The mechanism is thought to be primarily due to hydrophobic interactions. I don't think it is understood how exactly this works, except that the final protein-SDS complex is the (entropically?) favored state.

There is a review by Daniel Otzen titled "Protein–surfactant interactions: A tale of many states" that might be of interest, summarizing more recent findings.

https://www.researchgate.net/post/Can_anyone_tell_me_what_kind_of_interaction_there_is_between_SDS_and_proteins_in_SDS-PAGE

http://www.sciencedirect.com/science/article/pii/S1570963911000549

SDS-Polyacrylamide Gel Electrophoresis, or SDS-PAGE for short, is the technique where proteins are denatured and linearized, then run across a current through a thin gel, which separates the proteins by size. SDS-PAGE is a key step in many experiments including:

Western Blots

Separating proteins for mass spectrometry

Determining protein purity (such as after an immunoprecipitation or protein purification)

Examining protein size

Quantifying protein abundance

Visualizing post-translational modifications

…. Basically just about any experiment where you need to know something about your favorite proteins. SDS-PAGE is an essential lab tool you’ll want to master. And part of mastering it is understanding how it works.

Unraveling the Proteins

The first step in running a denaturing gel is to denature your proteins. This is accomplished using:

SDS

When you have your proteins in hand — whether they are from a cell lysate or purified sample — denaturing your proteins is the first step and for this you need Sodium dodecyl sulfate (SDS). SDS is the main star of the denaturing protein gel. SDS is a detergent composed of a hydrophobic hydrocarbon tail attached to an ionic sulphate group and a key component of loading buffer,. When SDS meets up with your protein, SDS’s hydrocarbon tail dissolves any hydrophobic region of the protein, while the sulfate end breaks non-covalent ionic bonds. This causes your protein to lose its secondary and tertiary structure, and well…unfold. Once surrounded by SDS, your previously carefully folded protein becomes loose and long, just like overcooked spaghetti.

A Reducing Agent

Also in the denaturing mix is the noxious β-mercaptoethanol (β-me). Its job is to break disulphide bonds, which further spaghettifies your protein. Its strong smell also lets everyone else in the lab know you’re doing a protein gel!

Heat

The final factor in denaturing your protein is heat. Typically, you will boil your protein samples in the loading buffer (containing Tris-HCl, SDS, bromophenol blue, glycerol, and ?-me) before loading them in your gel. This helps to completely denature the proteins and also helps with physically loading the gel. Protein samples frequently are gummy, particularly if the protein prep is from cell or tissue extracts and therefore contains DNA. Boiling homogenates your sample, as the heat melts any DNA in the prep, in turn making it less gummy and easier to load on the gel.

Separating the Proteins

Now that your proteins are nice and linear, it’s time to run them out on your polyacrylamide gel using electricity. That’s right it is time for PolyAcrylamide Gel Electrophoresis or PAGE.

The Resolving Gel

The main component of PAGE is the resolving acrylamide gel. Acrylamide gels are composed of SDS, buffer, ammonium persulfate, and TEMED. This mixture is poured between two closely spaced plates, forming a thin gel. Once polymerized this mix creates a sieve-like network that the proteins can then travel through. As the proteins run through the gel, they will work through the mesh structure of the gel. Larger proteins take longer to navigate through the gel, while smaller proteins move faster. Therefore, you can adjust how much proteins will separate by changing the percentage of acrylamide in the gel. Less acrylamide means a gel with larger pores, which good for large proteins. More acrylamide means a gel with smaller pores, which is great for separating smaller proteins.

The Current

The proteins don’t move through the gel by their own volition. Instead you must subject your gel to an electric current, with the negative charge at the top where the proteins are loaded and the positive charge at the bottom. SDS-coated proteins have a large negative charge (thanks to the SDS), thus the proteins are attracted to the positive charge and move from top to bottom.

The Stacking Gel

A stacking gel is poured at the top of the gel. The stacking gel is made of the same stuff as the resolving gel but with a lower concentration of acrylamide. It is poured, after your resolving gel polymerizes, immediately before loading the gel. This is where you place your loading comb, which will create neat wells for your protein sample. A decent stacking gel is important to ensure crisp, sharp bands on your gel. The stacking gel ensures that, regardless of protein size and sample volume, all your proteins enter the gel at the same time.

SDS makes your protein in linearized form so that it can run in SDS-PAGE...It will not denature..If SDS would have denatured the protein, there is no use of SDS-PAGE.