You are working in a biotechnology lab and are analyzing DNA. You obtain a sample of a short dodecamer of DNA that contains 12 base pairs. (a) What must the ratio of adenine to thymine be in your sample? (b) What must the ratio of cytosine to guanine be in your sample? (c) Assume the counterions present in your DNA solution are sodium ions. How many sodium ions must there be per dodecamer? Assume the \(5^{\prime}\) end phosphates each bear \(a-1\) charge.

Since adenine pairs with thymine in a DNA double helix, the ratio of adenine to thymine in the dodecamer DNA sequence must be 1:1. In other words, there is one adenine molecule for every thymine molecule in the DNA sample.

Similar to part (a), since cytosine pairs with guanine in a DNA double helix, the ratio of cytosine to guanine in the dodecamer DNA sequence must also be 1:1. In other words, there is one cytosine molecule for every guanine molecule in the DNA sample.

To calculate the number of sodium ions per dodecamer, we first need to understand that the negatively charged phosphate groups in DNA are neutralized by the positively charged sodium ions. In a dodecamer, there are 11 phosphate groups per strand, bringing a total of 22 phosphate groups for both the strands. At the 5' ends of the DNA, the phosphates each bear a negative charge. Since there are 2 strands, there will be 2 phosphates with \((a - 1)\) charge. Let's assume \((a - 1)\) charge is -1. Therefore, there will be 2 sodium ions neutralizing the negative charges in the 5' ends. Now, there are 20 remaining phosphate groups in the dodecamer with 1 negative charge each. These phosphate groups will be neutralized by 20 sodium ions. Hence, the total number of sodium ions required per dodecamer is the sum of sodium ions neutralizing the 5' end phosphates and the remaining phosphate groups, which is 2 + 20 = 22.