Does the binding pattern change if the scFv was converted into the Fab or whole antibody? What about other characteristics, such as the affinity, specificity, stability?
The specificity is determined by the paratope which is the same in scFv Fab and full size Ab. Affinity can differ (!) as a result of VH-VL interaction that can affect activity (scFv can be in an open binding incompetent conformation or a closed binding competent conformation). In the Fab the constant domains align the VH and VL and thus Fabs are generally better than scFv. The full size Ab is bivalent and has effector functions. Moreover, it is a better reagent simply because you have very good polyclonal secondary antibodies. If you can go with the Fab for affinity measurements (clean 1:1 binding) and use the fullsize Ab for classical immunological assays (ELISA, Wblot, FACS, IHC etc.). Special assays may favor other formats but then you are getting into delicate performance details subject to protein engineering a tailored antibody for your application.
See "Röthlisberger, D., Honegger, A., and Plückthun, A. (2005). Domain interactions in the Fab fragment: A comparative evaluation of the single-chain Fv and Fab format engineered with variable domains of different stability. J Mol Biol 347, 773-789." for a detailed analysis of the effect of domain interactions on stability (Article Domain Interactions in the Fab Fragment: A Comparative Evalu...
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The affinity of the antibody-antigen interaction usually does not change (with a few exceptions), however, in full antibody formats, the multiple binding sites will give you avidity effects yielding a better apparent affinity on multivalent or immobilized antigens.