Oxygen has the right atomic configuration (of a number of protons with a collective positive charge of eight strongly attracting electrons, a small number of electrons, so that the electrons are highly attracted to the protons in the nucleus and not shielded by repelling each other, and is close to filling its outer orbital, so that two additional electrons beyond six in the outer orbital are very stable causing them to spend more time with the oxygen nucleus (why eight valence electrons are so stable gets into a discussion of spherical harmonics [1] and quantum mechanical topics of Schrödinger's equation [2] and electron spin [3], which is not going to happen here)) so that it has a very high electronegativity (second only to flourine [4]) and tends to have a partial negative charge when covalently bonded to other elements.

This partial negative charge of oxygen results in a number of important phenomenon such as hydrogen bonding (in water partially positive hydrogen is attracted to partially negative oxygen of other molecules causing water to expand when it freezes contrary to the behavior of most molecules; this also causes the two strands of DNA to bind with each other) and being miscible with polar as opposed to nonpolar liquids.

Biological molecules have various levels of ability to remain in solution in water. This can be adjusted with alcohols, salts, silica, and resins that interact with the water and the biological molecules, at various levels to separate nucleic acids (DNA and RNA) from the mix of lipids, carbohydrates, proteins, and other biological molecules (metabolites and natural products) resulting from cell lysis.

The phosphate-sugar backbone of DNA is negatively charged, largely because of the phosphate oxygen atoms and oxygen's electronegativity. This allows a large amount of DNA to remain in solution in pure water. However, the DNA molecule is also made up of sugars and bases that contribute less solubility to the entire molecule.

Salts are made up of ionic compounds that will generally dissolve in water and result in negatively charged and positively charged components (ions). This does two things. The positive charged ions closely associate with the negative phosphates of a nucleic acid, acting to essentially cancel out part of their charge. Negatively charged DNA (and RNA) normally repel each other and the positive salt ions allow the DNA to clump together in solution. The ions also have a higher affinity for the charged water molecules and if present at high enough concentrations sequesters the water away from the DNA (see [5] and [6] for more extreme examples where alcohol can be separated from water using salt), making the nucleic acids slightly less soluble in water.

Alcohols have some partially polar properties (are hydrophilic and can dissolve in water) but are much less polar than pure water (the bound hydrocarbons shift the molecule more towards the hydrophobic direction). Nucleic acids are less soluble in a mixture of alcohol and water and insoluble in pure alcohol. Thus, increasing the alcohol content of a solution of water and DNA is also a method to precipitate the DNA out of solution.

Finally, temperature plays a role. DNA is less soluble at lower temperatures (less kinetic energy is available to disrupt in intermolecular attracting forces that separate DNA from water). Often in protocols alcohol is chilled to a lower temperature to promote DNA precipitation.

This suggests purifying nucleic acids by combining a few steps. First mixing cell lysate in water with little to no salt or alcohol to dissolve the nucleic acids in solution (usually salt is included from the beginning and alcohol concentration is used to modify solubility. Spinning down or washing the insoluble biological molecules away from the DNA solution. (Perhaps include a low initial alcohol concentration to remove more biological molecules that are soluble in water but less so than DNA.) Then increasing the concentration of salt and alcohol, and chilling the mixture on ice, to precipitate out the DNA (but not raising the alcohol concentration so high that other highly soluble biological molecules are precipitated out of solution). This often results in a DNA pellet or DNA bound to a surface such as silica. This can be washed briefly with cold ethanol to remove the salt ions and other impurities. Then the resulting DNA is resuspended in a water solution that may or may not contain buffer depending on what it will be used for next. This solution will contain a mixture of DNA and RNA as well as some biological molecules that were co-extracted as well as small amounts of residual salts and alcohol. It should be stored frozen.

Home Protocol

This can be done at home in a kitchen with table salt (NaCl), dishwashing liquid (to disrupt (lyse) cell membranes and release DNA), cheesecloth or a coffee filter (to remove large particles), and rubbing alcohol (isopropyl alcohol). Often this is done with commercial strawberries as a demonstration with colder less dense alcohol layered above a more dense salt-water-DNA solution. The DNA precipitates out of solution at the boundary between the two layers and can be spooled onto a stick and weighed.

Chill isopropyl (rubbing) alcohol in the freezer.
Mash up 2-3 strawberries into a paste.
Mix 1/2 cup of water, 1 teaspoon of salt, and 1 tablespoon of dishwashing liquid. This is your DNA extraction mix.
Add the same number of tablespoons of extraction mix as starting strawberries to the strawberry paste and mix well.
Filter the strawberry paste through cheese cloth, a cloth, or a coffee filter.
Tilt the container and carefully pour a layer of cold rubbing alcohol down the side so that the liquids do not mix.
Whitish DNA should precipitate at the boundary between the two liquid layers.
Use a wooden bamboo skewer to try to lift and spool the DNA out of the liquid.