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Chapter 31: Problem 5

The GroEL ring has a 5 -nm central cavity. Calculate the maximum molecular weight for a spherical protein that can just fit in this cavity, assuming the density of the protein is \(1.25 \mathrm{g} / \mathrm{mL}\)

Short Answer

Expert verified
The maximum molecular weight for a spherical protein that can just fit in the GroEL ring's central cavity is approximately \(6.55 \times 10^{23}\) Da (daltons) or amu (atomic mass units).

Step by step solution

01

Calculate the Sphere's Volume

The sphere's volume is given by \( \frac{4}{3} \pi r^3 \). Given that \( r = 5 \) nm = 0.0000005 cm, the volume in cubic centimetres is \( V = \frac{4}{3} \pi (0.0000005 \mathrm{cm})^3 = 5.24 \times 10^{-16} \mathrm{cm^3} \) or 5.24 picolitres.
02

Convert Density to g/L and Find Mass

The given density is 1.25 g/mL, or 1250 g/L. The mass of the protein that would exactly fill this sphere is given by \( mass = density \times volume \). Hence, the mass equates to \( 1250 \mathrm{g/L} \times 5.24 \times 10^{-16} \mathrm{L} = 6.55 \times 10^{-13} \) g.
03

Calculate Molecular Weight

The molecular weight will be the mass divided by the number of moles, but converting grams to daltons (or atomic mass units - amu) is required. 1 g/mol = 6.022 x 10^23 g/mol. Divide the mass by Avogadro's number gives \( \frac{6.55 \times 10^{-13}}{6.022 \times 10^{23}} \) moles = 10^-36 moles. Thus, the molecular weight is \( \frac{6.55 \times 10^{-13}}{10^{-36}} = 6.55 \times 10^{23} \) Da or amu.

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Most popular questions from this chapter

(Integrates with Chapter 30 .) Human rhodanese \((33 \mathrm{kD})\) consists of 296 amino acid residues. Approximately how many ATP equivalents are consumed in the synthesis of the rhodanese polypeptide chain from its constituent amino acids and the folding of this chain into an active tertiary structure?

A single proteolytic break in a polypeptide chain of a native protein is often sufficient to initiate its total degradation. What does this fact suggest to you regarding the structural consequences of proteolytic nicks in proteins?

Many multidomain proteins apparently do not require chaperones to attain the fully folded conformations. Suggest a rational scenario for chaperonc- independent folding of such proteins.

Protein molecules, like all molecules, can be characterized in terms of general properties such as size, shape, charge, solubility/hydrophobicity, Consider the influence of each of these general features on the likelihood of whether folding of a particular protein will require chaperone assistance or not. Be specific regarding just Hsp 70 chaperones or Hsp 70 chaperones and Hsp 60 chaperonins.

The cross-talk between phosphorylation and ubiquitination in protein degradation processes is encapsulated in the concept of the "phosphodegron." What is a phosphodegron, and how does phosphorylation serve as a recognition signal for protein degradation? (A good reference on the phosphodegron and crosstalk between phosphorylation and ubiquitination is Hunter, \(\mathrm{T}\)., 2007 . The age of crosstalk: Phosphorylation, ubiquitination, and beyond. Molecular Cell \(28: 730-738 .\)
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