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Physical Biology of the Cell

Rob Phillips, Jane Kondev, Julie Theriot

Chapter 4

ho: "Bless the Little Beasties" - all with Video Answers

Educators


Chapter Questions

02:03

Problem 1

(a) As in Problem $2.6,$ obtain the atomic coordinates for hemoglobin and myoglobin. Measure their dimensions, identify the different subunits and the heme groups.
(b) Expand the analysis of hemoglobin on $\mathrm{p} .143 \mathrm{by}$ calculating the mean spacing between hemoglobin molecules inside a red blood cell. How does this spacing compare with the size of a hemoglobin molecule?
(c) Typical results for a complete blood count (CBC) are shown in Table $4.1 .$ Assume that an adult has roughly 5 L of blood in his or her body. Based on these values, estimate:
(i) the number of red blood cells;
(ii) the percentage in volume they represent in the blood;
(iii) their mean spacing;
(iv) the total amount of hemoglobin in the blood;
(v) the number of hemoglobin molecules per cell;
(vi) the number of white blood cells in the blood.

Sana Riaz
Sana Riaz
Numerade Educator
02:21

Problem 2

(a) An estimate for the number of phages on Earth can be obtained using data from Bergh et al. $(1989) .$ By taking water samples from lakes and oceans and counting the various phages, one arrives at counts of the order of $10^{6}-10^{7}$ phages/mL. Using reasonable assumptions about the amount of water on Earth, make an estimate of the number of phages.
(b) Work out the mass of all of the phage particles on the Earth using your result from (a).
(Problem suggested by Sherwood Casjens.)

Narayan Hari
Narayan Hari
Numerade Educator
02:30

Problem 3

Three successive nucleotides along a DNA molecule, called a codon, encode one amino acid. The weight of an $E .$ coli DNA molecule is about $3.1 \times 10^{9}$ daltons. The average weight of a nucleotide pair is 660 daltons, and each nucleotide pair contributes $0.34 \mathrm{nm}$ to the overall DNA length.
(a) What fraction of the mass of an $E$. coli cell corresponds to its genomic DNA?
(b) Calculate the length of the $E .$ coli DNA. Comment on how it compares with the size of a single $E .$ coli cell.
(c) Assume that the average protein in $E .$ coli is a chain of 300 amino acids. What is the maximum number of proteins that can be coded by the $E .$ coli DNA?
(d) $\mathrm{On}$ an alien world, the genetic code consists of two base pairs per codon. There are still four different bases. How many different amino acids can be encoded?

Sana Riaz
Sana Riaz
Numerade Educator
02:58

Problem 4

In Section $4.6 .1,$ we briefly described Sturtevant's analysis of mutant flies that culminated in the generation of the first chromosome map. In Table $4.2,$ we show the crossover data associated with the different mutations that he used to draw the map. A crossover refers to a chromosomal rearrangement in which parts of two chromosomes exchange DNA. An illustration of the process is shown in Figure $4.26 .$ The six factors looked at by Sturtevant are $\mathrm{B}$, $\mathrm{C}$, O, $P, R,$ and $M .$ Flies recessive in $B$, the black factor, have a yellow body color. Factors $C$ and $O$ are completely linked, they always go together and flies recessive in both of these factors have white eyes. A fly recessive in factor P has vermilion eyes instead of the ordinary red eyes. Finally, flies recessive in $\mathrm{R}$ have rudimentary wings and those recessive in M have miniature wings. For example, the fraction of flies that presented a crossover of the $\mathrm{B}$ and $\mathrm{P}$ factors is denoted as BP. Assume that the frequency of recombination is proportional to the distance between loci on the chromosome.
Reproduce Sturtevant's conclusions by drawing your own map using the first seven data points from Table 4.2
Keep in mind that shorter "distances" are more reliable than longer ones because the latter are more prone to double crossings. Are distances additive? For example, can you predict the distance between $\mathrm{B}$ and $\mathrm{P}$ from looking at the distances $\mathrm{B}(\mathrm{C}, \mathrm{O})$ and $(\mathrm{C}, \mathrm{O}) \mathrm{P} ?$ What is the interpretation of the two last data points from Table $4.2 ?$

Sana Riaz
Sana Riaz
Numerade Educator
02:58

Problem 5

In a set of classic experiments, the second chromosome of
D. melanogaster was mutagenized and the effects of these mutations characterized based on their phenotype in embryonic development. The experimenters found 272 mutants with phenotypes visibly different from wild-type embryos. However, when they determined the location of the mutations using the method outlined in Figure 4.21 and worked out in Problem $4.4,$ they discovered that these mutations only mapped to 61 different positions or loci on that chromosome. Figure 4.27 shows how, as more mutants were scored, ever more mutants corresponded to previously identified loci. Using a model that assumes a uniform probability of mutation in any locus, calculate the number of new loci found as a function of the number of mutants isolated. Explain the saturation effect and plot your results against the data. Provide a judgment on whether it is useful to continue searching for loci. (Hint: Start by writing down the probability that a specific locus has not been mapped after scoring the first M mutants). Relevant data for this problem are provided on the book's website.

Sana Riaz
Sana Riaz
Numerade Educator
02:53

Problem 6

In a classic experiment, it was discovered that eukaryotic genomic DNA codes for proteins in a noncontinuous fashion, culminating in the idea of introns, regions in a given gene that are actually spliced out of the mRNA molecule before translation. The concept of the experiment was to hybridize the unspliced DNA with a DNA mimic of the spliced mRNA. Using Figure 4.28 , estimate the sizes of the spliced regions.

Mikayla Stephens
Mikayla Stephens
Numerade Educator
03:23

Problem 7

In this problem, we will compute the probabilities of finding specific DNA sequences in a perfectly random genome, for which we assume that the four different nucleotides appear randomly and with equal probability.
(a) From the genetic code shown in Figure $1.4,$ compute the probability that a randomly chosen sequence of three nucleotides will correspond to a stop codon. Similarly, what is the probability of a randomly chosen sequence corresponding to a start codon?
(b) A reading frame refers to one of three possible ways that a sequence of DNA can be divided into consecutive triplets of nucleotides. An open reading frame (ORF) is a reading frame that contains a start codon and does not contain a stop codon for at least some minimal length of codons. Derive a formula for the probability of an ORF having a length of $N$ codons (not including the stop codon).
(c) The genome of $E .$ coli is approximately $5 \times 10^{6}$ bp long and is circular. Again assuming a that the genome is a random configuration of base pairs, how many ORFs of length 1000 bp (a typical protein size) would be expected by chance? Note that there are six possible reading frames.
(Problem courtesy of Sharad Ramanathan)

Sana Riaz
Sana Riaz
Numerade Educator