Twenty-Third Annual Meeting February 26–28, 1979 Peachtree Plaza Hotel, Atlanta, Georgia
A method is given for the generation of fluorescence anisotropy decay curves for model macromolecules consisting of two rigid subunits connected by a hinge. To begin with, the elements of the resistance tensor must be determined either analytically or numerically, since the diffu ¶ion tensor depends both on these coefficients and on the bend angle restoring force . In order to apply the Belford equation, the average rotational diffusion coefficients must be calculated in a way that takes into
... count the dependence of the resistance tensor on the particle shape, which changes stochastically. Specifically, the averaging procedure must include three considerations: A procedure has been developed which generates possible three-dimensional conformations of variable regions of immunoglobulins. Since these proteins share the same three-dimensional structure except at their binding sites, the prediction of the conformation of an immunoglobulin's variable region reduces to the prediction of the conformation of the six hypervariable regions. An immunoglobulin whose atomic coordinates have been determined by x-ray diffraction analysis is used as a model for the framework; each hypervariable loop must then be of the proper length and orientation such that it can hook onto the framework. Several possible (4,q) angle choices for each residue in the hypervariable regions are made using the Wu-Kabat (40,) angle selection procedure. An initial choice of the conformation of each hypervariable region is found by searching for the permutation of (40,f) angle pairs which produces a chain with roughly the desired length and amino and carboxyl terminal orientations. This initial choice is refined by allowing each individual angle to vary within +30 degrees. A fitting procedure based on a least squares fit then locates angle modifications which generate improved fits to the framework. As each hypervariable region's backbone conformation is predicted, steric hindrance is searched for and corrected. Finally, the hypervariable regions must combine with each other such that a binding pocket which can accomodate any known antigens is formed. The application of this technique to the immunoglobulin MOPC-315 has successfully produced a possible binding site structure. Expressions are derived for the time-dependent relaxation behavior of a monodisperse suspension of arbitrarily shaped rigid bodies, after initial alignment by an electric field in a Kerr cell. The analysis predicts that five exponential terms are required for a complete description of birefringence, linear dichroism, and optical rotation decay phenomena in a force-free rotational diffusion process. The overall relaxation expression can be partitioned into one factor called the distribution factor and another called the anisotropy factor. The distribution factor depends on the initial alignment conditions, as determined by the particular experimental technique employed. Consideration of this factor alone permits application to other alignments, e.g. by hydrodynamic flow or magnetic fields. The anisotropy factor involves the light scattering, absorption, or optical rotation properties of the body. Because of this partitioning, symmetry considerations can be applied independently to the anisotropy and distribution factors. Symmetry constraints that involve special relationships between tensor components of these factors and the diffusion tensor lead to a reduction in the number of required exponential terms. A particular symmetry led to the "two exponential" results of a previous treatment. Furthermore, we have obtained the explicit form for the coefficients of the exponential relaxation terms. Since these, as well as the rotational diffusion coefficients, can undergo changes with varying environmental conditions, they should be considered as important indicies of changes in macromolecular conformation. Our results demonstrate that the presence of three or more exponential terms in time-dependent birefringence measurements is not a sufficient criterion for determining macromolecular flexibility. A general ellipsoidally-shaped body, or more commonly, an ellipsoid of revolution, serves as a convenient model for evaluating the rotational diffusion properties of macromolecules. If Perrin's equations for general ellipsoids can be shown to generate all possible rotational diffusion coefficients, then there would exist at least one equivalent general ellipsoidal shape for every arbitrarily-shaped rigid body. We evaluated the problem by first generating a space, r-space, representing all possible ellipsoidal shapes. We then generated another space, D-space, representing all possible combinations of rotational diffusion coefficients. We then mapped r-space onto D-space. Ellipsoidal shapes map onto diffusion space in a well-defined manner. The mapping is either 1:1, 2:1, or 3:1; several distinctly different regions of r-space map onto the same regions of D-space. Not all of D-space is covered by the mapping from r-space. Therefore, there are combinations of rotational diffusion coefficients that cannot be generated from ellipsoidally-shaped bodies. Examples of kinds of bodies that cannot be represented by an equivalent ellipsoidally-shaped body are bent rods, or two or more spheres connected by rigid arms. The three rotational diffusion coefficients generate five time constants. For ellipsoidally-shaped bodies, two pairs of time constants are almost degenerate. However, for diffusion coefficient sets that cannot be represented by a general ellipsoid, such degeneracy of the time constants may not occur. Therefore, the observation of more than three time constants in time-resolved experiments is not a sufficient criterion of macromolecular flexibility. (Supported by grants from the Sid W. Richardson Foundation and the NIH-HL-16678.) 60201. Manganoglobin, in which manganese porphyrins have been substituted for the heme prosthetic group, cooperatively and reversibly binds some small molecules but not oxygen. However, Mn(II) porphyrins do bind 02 reversibly at -800C in organic solvents to form pentacoordinated complexes in contrast to the hexacoordinated 02 complexes formed by iron and cobalt porphyrins. The reaction with 02 transforms the Mn(II) porphyrin spectrum from the normal to "hyper" type with a split Soret band typical of Mn(III) porphyrins. EPR spectra indicate a spin change from S = 5/2 to S = 3/2 and 170 substitution indicates little unpaired spin density on the 02. Analysis of the EPR data suggested that the 02 molecule binds to the Mn in the Griffith mode (edge-on, parallel to the porphyrin plane) and that the complexes could be formally described as Mn(IV)02m.1 However, published ab initio calculations2 predict instead that Mn(III)02_ should be the most stable configuration, with 02 bound in the Pauling mode (end-on, bent). Charge iterative extended HUckel calculations are reported here for both the Griffith and Pauling models for 02 Mn porphins, in which the 0-0, Mn-0, out of plane Mn distances and the 0-0 orientation above the porphinato plane have been varied. All of the experimental results can be explained in terms of the Griffith model but not the Pauling model. Furthermore, our calculations suggest that the ab initio results may simply be due to the use of too short an 0-0 distance. We conclude therefore that, unlike Co(II) and Fe(II) porphyrins, Mn(II) porphyrins bind oxygen in the Griffith mode in a manner similar to that found for Ti porphyrins. 1 B.M. Hoffman, et al. JACS 98 5473 (1976). 2 A. Dedieu et al. JACS, 99, 8050 (1977).