Let's break down and solve each question step by step: --- ### **Question 1: For the amino acid structure of leucine, the carbon at position 5 is also commonly correctly called a(n):** #### **Step 1: Identify the carbon at position 5** - The carbons in the side chain of leucine are labeled as follows: - Carbon 1: Carboxyl carbon - Carbon 2: Alpha carbon (attached to -NH2 group) - Carbon 3: Beta carbon - Carbon 4: Gamma carbon - Carbon 5: Delta carbon **Explanation:** In amino acid nomenclature, the side chain carbons are named in order: alpha (adjacent to the -COOH), beta, gamma, delta, etc. The carbon at position 5 is the fourth carbon away from the alpha carbon, making it the **delta carbon**. #### **Step 2: Check the options** - The correct answer is: **delta carbon** #### **Step 3: Confirm if any other names apply** - The carbon at position 5 is not the carboxyl, chiral, or nitrogenous carbon. It's not alpha, beta, or gamma either. **Final Answer for Q1:** - **delta carbon** --- ### **Question 2: Protein folding time calculation (Leventhal's paradox)** #### **Step 1: Calculate total number of conformations** - For a 210-residue polypeptide, each residue can have 4 conformations: - Total conformations = \( 4^{210} \) **Explanation:** Every amino acid in the chain can be in 4 different states. For 210 amino acids, the total number of possibilities is \( 4^{210} \). #### **Step 2: Calculate time to sample all conformations** - Sampling rate = \( 10^{15} \) conformations/sec - Time (in seconds) = \( \frac{4^{210}}{10^{15}} \) **Explanation:** Divide the total conformations by the number sampled per second to get the total time in seconds. #### **Step 3: Convert seconds to hours and simplify** - \( 4^{210} = (2^2)^{210} = 2^{420} \) - So, time (in seconds) = \( \frac{2^{420}}{10^{15}} \) - \( 2^{10} \approx 10^3 \), so \( 2^{420} \approx 10^{126} \) - Time (in seconds) ≈ \( \frac{10^{126}}{10^{15}} = 10^{111} \) seconds - Convert to hours: \( \frac{10^{111}}{3600} \approx 10^{108} \) hours **Check the options:** Closest match is **\( 8 \times 10^{107} \)**. **Final Answer for Q2:** - **\( 8 \times 10^{107} \)** --- ## **Final Answers** ### **1. The carbon at position 5 is:** - **delta carbon** ### **2. Folding time according to Leventhal:** - **\( 8 \times 10^{107} \) hours**

The first question relies on the concept of amino acid nomenclature and the systematic naming of carbon atoms in the side chain based on their position relative to the alpha carbon. Recognizing that the side chain carbons are labeled sequentially as beta, gamma, delta, etc., allows identification of the carbon at position 5 as the delta carbon. The second question employs principles of combinatorial chemistry and exponential calculations, where the total possible conformations of a polypeptide are determined by raising the number of conformations per residue to the power of the number of residues. It then uses logarithmic approximations and unit conversions to estimate the immense time required for the protein to sample all conformations, highlighting the complexity of protein folding and the improbability of exhaustive sampling within realistic timescales.