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Lehninger Principles of Biochemistry

David L. Nelson, Michael M. Cox

Chapter 1

The Foundations of Biochemistry - all with Video Answers

Educators

Chapter Questions

09:21

Problem 1

The Size of Cells and Their Components
(a) If you were to magnify a cell 10,000 -fold (typical of the magnification achieved using an electron microscope), how big would it appear? Assume you are viewing a "typical" eukaryotic cell with a cellular diameter of $50 \mu \mathrm{m}$.
(b) If this cell were a muscle cell (myocyte), how many molecules of actin could it hold? Assume the cell is spherical and no other cellular components are present; actin molecules are spherical, with a diameter of $3.6 \mathrm{nm}$. (The volume of a sphere is $4 / 3 \pi r^{3}$.)
(c) If this were a liver cell (hepatocyte) of the same dimensions, how many mitochondria could it hold? Assume the cell is spherical; no other cellular components are present; and the mitochondria are spherical, with a diameter of $1.5 \mu \mathrm{m}$
(d) Glucose is the major energy-yielding nutrient for most cells. Assuming a cellular concentration of $1 \mathrm{M}$ (that is, 1 millimole/L), calculate how many molecules of glucose would be present in our hypothetical (and spherical) eukaryotic cell. (Avogadro's number, the number of molecules in 1 mol of a nonionized substance, is $6.02 \times 10^{23}$.
(e) Hexokinase is an important enzyme in the metabolism of glucose. If the concentration of hexokinase in our eukaryotic cell is $20 \mu \mathrm{M},$ how many glucose molecules are present per hexokinase molecule?

Lara Gossage
Lara Gossage
Numerade Educator
09:30

Problem 2

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. The volume of a cylinder is $\pi r^{2} h,$ where $h$ is the height of the cylinder.
(a) If the average density of $E$. coli (mostly water) is $1.1 \times 10^{3} \mathrm{g} / \mathrm{L}$, what is the mass of a single cell?
(b) $E .$ coli has a protective cell envelope $10 \mathrm{nm}$ thick. What percentage of the total volume of the bacterium does the cell envelope occupy?
(c) $E .$ 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?

Lara Gossage
Lara Gossage
Numerade Educator
06:20

Problem 3

Genetic Information in $\boldsymbol{E}$. coli DNA The genetic information contained in DNA consists of a linear sequence of coding units, known as codons. Each codon is a specific sequence of three deoxyribonucleotides (three deoxyribonucleotide pairs in doublestranded DNA), and each codon codes for a single amino acid unit in a protein. 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. (a) Calculate the length of an $E$. coli DNA molecule. Compare the length of the DNA molecule with the cell dimensions (see Problem 2). How does the DNA molecule fit into the cell?
(b) Assume that the average protein in $E$. coli consists of a chain of 400 amino acids. What is the maximum number of proteins that can be coded by an $E$. coli DNA molecule?

Niamat Khuda
Niamat Khuda
Numerade Educator
07:18

Problem 4

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 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) Why does 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. Compare it with the surface-to-volume ratio for a globular amoeba, a large eukaryotic cell (diameter $150 \mu \mathrm{m}$ ). The surface area of a sphere is $4 \pi r^{2}$

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:52

Problem 5

Fast Axonal Transport Neurons have long thin processes called axons, structures specialized for conducting signals throughout the organism's nervous system. Some axonal processes can be as long as $2 \mathrm{m}-$ for example, the axons that originate in your spinal cord and terminate in the muscles of your toes. 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?

Niamat Khuda
Niamat Khuda
Numerade Educator
01:20

Problem 6

Is Synthetic Vitamin C as Good as the Natural Vitamin? A claim put forth by some purveyors of health foods is that vitamins obtained from natural sources are more healthful than those obtained by chemical synthesis. For example, pure L-ascorbic acid (vitamin C) extracted from rose hips is better than pure L-ascorbic acid manufactured in a chemical plant. Are the vitamins from the two sources different? Can the body distinguish a vitamin's source?

