I have been working with recombinant DNA binding nucleases (pI 5) expressed in E.coli that go in insoluble fraction. So i purify them form inclusion bodies.
Combination of High pH buffer ( 2 units higher than the pI of protein) and low detergent or urea worked very well for all my insoluble proteins.
CHAPS or CHAPSO works best while N-Lauryl Sarcosine less than 0.3% can easily be removed by dialysis.
After induction once cells are harvested, I resuspend the pellet in native buffer (40mM Tris-HCl (pH 9.0), 500 mM NaCl, and 0.1% N-Lauryl Sarcosine (Buffer A) supplemented with 10 mM PMSF and 0.2 mg/ml lysozyme and leave on ice for 30 minutes. Harvested cells are sonicated and the lysate is incubated on ice for 30 minutes to allow solubilisation of insoluble recombinant protein. This is followed by centrifugation at 13,000 rpm for 30 minutes at 4°C. The supernatant is applied to a nickel NTA column (Amersham Biosciences) equilibrated with buffer A, and protein is eluted using 10–500 mM imidazole gradient. Purified fractions are pooled and extensively dialysed against the dialysis buffer (40 mM Tris-HCl (pH 8.0), 50 mM NaCl and 2 mM DTT).
Following this method, all my proteins retained their respective biological activities associated with them like DNA binding, nuclease etc.
I agree with Taran that CHAPS and CHAPSO are good choices. The reason is the small size of their micelles. You can also remove Triton X-100 using Bio-beads.
low CMC detergent are harder to remove and high CMC (smaller micelles) are easier to remove. Problem is that high CMC detergent are usually harsher for the proteins and can kill the functionality of it. Same can be true for zwitterionic detergents. So if harsh detergent do not kill the function of your protein, I would go for them.
Try first zwitterionic as suggested CHAPS or similar. If its not good go for short carbon chain detergent as beta OG. If its still too harsh you can try mild maltoside family detergent as DM or DDM knowing that ,even DDM, can be removed with Bio beads in the worst case.
High CMC detergent (like TX100, OG, CHAPS) are easier to remove than low CMC detergent (like DDM, C12E8) as it could be easy to dilute a bit your sample to decrease their concentrations below their CMC (monomers could be eliminated by ultrafiltration, SEC or dialysis). However, those detergent are sometimes not good for protein long-term stability.
Removal of low CMC detegent could be achieved by using biobeads (see papers from Rigaud and colleagues in the 80's). It is a very efficient method. One drawback should be that sometimes, biobeads bound proteins too as biobeads are hydrophobic...
Note that if you would like to "only" detergent removal (and protein relipidation) or if you would like to proceed to a real reconstitution, methods should be different. You will found all the references you need in the following review (le Maire and al. BBA 2000).