David F. J. Tees, Ph.D.
Assistant Professor
Ohio University
In the work described in the two preceding chapters, break-up of doublets of antibody-agglutinated particles, either SSRC or antigen linked latex spheres, has been studied. Individual doublets were exposed to known hydrodynamic forces and the time required for the doublets to break up was measured.
The finding that there is a distribution of break-up times when a defined maximum force is applied either relatively slowly, as in the halted rapid acceleration in Poiseuille flow, or virtually instantaneously, as in the Rheoscope, shows that the notion of a "force per bond" can only serve as a convenient shorthand for what is actually a force dependence of the lifetime for bond break-up. The inherent stochastic nature of the lifetime of antigen-antibody bonds as demonstrated by Evans et al. (1991) has thus been confirmed for both SSRC and antigen linked spheres.
In the course of an attempt to determine the locus of bond break-up in Chapter 3 of this thesis, it was found that doublets of latex microspheres with covalently coupled blood group antigen were significantly less sensitive to force than were SSRC. To achieve equivalent fractions of break-up with antigen spheres required ~ 2´ the force needed for SSRC at both 75 and 150 pM IgM. Using Bell’s (1978) two parameter theory (Eq. 11 in Chapter 1) for the force dependence of the bond lifetime, a simulation of doublet break-up in shear flow was developed. Using the simulation to account for the periodic application of force on doublets in shear flow, model parameters that provide the best fit to the SSRC and antigen sphere data were found. The values of Eo and ro, the depth and range of the energy minimum representing the bond, and <Nb>, the average number of Poisson distributed bonds, were found to be 0.9 eV, 0.4 nm and 4 bonds (with an effectively infinite formation time = 100 s) respectively, for SSRC at 150 pM IgM. By contrast, the corresponding values for the antigen spheres at the same [IgM] were 0.8 eV, 0.12 nm and 2.5 bonds [with a formation time of only 2 s which is still a slow formation rate; break-up is relatively insensitive to tf > 1 s (see Appendix 3)]. The markedly different ro shows that the antigen spheres and the SSRC differ due to a change in bond character and not to a increase in the number of bonds linking doublets: in fact, <Nb> is less for the antigen spheres.
The simplest explanation for the difference is that in the case of the antigen spheres, antigen-antibody bonds linking doublets are being broken. The greater sensitivity of the bond to force for the SSRC represents extraction of the antigen (which is linked to glycolipids as well as to the glutaraldehyde crosslinked glycoproteins) from the lipid bilayer, as has been found for SSRC previously using both micropipette aspiration (Evans et al., 1991) and shear flow (Xia et al., 1994). The ro found for break-up of doublets of latex spheres is 3 ´ smaller than that for doublets of SSRC. The value of 0.12 nm is also smaller than that predicted by Bell (1978) for an antigen-antibody bond (0.3 nm). It is comparable to that found for selectin-carbohydrate bonds (0.05 nm) by Alon et al. (1995). They suggest that protein-carbohydrate bonds (such as the antibody-blood group B antigen bond) may be of shorter range than the bonds in protein-protein adhesive interactions. As mentioned in Chapter 2, however, the ro for antigen extraction from the cell membrane would be expected to be of the order of the width of one leaflet of the lipid bilayer (~ 2 nm). The ro of 0.4 nm found for SSRC doublet break-up, therefore, seems rather small to be the range of the interaction represented by antigen extraction from the cell membrane.
Alternate explanations for the difference in bond character between SSRC and antigen spheres are more speculative. A clear effect of increased fraction of break-up with increased suspending medium viscosity was seen for antigen spheres in Dextran, highlighting the effect that properties of the suspending medium can have on aggregation. It seems that the effect of increased viscosity was largely due to the increased exposure time to force in each rotation, combined with inhibited bond formation due to increasing adsorbed Dextran. In spite of this, it is unfortunate that problems with sedimentation required a change of suspending medium between the two parts of this work. Although the viscosities of the sucrose and Dextran 40 suspending media were matched, it is possible that there was an effect of the nature of the viscous co-solvent [small molecule (sucrose) vs large molecule (dextran)] on the antigen-antibody chemical environment, similar to that which has been suggested to affect protein structural fluctuations (Almagor et al., 1990).
Another possible complication is extraction of strands of latex from the microsphere. Latex spheres deposited on and adhering non-specifically to glass surfaces, subjected to oscillating or turbulent flows, move around a fixed point as if tethered to the surface by long, invisible elastic connections. This was interpreted as being due to extraction of bundles of entangled polymer chains (Dabros et al., 1994). Extraction might explain the difference in results between antigen spheres made with microspheres from two different companies. Since the antigen-antibody bond strength is expected to vary with pH, the observation of such variation provides at least some evidence that the antibody-antigen bond is broken for antigen spheres made from the IDC spheres.
(i) Extension of the previous work on the distribution of forces at break-up in accelerating Poiseuille flow of polyclonal antiserum agglutinated sphered swollen red blood cells to monoclonal antibodies.
