2. As we've seen previously, peptide bonds involving the amino acid proline can populate both "trans" and "cis" isomers. trans-Pro cis-Pro This isomerization reaction can be the rate-limiting step in protein folding. Depending on the protein sequence, the relative favorability of the trans and cis states can change. For Pro-117 in the protein staphylococcal nuclease, the rates of the forward and reverse reactions are: ktrans-cis = 3.1 x 10-2 and keis→trans = 2.5 x 10-3 s-1. (a) What is AG" for this reaction? (b) A prolyl isomeriase enzyme increases the rate of the forward reaction to kcat,trans+cis = 2.6 s-. What is the new rate constant for the reverse reaction (kcat,cis→trans)? = 2.6 s-1, KM = 1.9 µM. If (c) This prolyl isomerase is a Michaelis-Menten enzyme with kcat you have 1 nM enzyme, what is Vo for [S]o = 0.7 µM? What about [S]o = 30 µM? For each condition, what limits the reaction speed?
2. As we've seen previously, peptide bonds involving the amino acid proline can populate both "trans" and "cis" isomers. trans-Pro cis-Pro This isomerization reaction can be the rate-limiting step in protein folding. Depending on the protein sequence, the relative favorability of the trans and cis states can change. For Pro-117 in the protein staphylococcal nuclease, the rates of the forward and reverse reactions are: ktrans-cis = 3.1 x 10-2 and keis→trans = 2.5 x 10-3 s-1. (a) What is AG" for this reaction? (b) A prolyl isomeriase enzyme increases the rate of the forward reaction to kcat,trans+cis = 2.6 s-. What is the new rate constant for the reverse reaction (kcat,cis→trans)? = 2.6 s-1, KM = 1.9 µM. If (c) This prolyl isomerase is a Michaelis-Menten enzyme with kcat you have 1 nM enzyme, what is Vo for [S]o = 0.7 µM? What about [S]o = 30 µM? For each condition, what limits the reaction speed?
Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Chapter1: Biochemistry: An Evolving Science
Section: Chapter Questions
Problem 1P
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![**Peptide Bond Isomerization in Protein Folding**
Peptide bonds involving the amino acid proline can exist in both "trans" and "cis" isomeric forms. The isomerization reaction between these forms can be a rate-limiting step in protein folding. In certain proteins, such as staphylococcal nuclease with a specific proline residue (Pro-117), the rates of transformation between these isomers are given by the following constants:
- Forward reaction (\(k_\text{{trans→cis}}\)): \(3.1 \times 10^{-2}\, \text{s}^{-1}\)
- Reverse reaction (\(k_\text{{cis→trans}}\)): \(2.5 \times 10^{-3}\, \text{s}^{-1}\)
The diagram illustrates the chemical structures of the trans and cis isomers of proline, alongside the equilibrium between them.
### Questions:
**(a)** What is \(\Delta G^\circ\) for this reaction?
**(b)** A prolyl isomerase enzyme increases the rate of the forward reaction to \(k_\text{{cat, trans→cis}} = 2.6\, \text{s}^{-1}\).
- What is the new rate constant for the reverse reaction (\(k_\text{{cat, cis→trans}}\))?
**(c)** This prolyl isomerase follows Michaelis-Menten kinetics with:
- \(k_\text{{cat}} = 2.6\, \text{s}^{-1}\)
- \(K_M = 1.9\, \mu\text{M}\)
Given:
- Enzyme concentration \(= 1\, \text{nM}\)
Evaluate \(V_0\) for the following substrate concentrations:
- \([S]_0 = 0.7\, \mu\text{M}\)
- \([S]_0 = 30\, \mu\text{M}\)
For each condition, identify what limits the reaction speed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c5565a-787b-43d3-b23e-780453faf6da%2F31430967-aefd-467a-9f36-db8d3d53083b%2F7xwrdeq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Peptide Bond Isomerization in Protein Folding**
Peptide bonds involving the amino acid proline can exist in both "trans" and "cis" isomeric forms. The isomerization reaction between these forms can be a rate-limiting step in protein folding. In certain proteins, such as staphylococcal nuclease with a specific proline residue (Pro-117), the rates of transformation between these isomers are given by the following constants:
- Forward reaction (\(k_\text{{trans→cis}}\)): \(3.1 \times 10^{-2}\, \text{s}^{-1}\)
- Reverse reaction (\(k_\text{{cis→trans}}\)): \(2.5 \times 10^{-3}\, \text{s}^{-1}\)
The diagram illustrates the chemical structures of the trans and cis isomers of proline, alongside the equilibrium between them.
### Questions:
**(a)** What is \(\Delta G^\circ\) for this reaction?
**(b)** A prolyl isomerase enzyme increases the rate of the forward reaction to \(k_\text{{cat, trans→cis}} = 2.6\, \text{s}^{-1}\).
- What is the new rate constant for the reverse reaction (\(k_\text{{cat, cis→trans}}\))?
**(c)** This prolyl isomerase follows Michaelis-Menten kinetics with:
- \(k_\text{{cat}} = 2.6\, \text{s}^{-1}\)
- \(K_M = 1.9\, \mu\text{M}\)
Given:
- Enzyme concentration \(= 1\, \text{nM}\)
Evaluate \(V_0\) for the following substrate concentrations:
- \([S]_0 = 0.7\, \mu\text{M}\)
- \([S]_0 = 30\, \mu\text{M}\)
For each condition, identify what limits the reaction speed.
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