Some theoretical considerations regarding the effects of steric hindrance and intrinsic global coupling on the flexibility of Fc-anchored immunoglobulins

Nanosecond fluorescence depolarization studies reported in the accompanying companion paper showed that the long rotational correlation time, phi L, increased somewhat when rabbit IgG anti-dansyl antibodies were anchored in staphylococcal protein A (SpA) soluble complexes. The increases in phi L upon anchoring IgG probably resulted from "global coupling" effects caused by: increased steric hindrance of the antibody segments in the SpA complexes and intrinsic structural constraints already present in the monomeric IgG. Global coupling results from a restriction in the angular range of a flexible segment and is manifest when flexible motions alone cannot depolarize all of the fluorescence, so that the slower global tumbling of the entire particle is also required. Such effects cannot be resolved directly from experimental anisotropy data, however, because only a single long correlation time, phi L, is well defined over the limited time range of most fluorophores. In this paper, estimates of the anisotropy contributions from flexible and global motions of the IgG-SpA complexes are determined by contrasting theoretical and measured decays. For this analysis it was assumed that each of the experimental phi L-values is a weighted composite of the rotational correlation time associated with the less restricted flexible motions of the Fab arms, phi F, and the correlation time associated with global tumbling of the entire particle, phi G. A general two-exponential expression was used to relate phi F and phi G to phi L. This approach was meaningful because phi G-values of the various SpA complexes had been calculated from hydrodynamic measurements. The theoretical decays clearly show that, even if phi G is much longer than phi F, these two rotational motions still cannot be resolved over the experimentally accessible time range. Families of emission anisotropy decay curves for IgG antibodies with different amounts of intrinsic global coupling and for anchored antibodies with different amounts of steric hindrance were simulated by varying the preexponential weighting factors of the flexible and global terms. By comparing the calculated curves with the measured decays, it is evident that the rabbit IgG anti-dansyl antibodies do not have much intrinsic global coupling, but rather they are highly flexible. The curves also indicate that even for the exceptionally compact IgG4-SpA2 17-S complex, which showed the most steric hindrance in electron micrographs, the appropriate phi G weighting factor is only 0.28. Thus, as supposed earlier, the anchored antibodies exhibit considerable segmental flexibility. In closing, the above concepts are used to examine the results of