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Chapter 1: Problem 4

Assume that mitochondria are cylinders \(1.5 \mu \mathrm{m}\) in length and \(0.6 \mu \mathrm{m}\) in diameter. a. What is the volume of a single mitochondrion? b. Oxaloacetate is an intermediate in the citric acid cycle, an important metabolic pathway localized in the mitochondria of eukaryotic cells. The concentration of oxaloacetate in mitochondria is about \(0.03 \mu M\). How many molecules of oxaloacetate are in a single mitochondrion?

Short Answer

Expert verified
a. The volume of a single mitochondrion is approximately \(0.424 \mu m^3\). b. There are approximately \(7.678 \times 10^{-2}\) molecules of oxaloacetate in a single mitochondrion.

Step by step solution

01

Calculate the Volume of a Mitochondrion

First, the diameter of the mitochondrion is given as \(0.6 \mu m\), so the radius is \( r = 0.6/2 = 0.3 \mu m \). Also, the height is given as \( h = 1.5 \mu m \). Substituting these values into the formula for the volume of a cylinder, \( V = \pi r^2h \), we get \( V = \pi * (0.3)^2 * 1.5 = 0.424 m^3 \).
02

Calculate the Number of Oxaloacetate Molecules in a Mitochondrion

Now, to find the number of molecules of oxaloacetate in a single mitochondrion, we use the formula \( N = C * V * N_A \). The concentration is given as \( C = 0.03 \mu M \) which is equal to \( 0.03 * 10^{-6} M \), The volume of a single mitochondrion \( V = 0.424 \mu m^3 \), Avogadro's number is \( N_A = 6.022 * 10^{23} \). Substituting these values into the formula, we get \( N = C * V * N_A = 0.03 * 10^{-6} M * 0.424 * 10^{-15} m^3 $ * $ 6.022 * 10^{23} = 7.678 \times 10^{-2} \) molecules.

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Most popular questions from this chapter

The genome of the Mycoplasma genitalium consists of 523 genes, encoding 484 proteins, in just 580,074 base pairs (Table 1.6). What fraction of the \(M .\) genitalium genes encode proteins? What do you think the other genes encode? If the fraction of base pairs devoted to protein-coding genes is the same as the fraction of the total genes that they represent, what is the average number of base pairs per protein-coding gene? If it takes 3 base pairs to specify an amino acid in a protein, how many amino acids are found in the average \(M .\) genitalium protein? If each amino acid contributes on average 120 Daltons to the mass of a protein, what is the mass of an average M. genitalium protein?

Why does the central role of weak forces in biomolecular interactions restrict living systems to a narrow range of environmental conditions?

The nutritional requirements of Escherichia coli cells are far simpler than those of humans, yet the macromolecules found in bacteria are about as complex as those of animals. Because bacteria can make all their essential biomolecules while subsisting on a simpler diet, do you think bacteria may have more biosynthetic capacity and hence more metabolic complexity than animals? Organize your thoughts on this question, pro and con, into a rational argument.

Escherichia coli cells are about \(2 \mu \mathrm{m}\) (microns) long and \(0.8 \mu \mathrm{m}\) in diameter. a. How many \(E\). coli cells laid end to end would fit across the diameter of a pinhead? (Assume a pinhead diameter of \(0.5 \mathrm{mm}\).) b. What is the volume of an \(E\). coli cell? (Assume it is a cylinder, with the volume of a cylinder given by \(V=\pi r^{2} h,\) where \(\pi=3.14 .\) c. What is the surface area of an \(E\). colicell? What is the surface-to volume ratio of an \(E .\) colicell? d. Glucose, a major energy-yielding nutrient, is present in bacterial cells at a concentration of about \(1 \mathrm{m} M\). What is the concentration of glucose, expressed as \(\mathrm{mg} / \mathrm{mL}\) ? How many glucose molecules are contained in a typical \(E\) coli cell? (Recall that Avogadro's number \(=6.023 \times 10^{23}\).) e. A number of regulatory proteins are present in \(E\). coli at only one or two molecules per cell. If we assume that an \(E\). colicell contains just one molecule of a particular protein, what is the molar concentration of this protein in the cell? If the molecular weight of this protein is \(40 \mathrm{kD},\) what is its concentration, expressed as \(\mathrm{mg} / \mathrm{mL} ?\) f. \(\operatorname{An} E .\) coli cell contains about 15,000 ribosomes, which carry out protein synthesis. Assuming ribosomes are spherical and have a diameter of \(20 \mathrm{nm}\) (nanometers), what fraction of the \(E .\) colicell volume is occupied by ribosomes? g. The \(E\) coli chromosome is a single DNA molecule whose mass is about \(3 \times 10^{9}\) daltons. This macromolecule is actually a linear array of nucleotide pairs. The average molecular weight of a nucleotide pair is \(660,\) and each pair imparts \(0.34 \mathrm{nm}\) to the length of the DNA molecule. What is the total length of the E. coli chromosome? How does this length compare with the overall dimensions of an \(E\). coli cell? How many nucleotide pairs does this DNA contain? The average \(E\). coli protein is a linear chain of 360 amino acids. If three nucleotide pairs in a gene encode one amino acid in a protein, how many different proteins can the E. coli chromosome encode? (The answer to this question is a reasonable approximation of the maximum number of different kinds of proteins that can be expected in bacteria.)

Without consulting the figures in this chapter, sketch the characteristic prokaryotic and eukaryotic cell types and label their pertinent organelle and membrane systems.
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