Prashant Bana
Prashant Bana
Numerade Educator
03:18

Problem 7

Identification of Functional Groups Figures $1-17$ and $1-18$ show some common functional groups of biomolecules. Because the properties and biological activities of biomolecules are largely determined by their functional groups, it is important to be able to identify them. In each of the compounds below, circle and identify by name each functional group.

Prashant Bana
Prashant Bana
Numerade Educator
08:53

Problem 8

Drug Activity and Stereochemistry The quantitative differences in biological activity between the two enantiomers of a compound are sometimes quite large. For example, the $\mathrm{D}$ isomer of the drug isoproterenol, used to treat mild asthma, is 50 to 80 times more effective as a bronchodilator than the $L$ isomer. Identify the chiral center in isoproterenol. Why do the two enantiomers have such radically different bioactivity?

Dr. Satish Ingale
Dr. Satish Ingale
Numerade Educator
05:30

Problem 9

Separating Biomolecules In studying a particular biomolecule (a protein, nucleic acid, carbohydrate, or lipid) in the laboratory, the biochemist first needs to separate it from other biomolecules in the sample-that is, to purify it. Specific purification techniques are described later in the book. However, by looking at the monomeric subunits of a biomolecule, you should have some ideas about the characteristics of the molecule that would allow you to separate it from other molecules. For example, how would you separate
(a) amino acids from fatty acids and (b) nucleotides from glucose?

Lara Gossage
Lara Gossage
Numerade Educator
04:25

Problem 10

Silicon-Based Life? Silicon is in the same group of the periodic table as carbon and, like carbon, can form up to four single bonds. Many science fiction stories have been based on the premise of silicon-based life. Is this realistic? What characteristics of silicon make it less well adapted than carbon as the central organizing element for life? To answer this question, consider what you have learned about carbon's bonding versatility, and refer to a beginning inorganic chemistry textbook for silicon's bonding properties.

Lara Gossage
Lara Gossage
Numerade Educator
07:31

Problem 11

Drug Action and Shape of Molecules Some years ago, two drug companies marketed a drug under the trade names Dexedrine and Benzedrine. The structure of the drug is shown below.
The physical properties (C, $\mathrm{H}$, and $\mathrm{N}$ analysis, melting point, solubility, etc.) of Dexedrine and Benzedrine were identical. The recommended oral dosage of Dexedrine (which is still available) was $5 \mathrm{mg} /$ day, but the recommended dosage of Benzedrine (no longer available - was twice that. Apparently it required considerably more Benzedrine than Dexedrine to yield the same physiological response. Explain this apparent contradiction.

Lara Gossage
Lara Gossage
Numerade Educator
05:59

Problem 12

Components of Complex Biomolecules Figure $1-11$ shows the major components of complex biomolecules. For each of the three important biomolecules below (shown in their ionized forms at physiological $\mathrm{pH}$ ), identify the constituents.
(a) Guanosine triphosphate (GTP), an energy-rich nucleotide that serves as a precursor to RNA:
(b) Methionine enkephalin, the brain's own opiate:
(c) Phosphatidylcholine, a component of many membranes:

Lara Gossage
Lara Gossage
Numerade Educator
08:03

Problem 13

Determination of the Structure of a Biomolecule An unknown substance, X, was isolated from rabbit muscle. Its structure was determined from the following observations and experiments. Qualitative analysis showed that $\mathrm{X}$ was composed entirely of $\mathrm{C}, \mathrm{H},$ 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 $X$ contained $40.00 \%$ C, $6.71 \%$ H, and $53.29 \%$ O by weight. The molecular mass of $X$, determined by mass spectrometry, was $90.00 \mathrm{u}$ (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; the solution 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?
(d) What is the structural significance of the observation that a solution of $X$ was
acidic? Which structures in (b) are consistent with the observation?
(e) What is the structure of $X ?$ Is more than one structure consistent with all the data?

Lara Gossage
Lara Gossage
Numerade Educator
07:12

Problem 14

Naming Stereoisomers with One Chiral Carbon Using the RS System Propranolol is a chiral compound. ( $R$ )-Propranolol is used as a contraceptive; (S)-propranolol is used totreat hypertension. Identify the chiral carbon in the structure below. Is this the $(R)$ or the $(S)$ isomer? Draw the other isomer.