(ii) Development of techniques for applying constant maximum forces in the travelling microtube (halted rapid acceleration in Poiseuille flow), and in the Rheoscope, thus confirming in a simple shear flow the stochastic nature of the bonds cross-linking doublets observed originally by Evans et al. (1991) using micropipette aspiration.
(iii) Development and characterization of latex microspheres with covalently coupled antigen.
(iv) Comparison of force and time dependence of break up of antigen spheres with SSRC to elucidate the locus of bond failure for antibody agglutinated red cells.
(v) Development of a Monte Carlo simulation of doublet break up in shear flow using the exponential model of Bell (1978) for the force dependence of the time to break-up. Demonstration that both SSRC and antigen sphere data can be well matched with such a model, but not with a power law model as suggested by Evans et al. (1991).
The experiments designed to elucidate the locus of bond failure for antibody agglutinated red blood cells still suffer from concern that the composition of the viscous co-solvent used to produce high viscosities in the suspending media may affect the kinetics of bond rupture. Population studies done to assess the importance of medium composition showed that there was much less aggregation of antigen spheres in sucrose than in Dextran. These experiments suffered from a differences in the rate of sedimentation which might have affected the rates and extents of aggregate formation. To assess whether an effect of medium composition exists, it would worthwhile to repeat the antigen sphere experiments in 19% Dextran 40 using SSRC, which, due to leakage of medium into the interior are not expected to exhibit the sedimentation problems seen with impermeable latex spheres. If the SSRC results are the same in Dextran as in sucrose, the effect of medium composition on break-up can be discarded.
The concern over latex strand extraction highlights the difficulty of ensuring that an adhesion molecule is firmly anchored to a substrate that is also firmly anchored. One possible method suggested to us (Dr. T. G. M. van de Ven, private communication) would be to covalently link the latex strands within the microsphere. This could be done using gamma radiation from a 60Co source to form radicals within individual latex microspheres which should then cause the strands to form crosslinks, effectively turning the sphere into a single giant, covalently bound molecule. The degree of crosslinking could be assessed by dissolving the latex in an organic solvent and determining the molecular mass before and after treatment. If successful, such internally crosslinked spheres could be coupled to antigen, time and force dependence of break-up examined as before and the results compared with the present antigen sphere results.
The purpose of the experiments described above has been to develop a technique by which any pair of antigen-antibody bonds can have the associated force dependence of bond lifetime assessed. The system used here was an antibody-carbohydrate bond, which is a well studied model receptor-ligand system. There are many other receptor-ligand pairs which are of current interest to the adhesion community at large. Several sets of receptor-ligand bonds are well characterized and of interest technologically. The Avidin-Biotin system is very widely used for affinity purification, as is the bond between Protein G and the IgG Fc domain. A study of the latter is well underway and will be completed shortly (Kwong, D., D. F. J. Tees, and H. L. Goldsmith, manuscript in preparation). Increasingly, purified adhesion molecules are becoming available, and examination of some of the pairs described in Chapter 1, such as LFA-1-ICAM-1 or P-selectin-PSGL-1 would make a very interesting study, if the molecules could be obtained in sufficient quantity.
The principal drawback to the method described in Chapters 2 and 3 for studying force dependence of bond lifetime is that it is very time intensive. To collect and analyze a full series of data at several antibody concentrations requires several months of diligent work. An alternative method which might produce results more quickly is a population study in the Rheoscope. The Rheoscope is filled with suspension, allowed to form doublets for a specified period of time (say 30 minutes), the number of doublets is assessed, then the suspension is sheared at a defined shear rate, and the number of doublets is counted again. The fraction of doublets broken-up can thus be derived as a function of the shear rate, which is related to the applied force using the theory given in Chapters 2 and 3. Instead of a single force, a range of forces will be applied, since the doublets exhibit a range of orbit constants. If the distribution of orbit constants is known, the simulation described above can be applied to try to fit the results, with the modification that break-up is simulated at constant shear rate, not constant maximum force, for a prescribed period of time, and not for a certain number of rotations.
Whether by population experiments or by the individual doublet method developed above, the model antigen-antibody system still has many features that are worthy of investigation. Studies of viscosity variation, pH variation and also variation with affinity constant, KD (by using different antibodies to the blood group B antigen) of the force dependence of the bond lifetime are all of theoretical interest, and would make an interesting project.
Almagor, A., S. Yedgar, and B. Gavish. 1990. Solvent viscosity effects on protein dynamics studied by ultrasonic absorption. Biorheology. 27:605-610.
Bell, G. I. 1978. Models for the specific adhesion of cells to cells. Science (Washington DC). 200:618-627.
Evans, E., D. Berk, and A. Leung. 1991. Detachment of agglutinin-bonded red blood cells I. Forces to rupture molecular-point attachments. Biophys. J. 59:838-848.
Xia, Z., H. L. Goldsmith, and T. G. M. van de Ven. 1994. Flow-induced detachment of red blood cells adhering to surfaces by specific antigen-antibody bonds. Biophys. J. 66:1222-1230.