SDS denatures the protein and does interact to some degree as Denis mentioned. The benefit of SDS is that it surrounds the protein resulting in an overall negative charge and a consistent protein shape. Thus, migration through the gel is depended on size only, and is not influenced by innate secondary, tertiary conformations, or side chain charges. Essentially SDS eliminates confounding characteristics of the protein, so size is the migration factor.

To my knowledge, the hydrophobic hydrocarbonated portion of SDS interacts with hydrophobic regions on denaturated proteins.

SDS denatures the protein and does interact to some degree as Denis mentioned. The benefit of SDS is that it surrounds the protein resulting in an overall negative charge and a consistent protein shape. Thus, migration through the gel is depended on size only, and is not influenced by innate secondary, tertiary conformations, or side chain charges. Essentially SDS eliminates confounding characteristics of the protein, so size is the migration factor.

Hi,

The saturated hydrocarbone chain of SDS molecules binds to protein surface through hydrophobic interactions then masking all positive and negative charges of the protein. The sodium sulfate moiety of SDS is then disposed facing solvent and conferring a net negative electrostatic charge to protein leaving it unable to interact with other SDS-bound peptides.

In addition to the other things mentioned, SDS binds to polypeptides in a constant weight ratio of 1.4 g SDS/g of polypeptide. The three things that effect mobility in the gel are size (molecular weight), shape, and charge. The samples are boiled in sample buffer, which has SDS and a reducing agent such as DTT or beta-mercaptoethanol, prior to loading on the gel. The purpose of this is to denature all the samples, so all proteins theoretically run as linear rods (theoretically). The SDS coats all samples and gives them a net negative charge. In this way, you have controlled for all of the variables, except for one, which is molecular weight, which you can determine roughly by running protein standards in one lane of the gel, and your samples in the other lanes.

Be mindful of the affinity/avidity of your reagents used to visualise the proteins you have separated by PAGE. As with antibody, Coomassie has varying affinity for proteins depending on alanine and (a few othe aa) content

It has been rigthly quoted by Denis that the interaction between the protein and SDS is basically hyrophobic interaction. However the binding of SDS with highly negatively charged proteins do create some problems due to repulsion of negative charges placed on SDS and protein both... Here is very basic paper from 1970's to make your understanding more clear.

Here is one more paper for your reference

Hi, I agree with above info. and I would like to mention that the SDS is not only in the loading buffer but also in the SDS- PAGE running buffer.

From what i know, SDS is an anionic detergent which binds failry uniformly to a linearized protein. Therefore , it gives all the proteins in the sample the same charge to mass ratio. The interaction between SDS and the protein can be expected to be hydrophobic (based on how detergents work). Now when you run a PAGE the proteins separate only based on the size and not based on the charge on the molecule.  

Typically after SDS-PAGE we transfer to a membrane in a SDS-free transfer buffer which can allow some re-naturation of the protein, hopefully the epitope for an antibody of interest. mAbs are rated for their ability to recognize their epitopes in various situations like IHC, ELISA, WB etc and this is mostly related to how complex or structurally-reliant the epitope is, maybe involving loops in a strand of amino acids present in close proximity when not denatured, as compared to a lineraer epitope relying simply on the amino acids being in sequence. All epitopes are 3D but some require that the protein must be in tact for the epitope to be recognised.

Some mAbs work well in either conditions if the altered epitope is still of suitable affinity for the assay wash conditions and overall stringent limits