Two different views of a cyanine dye binding to the minor groove of DNA

A lot of research is being done on molecules that bind to DNA. The figure above shows one common binding mode, in which the molecule sticks into a groove of DNA. The binding is especially interesting if it is "sequence specific", such that the molecule binds only to specific sequences of DNA base pairs. Such molecules can be used as diagnostics, to indicate if a certain type of DNA is present in a sample. Often the molecule will change color when it binds, and this makes it easy to identify genes associated with certain viral infections. Another use of molecules that bind to DNA is to create drugs that bind to specific genes and prevent them from being expressed.

You work for new startup biotechnology company. They have invented a new molecular dye, code-named dye_a, that binds selectively to a portion of viral DNA that we will can DNA_a. The dye is a weak acid that can exist in both protonated (HDye_a⁺) and deprotonated (Dye_a) forms. These are related by a standard weak-acid reaction:

HDye_a⁺ + H₂O <==> Dye^a + H₃O⁺

HDye_a⁺ intercalates into DNA according to the equilibrium reaction,

HDye_a⁺ + DNA_a <==> Hdye_a⁺-DNA_a

where Hdye_a⁺-DNA_a means a single molecule consisting of HDye_a⁺ bound to DNA_a.

Your company is building an apparatus that can tell whether water is contaminated with the viral DNA (DNA_a). To calibrate the instrument, your co-workers would like a solution in which [Hdye_a⁺-DNA_a]/[DNA_a] = 1. Due to the nature of the experiment, the calibration solution must also be stable to additions of small amounts of acid or base.

Use the Virtual Lab to make a 100ml solution such that:

a) The addition of 1ml of 0.1M Dye solution and 1ml of 10^-3M DNA leads to a solution with half the DNA bound to the dye:

[Hdye_a⁺-DNA_a]/[DNA_a] = 1 ± 0.05

b) Addition of 0.1ml of 1M NaOH, or 0.1ml of 1M HCl maintains the same ratio:

[Hdye_a⁺-DNA_a]/[DNA_a] = 1 ± 0.05

Please list the solutions you mixed together to get the 100ml solution (please give the stockroom solution names, and the amounts, and check that your volumes sum to 100ml). Please also explain how you arrived at your answer.