Noah Boudrie
Noah Boudrie
Numerade Educator
04:11

Problem 15

Naming Stereoisomers with Two Chiral Carbons Using the RS System The $(R, R)$ isomer of methylphenidate (Ritalin) is used to treat attention deficit hyperactivity disorder (ADHD). The $(S, S)$ isomer is an antidepressant. Identify the two chiral carbons in the structure below. Is this the $(R, R)$ or the $(S, S)$ isomer? Draw the other isomer.

CB
Christopher Bazell
Numerade Educator
03:01

Problem 16

Interaction of Sweet-Tasting Molecules with Taste Receptors Many compounds taste sweet to humans. Sweet taste results when a molecule binds to the sweet receptor, one type of taste receptor, on the surface of certain tongue cells. The stronger the binding, the lower the concentration required to saturate the receptor and the sweeter a given concentration of that substance tastes. The standard free-energy change, $\Delta G^{\circ},$ of the binding reaction between a sweet molecule and a sweet receptor can be measured in kilojoules or kilocalories per mole.
Sweet taste can be quantified in units of "molar relative sweetness" (MRS), a measure that compares the sweetness of a substance to the sweetness of sucrose. For example, saccharin has an MRS of $161 ;$ this means that saccharin is 161 times sweeter than sucrose. In practical terms, this is measured by asking human subjects to compare the sweetness of solutions containing different concentrations of each compound. Sucrose and saccharin taste equally sweet when sucrose is at a concentration 161 times higher than that of saccharin.
(a) What is the relationship between MRS and the $\Delta G^{\circ}$ of the binding reaction? Specifically, would a more negative $\Delta G^{\circ}$ correspond to a higher or lower MRS? Explain your reasoning.
Shown below are the structures of 10 compounds, all of which taste sweet to humans. The MRS and $\Delta G^{\circ}$ for binding to the sweet receptor are given for each substance.
Morini, Bassoli, and Temussi (2005) used computer-based methods (often referred to as "in silico" methods) to model the binding of sweet molecules to the sweet receptor.
(b) Why is it useful to have a computer model to predict the sweetness of molecules, instead of a human- or animal-based taste assay? In earlier work, Schallenberger and Acree (1967) had suggested that all sweet molecules include an "AH-B" structural group, in which "A and B are electronegative atoms separated by a distance of greater than $2.5 \AA[0.25 \mathrm{nm}]$ but less than $4 \AA[0.4 \mathrm{nm}] . \mathrm{H}$ is a hydrogen atom attached to one of the electronegative atoms by a covalent bond."
(c) Given that the length of a "typical" single bond is about $0.15 \mathrm{nm}$, identify the AH-B group(s) in each of the molecules shown above.
(d) Based on your findings from (c), give two objections to the statement that "molecules containing an AH-B structure will taste sweet."
(e) For two of the molecules shown here, the AH-B model $c a n$ be used to explain the difference in MRS and $\Delta G^{\circ} .$ Which two molecules are these, and how would you use them to support the AH-B model?
(f) Several of the molecules have closely related structures but very different MRS and $\Delta G^{\circ}$ values. Give two such examples, and use these to argue that the AH-B model is unable to explain the observed differences in sweetness.
In their computer-modeling study, Morini and coauthors used the three-dimensional structure of the sweet receptor and a molecular dynamics modeling program called GRAMM to predict the $\Delta G^{\circ}$ of binding of sweet molecules to the sweet receptor. First, they "trained" their model-that is, they refined the parameters so that the $\Delta G^{\circ}$ values predicted by the model matched the known $\Delta G^{\circ}$ values for one set of sweet molecules (the "training set"' . They then "tested" the model by asking it to predict the $\Delta G^{\circ}$ values for a new set of molecules (the "test set").
(g) Why did Morini and colleagues need to test their model against a different set of molecules from the set it was trained on?
(h) The researchers found that the predicted $\Delta G^{\circ}$ values for the test set differed from the actual values by, on average, $1.3 \mathrm{kcal} / \mathrm{mol}$. Using the values given with the molecular structures, estimate the resulting error in MRS values.

Sana Riaz
Sana Riaz
Numerade Educator