

What and Where: Construction Plans for Cells and Organisms - all with Video Answers

Educators

Chapter Questions

Problem 1

We made a simple estimate of the mass of an $E$. coll cell by assuming that such cells have the same density of water. However, a more reasonable estimate is that the density of the macromolecules of the cell is 1.3 times that of water $(\mathrm{BNID} 101502,104272) .$ As a result, the estimate of the mass of an $E$ coli cell is off by a bit. Using that two-thirds of the mass is water and that the remaining one-third is macromolecular, compute the percentage error made by treating the macromolecular density as the same as that of water.

Prashant Bana

Prashant Bana

Numerade Educator

Problem 2

Make an estimate of the composition of carbon, hydrogen, oxygen, and nitrogen in the dry mass of a bacterium. Using knowledge of the size and mass of a bacterium, the fraction of that mass that is "dry mass" (that is, $\approx 30 \%$ ) and the chemical constituents of a cell, figure out the approximate small integers $(<10)$ for the composition $\mathrm{C}_{m} \mathrm{H}_{n} \mathrm{O}_{p} \mathrm{N}_{q},$ that is, find $m, n, p,$ and $q$

Josee Pacheco

Numerade Educator

Problem 3

(a) Use Figure 2.1 to justify the assumption that a typical bacterial cell (that is, $E$. coli) has a surface area of $6 \mu \mathrm{m}^{2}$ and a volume of $1 \mu \mathrm{m}^{3}$. Also, express this volume in femtoliters. Make a corresponding estimate of the mass of such a bacterium.
(b) Roughly $2-3 \mathrm{kg}$ of bacteria are harbored in your large intestine. Make an estimate of the total number of bacteria inhabiting your intestine. Estimate the total number of human cells in your body and compare the two figures.
(c) The claim is made (see Whitman et al., 1998 ) that in the top $200 \mathrm{m}$ of the world's oceans, there are roughly $10^{28}$ prokaryotes. Work out the total volume taken up by these cells in $\mathrm{m}^{3}$ and $\mathrm{km}^{3}$. Compute their mean spacing. How many such cells are there per milliliter of ocean water?

Josee Pacheco

Numerade Educator

Problem 4

(a) Estimate the volumes of the various amino acids in units of $\mathrm{nm}^{3}$.
(b) Estimate the mass of a "typical" amino acid in daltons. Justify your estimate by explaining how many of each type of atom you chose. Compare your estimate with the actual mass of several key amino acids such as glycine, proline, arginine, and tryptophan.
(c) On the basis of your result for part (b), deduce a rule of thumb for converting the mass of a protein (reported in kDa) into a corresponding number of residues. Apply this rule of thumb to myosin, G-actin, hemoglobin, and hexokinase and compare your results with the actual number of residues in each of these proteins. Relevant data for this problem are provided on the book's website.

Josee Pacheco

Numerade Educator

Problem 5

Minimal growth medium for bacteria such as $E$. coll includes various salts with characteristic concentrations in the $\mathrm{mM}$ range and a carbon source. The carbon source is typically glucose and it is used at $0.5 \%$ (a concentration of $0.5 \mathrm{g} / 100 \mathrm{mL}$ ). For nitrogen, minimal medium contains ammonium chloride $\left(\mathrm{NH}_{4} \mathrm{Cl}\right)$ with a concentration of $0.1 \mathrm{g} / 100 \mathrm{mL}$
(a) Make an estimate of the number of carbon atoms it takes to make up the macromolecular contents of a bacterium such as $E$. coli. Similarly, make an estimate of the number of nitrogens it takes to make up the macromolecular contents of a bacterium? What about phosphate?
(b) How many cells can be grown in a $5 \mathrm{mL}$ culture using minimal medium before the medium exhausts the carbon? How many cells can be grown in a $5 \mathrm{mL}$ culture using minimal medium before the medium exhausts the nitrogen? Note that this estimate will be flawed because it neglects the energy cost of synthesizing the macromolecules of the cell.
These shortcomings will be addressed in Chapter 5

Anand Jangid

Numerade Educator

Problem 6

(a) Obtain coordinates for several of the following molecules: ATP, phosphatidylcholine, B-DNA, Gractin, the lambda repressor/DNA complex or Lac repressor/DNA complex, hemoglobin, myoglobin, HIV gp120, green fluorescent protein (GFP), and RNA polymerase. You can find the coordinates on the book's website or by searching in the Protein Data Bank and various other Internet resources.
(b) Download a structural viewing code such as VMD (University of Illinois), Rasmol (University of Massachusetts), or DeepView (Swiss Institute of Bioinformatics) and create a plot of each of the molecules you downloaded above. Experiment with the orientation of the molecule and the different representations shown in Figure 2.32
(c) By looking at phosphatidylcholine, justify (or improve upon) the value of the area per lipid $\left(0.5 \mathrm{nm}^{2}\right)$ used in the chapter.
(d) Phosphoglycerate kinase is a key enzyme in the glycolysis pathway. One intriguing feature of such enzymes Is their enormity in comparison with the sizes of the molecules upon which they act (their "substrate"). This statement is made clear in Figure $5.5(\mathrm{p}, 195) .$ Obtain the coordinates for both phosphoglycerate kinase and glucose and examine the relative size of these molecules. The coordinates are provided on the book's website.

Josee Pacheco

Numerade Educator

Problem 7

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 $I=\alpha N$

Sana Riaz

Numerade Educator

Problem 8

(a) Estimate the total mass of an HIV virion by comparing its volume with that of an $E$, coli cell and assuming they have the same density.
(b) The HIV maturation process involves proteolytic clipping of the Gag polyprotein so that the capsid protein CA can form the shell surrounding the RNA genome and nucleocapsid $\mathrm{NC}$ can complex with the RNA itself. Using Figures 2.30 and 2.31 to obtain the capsid dimensions. estimate the number of CA proteins that are used to make the capsid and compare your result with the total number of Gag proteins.

Josee Pacheco

Numerade Educator

Problem 9

(a) Calculate the average volume and surface area of mitochondria in yeast based on the confocal microscopy image of Figure $2.18(\mathrm{C})$
(b) Estimate the area of the endoplasmic reticulum when it is in reticular form using a model for its structure of interpenetrating cylinders of diameter $d \approx 10 \mathrm{nm}$ separated by a distance $a \approx 60 \mathrm{nm},$ as shown in Figure 2.25

Sana Riaz

Numerade Educator

Problem 10

Using the figures of cells and their organelles provided on the book website, carry out estimates of the following:
(a) The number of nuclear pores in the nucleus of a pancreatic acinar cell.
(b) The spacing between mitochondrial lamellae and the relative area of the inner and outer mitochondrial membranes.
(c) The spacing and areal density of ribosomes in the rough endoplasmic reticulum of a pancreatic acinar cell.
(d) The DNA density in the head of a sperm.
(e) The volume available in the cytoplasm of a leukocyte.

Josee Pacheco

Numerade Educator