Chapter 1

The Size of Cells and Their Components A typical eukaryotic cell has a cellular diameter of \(50 \mu \mathrm{m}\). a. If you used an electron microscope to magnify this cell 10,000-fold, how big would the cell appear? b. If this cell were a liver cell (hepatocyte) with the same cellular diameter, how many mitochondria could the cell contain? Assume the cell is spherical; that the cell contains no other cellular components; and that each mitochondrion is spherical, with a diameter of \(1.5\) \(\mu \mathrm{m}\). (The volume of a sphere is \(4 / 3 \pi r^{3}\).) c. Glucose is the major energy-yielding nutrient for most cells. Assuming a cellular concentration of \(1 \mathrm{~mm}\)

Components of \(\boldsymbol{E}\). coli \(E\). coli cells are rod-shaped, about 2 \(\mu \mathrm{m}\) long, and \(0.8 \mu \mathrm{m}\) in diameter. E. coli has a protective envelope \(10 \mathrm{~nm}\) thick. The volume of a cylinder is \(\pi r^{2} h\), where \(h\) is the height of the cylinder. a. What percentage of the total volume of the bacterium does the cell envelope occupy? b. E. coli is capable of growing and multiplying rapidly because it contains some 15,000 spherical ribosomes (diameter \(18 \mathrm{~nm}\) ), which carry out protein synthesis. What percentage of the cell volume do the ribosomes occupy? c. The molecular weight of an \(E\). coli DNA molecule is about \(3.1 \times 10^{9} \mathrm{~g} / \mathrm{mol}\). The average molecular weight of a nucleotide pair is \(660 \mathrm{~g} / \mathrm{mol}\), and each nucleotide pair contributes \(0.34 \mathrm{~nm}\) to the length of DNA. Calculate the length of an \(E\). coli DNA molecule. Compare the length of the DNA molecule with the cell dimensions. Now, consider the photomicrograph showing the single DNA molecule of the bacterium \(E\). coli leaking out of a disrupted cell (Fig, 1-31b). How does the DNA molecule fit into the cell?

The High Rate of Bacterial Metabolism Bacterial cells have a much higher rate of metabolism than animal cells. Under ideal conditions, some bacteria double in size and divide every \(20 \mathrm{~min}\), whereas most animal cells under rapid growth conditions require 24 hours. The high rate of bacterial metabolism requires a high ratio of surface area to cell volume. a. How does the surface-to-volume ratio affect the maximum rate of metabolism? b. Calculate the surface-to-volume ratio for the spherical bacterium Neisseria gonorrhoeae (diameter \(0.5 \mu \mathrm{m}\) ), responsible for the disease gonorrhea. The surface area of a sphere is \(4 \pi r^{2}\). c. How many times greater is the surface-to-volume ratio of Neisseria gonorrhoeae compared to that of a globular amoeba, a large eukaryotic cell (diameter 150 \(\mu \mathrm{m}\) )?

Fast Axonal Transport Neurons have long thin processes called axons, structures specialized for conducting signals throughout the organism's nervous system. The axons that originate in a person's spinal cord and terminate in the muscles of the toes can be as long as \(2 \mathrm{~m}\). Small membrane- enclosed vesicles carrying materials essential to axonal function move along microtubules of the cytoskeleton, from the cell body to the tips of the axons. If the average velocity of a vesicle is \(1 \mu \mathrm{m} / \mathrm{s}\), how long does it take a vesicle to move from a cell body in the spinal cord to the axonal tip in the toes?

Possibility of Silicon-Based Life Carbon and silicon are in the same group on the periodic table, and both can form up to four single bonds. As such, many science fiction stories have been based on the premise of silicon-based life. Consider what you know about carbon's bonding versatility (refer to a beginning inorganic chemistry resource for silicon's bonding properties, if needed). What property of carbon makes it especially suitable for the chemistry of living organisms? What characteristics of silicon make it less well adapted than carbon as the central organizing element for life?

Stereochemistry and Drug Activity of Ibuprofen Ibuprofen is an over-the- counter drug that blocks the formation of a class of prostaglandins that cause inflammation and pain. Ibuprofen is available as a racemic mixture of \((R)\)-ibuprofen and \((S)\)-ibuprofen. In living organisms, an isomerase catalyzes the chiral inversion of the \((R)\)-enantiomer to the \((S)\) enantiomer. The reverse reaction does not occur at an appreciable rate. The accompanying figure represents the two enantiomers relative to the binding sites \(a, b\), and \(c\) in the isomerase enzyme that converts the \((R)\)-enantiomer to the (S)-enantiomer. All three sites recognize the corresponding functional groups of the \((R)\)-enantiomer of ibuprofen.

Three important biomolecules are depicted in their ionized forms at physiological \(\mathrm{pH}\). Identify the chemical constituents that are part of each molecule. a. Guanosine triphosphate (GTP), an energy-rich nucleotide that serves as a precursor to RNA:

Biomolecule Researchers isolated an unknown substance, \(X\), from rabbit muscle. They determined its structure from the following observations and experiments. Qualitative analysis showed that \(X\) was composed entirely of \(C, H\), and \(O\). \(A\) weighed sample of \(X\) was completely oxidized, and the \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}_{2}\) produced were measured; this quantitative analysis revealed that \(\mathrm{X}\) contained \(40.00 \% \mathrm{C}, 6.71 \% \mathrm{H}\), and \(53.29 \% \mathrm{O}\) by weight. The molecular mass of \(\mathrm{X}\), determined by mass spectrometry, was \(90.00\) u (atomic mass units; see Box 1-1). Infrared spectroscopy showed that \(X\) contained one double bond. X dissolved readily in water to give an acidic solution that demonstrated optical activity when tested in a polarimeter. a. Determine the empirical and molecular formula of \(X\). b. Draw the possible structures of \(X\) that fit the molecular formula and contain one double bond. Consider only linear or branched structures and disregard cyclic structures. Note that oxygen makes very poor bonds to itself. c. What is the structural significance of the observed optical activity? Which structures in (b) are consistent with the observation?

State of Bacterial Spores A bacterial spore is metabolically inert and may remain so for years. Spores contain no measurable ATP, exclude water, and consume no oxygen. However, when a spore is transferred into an appropriate liquid medium, it germinates, makes ATP, and begins cell division within an hour. Is the spore dead, or is it alive? Explain your answer.

chemically unstable compared with its oxidation products, \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). a. What can one say about the standard free- energy change for this reaction? b. Why doesn't firewood stacked beside the fireplace undergo spontaneous combustion to its much more stable products? c. How can the activation energy be supplied to this reaction? d. Suppose you have an enzyme (firewoodase) that catalyzes the rapid conversion of firewood to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature. How does the enzyme accomplish that in thermodynamic terms?